%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU297+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n004.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 12:03:02 EDT 2023

% Result   : Theorem 43.39s 42.73s
% Output   : Proof 43.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU297+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n004.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 12:31:24 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 43.39/42.73  
% 43.39/42.73  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 43.39/42.73  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.39/42.73  %-----------------------------------------------------
% 43.39/42.73  ncf(matrix, plain, [(514 ^ _103173) ^ [] : [-(relation(510 ^ []))], (516 ^ _103173) ^ [] : [-(function(510 ^ []))], (519 ^ _103173) ^ [_103458] : [528 ^ _103173 : [(533 ^ _103173) ^ [] : [in(517 ^ [_103458], _103458)], (531 ^ _103173) ^ [] : [-(in(relation_image(510 ^ [], 517 ^ [_103458]), 509 ^ []))], (529 ^ _103173) ^ [] : [-(in(517 ^ [_103458], powerset(relation_dom(510 ^ []))))]], 520 ^ _103173 : [(523 ^ _103173) ^ [] : [in(517 ^ [_103458], powerset(relation_dom(510 ^ []))), in(relation_image(510 ^ [], 517 ^ [_103458]), 509 ^ [])], (521 ^ _103173) ^ [] : [-(in(517 ^ [_103458], _103458))]]], (512 ^ _103173) ^ [] : [-(element(509 ^ [], powerset(powerset(508 ^ []))))], !, (299 ^ _86319) ^ [] : [-(one_to_one(293 ^ []))], (358 ^ _86319) ^ [] : [-(relation(354 ^ []))], (356 ^ _86319) ^ [] : [-(empty(354 ^ []))], (188 ^ _86319) ^ [] : [-(ordinal(180 ^ []))], (235 ^ _86319) ^ [] : [-(function(231 ^ []))], (295 ^ _86319) ^ [] : [-(relation(293 ^ []))], (399 ^ _86319) ^ [_98860] : [-(empty(_98860)), 403 ^ _86319 : [(406 ^ _86319) ^ [] : [empty(402 ^ [_98860])], (404 ^ _86319) ^ [] : [-(element(402 ^ [_98860], powerset(_98860)))]]], (303 ^ _86319) ^ [] : [-(epsilon_transitive(293 ^ []))], (40 ^ _86319) ^ [_87657, _87659] : [-(one_to_one(_87657)), _87659 = _87657, one_to_one(_87659)], (411 ^ _86319) ^ [_99294] : [-(empty(407 ^ [_99294]))], (297 ^ _86319) ^ [] : [-(function(293 ^ []))], (193 ^ _86319) ^ [] : [empty(191 ^ [])], (367 ^ _86319) ^ [] : [empty(365 ^ [])], (138 ^ _86319) ^ [_90616, _90618] : [_90618 = _90616, -(powerset(_90618) = powerset(_90616))], (30 ^ _86319) ^ [_87362, _87364] : [-(finite(_87362)), _87364 = _87362, finite(_87364)], (218 ^ _86319) ^ [_93431, _93433] : [-(finite(relation_image(_93433, _93431))), relation(_93433), function(_93433), finite(_93431)], (277 ^ _86319) ^ [_95235] : [-(ordinal(_95235)), epsilon_transitive(_95235), epsilon_connected(_95235)], (253 ^ _86319) ^ [_94498] : [260 ^ _86319 : [(263 ^ _86319) ^ [] : [-(epsilon_connected(_94498))], (265 ^ _86319) ^ [] : [-(ordinal(_94498))], (267 ^ _86319) ^ [] : [-(natural(_94498))], (261 ^ _86319) ^ [] : [-(epsilon_transitive(_94498))]], empty(_94498), ordinal(_94498)], (4 ^ _86319) ^ [_86550, _86552] : [_86552 = _86550, -(_86550 = _86552)], (310 ^ _86319) ^ [] : [empty(308 ^ [])], (70 ^ _86319) ^ [_88542, _88544] : [-(ordinal(_88542)), _88544 = _88542, ordinal(_88544)], (431 ^ _86319) ^ [] : [true___, -(true___)], (173 ^ _86319) ^ [_91889] : [-(epsilon_connected(159 ^ [_91889]))], (381 ^ _86319) ^ [_98268] : [empty(_98268), 384 ^ _86319 : [(387 ^ _86319) ^ [] : [-(relation(relation_dom(_98268)))], (385 ^ _86319) ^ [] : [-(empty(relation_dom(_98268)))]]], (186 ^ _86319) ^ [] : [-(epsilon_connected(180 ^ []))], (161 ^ _86319) ^ [_91478] : [-(element(159 ^ [_91478], powerset(_91478)))], (233 ^ _86319) ^ [] : [-(relation(231 ^ []))], (197 ^ _86319) ^ [_92668] : [-(empty(_92668)), 201 ^ _86319 : [(206 ^ _86319) ^ [] : [-(finite(200 ^ [_92668]))], (204 ^ _86319) ^ [] : [empty(200 ^ [_92668])], (202 ^ _86319) ^ [] : [-(element(200 ^ [_92668], powerset(_92668)))]]], (371 ^ _86319) ^ [_97991] : [empty(relation_dom(_97991)), -(empty(_97991)), relation(_97991)], (124 ^ _86319) ^ [_90174, _90176, _90178, _90180] : [-(in(_90178, _90174)), in(_90180, _90176), _90180 = _90178, _90176 = _90174], (389 ^ _86319) ^ [_98533] : [empty(_98533), 392 ^ _86319 : [(397 ^ _86319) ^ [] : [-(ordinal(_98533))], (395 ^ _86319) ^ [] : [-(epsilon_connected(_98533))], (393 ^ _86319) ^ [] : [-(epsilon_transitive(_98533))]]], (324 ^ _86319) ^ [_96618] : [empty(_96618), -(function(_96618))], (337 ^ _86319) ^ [_97013] : [348 ^ _86319 : [(353 ^ _86319) ^ [] : [-(one_to_one(_97013))], (351 ^ _86319) ^ [] : [-(function(_97013))], (349 ^ _86319) ^ [] : [-(relation(_97013))]], relation(_97013), empty(_97013), function(_97013)], (80 ^ _86319) ^ [_88837, _88839] : [-(empty(_88837)), _88839 = _88837, empty(_88839)], (288 ^ _86319) ^ [] : [-(epsilon_transitive(286 ^ []))], (90 ^ _86319) ^ [_89160, _89162, _89164, _89166] : [-(element(_89164, _89160)), element(_89166, _89162), _89166 = _89164, _89162 = _89160], (269 ^ _86319) ^ [_94978] : [ordinal(_94978), 272 ^ _86319 : [(275 ^ _86319) ^ [] : [-(epsilon_connected(_94978))], (273 ^ _86319) ^ [] : [-(epsilon_transitive(_94978))]]], (450 ^ _86319) ^ [] : [-(relation(448 ^ []))], (454 ^ _86319) ^ [_100392] : [empty(powerset(_100392))], (208 ^ _86319) ^ [_93080] : [finite(_93080), 211 ^ _86319 : [(212 ^ _86319) ^ [_93212] : [element(_93212, powerset(_93080)), -(finite(_93212))]]], (163 ^ _86319) ^ [_91549] : [-(empty(159 ^ [_91549]))], (419 ^ _86319) ^ [_99586, _99588] : [in(_99588, _99586), in(_99586, _99588)], (182 ^ _86319) ^ [] : [empty(180 ^ [])], (195 ^ _86319) ^ [] : [-(finite(191 ^ []))], (307 ^ _86319) ^ [] : [-(ordinal(293 ^ []))], (10 ^ _86319) ^ [_86754, _86756, _86758] : [-(_86758 = _86754), _86758 = _86756, _86756 = _86754], (292 ^ _86319) ^ [] : [-(ordinal(286 ^ []))], (290 ^ _86319) ^ [] : [-(epsilon_connected(286 ^ []))], (104 ^ _86319) ^ [_89576, _89578] : [-(relation(_89576)), _89578 = _89576, relation(_89578)], (50 ^ _86319) ^ [_87952, _87954] : [-(epsilon_transitive(_87952)), _87954 = _87952, epsilon_transitive(_87954)], (369 ^ _86319) ^ [] : [-(relation(365 ^ []))], (20 ^ _86319) ^ [_87067, _87069] : [-(natural(_87067)), _87069 = _87067, natural(_87069)], (443 ^ _86319) ^ [] : [true___, -(true___)], (414 ^ _86319) ^ [] : [-(empty(412 ^ []))], (237 ^ _86319) ^ [] : [-(one_to_one(231 ^ []))], (312 ^ _86319) ^ [] : [-(epsilon_transitive(308 ^ []))], (301 ^ _86319) ^ [] : [-(empty(293 ^ []))], (417 ^ _86319) ^ [] : [empty(415 ^ [])], (177 ^ _86319) ^ [_92025] : [-(natural(159 ^ [_92025]))], (314 ^ _86319) ^ [] : [-(epsilon_connected(308 ^ []))], (114 ^ _86319) ^ [_89871, _89873] : [-(function(_89871)), _89873 = _89871, function(_89873)], (425 ^ _86319) ^ [] : [true___, -(true___)], (331 ^ _86319) ^ [] : [-(relation(329 ^ []))], (184 ^ _86319) ^ [] : [-(epsilon_transitive(180 ^ []))], (150 ^ _86319) ^ [_91060, _91062, _91064, _91066] : [-(relation_image(_91066, _91062) = relation_image(_91064, _91060)), _91066 = _91064, _91062 = _91060], (333 ^ _86319) ^ [] : [-(empty(329 ^ []))], (175 ^ _86319) ^ [_91957] : [-(ordinal(159 ^ [_91957]))], (171 ^ _86319) ^ [_91821] : [-(epsilon_transitive(159 ^ [_91821]))], (190 ^ _86319) ^ [] : [-(natural(180 ^ []))], (167 ^ _86319) ^ [_91685] : [-(function(159 ^ [_91685]))], (409 ^ _86319) ^ [_99243] : [-(element(407 ^ [_99243], powerset(_99243)))], (2 ^ _86319) ^ [_86443] : [-(_86443 = _86443)], (316 ^ _86319) ^ [] : [-(ordinal(308 ^ []))], (452 ^ _86319) ^ [] : [-(function(448 ^ []))], (360 ^ _86319) ^ [_97655] : [empty(_97655), -(relation(_97655))], (318 ^ _86319) ^ [_96432] : [empty(_96432), -(finite(_96432))], (437 ^ _86319) ^ [] : [true___, -(true___)], (179 ^ _86319) ^ [_92073] : [-(finite(159 ^ [_92073]))], (305 ^ _86319) ^ [] : [-(epsilon_connected(293 ^ []))], (165 ^ _86319) ^ [_91617] : [-(relation(159 ^ [_91617]))], (335 ^ _86319) ^ [] : [-(function(329 ^ []))], (456 ^ _86319) ^ [_100494, _100496, _100498] : [element(_100496, powerset(powerset(_100498))), relation(_100494), function(_100494), 472 ^ _86319 : [(473 ^ _86319) ^ [] : [-(469 ^ [_100494, _100496, _100498] = 470 ^ [_100494, _100496, _100498])], (477 ^ _86319) ^ [] : [-(469 ^ [_100494, _100496, _100498] = 471 ^ [_100494, _100496, _100498])], (481 ^ _86319) ^ [] : [470 ^ [_100494, _100496, _100498] = 471 ^ [_100494, _100496, _100498]], (479 ^ _86319) ^ [] : [-(in(relation_image(_100494, 471 ^ [_100494, _100496, _100498]), _100496))], (475 ^ _86319) ^ [] : [-(in(relation_image(_100494, 470 ^ [_100494, _100496, _100498]), _100496))]], 483 ^ _86319 : [(495 ^ _86319) ^ [_102248] : [-(in(_102248, 482 ^ [_100494, _100496, _100498])), 496 ^ _86319 : [(497 ^ _86319) ^ [_102372] : [in(_102372, powerset(relation_dom(_100494))), _102372 = _102248, in(relation_image(_100494, _102248), _100496)]]], (484 ^ _86319) ^ [_101780] : [in(_101780, 482 ^ [_100494, _100496, _100498]), 488 ^ _86319 : [(493 ^ _86319) ^ [] : [-(in(relation_image(_100494, _101780), _100496))], (491 ^ _86319) ^ [] : [-(487 ^ [_100494, _100496, _100498, _101780] = _101780)], (489 ^ _86319) ^ [] : [-(in(487 ^ [_100494, _100496, _100498, _101780], powerset(relation_dom(_100494))))]]]]], (169 ^ _86319) ^ [_91753] : [-(one_to_one(159 ^ [_91753]))], (60 ^ _86319) ^ [_88247, _88249] : [-(epsilon_connected(_88247)), _88249 = _88247, epsilon_connected(_88249)], (144 ^ _86319) ^ [_90834, _90836] : [_90836 = _90834, -(relation_dom(_90836) = relation_dom(_90834))], (239 ^ _86319) ^ [_94012] : [ordinal(_94012), 242 ^ _86319 : [(243 ^ _86319) ^ [_94152] : [element(_94152, _94012), 246 ^ _86319 : [(251 ^ _86319) ^ [] : [-(ordinal(_94152))], (249 ^ _86319) ^ [] : [-(epsilon_connected(_94152))], (247 ^ _86319) ^ [] : [-(epsilon_transitive(_94152))]]]]]], input).
% 43.39/42.73  ncf('1',plain,[-(relation(510 ^ []))],start(514 ^ 0)).
% 43.39/42.73  ncf('1.1',plain,[relation(510 ^ []), element(509 ^ [], powerset(powerset(508 ^ []))), function(510 ^ []), 473 : -(469 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 470 ^ [510 ^ [], 509 ^ [], 508 ^ []]), 484 : in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 482 ^ [510 ^ [], 509 ^ [], 508 ^ []]), 491 : -(487 ^ [510 ^ [], 509 ^ [], 508 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]] = 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]])],extension(456 ^ 1,bind([[_100494, _100496, _100498, _101780], [510 ^ [], 509 ^ [], 508 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]]))).
% 43.39/42.73  ncf('1.1.1',plain,[-(element(509 ^ [], powerset(powerset(508 ^ []))))],extension(512 ^ 2)).
% 43.39/42.73  ncf('1.1.2',plain,[-(function(510 ^ []))],extension(516 ^ 2)).
% 43.39/42.73  ncf('1.1.3',plain,[469 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 470 ^ [510 ^ [], 509 ^ [], 508 ^ []], -(470 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 469 ^ [510 ^ [], 509 ^ [], 508 ^ []])],extension(4 ^ 4,bind([[_86550, _86552], [470 ^ [510 ^ [], 509 ^ [], 508 ^ []], 469 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]))).
% 43.39/42.73  ncf('1.1.3.1',plain,[470 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 469 ^ [510 ^ [], 509 ^ [], 508 ^ []], -(470 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 471 ^ [510 ^ [], 509 ^ [], 508 ^ []]), 469 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 471 ^ [510 ^ [], 509 ^ [], 508 ^ []]],extension(10 ^ 5,bind([[_86754, _86756, _86758], [471 ^ [510 ^ [], 509 ^ [], 508 ^ []], 469 ^ [510 ^ [], 509 ^ [], 508 ^ []], 470 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]))).
% 43.39/42.73  ncf('1.1.3.1.1',plain,[470 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 471 ^ [510 ^ [], 509 ^ [], 508 ^ []]],extension(481 ^ 6)).
% 43.39/42.73  ncf('1.1.3.1.2',plain,[-(469 ^ [510 ^ [], 509 ^ [], 508 ^ []] = 471 ^ [510 ^ [], 509 ^ [], 508 ^ []])],extension(477 ^ 6)).
% 43.39/42.73  ncf('1.1.4',plain,[-(in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 482 ^ [510 ^ [], 509 ^ [], 508 ^ []])), 531 : -(in(relation_image(510 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]), 509 ^ []))],extension(519 ^ 4,bind([[_103458], [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]))).
% 43.39/42.73  ncf('1.1.4.1',plain,[in(relation_image(510 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]), 509 ^ []), 497 : in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], powerset(relation_dom(510 ^ []))), 497 : 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]] = 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 497 : -(in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 482 ^ [510 ^ [], 509 ^ [], 508 ^ []]))],extension(495 ^ 7,bind([[_102248, _102372], [517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]]))).
% 43.39/42.73  ncf('1.1.4.1.1',plain,[-(in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], powerset(relation_dom(510 ^ []))))],extension(529 ^ 10)).
% 43.39/42.73  ncf('1.1.4.1.2',plain,[-(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]] = 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]])],extension(2 ^ 10,bind([[_86443], [517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]]))).
% 43.39/42.73  ncf('1.1.4.1.3',plain,[in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 482 ^ [510 ^ [], 509 ^ [], 508 ^ []])],reduction('1.1')).
% 43.39/42.73  ncf('1.1.5',plain,[487 ^ [510 ^ [], 509 ^ [], 508 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]] = 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], -(in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], powerset(relation_dom(510 ^ [])))), in(487 ^ [510 ^ [], 509 ^ [], 508 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]], powerset(relation_dom(510 ^ []))), powerset(relation_dom(510 ^ [])) = powerset(relation_dom(510 ^ []))],extension(124 ^ 6,bind([[_90174, _90176, _90178, _90180], [powerset(relation_dom(510 ^ [])), powerset(relation_dom(510 ^ [])), 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 487 ^ [510 ^ [], 509 ^ [], 508 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]]]))).
% 43.39/42.73  ncf('1.1.5.1',plain,[in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], powerset(relation_dom(510 ^ []))), 523 : in(relation_image(510 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]), 509 ^ []), 533 : in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 482 ^ [510 ^ [], 509 ^ [], 508 ^ []])],extension(519 ^ 7,bind([[_103458], [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]]))).
% 43.39/42.73  ncf('1.1.5.1.1',plain,[-(in(relation_image(510 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]), 509 ^ []))],extension(493 ^ 10)).
% 43.39/42.73  ncf('1.1.5.1.2',plain,[-(in(517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]], 482 ^ [510 ^ [], 509 ^ [], 508 ^ []]))],lemmata('[1].x')).
% 43.39/42.73  ncf('1.1.5.2',plain,[-(in(487 ^ [510 ^ [], 509 ^ [], 508 ^ [], 517 ^ [482 ^ [510 ^ [], 509 ^ [], 508 ^ []]]], powerset(relation_dom(510 ^ []))))],extension(489 ^ 7)).
% 43.39/42.73  ncf('1.1.5.3',plain,[-(powerset(relation_dom(510 ^ [])) = powerset(relation_dom(510 ^ []))), relation_dom(510 ^ []) = relation_dom(510 ^ [])],extension(138 ^ 7,bind([[_90616, _90618], [relation_dom(510 ^ []), relation_dom(510 ^ [])]]))).
% 43.39/42.73  ncf('1.1.5.3.1',plain,[-(relation_dom(510 ^ []) = relation_dom(510 ^ []))],extension(2 ^ 8,bind([[_86443], [relation_dom(510 ^ [])]]))).
% 43.39/42.73  %-----------------------------------------------------
% 43.39/42.73  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------