%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.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 11:56:12 EDT 2023

% Result   : Theorem 37.03s 36.53s
% Output   : Proof 37.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.31  % Computer : n020.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May 18 18:59:47 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 37.03/36.53  
% 37.03/36.53  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 37.03/36.53  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.03/36.53  %-----------------------------------------------------
% 37.03/36.53  ncf(matrix, plain, [(466 ^ _66339) ^ [] : [-(ilf_type(464 ^ [], set_type))], (469 ^ _66339) ^ [] : [-(ilf_type(467 ^ [], set_type))], (472 ^ _66339) ^ [] : [-(ilf_type(470 ^ [], set_type))], (474 ^ _66339) ^ [] : [-(subset(464 ^ [], cross_product(467 ^ [], 470 ^ [])))], (476 ^ _66339) ^ [] : [ilf_type(464 ^ [], relation_type(467 ^ [], 470 ^ []))], (82 ^ _66339) ^ [_69023, _69025] : [_69025 = _69023, -(power_set(_69025) = power_set(_69023))], (88 ^ _66339) ^ [_69241, _69243] : [_69243 = _69241, -(member_type(_69243) = member_type(_69241))], (94 ^ _66339) ^ [_69487, _69489, _69491, _69493] : [-(ordered_pair(_69493, _69489) = ordered_pair(_69491, _69487)), _69493 = _69491, _69489 = _69487], (104 ^ _66339) ^ [_69818, _69820] : [_69820 = _69818, -(subset_type(_69820) = subset_type(_69818))], (110 ^ _66339) ^ [_70064, _70066, _70068, _70070] : [-(cross_product(_70070, _70066) = cross_product(_70068, _70064)), _70070 = _70068, _70066 = _70064], (120 ^ _66339) ^ [_70403, _70405, _70407, _70409] : [-(relation_type(_70409, _70405) = relation_type(_70407, _70403)), _70409 = _70407, _70405 = _70403], (2 ^ _66339) ^ [_66483] : [-(_66483 = _66483)], (4 ^ _66339) ^ [_66590, _66592] : [_66592 = _66590, -(_66590 = _66592)], (10 ^ _66339) ^ [_66794, _66796, _66798] : [-(_66798 = _66794), _66798 = _66796, _66796 = _66794], (20 ^ _66339) ^ [_67135, _67137, _67139, _67141] : [-(member(_67139, _67135)), member(_67141, _67137), _67141 = _67139, _67137 = _67135], (34 ^ _66339) ^ [_67551, _67553] : [-(empty(_67551)), _67553 = _67551, empty(_67553)], (44 ^ _66339) ^ [_67846, _67848] : [-(relation_like(_67846)), _67848 = _67846, relation_like(_67848)], (54 ^ _66339) ^ [_68169, _68171, _68173, _68175] : [-(subset(_68173, _68169)), subset(_68175, _68171), _68175 = _68173, _68171 = _68169], (68 ^ _66339) ^ [_68593, _68595, _68597, _68599] : [-(ilf_type(_68597, _68593)), ilf_type(_68599, _68595), _68599 = _68597, _68595 = _68593], (130 ^ _66339) ^ [_70742] : [ilf_type(_70742, set_type), 133 ^ _66339 : [(134 ^ _66339) ^ [_70919] : [ilf_type(_70919, set_type), 137 ^ _66339 : [(138 ^ _66339) ^ [_71111] : [ilf_type(_71111, subset_type(cross_product(_70742, _70919))), -(ilf_type(_71111, relation_type(_70742, _70919)))], (144 ^ _66339) ^ [_71313] : [ilf_type(_71313, relation_type(_70742, _70919)), -(ilf_type(_71313, subset_type(cross_product(_70742, _70919))))]]]]], (150 ^ _66339) ^ [_71547] : [ilf_type(_71547, set_type), 153 ^ _66339 : [(154 ^ _66339) ^ [_71688] : [ilf_type(_71688, set_type), -(ilf_type(157 ^ [_71547, _71688], relation_type(_71688, _71547)))]]], (161 ^ _66339) ^ [_71957] : [ilf_type(_71957, set_type), 164 ^ _66339 : [(165 ^ _66339) ^ [_72147] : [ilf_type(_72147, set_type), 168 ^ _66339 : [(169 ^ _66339) ^ [_72332] : [ilf_type(_72332, set_type), 172 ^ _66339 : [(173 ^ _66339) ^ [] : [member(_72332, cross_product(_71957, _72147)), 177 ^ _66339 : [(178 ^ _66339) ^ [] : [-(ilf_type(176 ^ [_71957, _72147, _72332], set_type))], (181 ^ _66339) ^ [] : [-(ilf_type(179 ^ [_71957, _72147, _72332], set_type))], (183 ^ _66339) ^ [] : [-(member(176 ^ [_71957, _72147, _72332], _71957))], (185 ^ _66339) ^ [] : [-(member(179 ^ [_71957, _72147, _72332], _72147))], (187 ^ _66339) ^ [] : [-(_72332 = ordered_pair(176 ^ [_71957, _72147, _72332], 179 ^ [_71957, _72147, _72332]))]]], (189 ^ _66339) ^ [] : [-(member(_72332, cross_product(_71957, _72147))), 190 ^ _66339 : [(191 ^ _66339) ^ [_73222] : [ilf_type(_73222, set_type), 194 ^ _66339 : [(195 ^ _66339) ^ [_73388] : [ilf_type(_73388, set_type), member(_73222, _71957), member(_73388, _72147), _72332 = ordered_pair(_73222, _73388)]]]]]]]]]]], (211 ^ _66339) ^ [_73895] : [ilf_type(_73895, set_type), 214 ^ _66339 : [(215 ^ _66339) ^ [_74031] : [ilf_type(_74031, set_type), -(ilf_type(cross_product(_73895, _74031), set_type))]]], (221 ^ _66339) ^ [_74240] : [ilf_type(_74240, set_type), 224 ^ _66339 : [(225 ^ _66339) ^ [_74396] : [ilf_type(_74396, set_type), 228 ^ _66339 : [(243 ^ _66339) ^ [] : [245 ^ _66339 : [(246 ^ _66339) ^ [] : [-(ilf_type(244 ^ [_74240, _74396], set_type))], (248 ^ _66339) ^ [] : [-(member(244 ^ [_74240, _74396], _74240))], (250 ^ _66339) ^ [] : [member(244 ^ [_74240, _74396], _74396)]], -(subset(_74240, _74396))], (229 ^ _66339) ^ [] : [subset(_74240, _74396), 232 ^ _66339 : [(233 ^ _66339) ^ [_74655] : [ilf_type(_74655, set_type), member(_74655, _74240), -(member(_74655, _74396))]]]]]]], (254 ^ _66339) ^ [_75315] : [ilf_type(_75315, set_type), 257 ^ _66339 : [(258 ^ _66339) ^ [_75451] : [ilf_type(_75451, set_type), -(ilf_type(ordered_pair(_75315, _75451), set_type))]]], (264 ^ _66339) ^ [_75660] : [ilf_type(_75660, set_type), 267 ^ _66339 : [(268 ^ _66339) ^ [_75805] : [ilf_type(_75805, set_type), 271 ^ _66339 : [(272 ^ _66339) ^ [] : [ilf_type(_75805, subset_type(_75660)), -(ilf_type(_75805, member_type(power_set(_75660))))], (278 ^ _66339) ^ [] : [ilf_type(_75805, member_type(power_set(_75660))), -(ilf_type(_75805, subset_type(_75660)))]]]]], (284 ^ _66339) ^ [_76276] : [ilf_type(_76276, set_type), -(ilf_type(287 ^ [_76276], subset_type(_76276)))], (291 ^ _66339) ^ [_76523] : [ilf_type(_76523, set_type), -(subset(_76523, _76523))], (297 ^ _66339) ^ [_76713] : [ilf_type(_76713, set_type), 300 ^ _66339 : [(301 ^ _66339) ^ [_76871] : [ilf_type(_76871, set_type), 304 ^ _66339 : [(319 ^ _66339) ^ [] : [321 ^ _66339 : [(322 ^ _66339) ^ [] : [-(ilf_type(320 ^ [_76713, _76871], set_type))], (324 ^ _66339) ^ [] : [-(member(320 ^ [_76713, _76871], _76713))], (326 ^ _66339) ^ [] : [member(320 ^ [_76713, _76871], _76871)]], -(member(_76713, power_set(_76871)))], (305 ^ _66339) ^ [] : [member(_76713, power_set(_76871)), 308 ^ _66339 : [(309 ^ _66339) ^ [_77134] : [ilf_type(_77134, set_type), member(_77134, _76713), -(member(_77134, _76871))]]]]]]], (330 ^ _66339) ^ [_77796] : [ilf_type(_77796, set_type), 333 ^ _66339 : [(334 ^ _66339) ^ [] : [empty(power_set(_77796))], (336 ^ _66339) ^ [] : [-(ilf_type(power_set(_77796), set_type))]]], (338 ^ _66339) ^ [_78066] : [ilf_type(_78066, set_type), 341 ^ _66339 : [(342 ^ _66339) ^ [_78214] : [-(empty(_78214)), ilf_type(_78214, set_type), 349 ^ _66339 : [(350 ^ _66339) ^ [] : [ilf_type(_78066, member_type(_78214)), -(member(_78066, _78214))], (356 ^ _66339) ^ [] : [member(_78066, _78214), -(ilf_type(_78066, member_type(_78214)))]]]]], (362 ^ _66339) ^ [_78765] : [-(ilf_type(369 ^ [_78765], member_type(_78765))), -(empty(_78765)), ilf_type(_78765, set_type)], (373 ^ _66339) ^ [_79098] : [ilf_type(_79098, set_type), 376 ^ _66339 : [(387 ^ _66339) ^ [] : [389 ^ _66339 : [(390 ^ _66339) ^ [] : [-(ilf_type(388 ^ [_79098], set_type))], (392 ^ _66339) ^ [] : [-(member(388 ^ [_79098], _79098))]], -(empty(_79098))], (377 ^ _66339) ^ [] : [empty(_79098), 380 ^ _66339 : [(381 ^ _66339) ^ [_79341] : [ilf_type(_79341, set_type), member(_79341, _79098)]]]]], (439 ^ _66339) ^ [_81344] : [-(relation_like(_81344)), empty(_81344), ilf_type(_81344, set_type)], (463 ^ _66339) ^ [_82095] : [-(ilf_type(_82095, set_type))], (449 ^ _66339) ^ [_81615] : [ilf_type(_81615, set_type), 452 ^ _66339 : [(453 ^ _66339) ^ [_81763] : [ilf_type(_81763, set_type), 456 ^ _66339 : [(457 ^ _66339) ^ [_81906] : [ilf_type(_81906, subset_type(cross_product(_81615, _81763))), -(relation_like(_81906))]]]]], (396 ^ _66339) ^ [_79801] : [ilf_type(_79801, set_type), 399 ^ _66339 : [(400 ^ _66339) ^ [] : [relation_like(_79801), 403 ^ _66339 : [(404 ^ _66339) ^ [_80073] : [ilf_type(_80073, set_type), member(_80073, _79801), 412 ^ _66339 : [(413 ^ _66339) ^ [] : [-(ilf_type(411 ^ [_79801, _80073], set_type))], (416 ^ _66339) ^ [] : [-(ilf_type(414 ^ [_79801, _80073], set_type))], (418 ^ _66339) ^ [] : [-(_80073 = ordered_pair(411 ^ [_79801, _80073], 414 ^ [_79801, _80073]))]]]]], (420 ^ _66339) ^ [] : [-(relation_like(_79801)), 422 ^ _66339 : [(423 ^ _66339) ^ [] : [-(ilf_type(421 ^ [_79801], set_type))], (425 ^ _66339) ^ [] : [-(member(421 ^ [_79801], _79801))], (427 ^ _66339) ^ [_80912] : [ilf_type(_80912, set_type), 430 ^ _66339 : [(431 ^ _66339) ^ [_81059] : [ilf_type(_81059, set_type), 421 ^ [_79801] = ordered_pair(_80912, _81059)]]]]]]]], input).
% 37.03/36.53  ncf('1',plain,[ilf_type(464 ^ [], relation_type(467 ^ [], 470 ^ []))],start(476 ^ 0)).
% 37.03/36.53  ncf('1.1',plain,[-(ilf_type(464 ^ [], relation_type(467 ^ [], 470 ^ []))), 138 : ilf_type(464 ^ [], subset_type(cross_product(467 ^ [], 470 ^ []))), 138 : ilf_type(470 ^ [], set_type), 134 : ilf_type(467 ^ [], set_type)],extension(130 ^ 1,bind([[_70742, _70919, _71111], [467 ^ [], 470 ^ [], 464 ^ []]]))).
% 37.03/36.53  ncf('1.1.1',plain,[-(ilf_type(464 ^ [], subset_type(cross_product(467 ^ [], 470 ^ [])))), 278 : ilf_type(464 ^ [], member_type(power_set(cross_product(467 ^ [], 470 ^ [])))), 278 : ilf_type(464 ^ [], set_type), 268 : ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)],extension(264 ^ 6,bind([[_75660, _75805], [cross_product(467 ^ [], 470 ^ []), 464 ^ []]]))).
% 37.03/36.53  ncf('1.1.1.1',plain,[-(ilf_type(464 ^ [], member_type(power_set(cross_product(467 ^ [], 470 ^ []))))), 356 : member(464 ^ [], power_set(cross_product(467 ^ [], 470 ^ []))), 356 : -(empty(power_set(cross_product(467 ^ [], 470 ^ [])))), 356 : ilf_type(power_set(cross_product(467 ^ [], 470 ^ [])), set_type), 342 : ilf_type(464 ^ [], set_type)],extension(338 ^ 11,bind([[_78066, _78214], [464 ^ [], power_set(cross_product(467 ^ [], 470 ^ []))]]))).
% 37.03/36.53  ncf('1.1.1.1.1',plain,[-(member(464 ^ [], power_set(cross_product(467 ^ [], 470 ^ [])))), 322 : -(ilf_type(320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])], set_type)), 319 : ilf_type(cross_product(467 ^ [], 470 ^ []), set_type), 301 : ilf_type(464 ^ [], set_type)],extension(297 ^ 16,bind([[_76713, _76871], [464 ^ [], cross_product(467 ^ [], 470 ^ [])]]))).
% 37.03/36.53  ncf('1.1.1.1.1.1',plain,[ilf_type(320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])], set_type), 233 : member(320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])], 464 ^ []), 233 : -(member(320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])], cross_product(467 ^ [], 470 ^ []))), 233 : subset(464 ^ [], cross_product(467 ^ [], 470 ^ [])), 229 : ilf_type(cross_product(467 ^ [], 470 ^ []), set_type), 225 : ilf_type(464 ^ [], set_type)],extension(221 ^ 23,bind([[_74240, _74396, _74655], [464 ^ [], cross_product(467 ^ [], 470 ^ []), 320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])]]]))).
% 37.03/36.53  ncf('1.1.1.1.1.1.1',plain,[-(member(320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])], 464 ^ []))],extension(324 ^ 30)).
% 37.03/36.53  ncf('1.1.1.1.1.1.2',plain,[member(320 ^ [464 ^ [], cross_product(467 ^ [], 470 ^ [])], cross_product(467 ^ [], 470 ^ []))],extension(326 ^ 30)).
% 37.03/36.53  ncf('1.1.1.1.1.1.3',plain,[-(subset(464 ^ [], cross_product(467 ^ [], 470 ^ [])))],extension(474 ^ 28)).
% 37.03/36.53  ncf('1.1.1.1.1.1.4',plain,[-(ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)), 215 : ilf_type(470 ^ [], set_type), 215 : ilf_type(467 ^ [], set_type)],extension(211 ^ 26,bind([[_73895, _74031], [467 ^ [], 470 ^ []]]))).
% 37.03/36.53  ncf('1.1.1.1.1.1.4.1',plain,[-(ilf_type(470 ^ [], set_type))],extension(472 ^ 29)).
% 37.03/36.53  ncf('1.1.1.1.1.1.4.2',plain,[-(ilf_type(467 ^ [], set_type))],extension(469 ^ 27)).
% 37.03/36.53  ncf('1.1.1.1.1.1.5',plain,[-(ilf_type(464 ^ [], set_type))],extension(466 ^ 24)).
% 37.03/36.53  ncf('1.1.1.1.1.2',plain,[-(ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)), 215 : ilf_type(470 ^ [], set_type), 215 : ilf_type(467 ^ [], set_type)],extension(211 ^ 19,bind([[_73895, _74031], [467 ^ [], 470 ^ []]]))).
% 37.03/36.53  ncf('1.1.1.1.1.2.1',plain,[-(ilf_type(470 ^ [], set_type))],extension(472 ^ 22)).
% 37.03/36.53  ncf('1.1.1.1.1.2.2',plain,[-(ilf_type(467 ^ [], set_type))],extension(469 ^ 20)).
% 37.03/36.53  ncf('1.1.1.1.1.3',plain,[-(ilf_type(464 ^ [], set_type))],extension(466 ^ 17)).
% 37.03/36.53  ncf('1.1.1.1.2',plain,[empty(power_set(cross_product(467 ^ [], 470 ^ []))), ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)],extension(330 ^ 14,bind([[_77796], [cross_product(467 ^ [], 470 ^ [])]]))).
% 37.03/36.53  ncf('1.1.1.1.2.1',plain,[-(ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)), 215 : ilf_type(470 ^ [], set_type), 215 : ilf_type(467 ^ [], set_type)],extension(211 ^ 15,bind([[_73895, _74031], [467 ^ [], 470 ^ []]]))).
% 37.03/36.53  ncf('1.1.1.1.2.1.1',plain,[-(ilf_type(470 ^ [], set_type))],extension(472 ^ 18)).
% 37.03/36.53  ncf('1.1.1.1.2.1.2',plain,[-(ilf_type(467 ^ [], set_type))],extension(469 ^ 16)).
% 37.03/36.53  ncf('1.1.1.1.3',plain,[-(ilf_type(power_set(cross_product(467 ^ [], 470 ^ [])), set_type)), ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)],extension(330 ^ 14,bind([[_77796], [cross_product(467 ^ [], 470 ^ [])]]))).
% 37.03/36.53  ncf('1.1.1.1.3.1',plain,[-(ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)), 215 : ilf_type(470 ^ [], set_type), 215 : ilf_type(467 ^ [], set_type)],extension(211 ^ 15,bind([[_73895, _74031], [467 ^ [], 470 ^ []]]))).
% 37.03/36.53  ncf('1.1.1.1.3.1.1',plain,[-(ilf_type(470 ^ [], set_type))],extension(472 ^ 18)).
% 37.03/36.53  ncf('1.1.1.1.3.1.2',plain,[-(ilf_type(467 ^ [], set_type))],extension(469 ^ 16)).
% 37.03/36.53  ncf('1.1.1.1.4',plain,[-(ilf_type(464 ^ [], set_type))],extension(466 ^ 12)).
% 37.03/36.53  ncf('1.1.1.2',plain,[-(ilf_type(464 ^ [], set_type))],extension(466 ^ 9)).
% 37.03/36.53  ncf('1.1.1.3',plain,[-(ilf_type(cross_product(467 ^ [], 470 ^ []), set_type)), 215 : ilf_type(470 ^ [], set_type), 215 : ilf_type(467 ^ [], set_type)],extension(211 ^ 7,bind([[_73895, _74031], [467 ^ [], 470 ^ []]]))).
% 37.03/36.53  ncf('1.1.1.3.1',plain,[-(ilf_type(470 ^ [], set_type))],extension(472 ^ 10)).
% 37.03/36.53  ncf('1.1.1.3.2',plain,[-(ilf_type(467 ^ [], set_type))],extension(469 ^ 8)).
% 37.03/36.53  ncf('1.1.2',plain,[-(ilf_type(470 ^ [], set_type))],extension(472 ^ 4)).
% 37.03/36.53  ncf('1.1.3',plain,[-(ilf_type(467 ^ [], set_type))],extension(469 ^ 2)).
% 37.03/36.53  %-----------------------------------------------------
% 37.03/36.53  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------