%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET813+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 11:56:28 EDT 2023

% Result   : Theorem 1.42s 2.41s
% Output   : Proof 1.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET813+4 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.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 19:21:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.42/2.41  
% 1.42/2.41  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.42/2.41  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.42/2.41  %-----------------------------------------------------
% 1.42/2.41  ncf(matrix, plain, [(612 ^ _75877) ^ [] : [-(member(610 ^ [], on))], (614 ^ _75877) ^ [] : [member(610 ^ [], suc(610 ^ []))], (136 ^ _75877) ^ [_80378, _80380] : [_80380 = _80378, -(power_set(_80380) = power_set(_80378))], (142 ^ _75877) ^ [_80624, _80626, _80628, _80630] : [-(intersection(_80630, _80626) = intersection(_80628, _80624)), _80630 = _80628, _80626 = _80624], (152 ^ _75877) ^ [_80983, _80985, _80987, _80989] : [-(difference(_80989, _80985) = difference(_80987, _80983)), _80989 = _80987, _80985 = _80983], (162 ^ _75877) ^ [_81342, _81344, _81346, _81348] : [-(unordered_pair(_81348, _81344) = unordered_pair(_81346, _81342)), _81348 = _81346, _81344 = _81342], (172 ^ _75877) ^ [_81673, _81675] : [_81675 = _81673, -(sum(_81675) = sum(_81673))], (178 ^ _75877) ^ [_81891, _81893] : [_81893 = _81891, -(product(_81893) = product(_81891))], (184 ^ _75877) ^ [_82165, _82167, _82169, _82171, _82173, _82175] : [-(initial_segment(_82175, _82171, _82167) = initial_segment(_82173, _82169, _82165)), _82175 = _82173, _82171 = _82169, _82167 = _82165], (198 ^ _75877) ^ [_82653, _82655, _82657, _82659] : [-(union(_82659, _82655) = union(_82657, _82653)), _82659 = _82657, _82655 = _82653], (208 ^ _75877) ^ [_82984, _82986] : [_82986 = _82984, -(singleton(_82986) = singleton(_82984))], (214 ^ _75877) ^ [_83182, _83184] : [_83184 = _83182, -(suc(_83184) = suc(_83182))], (2 ^ _75877) ^ [_76021] : [-(_76021 = _76021)], (4 ^ _75877) ^ [_76128, _76130] : [_76130 = _76128, -(_76128 = _76130)], (10 ^ _75877) ^ [_76332, _76334, _76336] : [-(_76336 = _76332), _76336 = _76334, _76334 = _76332], (20 ^ _75877) ^ [_76673, _76675, _76677, _76679] : [-(equal_set(_76677, _76673)), equal_set(_76679, _76675), _76679 = _76677, _76675 = _76673], (34 ^ _75877) ^ [_77117, _77119, _77121, _77123] : [-(strict_well_order(_77121, _77117)), strict_well_order(_77123, _77119), _77123 = _77121, _77119 = _77117], (48 ^ _75877) ^ [_77561, _77563, _77565, _77567] : [-(subset(_77565, _77561)), subset(_77567, _77563), _77567 = _77565, _77563 = _77561], (62 ^ _75877) ^ [_78033, _78035, _78037, _78039, _78041, _78043] : [-(least(_78041, _78037, _78033)), least(_78043, _78039, _78035), _78043 = _78041, _78039 = _78037, _78035 = _78033], (80 ^ _75877) ^ [_78614, _78616, _78618, _78620] : [-(strict_order(_78618, _78614)), strict_order(_78620, _78616), _78620 = _78618, _78616 = _78614], (94 ^ _75877) ^ [_79030, _79032] : [-(set(_79030)), _79032 = _79030, set(_79032)], (122 ^ _75877) ^ [_79942, _79944, _79946, _79948] : [-(member(_79946, _79942)), member(_79948, _79944), _79948 = _79946, _79944 = _79942], (104 ^ _75877) ^ [_79381, _79383, _79385, _79387, _79389, _79391] : [-(apply(_79389, _79385, _79381)), apply(_79391, _79387, _79383), _79391 = _79389, _79387 = _79385, _79383 = _79381], (230 ^ _75877) ^ [_83833, _83835] : [232 ^ _75877 : [(233 ^ _75877) ^ [] : [-(member(231 ^ [_83833, _83835], _83835))], (235 ^ _75877) ^ [] : [member(231 ^ [_83833, _83835], _83833)]], -(subset(_83835, _83833))], (220 ^ _75877) ^ [_83519, _83521] : [subset(_83521, _83519), 223 ^ _75877 : [(224 ^ _75877) ^ [_83656] : [member(_83656, _83521), -(member(_83656, _83519))]]], (239 ^ _75877) ^ [_84219, _84221] : [equal_set(_84221, _84219), 242 ^ _75877 : [(243 ^ _75877) ^ [] : [-(subset(_84221, _84219))], (245 ^ _75877) ^ [] : [-(subset(_84219, _84221))]]], (247 ^ _75877) ^ [_84456, _84458] : [-(equal_set(_84458, _84456)), subset(_84458, _84456), subset(_84456, _84458)], (257 ^ _75877) ^ [_84786, _84788] : [member(_84788, power_set(_84786)), -(subset(_84788, _84786))], (263 ^ _75877) ^ [_84952, _84954] : [subset(_84954, _84952), -(member(_84954, power_set(_84952)))], (269 ^ _75877) ^ [_85211, _85213, _85215] : [member(_85215, intersection(_85213, _85211)), 272 ^ _75877 : [(273 ^ _75877) ^ [] : [-(member(_85215, _85213))], (275 ^ _75877) ^ [] : [-(member(_85215, _85211))]]], (277 ^ _75877) ^ [_85462, _85464, _85466] : [-(member(_85466, intersection(_85464, _85462))), member(_85466, _85464), member(_85466, _85462)], (297 ^ _75877) ^ [_86090, _86092, _86094] : [298 ^ _75877 : [(299 ^ _75877) ^ [] : [member(_86094, _86092)], (301 ^ _75877) ^ [] : [member(_86094, _86090)]], -(member(_86094, union(_86092, _86090)))], (287 ^ _75877) ^ [_85822, _85824, _85826] : [member(_85826, union(_85824, _85822)), -(member(_85826, _85824)), -(member(_85826, _85822))], (305 ^ _75877) ^ [_86360] : [member(_86360, empty_set)], (307 ^ _75877) ^ [_86510, _86512, _86514] : [member(_86514, difference(_86510, _86512)), 310 ^ _75877 : [(311 ^ _75877) ^ [] : [-(member(_86514, _86510))], (313 ^ _75877) ^ [] : [member(_86514, _86512)]]], (315 ^ _75877) ^ [_86762, _86764, _86766] : [-(member(_86766, difference(_86762, _86764))), member(_86766, _86762), -(member(_86766, _86764))], (325 ^ _75877) ^ [_87111, _87113] : [member(_87113, singleton(_87111)), -(_87113 = _87111)], (331 ^ _75877) ^ [_87277, _87279] : [_87279 = _87277, -(member(_87279, singleton(_87277)))], (347 ^ _75877) ^ [_87804, _87806, _87808] : [348 ^ _75877 : [(349 ^ _75877) ^ [] : [_87808 = _87806], (351 ^ _75877) ^ [] : [_87808 = _87804]], -(member(_87808, unordered_pair(_87806, _87804)))], (337 ^ _75877) ^ [_87536, _87538, _87540] : [member(_87540, unordered_pair(_87538, _87536)), -(_87540 = _87538), -(_87540 = _87536)], (355 ^ _75877) ^ [_88133, _88135] : [member(_88135, sum(_88133)), 359 ^ _75877 : [(360 ^ _75877) ^ [] : [-(member(358 ^ [_88133, _88135], _88133))], (362 ^ _75877) ^ [] : [-(member(_88135, 358 ^ [_88133, _88135]))]]], (364 ^ _75877) ^ [_88444, _88446] : [-(member(_88446, sum(_88444))), 365 ^ _75877 : [(366 ^ _75877) ^ [_88538] : [member(_88538, _88444), member(_88446, _88538)]]], (384 ^ _75877) ^ [_89139, _89141] : [386 ^ _75877 : [(387 ^ _75877) ^ [] : [-(member(385 ^ [_89139, _89141], _89139))], (389 ^ _75877) ^ [] : [member(_89141, 385 ^ [_89139, _89141])]], -(member(_89141, product(_89139)))], (374 ^ _75877) ^ [_88821, _88823] : [member(_88823, product(_88821)), 377 ^ _75877 : [(378 ^ _75877) ^ [_88962] : [member(_88962, _88821), -(member(_88823, _88962))]]], (393 ^ _75877) ^ [_89553] : [member(_89553, on), 396 ^ _75877 : [(397 ^ _75877) ^ [] : [-(set(_89553))], (399 ^ _75877) ^ [] : [-(strict_well_order(member_predicate, _89553))], (401 ^ _75877) ^ [_89824] : [member(_89824, _89553), -(subset(_89824, _89553))]]], (407 ^ _75877) ^ [_89997] : [-(member(_89997, on)), set(_89997), strict_well_order(member_predicate, _89997), 417 ^ _75877 : [(418 ^ _75877) ^ [] : [-(member(416 ^ [_89997], _89997))], (420 ^ _75877) ^ [] : [subset(416 ^ [_89997], _89997)]]], (441 ^ _75877) ^ [_91121, _91123] : [-(strict_well_order(_91123, _91121)), strict_order(_91123, _91121), 447 ^ _75877 : [(448 ^ _75877) ^ [] : [-(subset(446 ^ [_91121, _91123], _91121))], (451 ^ _75877) ^ [] : [-(member(449 ^ [_91121, _91123], 446 ^ [_91121, _91123]))], (453 ^ _75877) ^ [_91574] : [least(_91574, _91123, 446 ^ [_91121, _91123])]]], (424 ^ _75877) ^ [_90535, _90537] : [strict_well_order(_90537, _90535), 427 ^ _75877 : [(428 ^ _75877) ^ [] : [-(strict_order(_90537, _90535))], (430 ^ _75877) ^ [_90761] : [-(least(437 ^ [_90535, _90537, _90761], _90537, _90761)), subset(_90761, _90535), 435 ^ _75877 : [(436 ^ _75877) ^ [_90932] : [member(_90932, _90761)]]]]], (473 ^ _75877) ^ [_92308, _92310, _92312] : [-(least(_92308, _92312, _92310)), member(_92308, _92310), 479 ^ _75877 : [(480 ^ _75877) ^ [] : [-(member(478 ^ [_92308, _92310, _92312], _92310))], (482 ^ _75877) ^ [] : [_92308 = 478 ^ [_92308, _92310, _92312]], (484 ^ _75877) ^ [] : [apply(_92312, _92308, 478 ^ [_92308, _92310, _92312])]]], (457 ^ _75877) ^ [_91797, _91799, _91801] : [least(_91797, _91801, _91799), 460 ^ _75877 : [(461 ^ _75877) ^ [] : [-(member(_91797, _91799))], (463 ^ _75877) ^ [_92021] : [member(_92021, _91799), -(_91797 = _92021), -(apply(_91801, _91797, _92021))]]], (488 ^ _75877) ^ [_92898, _92900] : [apply(member_predicate, _92900, _92898), -(member(_92900, _92898))], (494 ^ _75877) ^ [_93062, _93064] : [member(_93064, _93062), -(apply(member_predicate, _93064, _93062))], (571 ^ _75877) ^ [_96081] : [set(_96081), 574 ^ _75877 : [(575 ^ _75877) ^ [_96211] : [member(_96211, _96081), -(set(_96211))]]], (599 ^ _75877) ^ [_97086, _97088] : [member(_97086, suc(_97088)), -(member(_97086, union(_97088, singleton(_97088))))], (605 ^ _75877) ^ [_97262, _97264] : [member(_97262, union(_97264, singleton(_97264))), -(member(_97262, suc(_97264)))], (581 ^ _75877) ^ [_96483, _96485, _96487, _96489] : [member(_96483, initial_segment(_96489, _96487, _96485)), 584 ^ _75877 : [(585 ^ _75877) ^ [] : [-(member(_96483, _96485))], (587 ^ _75877) ^ [] : [-(apply(_96487, _96483, _96489))]]], (589 ^ _75877) ^ [_96746, _96748, _96750, _96752] : [-(member(_96746, initial_segment(_96752, _96750, _96748))), member(_96746, _96748), apply(_96750, _96746, _96752)], (540 ^ _75877) ^ [_94577, _94579] : [-(strict_order(_94579, _94577)), 545 ^ _75877 : [(546 ^ _75877) ^ [] : [-(member(543 ^ [_94577, _94579], _94577))], (548 ^ _75877) ^ [] : [-(member(544 ^ [_94577, _94579], _94577))], (550 ^ _75877) ^ [] : [-(apply(_94579, 543 ^ [_94577, _94579], 544 ^ [_94577, _94579]))], (552 ^ _75877) ^ [] : [-(apply(_94579, 544 ^ [_94577, _94579], 543 ^ [_94577, _94579]))]], 556 ^ _75877 : [(557 ^ _75877) ^ [] : [-(member(553 ^ [_94577, _94579], _94577))], (559 ^ _75877) ^ [] : [-(member(554 ^ [_94577, _94579], _94577))], (561 ^ _75877) ^ [] : [-(member(555 ^ [_94577, _94579], _94577))], (563 ^ _75877) ^ [] : [-(apply(_94579, 553 ^ [_94577, _94579], 554 ^ [_94577, _94579]))], (565 ^ _75877) ^ [] : [-(apply(_94579, 554 ^ [_94577, _94579], 555 ^ [_94577, _94579]))], (567 ^ _75877) ^ [] : [apply(_94579, 553 ^ [_94577, _94579], 555 ^ [_94577, _94579])]]], (500 ^ _75877) ^ [_93305, _93307] : [strict_order(_93307, _93305), 503 ^ _75877 : [(504 ^ _75877) ^ [_93551, _93553] : [member(_93553, _93305), member(_93551, _93305), apply(_93307, _93553, _93551), apply(_93307, _93551, _93553)], (518 ^ _75877) ^ [_93972, _93974, _93976] : [member(_93976, _93305), member(_93974, _93305), member(_93972, _93305), -(apply(_93307, _93976, _93972)), apply(_93307, _93976, _93974), apply(_93307, _93974, _93972)]]]], input).
% 1.42/2.41  ncf('1',plain,[member(610 ^ [], suc(610 ^ []))],start(614 ^ 0)).
% 1.42/2.41  ncf('1.1',plain,[-(member(610 ^ [], suc(610 ^ []))), member(610 ^ [], union(610 ^ [], singleton(610 ^ [])))],extension(605 ^ 1,bind([[_97262, _97264], [610 ^ [], 610 ^ []]]))).
% 1.42/2.41  ncf('1.1.1',plain,[-(member(610 ^ [], union(610 ^ [], singleton(610 ^ [])))), 301 : member(610 ^ [], singleton(610 ^ []))],extension(297 ^ 2,bind([[_86090, _86092, _86094], [singleton(610 ^ []), 610 ^ [], 610 ^ []]]))).
% 1.42/2.41  ncf('1.1.1.1',plain,[-(member(610 ^ [], singleton(610 ^ []))), 610 ^ [] = 610 ^ []],extension(331 ^ 5,bind([[_87277, _87279], [610 ^ [], 610 ^ []]]))).
% 1.42/2.41  ncf('1.1.1.1.1',plain,[-(610 ^ [] = 610 ^ [])],extension(2 ^ 6,bind([[_76021], [610 ^ []]]))).
% 1.42/2.41  %-----------------------------------------------------
% 1.42/2.41  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------