%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 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 11:56:15 EDT 2023

% Result   : Theorem 13.10s 13.77s
% Output   : Proof 13.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n004.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 18:52:24 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 13.10/13.77  
% 13.10/13.77  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 13.10/13.77  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.10/13.77  %-----------------------------------------------------
% 13.10/13.77  ncf(matrix, plain, [(450 ^ _63382) ^ [] : [-(ilf_type(448 ^ [], set_type))], (453 ^ _63382) ^ [] : [-(ilf_type(451 ^ [], set_type))], (455 ^ _63382) ^ [] : [ilf_type(empty_set, relation_type(448 ^ [], 451 ^ []))], (96 ^ _63382) ^ [_66512, _66514] : [_66514 = _66512, -(power_set(_66514) = power_set(_66512))], (102 ^ _63382) ^ [_66730, _66732] : [_66732 = _66730, -(member_type(_66732) = member_type(_66730))], (108 ^ _63382) ^ [_66948, _66950] : [_66950 = _66948, -(subset_type(_66950) = subset_type(_66948))], (114 ^ _63382) ^ [_67194, _67196, _67198, _67200] : [-(cross_product(_67200, _67196) = cross_product(_67198, _67194)), _67200 = _67198, _67196 = _67194], (124 ^ _63382) ^ [_67553, _67555, _67557, _67559] : [-(ordered_pair(_67559, _67555) = ordered_pair(_67557, _67553)), _67559 = _67557, _67555 = _67553], (134 ^ _63382) ^ [_67892, _67894, _67896, _67898] : [-(relation_type(_67898, _67894) = relation_type(_67896, _67892)), _67898 = _67896, _67894 = _67892], (2 ^ _63382) ^ [_63526] : [-(_63526 = _63526)], (4 ^ _63382) ^ [_63633, _63635] : [_63635 = _63633, -(_63633 = _63635)], (10 ^ _63382) ^ [_63837, _63839, _63841] : [-(_63841 = _63837), _63841 = _63839, _63839 = _63837], (20 ^ _63382) ^ [_64178, _64180, _64182, _64184] : [-(type(_64182, _64178)), type(_64184, _64180), _64184 = _64182, _64180 = _64178], (34 ^ _63382) ^ [_64622, _64624, _64626, _64628] : [-(subset(_64626, _64622)), subset(_64628, _64624), _64628 = _64626, _64624 = _64622], (48 ^ _63382) ^ [_65066, _65068, _65070, _65072] : [-(member(_65070, _65066)), member(_65072, _65068), _65072 = _65070, _65068 = _65066], (62 ^ _63382) ^ [_65482, _65484] : [-(empty(_65482)), _65484 = _65482, empty(_65484)], (72 ^ _63382) ^ [_65777, _65779] : [-(relation_like(_65777)), _65779 = _65777, relation_like(_65779)], (82 ^ _63382) ^ [_66080, _66082, _66084, _66086] : [-(ilf_type(_66084, _66080)), ilf_type(_66086, _66082), _66086 = _66084, _66082 = _66080], (144 ^ _63382) ^ [_68231] : [ilf_type(_68231, set_type), 147 ^ _63382 : [(148 ^ _63382) ^ [_68367] : [ilf_type(_68367, set_type), -(subset(empty_set, cross_product(_68231, _68367)))]]], (154 ^ _63382) ^ [_68576] : [ilf_type(_68576, set_type), 157 ^ _63382 : [(158 ^ _63382) ^ [_68753] : [ilf_type(_68753, set_type), 161 ^ _63382 : [(162 ^ _63382) ^ [_68945] : [ilf_type(_68945, subset_type(cross_product(_68576, _68753))), -(ilf_type(_68945, relation_type(_68576, _68753)))], (168 ^ _63382) ^ [_69147] : [ilf_type(_69147, relation_type(_68576, _68753)), -(ilf_type(_69147, subset_type(cross_product(_68576, _68753))))]]]]], (174 ^ _63382) ^ [_69381] : [ilf_type(_69381, set_type), 177 ^ _63382 : [(178 ^ _63382) ^ [_69522] : [ilf_type(_69522, set_type), -(ilf_type(181 ^ [_69381, _69522], relation_type(_69522, _69381)))]]], (185 ^ _63382) ^ [_69791] : [ilf_type(_69791, set_type), member(_69791, empty_set)], (191 ^ _63382) ^ [] : [-(empty(empty_set))], (193 ^ _63382) ^ [] : [-(type(empty_set, set_type))], (195 ^ _63382) ^ [_70088] : [ilf_type(_70088, set_type), 198 ^ _63382 : [(199 ^ _63382) ^ [_70224] : [ilf_type(_70224, set_type), -(ilf_type(cross_product(_70088, _70224), set_type))]]], (205 ^ _63382) ^ [_70433] : [ilf_type(_70433, set_type), 208 ^ _63382 : [(209 ^ _63382) ^ [_70578] : [ilf_type(_70578, set_type), 212 ^ _63382 : [(213 ^ _63382) ^ [] : [ilf_type(_70578, subset_type(_70433)), -(ilf_type(_70578, member_type(power_set(_70433))))], (219 ^ _63382) ^ [] : [ilf_type(_70578, member_type(power_set(_70433))), -(ilf_type(_70578, subset_type(_70433)))]]]]], (225 ^ _63382) ^ [_71049] : [ilf_type(_71049, set_type), -(ilf_type(228 ^ [_71049], subset_type(_71049)))], (232 ^ _63382) ^ [_71296] : [ilf_type(_71296, set_type), 235 ^ _63382 : [(236 ^ _63382) ^ [_71452] : [ilf_type(_71452, set_type), 239 ^ _63382 : [(254 ^ _63382) ^ [] : [256 ^ _63382 : [(257 ^ _63382) ^ [] : [-(ilf_type(255 ^ [_71296, _71452], set_type))], (259 ^ _63382) ^ [] : [-(member(255 ^ [_71296, _71452], _71296))], (261 ^ _63382) ^ [] : [member(255 ^ [_71296, _71452], _71452)]], -(subset(_71296, _71452))], (240 ^ _63382) ^ [] : [subset(_71296, _71452), 243 ^ _63382 : [(244 ^ _63382) ^ [_71711] : [ilf_type(_71711, set_type), member(_71711, _71296), -(member(_71711, _71452))]]]]]]], (265 ^ _63382) ^ [_72371] : [ilf_type(_72371, set_type), -(subset(_72371, _72371))], (271 ^ _63382) ^ [_72561] : [ilf_type(_72561, set_type), 274 ^ _63382 : [(285 ^ _63382) ^ [] : [287 ^ _63382 : [(288 ^ _63382) ^ [] : [-(ilf_type(286 ^ [_72561], set_type))], (290 ^ _63382) ^ [] : [-(member(286 ^ [_72561], _72561))]], -(empty(_72561))], (275 ^ _63382) ^ [] : [empty(_72561), 278 ^ _63382 : [(279 ^ _63382) ^ [_72804] : [ilf_type(_72804, set_type), member(_72804, _72561)]]]]], (294 ^ _63382) ^ [_73264] : [ilf_type(_73264, set_type), 297 ^ _63382 : [(298 ^ _63382) ^ [_73422] : [ilf_type(_73422, set_type), 301 ^ _63382 : [(316 ^ _63382) ^ [] : [318 ^ _63382 : [(319 ^ _63382) ^ [] : [-(ilf_type(317 ^ [_73264, _73422], set_type))], (321 ^ _63382) ^ [] : [-(member(317 ^ [_73264, _73422], _73264))], (323 ^ _63382) ^ [] : [member(317 ^ [_73264, _73422], _73422)]], -(member(_73264, power_set(_73422)))], (302 ^ _63382) ^ [] : [member(_73264, power_set(_73422)), 305 ^ _63382 : [(306 ^ _63382) ^ [_73685] : [ilf_type(_73685, set_type), member(_73685, _73264), -(member(_73685, _73422))]]]]]]], (327 ^ _63382) ^ [_74347] : [ilf_type(_74347, set_type), 330 ^ _63382 : [(331 ^ _63382) ^ [] : [empty(power_set(_74347))], (333 ^ _63382) ^ [] : [-(ilf_type(power_set(_74347), set_type))]]], (335 ^ _63382) ^ [_74617] : [ilf_type(_74617, set_type), 338 ^ _63382 : [(339 ^ _63382) ^ [_74765] : [-(empty(_74765)), ilf_type(_74765, set_type), 346 ^ _63382 : [(347 ^ _63382) ^ [] : [ilf_type(_74617, member_type(_74765)), -(member(_74617, _74765))], (353 ^ _63382) ^ [] : [member(_74617, _74765), -(ilf_type(_74617, member_type(_74765)))]]]]], (359 ^ _63382) ^ [_75316] : [-(ilf_type(366 ^ [_75316], member_type(_75316))), -(empty(_75316)), ilf_type(_75316, set_type)], (370 ^ _63382) ^ [_75649] : [ilf_type(_75649, set_type), 373 ^ _63382 : [(374 ^ _63382) ^ [] : [relation_like(_75649), 377 ^ _63382 : [(378 ^ _63382) ^ [_75921] : [ilf_type(_75921, set_type), member(_75921, _75649), 386 ^ _63382 : [(387 ^ _63382) ^ [] : [-(ilf_type(385 ^ [_75649, _75921], set_type))], (390 ^ _63382) ^ [] : [-(ilf_type(388 ^ [_75649, _75921], set_type))], (392 ^ _63382) ^ [] : [-(_75921 = ordered_pair(385 ^ [_75649, _75921], 388 ^ [_75649, _75921]))]]]]], (394 ^ _63382) ^ [] : [-(relation_like(_75649)), 396 ^ _63382 : [(397 ^ _63382) ^ [] : [-(ilf_type(395 ^ [_75649], set_type))], (399 ^ _63382) ^ [] : [-(member(395 ^ [_75649], _75649))], (401 ^ _63382) ^ [_76760] : [ilf_type(_76760, set_type), 404 ^ _63382 : [(405 ^ _63382) ^ [_76907] : [ilf_type(_76907, set_type), 395 ^ [_75649] = ordered_pair(_76760, _76907)]]]]]]], (413 ^ _63382) ^ [_77192] : [-(relation_like(_77192)), empty(_77192), ilf_type(_77192, set_type)], (447 ^ _63382) ^ [_78288] : [-(ilf_type(_78288, set_type))], (437 ^ _63382) ^ [_77978] : [ilf_type(_77978, set_type), 440 ^ _63382 : [(441 ^ _63382) ^ [_78114] : [ilf_type(_78114, set_type), -(ilf_type(ordered_pair(_77978, _78114), set_type))]]], (423 ^ _63382) ^ [_77463] : [ilf_type(_77463, set_type), 426 ^ _63382 : [(427 ^ _63382) ^ [_77611] : [ilf_type(_77611, set_type), 430 ^ _63382 : [(431 ^ _63382) ^ [_77754] : [ilf_type(_77754, subset_type(cross_product(_77463, _77611))), -(relation_like(_77754))]]]]]], input).
% 13.10/13.77  ncf('1',plain,[ilf_type(empty_set, relation_type(448 ^ [], 451 ^ []))],start(455 ^ 0)).
% 13.10/13.77  ncf('1.1',plain,[-(ilf_type(empty_set, relation_type(448 ^ [], 451 ^ []))), 162 : ilf_type(empty_set, subset_type(cross_product(448 ^ [], 451 ^ []))), 162 : ilf_type(451 ^ [], set_type), 158 : ilf_type(448 ^ [], set_type)],extension(154 ^ 1,bind([[_68576, _68753, _68945], [448 ^ [], 451 ^ [], empty_set]]))).
% 13.10/13.77  ncf('1.1.1',plain,[-(ilf_type(empty_set, subset_type(cross_product(448 ^ [], 451 ^ [])))), 219 : ilf_type(empty_set, member_type(power_set(cross_product(448 ^ [], 451 ^ [])))), 219 : ilf_type(empty_set, set_type), 209 : ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)],extension(205 ^ 6,bind([[_70433, _70578], [cross_product(448 ^ [], 451 ^ []), empty_set]]))).
% 13.10/13.77  ncf('1.1.1.1',plain,[-(ilf_type(empty_set, member_type(power_set(cross_product(448 ^ [], 451 ^ []))))), 353 : member(empty_set, power_set(cross_product(448 ^ [], 451 ^ []))), 353 : -(empty(power_set(cross_product(448 ^ [], 451 ^ [])))), 353 : ilf_type(power_set(cross_product(448 ^ [], 451 ^ [])), set_type), 339 : ilf_type(empty_set, set_type)],extension(335 ^ 11,bind([[_74617, _74765], [empty_set, power_set(cross_product(448 ^ [], 451 ^ []))]]))).
% 13.10/13.77  ncf('1.1.1.1.1',plain,[-(member(empty_set, power_set(cross_product(448 ^ [], 451 ^ [])))), 319 : -(ilf_type(317 ^ [empty_set, cross_product(448 ^ [], 451 ^ [])], set_type)), 316 : ilf_type(cross_product(448 ^ [], 451 ^ []), set_type), 298 : ilf_type(empty_set, set_type)],extension(294 ^ 16,bind([[_73264, _73422], [empty_set, cross_product(448 ^ [], 451 ^ [])]]))).
% 13.10/13.77  ncf('1.1.1.1.1.1',plain,[ilf_type(317 ^ [empty_set, cross_product(448 ^ [], 451 ^ [])], set_type), member(317 ^ [empty_set, cross_product(448 ^ [], 451 ^ [])], empty_set)],extension(185 ^ 23,bind([[_69791], [317 ^ [empty_set, cross_product(448 ^ [], 451 ^ [])]]]))).
% 13.10/13.77  ncf('1.1.1.1.1.1.1',plain,[-(member(317 ^ [empty_set, cross_product(448 ^ [], 451 ^ [])], empty_set))],extension(321 ^ 24)).
% 13.10/13.77  ncf('1.1.1.1.1.2',plain,[-(ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)), 199 : ilf_type(451 ^ [], set_type), 199 : ilf_type(448 ^ [], set_type)],extension(195 ^ 19,bind([[_70088, _70224], [448 ^ [], 451 ^ []]]))).
% 13.10/13.77  ncf('1.1.1.1.1.2.1',plain,[-(ilf_type(451 ^ [], set_type))],extension(453 ^ 22)).
% 13.10/13.77  ncf('1.1.1.1.1.2.2',plain,[-(ilf_type(448 ^ [], set_type))],extension(450 ^ 20)).
% 13.10/13.77  ncf('1.1.1.1.1.3',plain,[-(ilf_type(empty_set, set_type))],extension(447 ^ 17,bind([[_78288], [empty_set]]))).
% 13.10/13.77  ncf('1.1.1.1.2',plain,[empty(power_set(cross_product(448 ^ [], 451 ^ []))), ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)],extension(327 ^ 14,bind([[_74347], [cross_product(448 ^ [], 451 ^ [])]]))).
% 13.10/13.77  ncf('1.1.1.1.2.1',plain,[-(ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)), 199 : ilf_type(451 ^ [], set_type), 199 : ilf_type(448 ^ [], set_type)],extension(195 ^ 15,bind([[_70088, _70224], [448 ^ [], 451 ^ []]]))).
% 13.10/13.77  ncf('1.1.1.1.2.1.1',plain,[-(ilf_type(451 ^ [], set_type))],extension(453 ^ 18)).
% 13.10/13.77  ncf('1.1.1.1.2.1.2',plain,[-(ilf_type(448 ^ [], set_type))],extension(450 ^ 16)).
% 13.10/13.77  ncf('1.1.1.1.3',plain,[-(ilf_type(power_set(cross_product(448 ^ [], 451 ^ [])), set_type)), ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)],extension(327 ^ 14,bind([[_74347], [cross_product(448 ^ [], 451 ^ [])]]))).
% 13.10/13.77  ncf('1.1.1.1.3.1',plain,[-(ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)), 199 : ilf_type(451 ^ [], set_type), 199 : ilf_type(448 ^ [], set_type)],extension(195 ^ 15,bind([[_70088, _70224], [448 ^ [], 451 ^ []]]))).
% 13.10/13.77  ncf('1.1.1.1.3.1.1',plain,[-(ilf_type(451 ^ [], set_type))],extension(453 ^ 18)).
% 13.10/13.77  ncf('1.1.1.1.3.1.2',plain,[-(ilf_type(448 ^ [], set_type))],extension(450 ^ 16)).
% 13.10/13.77  ncf('1.1.1.1.4',plain,[-(ilf_type(empty_set, set_type))],extension(447 ^ 12,bind([[_78288], [empty_set]]))).
% 13.10/13.77  ncf('1.1.1.2',plain,[-(ilf_type(empty_set, set_type))],extension(447 ^ 9,bind([[_78288], [empty_set]]))).
% 13.10/13.77  ncf('1.1.1.3',plain,[-(ilf_type(cross_product(448 ^ [], 451 ^ []), set_type)), 199 : ilf_type(451 ^ [], set_type), 199 : ilf_type(448 ^ [], set_type)],extension(195 ^ 7,bind([[_70088, _70224], [448 ^ [], 451 ^ []]]))).
% 13.10/13.77  ncf('1.1.1.3.1',plain,[-(ilf_type(451 ^ [], set_type))],extension(453 ^ 10)).
% 13.10/13.77  ncf('1.1.1.3.2',plain,[-(ilf_type(448 ^ [], set_type))],extension(450 ^ 8)).
% 13.10/13.77  ncf('1.1.2',plain,[-(ilf_type(451 ^ [], set_type))],extension(453 ^ 4)).
% 13.10/13.77  ncf('1.1.3',plain,[-(ilf_type(448 ^ [], set_type))],extension(450 ^ 2)).
% 13.10/13.77  %-----------------------------------------------------
% 13.10/13.77  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------