%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 11:56:13 EDT 2023

% Result   : Theorem 69.63s 67.52s
% Output   : Proof 69.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 19:07:29 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 69.63/67.52  
% 69.63/67.52  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 69.63/67.52  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.63/67.52  %-----------------------------------------------------
% 69.63/67.52  ncf(matrix, plain, [(522 ^ _96133) ^ [] : [-(ilf_type(520 ^ [], set_type))], (530 ^ _96133) ^ [] : [-(member(ordered_pair(520 ^ [], 523 ^ []), 526 ^ []))], (532 ^ _96133) ^ [] : [member(520 ^ [], 514 ^ []), member(523 ^ [], 517 ^ [])], (525 ^ _96133) ^ [] : [-(ilf_type(523 ^ [], set_type))], (516 ^ _96133) ^ [] : [-(ilf_type(514 ^ [], set_type))], (519 ^ _96133) ^ [] : [-(ilf_type(517 ^ [], set_type))], (528 ^ _96133) ^ [] : [-(ilf_type(526 ^ [], relation_type(514 ^ [], 517 ^ [])))], !, (295 ^ _78450) ^ [_88832] : [ilf_type(_88832, set_type), -(ilf_type(298 ^ [_88832], subset_type(_88832)))], (74 ^ _78450) ^ [_80914, _80916, _80918, _80920] : [-(unordered_pair(_80920, _80916) = unordered_pair(_80918, _80914)), _80920 = _80918, _80916 = _80914], (275 ^ _78450) ^ [_88216] : [ilf_type(_88216, set_type), 278 ^ _78450 : [(279 ^ _78450) ^ [_88361] : [ilf_type(_88361, set_type), 282 ^ _78450 : [(289 ^ _78450) ^ [] : [ilf_type(_88361, member_type(power_set(_88216))), -(ilf_type(_88361, subset_type(_88216)))], (283 ^ _78450) ^ [] : [ilf_type(_88361, subset_type(_88216)), -(ilf_type(_88361, member_type(power_set(_88216))))]]]]], (30 ^ _78450) ^ [_79493, _79495] : [-(relation_like(_79493)), _79495 = _79493, relation_like(_79495)], (68 ^ _78450) ^ [_80668, _80670] : [_80670 = _80668, -(singleton(_80670) = singleton(_80668))], (423 ^ _78450) ^ [_92882] : [ilf_type(_92882, set_type), 426 ^ _78450 : [(427 ^ _78450) ^ [] : [empty(_92882), 430 ^ _78450 : [(431 ^ _78450) ^ [_93125] : [ilf_type(_93125, set_type), member(_93125, _92882)]]], (437 ^ _78450) ^ [] : [439 ^ _78450 : [(442 ^ _78450) ^ [] : [-(member(438 ^ [_92882], _92882))], (440 ^ _78450) ^ [] : [-(ilf_type(438 ^ [_92882], set_type))]], -(empty(_92882))]]], (499 ^ _78450) ^ [_95399] : [ilf_type(_95399, set_type), 502 ^ _78450 : [(503 ^ _78450) ^ [_95547] : [ilf_type(_95547, set_type), 506 ^ _78450 : [(507 ^ _78450) ^ [_95690] : [ilf_type(_95690, subset_type(cross_product(_95399, _95547))), -(relation_like(_95690))]]]]], (40 ^ _78450) ^ [_79816, _79818, _79820, _79822] : [-(ilf_type(_79820, _79816)), ilf_type(_79822, _79818), _79822 = _79820, _79818 = _79816], (265 ^ _78450) ^ [_87862] : [ilf_type(_87862, set_type), 268 ^ _78450 : [(269 ^ _78450) ^ [_88001] : [ilf_type(_88001, set_type), -(unordered_pair(_87862, _88001) = unordered_pair(_88001, _87862))]]], (54 ^ _78450) ^ [_80240, _80242, _80244, _80246] : [-(member(_80244, _80240)), member(_80246, _80242), _80246 = _80244, _80242 = _80240], (380 ^ _78450) ^ [_91580] : [ilf_type(_91580, set_type), 383 ^ _78450 : [(386 ^ _78450) ^ [] : [-(ilf_type(power_set(_91580), set_type))], (384 ^ _78450) ^ [] : [empty(power_set(_91580))]]], (412 ^ _78450) ^ [_92549] : [-(ilf_type(419 ^ [_92549], member_type(_92549))), -(empty(_92549)), ilf_type(_92549, set_type)], (239 ^ _78450) ^ [_86978] : [ilf_type(_86978, set_type), -(ilf_type(singleton(_86978), set_type))], (513 ^ _78450) ^ [_95879] : [-(ilf_type(_95879, set_type))], (198 ^ _78450) ^ [_85418] : [ilf_type(_85418, set_type), 201 ^ _78450 : [(202 ^ _78450) ^ [_85554] : [ilf_type(_85554, set_type), -(ilf_type(ordered_pair(_85418, _85554), set_type))]]], (347 ^ _78450) ^ [_90497] : [ilf_type(_90497, set_type), 350 ^ _78450 : [(351 ^ _78450) ^ [_90655] : [ilf_type(_90655, set_type), 354 ^ _78450 : [(355 ^ _78450) ^ [] : [member(_90497, power_set(_90655)), 358 ^ _78450 : [(359 ^ _78450) ^ [_90918] : [ilf_type(_90918, set_type), member(_90918, _90497), -(member(_90918, _90655))]]], (369 ^ _78450) ^ [] : [371 ^ _78450 : [(376 ^ _78450) ^ [] : [member(370 ^ [_90497, _90655], _90655)], (374 ^ _78450) ^ [] : [-(member(370 ^ [_90497, _90655], _90497))], (372 ^ _78450) ^ [] : [-(ilf_type(370 ^ [_90497, _90655], set_type))]], -(member(_90497, power_set(_90655)))]]]]], (122 ^ _78450) ^ [_82625, _82627, _82629, _82631] : [-(ordered_pair(_82631, _82627) = ordered_pair(_82629, _82625)), _82631 = _82629, _82627 = _82625], (446 ^ _78450) ^ [_93585] : [ilf_type(_93585, set_type), 449 ^ _78450 : [(470 ^ _78450) ^ [] : [-(relation_like(_93585)), 472 ^ _78450 : [(477 ^ _78450) ^ [_94696] : [ilf_type(_94696, set_type), 480 ^ _78450 : [(481 ^ _78450) ^ [_94843] : [ilf_type(_94843, set_type), 471 ^ [_93585] = ordered_pair(_94696, _94843)]]], (475 ^ _78450) ^ [] : [-(member(471 ^ [_93585], _93585))], (473 ^ _78450) ^ [] : [-(ilf_type(471 ^ [_93585], set_type))]]], (450 ^ _78450) ^ [] : [relation_like(_93585), 453 ^ _78450 : [(454 ^ _78450) ^ [_93857] : [ilf_type(_93857, set_type), member(_93857, _93585), 462 ^ _78450 : [(468 ^ _78450) ^ [] : [-(_93857 = ordered_pair(461 ^ [_93585, _93857], 464 ^ [_93585, _93857]))], (466 ^ _78450) ^ [] : [-(ilf_type(464 ^ [_93585, _93857], set_type))], (463 ^ _78450) ^ [] : [-(ilf_type(461 ^ [_93585, _93857], set_type))]]]]]]], (228 ^ _78450) ^ [_86568] : [ilf_type(_86568, set_type), 231 ^ _78450 : [(232 ^ _78450) ^ [_86709] : [ilf_type(_86709, set_type), -(ilf_type(235 ^ [_86568, _86709], relation_type(_86709, _86568)))]]], (102 ^ _78450) ^ [_81927, _81929, _81931, _81933] : [-(cross_product(_81933, _81929) = cross_product(_81931, _81927)), _81933 = _81931, _81929 = _81927], (96 ^ _78450) ^ [_81681, _81683] : [_81683 = _81681, -(subset_type(_81683) = subset_type(_81681))], (112 ^ _78450) ^ [_82286, _82288, _82290, _82292] : [-(relation_type(_82292, _82288) = relation_type(_82290, _82286)), _82292 = _82290, _82288 = _82286], (4 ^ _78450) ^ [_78681, _78683] : [_78683 = _78681, -(_78681 = _78683)], (2 ^ _78450) ^ [_78574] : [-(_78574 = _78574)], (132 ^ _78450) ^ [_82970] : [ilf_type(_82970, set_type), 135 ^ _78450 : [(136 ^ _78450) ^ [_83143] : [ilf_type(_83143, set_type), 139 ^ _78450 : [(140 ^ _78450) ^ [_83311] : [ilf_type(_83311, set_type), 143 ^ _78450 : [(144 ^ _78450) ^ [_83474] : [ilf_type(_83474, set_type), 147 ^ _78450 : [(156 ^ _78450) ^ [] : [-(member(ordered_pair(_82970, _83143), cross_product(_83311, _83474))), member(_82970, _83311), member(_83143, _83474)], (148 ^ _78450) ^ [] : [member(ordered_pair(_82970, _83143), cross_product(_83311, _83474)), 151 ^ _78450 : [(154 ^ _78450) ^ [] : [-(member(_83143, _83474))], (152 ^ _78450) ^ [] : [-(member(_82970, _83311))]]]]]]]]]]], (84 ^ _78450) ^ [_81245, _81247] : [_81247 = _81245, -(power_set(_81247) = power_set(_81245))], (166 ^ _78450) ^ [_84161] : [ilf_type(_84161, set_type), 169 ^ _78450 : [(170 ^ _78450) ^ [_84344] : [ilf_type(_84344, set_type), 173 ^ _78450 : [(174 ^ _78450) ^ [_84522] : [ilf_type(_84522, set_type), 177 ^ _78450 : [(178 ^ _78450) ^ [_84695] : [ilf_type(_84695, set_type), 181 ^ _78450 : [(182 ^ _78450) ^ [_84863] : [ilf_type(_84863, set_type), 185 ^ _78450 : [(192 ^ _78450) ^ [] : [_84863 = unordered_pair(unordered_pair(_84522, _84695), singleton(_84522)), -(_84863 = ordered_pair(_84522, _84695))], (186 ^ _78450) ^ [] : [_84863 = ordered_pair(_84522, _84695), -(_84863 = unordered_pair(unordered_pair(_84522, _84695), singleton(_84522)))]]]]]]]]]]], (20 ^ _78450) ^ [_79198, _79200] : [-(empty(_79198)), _79200 = _79198, empty(_79200)], (208 ^ _78450) ^ [_85763] : [ilf_type(_85763, set_type), 211 ^ _78450 : [(212 ^ _78450) ^ [_85940] : [ilf_type(_85940, set_type), 215 ^ _78450 : [(222 ^ _78450) ^ [_86334] : [ilf_type(_86334, relation_type(_85763, _85940)), -(ilf_type(_86334, subset_type(cross_product(_85763, _85940))))], (216 ^ _78450) ^ [_86132] : [ilf_type(_86132, subset_type(cross_product(_85763, _85940))), -(ilf_type(_86132, relation_type(_85763, _85940)))]]]]], (90 ^ _78450) ^ [_81463, _81465] : [_81465 = _81463, -(member_type(_81465) = member_type(_81463))], (245 ^ _78450) ^ [_87172] : [ilf_type(_87172, set_type), 248 ^ _78450 : [(249 ^ _78450) ^ [_87308] : [ilf_type(_87308, set_type), -(ilf_type(cross_product(_87172, _87308), set_type))]]], (388 ^ _78450) ^ [_91850] : [ilf_type(_91850, set_type), 391 ^ _78450 : [(392 ^ _78450) ^ [_91998] : [-(empty(_91998)), ilf_type(_91998, set_type), 399 ^ _78450 : [(406 ^ _78450) ^ [] : [member(_91850, _91998), -(ilf_type(_91850, member_type(_91998)))], (400 ^ _78450) ^ [] : [ilf_type(_91850, member_type(_91998)), -(member(_91850, _91998))]]]]], (302 ^ _78450) ^ [_89079] : [ilf_type(_89079, set_type), 305 ^ _78450 : [(306 ^ _78450) ^ [_89235] : [ilf_type(_89235, set_type), 309 ^ _78450 : [(310 ^ _78450) ^ [] : [_89079 = _89235, 313 ^ _78450 : [(314 ^ _78450) ^ [_89494] : [ilf_type(_89494, set_type), 317 ^ _78450 : [(324 ^ _78450) ^ [] : [member(_89494, _89235), -(member(_89494, _89079))], (318 ^ _78450) ^ [] : [member(_89494, _89079), -(member(_89494, _89235))]]]]], (330 ^ _78450) ^ [] : [-(_89079 = _89235), 332 ^ _78450 : [(335 ^ _78450) ^ [] : [336 ^ _78450 : [(339 ^ _78450) ^ [] : [member(331 ^ [_89079, _89235], _89235)], (337 ^ _78450) ^ [] : [-(member(331 ^ [_89079, _89235], _89079))]], 340 ^ _78450 : [(343 ^ _78450) ^ [] : [member(331 ^ [_89079, _89235], _89079)], (341 ^ _78450) ^ [] : [-(member(331 ^ [_89079, _89235], _89235))]]], (333 ^ _78450) ^ [] : [-(ilf_type(331 ^ [_89079, _89235], set_type))]]]]]]], (10 ^ _78450) ^ [_78885, _78887, _78889] : [-(_78889 = _78885), _78889 = _78887, _78887 = _78885], (255 ^ _78450) ^ [_87517] : [ilf_type(_87517, set_type), 258 ^ _78450 : [(259 ^ _78450) ^ [_87653] : [ilf_type(_87653, set_type), -(ilf_type(unordered_pair(_87517, _87653), set_type))]]], (489 ^ _78450) ^ [_95128] : [-(relation_like(_95128)), empty(_95128), ilf_type(_95128, set_type)]], input).
% 69.63/67.52  ncf('1',plain,[-(member(ordered_pair(520 ^ [], 523 ^ []), 526 ^ []))],start(530 ^ 0)).
% 69.63/67.52  ncf('1.1',plain,[member(ordered_pair(520 ^ [], 523 ^ []), 526 ^ []), 359 : ilf_type(ordered_pair(520 ^ [], 523 ^ []), set_type), 359 : -(member(ordered_pair(520 ^ [], 523 ^ []), cross_product(514 ^ [], 517 ^ []))), 359 : member(526 ^ [], power_set(cross_product(514 ^ [], 517 ^ []))), 355 : ilf_type(cross_product(514 ^ [], 517 ^ []), set_type), 351 : ilf_type(526 ^ [], set_type)],extension(347 ^ 1,bind([[_90497, _90655, _90918], [526 ^ [], cross_product(514 ^ [], 517 ^ []), ordered_pair(520 ^ [], 523 ^ [])]]))).
% 69.63/67.52  ncf('1.1.1',plain,[-(ilf_type(ordered_pair(520 ^ [], 523 ^ []), set_type))],extension(513 ^ 8,bind([[_95879], [ordered_pair(520 ^ [], 523 ^ [])]]))).
% 69.63/67.52  ncf('1.1.2',plain,[member(ordered_pair(520 ^ [], 523 ^ []), cross_product(514 ^ [], 517 ^ [])), 154 : -(member(523 ^ [], 517 ^ [])), 148 : ilf_type(517 ^ [], set_type), 144 : ilf_type(514 ^ [], set_type), 140 : ilf_type(523 ^ [], set_type), 136 : ilf_type(520 ^ [], set_type)],extension(132 ^ 8,bind([[_82970, _83143, _83311, _83474], [520 ^ [], 523 ^ [], 514 ^ [], 517 ^ []]]))).
% 69.63/67.52  ncf('1.1.2.1',plain,[member(523 ^ [], 517 ^ []), member(520 ^ [], 514 ^ [])],extension(532 ^ 19)).
% 69.63/67.52  ncf('1.1.2.1.1',plain,[-(member(520 ^ [], 514 ^ []))],extension(152 ^ 20)).
% 69.63/67.52  ncf('1.1.2.2',plain,[-(ilf_type(517 ^ [], set_type))],extension(519 ^ 15)).
% 69.63/67.52  ncf('1.1.2.3',plain,[-(ilf_type(514 ^ [], set_type))],extension(516 ^ 13)).
% 69.63/67.52  ncf('1.1.2.4',plain,[-(ilf_type(523 ^ [], set_type))],extension(525 ^ 11)).
% 69.63/67.52  ncf('1.1.2.5',plain,[-(ilf_type(520 ^ [], set_type))],extension(522 ^ 9)).
% 69.63/67.52  ncf('1.1.3',plain,[-(member(526 ^ [], power_set(cross_product(514 ^ [], 517 ^ [])))), 400 : ilf_type(526 ^ [], member_type(power_set(cross_product(514 ^ [], 517 ^ [])))), 400 : -(empty(power_set(cross_product(514 ^ [], 517 ^ [])))), 400 : ilf_type(power_set(cross_product(514 ^ [], 517 ^ [])), set_type), 392 : ilf_type(526 ^ [], set_type)],extension(388 ^ 6,bind([[_91850, _91998], [526 ^ [], power_set(cross_product(514 ^ [], 517 ^ []))]]))).
% 69.63/67.52  ncf('1.1.3.1',plain,[-(ilf_type(526 ^ [], member_type(power_set(cross_product(514 ^ [], 517 ^ []))))), 283 : ilf_type(526 ^ [], subset_type(cross_product(514 ^ [], 517 ^ []))), 283 : ilf_type(526 ^ [], set_type), 279 : ilf_type(cross_product(514 ^ [], 517 ^ []), set_type)],extension(275 ^ 11,bind([[_88216, _88361], [cross_product(514 ^ [], 517 ^ []), 526 ^ []]]))).
% 69.63/67.52  ncf('1.1.3.1.1',plain,[-(ilf_type(526 ^ [], subset_type(cross_product(514 ^ [], 517 ^ [])))), 222 : ilf_type(526 ^ [], relation_type(514 ^ [], 517 ^ [])), 222 : ilf_type(517 ^ [], set_type), 212 : ilf_type(514 ^ [], set_type)],extension(208 ^ 16,bind([[_85763, _85940, _86334], [514 ^ [], 517 ^ [], 526 ^ []]]))).
% 69.63/67.52  ncf('1.1.3.1.1.1',plain,[-(ilf_type(526 ^ [], relation_type(514 ^ [], 517 ^ [])))],extension(528 ^ 21)).
% 69.63/67.52  ncf('1.1.3.1.1.2',plain,[-(ilf_type(517 ^ [], set_type))],extension(519 ^ 19)).
% 69.63/67.52  ncf('1.1.3.1.1.3',plain,[-(ilf_type(514 ^ [], set_type))],extension(516 ^ 17)).
% 69.63/67.52  ncf('1.1.3.1.2',plain,[-(ilf_type(526 ^ [], set_type))],extension(513 ^ 14,bind([[_95879], [526 ^ []]]))).
% 69.63/67.52  ncf('1.1.3.1.3',plain,[-(ilf_type(cross_product(514 ^ [], 517 ^ []), set_type))],extension(513 ^ 12,bind([[_95879], [cross_product(514 ^ [], 517 ^ [])]]))).
% 69.63/67.52  ncf('1.1.3.2',plain,[empty(power_set(cross_product(514 ^ [], 517 ^ []))), ilf_type(cross_product(514 ^ [], 517 ^ []), set_type)],extension(380 ^ 9,bind([[_91580], [cross_product(514 ^ [], 517 ^ [])]]))).
% 69.63/67.52  ncf('1.1.3.2.1',plain,[-(ilf_type(cross_product(514 ^ [], 517 ^ []), set_type))],extension(513 ^ 10,bind([[_95879], [cross_product(514 ^ [], 517 ^ [])]]))).
% 69.63/67.52  ncf('1.1.3.3',plain,[-(ilf_type(power_set(cross_product(514 ^ [], 517 ^ [])), set_type)), ilf_type(cross_product(514 ^ [], 517 ^ []), set_type)],extension(380 ^ 9,bind([[_91580], [cross_product(514 ^ [], 517 ^ [])]]))).
% 69.63/67.52  ncf('1.1.3.3.1',plain,[-(ilf_type(cross_product(514 ^ [], 517 ^ []), set_type))],extension(513 ^ 10,bind([[_95879], [cross_product(514 ^ [], 517 ^ [])]]))).
% 69.63/67.52  ncf('1.1.3.4',plain,[-(ilf_type(526 ^ [], set_type))],extension(513 ^ 7,bind([[_95879], [526 ^ []]]))).
% 69.63/67.52  ncf('1.1.4',plain,[-(ilf_type(cross_product(514 ^ [], 517 ^ []), set_type))],extension(513 ^ 4,bind([[_95879], [cross_product(514 ^ [], 517 ^ [])]]))).
% 69.63/67.52  ncf('1.1.5',plain,[-(ilf_type(526 ^ [], set_type))],extension(513 ^ 2,bind([[_95879], [526 ^ []]]))).
% 69.63/67.52  %-----------------------------------------------------
% 69.63/67.52  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------