%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU252+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 12:02:53 EDT 2023

% Result   : Theorem 1.49s 2.42s
% Output   : Proof 1.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU252+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % 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 12:21:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.49/2.42  
% 1.49/2.42  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.49/2.42  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.49/2.42  %-----------------------------------------------------
% 1.49/2.42  ncf(matrix, plain, [(471 ^ _69840) ^ [] : [-(relation(469 ^ []))], (473 ^ _69840) ^ [] : [-(reflexive(469 ^ []))], (475 ^ _69840) ^ [] : [reflexive(relation_restriction(469 ^ [], 468 ^ []))], (98 ^ _69840) ^ [_72997, _72999, _73001, _73003] : [-(unordered_pair(_73003, _72999) = unordered_pair(_73001, _72997)), _73003 = _73001, _72999 = _72997], (108 ^ _69840) ^ [_73328, _73330] : [_73330 = _73328, -(singleton(_73330) = singleton(_73328))], (114 ^ _69840) ^ [_73546, _73548] : [_73548 = _73546, -(relation_dom(_73548) = relation_dom(_73546))], (120 ^ _69840) ^ [_73764, _73766] : [_73766 = _73764, -(relation_rng(_73766) = relation_rng(_73764))], (126 ^ _69840) ^ [_74010, _74012, _74014, _74016] : [-(ordered_pair(_74016, _74012) = ordered_pair(_74014, _74010)), _74016 = _74014, _74012 = _74010], (136 ^ _69840) ^ [_74369, _74371, _74373, _74375] : [-(cartesian_product2(_74375, _74371) = cartesian_product2(_74373, _74369)), _74375 = _74373, _74371 = _74369], (146 ^ _69840) ^ [_74700, _74702] : [_74702 = _74700, -(relation_field(_74702) = relation_field(_74700))], (152 ^ _69840) ^ [_74946, _74948, _74950, _74952] : [-(set_union2(_74952, _74948) = set_union2(_74950, _74946)), _74952 = _74950, _74948 = _74946], (162 ^ _69840) ^ [_75305, _75307, _75309, _75311] : [-(set_intersection2(_75311, _75307) = set_intersection2(_75309, _75305)), _75311 = _75309, _75307 = _75305], (172 ^ _69840) ^ [_75644, _75646, _75648, _75650] : [-(relation_restriction(_75650, _75646) = relation_restriction(_75648, _75644)), _75650 = _75648, _75646 = _75644], (2 ^ _69840) ^ [_69984] : [-(_69984 = _69984)], (4 ^ _69840) ^ [_70091, _70093] : [_70093 = _70091, -(_70091 = _70093)], (10 ^ _69840) ^ [_70295, _70297, _70299] : [-(_70299 = _70295), _70299 = _70297, _70297 = _70295], (20 ^ _69840) ^ [_70608, _70610] : [-(function(_70608)), _70610 = _70608, function(_70610)], (30 ^ _69840) ^ [_70903, _70905] : [-(one_to_one(_70903)), _70905 = _70903, one_to_one(_70905)], (40 ^ _69840) ^ [_71226, _71228, _71230, _71232] : [-(element(_71230, _71226)), element(_71232, _71228), _71232 = _71230, _71228 = _71226], (54 ^ _69840) ^ [_71670, _71672, _71674, _71676] : [-(in(_71674, _71670)), in(_71676, _71672), _71676 = _71674, _71672 = _71670], (68 ^ _69840) ^ [_72086, _72088] : [-(empty(_72086)), _72088 = _72086, empty(_72088)], (78 ^ _69840) ^ [_72381, _72383] : [-(relation(_72381)), _72383 = _72381, relation(_72383)], (88 ^ _69840) ^ [_72656, _72658] : [-(reflexive(_72656)), _72658 = _72656, reflexive(_72658)], (182 ^ _69840) ^ [_76013, _76015] : [in(_76015, _76013), in(_76013, _76015)], (188 ^ _69840) ^ [_76210] : [empty(_76210), -(function(_76210))], (194 ^ _69840) ^ [_76396] : [205 ^ _69840 : [(206 ^ _69840) ^ [] : [-(relation(_76396))], (208 ^ _69840) ^ [] : [-(function(_76396))], (210 ^ _69840) ^ [] : [-(one_to_one(_76396))]], relation(_76396), empty(_76396), function(_76396)], (212 ^ _69840) ^ [_76888, _76890] : [-(unordered_pair(_76890, _76888) = unordered_pair(_76888, _76890))], (214 ^ _69840) ^ [_76988, _76990] : [-(set_union2(_76990, _76988) = set_union2(_76988, _76990))], (216 ^ _69840) ^ [_77088, _77090] : [-(set_intersection2(_77090, _77088) = set_intersection2(_77088, _77090))], (218 ^ _69840) ^ [_77188, _77190] : [-(ordered_pair(_77190, _77188) = unordered_pair(unordered_pair(_77190, _77188), singleton(_77190)))], (220 ^ _69840) ^ [_77294] : [relation(_77294), -(relation_field(_77294) = set_union2(relation_dom(_77294), relation_rng(_77294)))], (226 ^ _69840) ^ [_77500] : [relation(_77500), 229 ^ _69840 : [(230 ^ _69840) ^ [_77619] : [-(relation_restriction(_77500, _77619) = set_intersection2(_77500, cartesian_product2(_77619, _77619)))]]], (232 ^ _69840) ^ [] : [true___, -(true___)], (238 ^ _69840) ^ [] : [true___, -(true___)], (244 ^ _69840) ^ [] : [true___, -(true___)], (250 ^ _69840) ^ [] : [true___, -(true___)], (256 ^ _69840) ^ [] : [true___, -(true___)], (262 ^ _69840) ^ [_78337, _78339] : [relation(_78339), -(relation(relation_restriction(_78339, _78337)))], (268 ^ _69840) ^ [] : [true___, -(true___)], (274 ^ _69840) ^ [] : [true___, -(true___)], (280 ^ _69840) ^ [] : [true___, -(true___)], (286 ^ _69840) ^ [] : [true___, -(true___)], (292 ^ _69840) ^ [] : [true___, -(true___)], (298 ^ _69840) ^ [] : [true___, -(true___)], (305 ^ _69840) ^ [_79273] : [-(element(303 ^ [_79273], _79273))], (307 ^ _69840) ^ [] : [-(empty(empty_set))], (309 ^ _69840) ^ [_79422, _79424] : [empty(ordered_pair(_79424, _79422))], (311 ^ _69840) ^ [_79533, _79535] : [-(empty(_79535)), empty(set_union2(_79535, _79533))], (317 ^ _69840) ^ [_79749, _79751] : [-(empty(_79751)), empty(set_union2(_79749, _79751))], (323 ^ _69840) ^ [_79950, _79952] : [-(set_union2(_79952, _79952) = _79952)], (325 ^ _69840) ^ [_80047, _80049] : [-(set_intersection2(_80049, _80049) = _80049)], (327 ^ _69840) ^ [_80145] : [relation(_80145), 330 ^ _69840 : [(341 ^ _69840) ^ [] : [343 ^ _69840 : [(344 ^ _69840) ^ [] : [-(in(342 ^ [_80145], relation_field(_80145)))], (346 ^ _69840) ^ [] : [in(ordered_pair(342 ^ [_80145], 342 ^ [_80145]), _80145)]], -(reflexive(_80145))], (331 ^ _69840) ^ [] : [reflexive(_80145), 334 ^ _69840 : [(335 ^ _69840) ^ [_80389] : [in(_80389, relation_field(_80145)), -(in(ordered_pair(_80389, _80389), _80145))]]]]], (351 ^ _69840) ^ [] : [-(relation(349 ^ []))], (353 ^ _69840) ^ [] : [-(function(349 ^ []))], (356 ^ _69840) ^ [] : [-(empty(354 ^ []))], (359 ^ _69840) ^ [] : [-(relation(357 ^ []))], (361 ^ _69840) ^ [] : [-(empty(357 ^ []))], (363 ^ _69840) ^ [] : [-(function(357 ^ []))], (366 ^ _69840) ^ [] : [empty(364 ^ [])], (369 ^ _69840) ^ [] : [-(relation(367 ^ []))], (371 ^ _69840) ^ [] : [-(function(367 ^ []))], (373 ^ _69840) ^ [] : [-(one_to_one(367 ^ []))], (375 ^ _69840) ^ [_81687, _81689, _81691, _81693] : [in(ordered_pair(_81693, _81691), cartesian_product2(_81689, _81687)), 378 ^ _69840 : [(379 ^ _69840) ^ [] : [-(in(_81693, _81689))], (381 ^ _69840) ^ [] : [-(in(_81691, _81687))]]], (383 ^ _69840) ^ [_81952, _81954, _81956, _81958] : [-(in(ordered_pair(_81958, _81956), cartesian_product2(_81954, _81952))), in(_81958, _81954), in(_81956, _81952)], (393 ^ _69840) ^ [_82299, _82301, _82303] : [relation(_82299), 396 ^ _69840 : [(397 ^ _69840) ^ [] : [in(_82303, relation_restriction(_82299, _82301)), 400 ^ _69840 : [(401 ^ _69840) ^ [] : [-(in(_82303, _82299))], (403 ^ _69840) ^ [] : [-(in(_82303, cartesian_product2(_82301, _82301)))]]], (405 ^ _69840) ^ [] : [-(in(_82303, relation_restriction(_82299, _82301))), in(_82303, _82299), in(_82303, cartesian_product2(_82301, _82301))]]], (415 ^ _69840) ^ [_82969, _82971, _82973] : [relation(_82969), in(_82973, relation_field(relation_restriction(_82969, _82971))), 422 ^ _69840 : [(423 ^ _69840) ^ [] : [-(in(_82973, relation_field(_82969)))], (425 ^ _69840) ^ [] : [-(in(_82973, _82971))]]], (427 ^ _69840) ^ [_83338] : [-(set_union2(_83338, empty_set) = _83338)], (429 ^ _69840) ^ [_83448, _83450] : [in(_83450, _83448), -(element(_83450, _83448))], (435 ^ _69840) ^ [_83629] : [-(set_intersection2(_83629, empty_set) = empty_set)], (437 ^ _69840) ^ [_83739, _83741] : [element(_83741, _83739), -(empty(_83739)), -(in(_83741, _83739))], (447 ^ _69840) ^ [_84023] : [empty(_84023), -(_84023 = empty_set)], (453 ^ _69840) ^ [_84225, _84227] : [in(_84227, _84225), empty(_84225)], (459 ^ _69840) ^ [_84412, _84414] : [empty(_84414), -(_84414 = _84412), empty(_84412)]], input).
% 1.49/2.42  ncf('1',plain,[reflexive(relation_restriction(469 ^ [], 468 ^ []))],start(475 ^ 0)).
% 1.49/2.42  ncf('1.1',plain,[-(reflexive(relation_restriction(469 ^ [], 468 ^ []))), 344 : -(in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], relation_field(relation_restriction(469 ^ [], 468 ^ [])))), 341 : relation(relation_restriction(469 ^ [], 468 ^ []))],extension(327 ^ 1,bind([[_80145], [relation_restriction(469 ^ [], 468 ^ [])]]))).
% 1.49/2.42  ncf('1.1.1',plain,[in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], relation_field(relation_restriction(469 ^ [], 468 ^ []))), relation(469 ^ []), 423 : -(in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], relation_field(469 ^ [])))],extension(415 ^ 6,bind([[_82969, _82971, _82973], [469 ^ [], 468 ^ [], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]]]))).
% 1.49/2.42  ncf('1.1.1.1',plain,[-(relation(469 ^ []))],extension(471 ^ 7)).
% 1.49/2.42  ncf('1.1.1.2',plain,[in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], relation_field(469 ^ [])), 335 : -(in(ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]), 469 ^ [])), 335 : reflexive(469 ^ []), 331 : relation(469 ^ [])],extension(327 ^ 9,bind([[_80145, _80389], [469 ^ [], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]]]))).
% 1.49/2.42  ncf('1.1.1.2.1',plain,[in(ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]), 469 ^ []), 405 : -(in(ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]), relation_restriction(469 ^ [], 468 ^ []))), 405 : in(ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]), cartesian_product2(468 ^ [], 468 ^ [])), 405 : relation(469 ^ [])],extension(393 ^ 14,bind([[_82299, _82301, _82303], [469 ^ [], 468 ^ [], ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])])]]))).
% 1.49/2.42  ncf('1.1.1.2.1.1',plain,[in(ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]), relation_restriction(469 ^ [], 468 ^ [])), 341 : -(reflexive(relation_restriction(469 ^ [], 468 ^ []))), 341 : relation(relation_restriction(469 ^ [], 468 ^ []))],extension(327 ^ 17,bind([[_80145], [relation_restriction(469 ^ [], 468 ^ [])]]))).
% 1.49/2.42  ncf('1.1.1.2.1.1.1',plain,[reflexive(relation_restriction(469 ^ [], 468 ^ []))],reduction('1')).
% 1.49/2.42  ncf('1.1.1.2.1.1.2',plain,[-(relation(relation_restriction(469 ^ [], 468 ^ []))), relation(469 ^ [])],extension(262 ^ 18,bind([[_78337, _78339], [468 ^ [], 469 ^ []]]))).
% 1.49/2.42  ncf('1.1.1.2.1.1.2.1',plain,[-(relation(469 ^ []))],lemmata('[1, 1].x')).
% 1.49/2.42  ncf('1.1.1.2.1.2',plain,[-(in(ordered_pair(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]), cartesian_product2(468 ^ [], 468 ^ []))), in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 468 ^ []), in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 468 ^ [])],extension(383 ^ 17,bind([[_81952, _81954, _81956, _81958], [468 ^ [], 468 ^ [], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 342 ^ [relation_restriction(469 ^ [], 468 ^ [])]]]))).
% 1.49/2.42  ncf('1.1.1.2.1.2.1',plain,[-(in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 468 ^ []))],extension(425 ^ 18)).
% 1.49/2.42  ncf('1.1.1.2.1.2.2',plain,[-(in(342 ^ [relation_restriction(469 ^ [], 468 ^ [])], 468 ^ []))],lemmata('[1, 2, 1, 1, 1].x')).
% 1.49/2.42  ncf('1.1.1.2.1.3',plain,[-(relation(469 ^ []))],lemmata('[1, 1].x')).
% 1.49/2.42  ncf('1.1.1.2.2',plain,[-(reflexive(469 ^ []))],extension(473 ^ 12)).
% 1.49/2.42  ncf('1.1.1.2.3',plain,[-(relation(469 ^ []))],lemmata('[1, 1].x')).
% 1.49/2.42  ncf('1.1.2',plain,[-(relation(relation_restriction(469 ^ [], 468 ^ []))), relation(469 ^ [])],extension(262 ^ 2,bind([[_78337, _78339], [468 ^ [], 469 ^ []]]))).
% 1.49/2.42  ncf('1.1.2.1',plain,[-(relation(469 ^ []))],extension(471 ^ 3)).
% 1.49/2.42  %-----------------------------------------------------
% 1.49/2.42  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------