%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n009.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 12:02:04 EDT 2023

% Result   : Theorem 45.84s 44.80s
% Output   : Proof 45.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n009.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 12:46:48 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 45.84/44.80  
% 45.84/44.80  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 45.84/44.80  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.84/44.80  %-----------------------------------------------------
% 45.84/44.80  ncf(matrix, plain, [(439 ^ _88492) ^ [] : [448 ^ _88492 : [(453 ^ _88492) ^ [] : [in(432 ^ [], relation_dom(relation_composition(433 ^ [], identity_relation(431 ^ []))))], (451 ^ _88492) ^ [] : [-(in(apply(433 ^ [], 432 ^ []), 431 ^ []))], (449 ^ _88492) ^ [] : [-(in(432 ^ [], relation_dom(433 ^ [])))]], 440 ^ _88492 : [(443 ^ _88492) ^ [] : [in(432 ^ [], relation_dom(433 ^ [])), in(apply(433 ^ [], 432 ^ []), 431 ^ [])], (441 ^ _88492) ^ [] : [-(in(432 ^ [], relation_dom(relation_composition(433 ^ [], identity_relation(431 ^ [])))))]]], (437 ^ _88492) ^ [] : [-(function(433 ^ []))], (435 ^ _88492) ^ [] : [-(relation(433 ^ []))], !, (168 ^ _74401) ^ [_79882] : [-(relation(identity_relation(_79882)))], (118 ^ _74401) ^ [_78236, _78238] : [_78238 = _78236, -(identity_relation(_78238) = identity_relation(_78236))], (140 ^ _74401) ^ [_79029, _79031] : [in(_79031, _79029), in(_79029, _79031)], (233 ^ _74401) ^ [_81853] : [empty(_81853), 236 ^ _74401 : [(239 ^ _74401) ^ [] : [-(relation(relation_dom(_81853)))], (237 ^ _74401) ^ [] : [-(empty(relation_dom(_81853)))]]], (4 ^ _74401) ^ [_74632, _74634] : [_74634 = _74632, -(_74632 = _74634)], (263 ^ _74401) ^ [_82794] : [-(empty(_82794)), 267 ^ _74401 : [(270 ^ _74401) ^ [] : [empty(266 ^ [_82794])], (268 ^ _74401) ^ [] : [-(element(266 ^ [_82794], powerset(_82794)))]]], (213 ^ _74401) ^ [] : [-(empty(empty_set))], (335 ^ _74401) ^ [_85151, _85153] : [element(_85153, _85151), -(empty(_85151)), -(in(_85153, _85151))], (215 ^ _74401) ^ [_81327] : [-(relation(identity_relation(_81327)))], (278 ^ _74401) ^ [] : [-(relation(274 ^ []))], (286 ^ _74401) ^ [] : [empty(284 ^ [])], (191 ^ _74401) ^ [_80653, _80655] : [206 ^ _74401 : [(209 ^ _74401) ^ [] : [-(function(relation_composition(_80655, _80653)))], (207 ^ _74401) ^ [] : [-(relation(relation_composition(_80655, _80653)))]], relation(_80655), function(_80655), relation(_80653), function(_80653)], (345 ^ _74401) ^ [_85449, _85451] : [relation(_85449), function(_85449), 352 ^ _74401 : [(365 ^ _74401) ^ [] : [-(_85449 = identity_relation(_85451)), relation_dom(_85449) = _85451, 371 ^ _74401 : [(374 ^ _74401) ^ [] : [apply(_85449, 370 ^ [_85449, _85451]) = 370 ^ [_85449, _85451]], (372 ^ _74401) ^ [] : [-(in(370 ^ [_85449, _85451], _85451))]]], (353 ^ _74401) ^ [] : [_85449 = identity_relation(_85451), 356 ^ _74401 : [(359 ^ _74401) ^ [_85868] : [in(_85868, _85451), -(apply(_85449, _85868) = _85868)], (357 ^ _74401) ^ [] : [-(relation_dom(_85449) = _85451)]]]]], (295 ^ _74401) ^ [_83913, _83915] : [in(_83915, _83913), -(element(_83915, _83913))], (211 ^ _74401) ^ [_81175] : [empty(powerset(_81175))], (173 ^ _74401) ^ [_80112, _80114] : [180 ^ _74401 : [(183 ^ _74401) ^ [] : [-(relation(relation_composition(_80112, _80114)))], (181 ^ _74401) ^ [] : [-(empty(relation_composition(_80112, _80114)))]], empty(_80114), relation(_80112)], (158 ^ _74401) ^ [_79612, _79614] : [-(relation(relation_composition(_79614, _79612))), relation(_79614), relation(_79612)], (276 ^ _74401) ^ [] : [empty(274 ^ [])], (171 ^ _74401) ^ [_80000] : [-(element(169 ^ [_80000], _80000))], (78 ^ _74401) ^ [_76922, _76924] : [-(function(_76922)), _76924 = _76922, function(_76924)], (146 ^ _74401) ^ [_79226] : [empty(_79226), -(function(_79226))], (256 ^ _74401) ^ [] : [-(function(252 ^ []))], (20 ^ _74401) ^ [_75149, _75151] : [-(relation_empty_yielding(_75149)), _75151 = _75149, relation_empty_yielding(_75151)], (289 ^ _74401) ^ [] : [-(relation(287 ^ []))], (10 ^ _74401) ^ [_74836, _74838, _74840] : [-(_74840 = _74836), _74840 = _74838, _74838 = _74836], (130 ^ _74401) ^ [_78680, _78682, _78684, _78686] : [-(apply(_78686, _78682) = apply(_78684, _78680)), _78686 = _78684, _78682 = _78680], (259 ^ _74401) ^ [] : [-(empty(257 ^ []))], (291 ^ _74401) ^ [] : [-(relation_empty_yielding(287 ^ []))], (283 ^ _74401) ^ [_83467] : [-(empty(279 ^ [_83467]))], (124 ^ _74401) ^ [_78454, _78456] : [_78456 = _78454, -(relation_dom(_78456) = relation_dom(_78454))], (422 ^ _74401) ^ [_87910, _87912] : [empty(_87912), -(_87912 = _87910), empty(_87910)], (400 ^ _74401) ^ [_87225, _87227, _87229] : [in(_87229, _87227), element(_87227, powerset(_87225)), empty(_87225)], (187 ^ _74401) ^ [] : [-(relation(empty_set))], (273 ^ _74401) ^ [] : [-(empty(271 ^ []))], (223 ^ _74401) ^ [_81576] : [empty(relation_dom(_81576)), -(empty(_81576)), relation(_81576)], (68 ^ _74401) ^ [_76627, _76629] : [-(relation(_76627)), _76629 = _76627, relation(_76629)], (44 ^ _74401) ^ [_75916, _75918, _75920, _75922] : [-(element(_75920, _75916)), element(_75922, _75918), _75922 = _75920, _75918 = _75916], (217 ^ _74401) ^ [_81372] : [-(function(identity_relation(_81372)))], (241 ^ _74401) ^ [_82132, _82134] : [248 ^ _74401 : [(251 ^ _74401) ^ [] : [-(relation(relation_composition(_82134, _82132)))], (249 ^ _74401) ^ [] : [-(empty(relation_composition(_82134, _82132)))]], empty(_82134), relation(_82132)], (301 ^ _74401) ^ [_84123, _84125] : [relation(_84123), function(_84123), 308 ^ _74401 : [(309 ^ _74401) ^ [_84373] : [relation(_84373), function(_84373), 316 ^ _74401 : [(325 ^ _74401) ^ [] : [-(in(_84125, relation_dom(relation_composition(_84373, _84123)))), in(_84125, relation_dom(_84373)), in(apply(_84373, _84125), relation_dom(_84123))], (317 ^ _74401) ^ [] : [in(_84125, relation_dom(relation_composition(_84373, _84123))), 320 ^ _74401 : [(323 ^ _74401) ^ [] : [-(in(apply(_84373, _84125), relation_dom(_84123)))], (321 ^ _74401) ^ [] : [-(in(_84125, relation_dom(_84373)))]]]]]]], (378 ^ _74401) ^ [_86502, _86504] : [element(_86504, powerset(_86502)), -(subset(_86504, _86502))], (390 ^ _74401) ^ [_86898, _86900, _86902] : [-(element(_86902, _86898)), in(_86902, _86900), element(_86900, powerset(_86898))], (189 ^ _74401) ^ [] : [-(relation_empty_yielding(empty_set))], (293 ^ _74401) ^ [_83804, _83806] : [-(subset(_83806, _83806))], (185 ^ _74401) ^ [] : [-(empty(empty_set))], (88 ^ _74401) ^ [_77225, _77227, _77229, _77231] : [-(in(_77229, _77225)), in(_77231, _77227), _77231 = _77229, _77227 = _77225], (221 ^ _74401) ^ [] : [-(relation(empty_set))], (219 ^ _74401) ^ [] : [-(empty(empty_set))], (281 ^ _74401) ^ [_83416] : [-(element(279 ^ [_83416], powerset(_83416)))], (30 ^ _74401) ^ [_75472, _75474, _75476, _75478] : [-(subset(_75476, _75472)), subset(_75478, _75474), _75478 = _75476, _75474 = _75472], (410 ^ _74401) ^ [_87521] : [empty(_87521), -(_87521 = empty_set)], (254 ^ _74401) ^ [] : [-(relation(252 ^ []))], (102 ^ _74401) ^ [_77659, _77661] : [_77661 = _77659, -(powerset(_77661) = powerset(_77659))], (261 ^ _74401) ^ [] : [-(relation(257 ^ []))], (58 ^ _74401) ^ [_76332, _76334] : [-(empty(_76332)), _76334 = _76332, empty(_76334)], (416 ^ _74401) ^ [_87723, _87725] : [in(_87725, _87723), empty(_87723)], (384 ^ _74401) ^ [_86668, _86670] : [subset(_86670, _86668), -(element(_86670, powerset(_86668)))], (152 ^ _74401) ^ [_79412] : [empty(_79412), -(relation(_79412))], (108 ^ _74401) ^ [_77905, _77907, _77909, _77911] : [-(relation_composition(_77911, _77907) = relation_composition(_77909, _77905)), _77911 = _77909, _77907 = _77905], (2 ^ _74401) ^ [_74525] : [-(_74525 = _74525)]], input).
% 45.84/44.80  ncf('1',plain,[453 : in(432 ^ [], relation_dom(relation_composition(433 ^ [], identity_relation(431 ^ [])))), 441 : -(in(432 ^ [], relation_dom(relation_composition(433 ^ [], identity_relation(431 ^ [])))))],start(439 ^ 0)).
% 45.84/44.80  ncf('1.1',plain,[-(in(432 ^ [], relation_dom(relation_composition(433 ^ [], identity_relation(431 ^ []))))), 325 : in(432 ^ [], relation_dom(433 ^ [])), 325 : in(apply(433 ^ [], 432 ^ []), relation_dom(identity_relation(431 ^ []))), 325 : relation(433 ^ []), 325 : function(433 ^ []), 309 : relation(identity_relation(431 ^ [])), 309 : function(identity_relation(431 ^ []))],extension(301 ^ 3,bind([[_84123, _84125, _84373], [identity_relation(431 ^ []), 432 ^ [], 433 ^ []]]))).
% 45.84/44.80  ncf('1.1.1',plain,[-(in(432 ^ [], relation_dom(433 ^ [])))],extension(449 ^ 8)).
% 45.84/44.80  ncf('1.1.2',plain,[-(in(apply(433 ^ [], 432 ^ []), relation_dom(identity_relation(431 ^ [])))), in(apply(433 ^ [], 432 ^ []), 431 ^ []), apply(433 ^ [], 432 ^ []) = apply(433 ^ [], 432 ^ []), 431 ^ [] = relation_dom(identity_relation(431 ^ []))],extension(88 ^ 8,bind([[_77225, _77227, _77229, _77231], [relation_dom(identity_relation(431 ^ [])), 431 ^ [], apply(433 ^ [], 432 ^ []), apply(433 ^ [], 432 ^ [])]]))).
% 45.84/44.80  ncf('1.1.2.1',plain,[-(in(apply(433 ^ [], 432 ^ []), 431 ^ []))],extension(451 ^ 9)).
% 45.84/44.80  ncf('1.1.2.2',plain,[-(apply(433 ^ [], 432 ^ []) = apply(433 ^ [], 432 ^ [])), 433 ^ [] = 433 ^ [], 432 ^ [] = 432 ^ []],extension(130 ^ 9,bind([[_78680, _78682, _78684, _78686], [432 ^ [], 432 ^ [], 433 ^ [], 433 ^ []]]))).
% 45.84/44.80  ncf('1.1.2.2.1',plain,[-(433 ^ [] = 433 ^ [])],extension(2 ^ 10,bind([[_74525], [433 ^ []]]))).
% 45.84/44.80  ncf('1.1.2.2.2',plain,[-(432 ^ [] = 432 ^ [])],extension(2 ^ 10,bind([[_74525], [432 ^ []]]))).
% 45.84/44.80  ncf('1.1.2.3',plain,[-(431 ^ [] = relation_dom(identity_relation(431 ^ []))), relation_dom(identity_relation(431 ^ [])) = 431 ^ []],extension(4 ^ 9,bind([[_74632, _74634], [431 ^ [], relation_dom(identity_relation(431 ^ []))]]))).
% 45.84/44.80  ncf('1.1.2.3.1',plain,[-(relation_dom(identity_relation(431 ^ [])) = 431 ^ []), 353 : identity_relation(431 ^ []) = identity_relation(431 ^ []), 353 : relation(identity_relation(431 ^ [])), 353 : function(identity_relation(431 ^ []))],extension(345 ^ 10,bind([[_85449, _85451], [identity_relation(431 ^ []), 431 ^ []]]))).
% 45.84/44.80  ncf('1.1.2.3.1.1',plain,[-(identity_relation(431 ^ []) = identity_relation(431 ^ []))],extension(2 ^ 13,bind([[_74525], [identity_relation(431 ^ [])]]))).
% 45.84/44.80  ncf('1.1.2.3.1.2',plain,[-(relation(identity_relation(431 ^ [])))],extension(168 ^ 11,bind([[_79882], [431 ^ []]]))).
% 45.84/44.80  ncf('1.1.2.3.1.3',plain,[-(function(identity_relation(431 ^ [])))],extension(217 ^ 11,bind([[_81372], [431 ^ []]]))).
% 45.84/44.80  ncf('1.1.3',plain,[-(relation(433 ^ []))],extension(435 ^ 6)).
% 45.84/44.80  ncf('1.1.4',plain,[-(function(433 ^ []))],extension(437 ^ 6)).
% 45.84/44.80  ncf('1.1.5',plain,[-(relation(identity_relation(431 ^ [])))],extension(168 ^ 4,bind([[_79882], [431 ^ []]]))).
% 45.84/44.80  ncf('1.1.6',plain,[-(function(identity_relation(431 ^ [])))],extension(217 ^ 4,bind([[_81372], [431 ^ []]]))).
% 45.84/44.80  ncf('1.2',plain,[in(432 ^ [], relation_dom(relation_composition(433 ^ [], identity_relation(431 ^ [])))), 323 : -(in(apply(433 ^ [], 432 ^ []), relation_dom(identity_relation(431 ^ [])))), 317 : relation(433 ^ []), 317 : function(433 ^ []), 309 : relation(identity_relation(431 ^ [])), 309 : function(identity_relation(431 ^ []))],extension(301 ^ 3,bind([[_84123, _84125, _84373], [identity_relation(431 ^ []), 432 ^ [], 433 ^ []]]))).
% 45.84/44.80  ncf('1.2.1',plain,[in(apply(433 ^ [], 432 ^ []), relation_dom(identity_relation(431 ^ []))), -(in(apply(433 ^ [], 432 ^ []), 431 ^ [])), apply(433 ^ [], 432 ^ []) = apply(433 ^ [], 432 ^ []), relation_dom(identity_relation(431 ^ [])) = 431 ^ []],extension(88 ^ 10,bind([[_77225, _77227, _77229, _77231], [431 ^ [], relation_dom(identity_relation(431 ^ [])), apply(433 ^ [], 432 ^ []), apply(433 ^ [], 432 ^ [])]]))).
% 45.84/44.80  ncf('1.2.1.1',plain,[in(apply(433 ^ [], 432 ^ []), 431 ^ []), in(432 ^ [], relation_dom(433 ^ []))],extension(443 ^ 11)).
% 45.84/44.80  ncf('1.2.1.1.1',plain,[-(in(432 ^ [], relation_dom(433 ^ [])))],extension(321 ^ 12)).
% 45.84/44.80  ncf('1.2.1.2',plain,[-(apply(433 ^ [], 432 ^ []) = apply(433 ^ [], 432 ^ [])), 433 ^ [] = 433 ^ [], 432 ^ [] = 432 ^ []],extension(130 ^ 11,bind([[_78680, _78682, _78684, _78686], [432 ^ [], 432 ^ [], 433 ^ [], 433 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.2.1',plain,[-(433 ^ [] = 433 ^ [])],extension(2 ^ 12,bind([[_74525], [433 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.2.2',plain,[-(432 ^ [] = 432 ^ [])],extension(2 ^ 12,bind([[_74525], [432 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.3',plain,[-(relation_dom(identity_relation(431 ^ [])) = 431 ^ []), 353 : identity_relation(431 ^ []) = identity_relation(431 ^ []), 353 : relation(identity_relation(431 ^ [])), 353 : function(identity_relation(431 ^ []))],extension(345 ^ 11,bind([[_85449, _85451], [identity_relation(431 ^ []), 431 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.3.1',plain,[-(identity_relation(431 ^ []) = identity_relation(431 ^ [])), 431 ^ [] = 431 ^ []],extension(118 ^ 14,bind([[_78236, _78238], [431 ^ [], 431 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.3.1.1',plain,[-(431 ^ [] = 431 ^ [])],extension(2 ^ 15,bind([[_74525], [431 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.3.2',plain,[-(relation(identity_relation(431 ^ [])))],extension(168 ^ 12,bind([[_79882], [431 ^ []]]))).
% 45.84/44.80  ncf('1.2.1.3.3',plain,[-(function(identity_relation(431 ^ [])))],extension(217 ^ 12,bind([[_81372], [431 ^ []]]))).
% 45.84/44.80  ncf('1.2.2',plain,[-(relation(433 ^ []))],extension(435 ^ 6)).
% 45.84/44.80  ncf('1.2.3',plain,[-(function(433 ^ []))],extension(437 ^ 6)).
% 45.84/44.80  ncf('1.2.4',plain,[-(relation(identity_relation(431 ^ [])))],extension(168 ^ 4,bind([[_79882], [431 ^ []]]))).
% 45.84/44.80  ncf('1.2.5',plain,[-(function(identity_relation(431 ^ [])))],extension(217 ^ 4,bind([[_81372], [431 ^ []]]))).
% 45.84/44.80  %-----------------------------------------------------
% 45.84/44.80  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------