%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET992+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n012.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 11:56:47 EDT 2023

% Result   : Theorem 46.97s 45.83s
% Output   : Proof 46.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET992+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n012.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 18:54:02 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 46.97/45.83  
% 46.97/45.83  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 46.97/45.83  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.97/45.83  %-----------------------------------------------------
% 46.97/45.83  ncf(matrix, plain, [(424 ^ _83191) ^ [] : [-(function(420 ^ []))], (426 ^ _83191) ^ [] : [-(relation_dom(420 ^ []) = singleton(419 ^ []))], (428 ^ _83191) ^ [] : [relation_rng(420 ^ []) = singleton(apply(420 ^ [], 419 ^ []))], (422 ^ _83191) ^ [] : [-(relation(420 ^ []))], !, (82 ^ _68964) ^ [_71634, _71636] : [-(relation(_71634)), _71636 = _71634, relation(_71636)], (285 ^ _68964) ^ [_78553] : [empty(_78553), 288 ^ _68964 : [(291 ^ _68964) ^ [] : [-(relation(relation_rng(_78553)))], (289 ^ _68964) ^ [] : [-(empty(relation_rng(_78553)))]]], (148 ^ _68964) ^ [_73834] : [empty(_73834), -(relation(_73834))], (255 ^ _68964) ^ [] : [-(relation(empty_set))], (10 ^ _68964) ^ [_69399, _69401, _69403] : [-(_69403 = _69399), _69403 = _69401, _69401 = _69399], (142 ^ _68964) ^ [_73648] : [empty(_73648), -(function(_73648))], (20 ^ _68964) ^ [_69712, _69714] : [-(relation_empty_yielding(_69712)), _69714 = _69712, relation_empty_yielding(_69714)], (277 ^ _68964) ^ [_78288] : [empty(_78288), 280 ^ _68964 : [(283 ^ _68964) ^ [] : [-(relation(relation_dom(_78288)))], (281 ^ _68964) ^ [] : [-(empty(relation_dom(_78288)))]]], (329 ^ _68964) ^ [] : [-(relation(327 ^ []))], (326 ^ _68964) ^ [] : [empty(324 ^ [])], (267 ^ _68964) ^ [_78011] : [empty(relation_rng(_78011)), -(empty(_78011)), relation(_78011)], (303 ^ _68964) ^ [_79116] : [-(empty(_79116)), 307 ^ _68964 : [(310 ^ _68964) ^ [] : [empty(306 ^ [_79116])], (308 ^ _68964) ^ [] : [-(element(306 ^ [_79116], powerset(_79116)))]]], (313 ^ _68964) ^ [] : [-(empty(311 ^ []))], (351 ^ _68964) ^ [_80743, _80745] : [-(_80745 = _80743), 355 ^ _68964 : [(358 ^ _68964) ^ [] : [in(352 ^ [_80743, _80745], _80743)], (356 ^ _68964) ^ [] : [-(in(352 ^ [_80743, _80745], _80745))]], 359 ^ _68964 : [(362 ^ _68964) ^ [] : [in(352 ^ [_80743, _80745], _80745)], (360 ^ _68964) ^ [] : [-(in(352 ^ [_80743, _80745], _80743))]]], (331 ^ _68964) ^ [] : [-(relation_empty_yielding(327 ^ []))], (2 ^ _68964) ^ [_69088] : [-(_69088 = _69088)], (410 ^ _68964) ^ [_82710, _82712] : [empty(_82712), -(_82712 = _82710), empty(_82710)], (321 ^ _68964) ^ [_79738] : [-(element(319 ^ [_79738], powerset(_79738)))], (249 ^ _68964) ^ [] : [-(empty(empty_set))], (323 ^ _68964) ^ [_79789] : [-(empty(319 ^ [_79789]))], (333 ^ _68964) ^ [_80126, _80128] : [-(subset(_80128, _80128))], (102 ^ _68964) ^ [_72222, _72224] : [_72224 = _72222, -(powerset(_72224) = powerset(_72222))], (372 ^ _68964) ^ [_81468, _81470] : [subset(_81470, _81468), -(element(_81470, powerset(_81468)))], (58 ^ _68964) ^ [_70923, _70925, _70927, _70929] : [-(in(_70927, _70923)), in(_70929, _70925), _70929 = _70927, _70925 = _70923], (398 ^ _68964) ^ [_82321] : [empty(_82321), -(_82321 = empty_set)], (294 ^ _68964) ^ [] : [-(relation(292 ^ []))], (72 ^ _68964) ^ [_71339, _71341] : [-(empty(_71339)), _71341 = _71339, empty(_71341)], (335 ^ _68964) ^ [_80235, _80237] : [in(_80237, _80235), -(element(_80237, _80235))], (404 ^ _68964) ^ [_82523, _82525] : [in(_82525, _82523), empty(_82523)], (296 ^ _68964) ^ [] : [-(function(292 ^ []))], (92 ^ _68964) ^ [_71909, _71911] : [-(function(_71909)), _71911 = _71909, function(_71911)], (247 ^ _68964) ^ [_77401] : [empty(powerset(_77401))], (30 ^ _68964) ^ [_70035, _70037, _70039, _70041] : [-(subset(_70039, _70035)), subset(_70041, _70037), _70041 = _70039, _70037 = _70035], (126 ^ _68964) ^ [_73102, _73104, _73106, _73108] : [-(apply(_73108, _73104) = apply(_73106, _73102)), _73108 = _73106, _73104 = _73102], (120 ^ _68964) ^ [_72876, _72878] : [_72878 = _72876, -(singleton(_72878) = singleton(_72876))], (378 ^ _68964) ^ [_81698, _81700, _81702] : [-(element(_81702, _81698)), in(_81702, _81700), element(_81700, powerset(_81698))], (301 ^ _68964) ^ [] : [-(relation(297 ^ []))], (253 ^ _68964) ^ [] : [-(empty(empty_set))], (114 ^ _68964) ^ [_72658, _72660] : [_72660 = _72658, -(relation_rng(_72660) = relation_rng(_72658))], (251 ^ _68964) ^ [_77532] : [empty(singleton(_77532))], (245 ^ _68964) ^ [] : [-(relation_empty_yielding(empty_set))], (239 ^ _68964) ^ [_77156] : [-(element(237 ^ [_77156], _77156))], (154 ^ _68964) ^ [_74063, _74065] : [_74063 = singleton(_74065), 157 ^ _68964 : [(164 ^ _68964) ^ [_74405] : [_74405 = _74065, -(in(_74405, _74063))], (158 ^ _68964) ^ [_74233] : [in(_74233, _74063), -(_74233 = _74065)]]], (257 ^ _68964) ^ [_77734] : [empty(relation_dom(_77734)), -(empty(_77734)), relation(_77734)], (185 ^ _68964) ^ [_75106] : [relation(_75106), function(_75106), 192 ^ _68964 : [(193 ^ _68964) ^ [_75378] : [_75378 = relation_rng(_75106), 196 ^ _68964 : [(206 ^ _68964) ^ [_75908] : [-(in(_75908, _75378)), 207 ^ _68964 : [(208 ^ _68964) ^ [_76011] : [in(_76011, relation_dom(_75106)), _75908 = apply(_75106, _76011)]]], (197 ^ _68964) ^ [_75566] : [in(_75566, _75378), 201 ^ _68964 : [(204 ^ _68964) ^ [] : [-(_75566 = apply(_75106, 200 ^ [_75106, _75378, _75566]))], (202 ^ _68964) ^ [] : [-(in(200 ^ [_75106, _75378, _75566], relation_dom(_75106)))]]]]], (216 ^ _68964) ^ [_76260] : [-(_76260 = relation_rng(_75106)), 229 ^ _68964 : [(234 ^ _68964) ^ [] : [in(217 ^ [_75106, _76260], _76260)], (232 ^ _68964) ^ [] : [-(217 ^ [_75106, _76260] = apply(_75106, 228 ^ [_75106, _76260]))], (230 ^ _68964) ^ [] : [-(in(228 ^ [_75106, _76260], relation_dom(_75106)))]], 220 ^ _68964 : [(223 ^ _68964) ^ [_76555] : [in(_76555, relation_dom(_75106)), 217 ^ [_75106, _76260] = apply(_75106, _76555)], (221 ^ _68964) ^ [] : [-(in(217 ^ [_75106, _76260], _76260))]]]]], (108 ^ _68964) ^ [_72440, _72442] : [_72442 = _72440, -(relation_dom(_72442) = relation_dom(_72440))], (136 ^ _68964) ^ [_73451, _73453] : [in(_73453, _73451), in(_73451, _73453)], (170 ^ _68964) ^ [_74584, _74586] : [-(_74584 = singleton(_74586)), 174 ^ _68964 : [(177 ^ _68964) ^ [] : [171 ^ [_74584, _74586] = _74586], (175 ^ _68964) ^ [] : [-(in(171 ^ [_74584, _74586], _74584))]], 178 ^ _68964 : [(181 ^ _68964) ^ [] : [in(171 ^ [_74584, _74586], _74584)], (179 ^ _68964) ^ [] : [-(171 ^ [_74584, _74586] = _74586)]]], (316 ^ _68964) ^ [] : [empty(314 ^ [])], (341 ^ _68964) ^ [_80445, _80447] : [element(_80447, _80445), -(empty(_80445)), -(in(_80447, _80445))], (243 ^ _68964) ^ [] : [-(relation(empty_set))], (299 ^ _68964) ^ [] : [-(empty(297 ^ []))], (4 ^ _68964) ^ [_69195, _69197] : [_69197 = _69195, -(_69195 = _69197)], (388 ^ _68964) ^ [_82025, _82027, _82029] : [in(_82029, _82027), element(_82027, powerset(_82025)), empty(_82025)], (366 ^ _68964) ^ [_81302, _81304] : [element(_81304, powerset(_81302)), -(subset(_81304, _81302))], (318 ^ _68964) ^ [] : [-(relation(314 ^ []))], (44 ^ _68964) ^ [_70479, _70481, _70483, _70485] : [-(element(_70483, _70479)), element(_70485, _70481), _70485 = _70483, _70481 = _70479], (241 ^ _68964) ^ [] : [-(empty(empty_set))]], input).
% 46.97/45.83  ncf('1',plain,[-(function(420 ^ []))],start(424 ^ 0)).
% 46.97/45.83  ncf('1.1',plain,[function(420 ^ []), relation(420 ^ []), 193 : relation_rng(420 ^ []) = relation_rng(420 ^ []), 197 : in(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], relation_rng(420 ^ [])), 204 : -(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]))],extension(185 ^ 1,bind([[_75106, _75378, _75566], [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]]))).
% 46.97/45.83  ncf('1.1.1',plain,[-(relation(420 ^ []))],extension(422 ^ 2)).
% 46.97/45.83  ncf('1.1.2',plain,[-(relation_rng(420 ^ []) = relation_rng(420 ^ [])), 358 : in(352 ^ [relation_rng(420 ^ []), relation_rng(420 ^ [])], relation_rng(420 ^ [])), 362 : in(352 ^ [relation_rng(420 ^ []), relation_rng(420 ^ [])], relation_rng(420 ^ []))],extension(351 ^ 4,bind([[_80743, _80745], [relation_rng(420 ^ []), relation_rng(420 ^ [])]]))).
% 46.97/45.83  ncf('1.1.2.1',plain,[-(in(352 ^ [relation_rng(420 ^ []), relation_rng(420 ^ [])], relation_rng(420 ^ [])))],extension(356 ^ 7)).
% 46.97/45.83  ncf('1.1.2.2',plain,[-(in(352 ^ [relation_rng(420 ^ []), relation_rng(420 ^ [])], relation_rng(420 ^ [])))],extension(360 ^ 7)).
% 46.97/45.83  ncf('1.1.3',plain,[-(in(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], relation_rng(420 ^ []))), -(relation_rng(420 ^ []) = singleton(apply(420 ^ [], 419 ^ []))), 179 : -(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ []))],extension(170 ^ 6,bind([[_74584, _74586], [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]))).
% 46.97/45.83  ncf('1.1.3.1',plain,[relation_rng(420 ^ []) = singleton(apply(420 ^ [], 419 ^ []))],extension(428 ^ 7)).
% 46.97/45.83  ncf('1.1.3.2',plain,[171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ []), 208 : in(419 ^ [], relation_dom(420 ^ [])), 208 : -(in(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], relation_rng(420 ^ [])))],extension(206 ^ 9,bind([[_75908, _76011], [171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], 419 ^ []]]))).
% 46.97/45.83  ncf('1.1.3.2.1',plain,[-(in(419 ^ [], relation_dom(420 ^ []))), 164 : 419 ^ [] = 419 ^ [], 164 : relation_dom(420 ^ []) = singleton(419 ^ [])],extension(154 ^ 12,bind([[_74063, _74065, _74405], [relation_dom(420 ^ []), 419 ^ [], 419 ^ []]]))).
% 46.97/45.83  ncf('1.1.3.2.1.1',plain,[-(419 ^ [] = 419 ^ [])],extension(2 ^ 15,bind([[_69088], [419 ^ []]]))).
% 46.97/45.83  ncf('1.1.3.2.1.2',plain,[-(relation_dom(420 ^ []) = singleton(419 ^ []))],extension(426 ^ 13)).
% 46.97/45.83  ncf('1.1.3.2.2',plain,[in(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], relation_rng(420 ^ []))],reduction('1.1')).
% 46.97/45.83  ncf('1.1.4',plain,[171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]), -(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ [])), apply(420 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]) = apply(420 ^ [], 419 ^ [])],extension(10 ^ 8,bind([[_69399, _69401, _69403], [apply(420 ^ [], 419 ^ []), apply(420 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]]))).
% 46.97/45.83  ncf('1.1.4.1',plain,[171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ []), -(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]), apply(420 ^ [], 419 ^ []) = 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]],extension(10 ^ 9,bind([[_69399, _69401, _69403], [171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], apply(420 ^ [], 419 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]]))).
% 46.97/45.83  ncf('1.1.4.1.1',plain,[171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], -(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ [])), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ [])],extension(10 ^ 10,bind([[_69399, _69401, _69403], [apply(420 ^ [], 419 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]]))).
% 46.97/45.83  ncf('1.1.4.1.1.1',plain,[171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ []), -(relation_rng(420 ^ []) = singleton(apply(420 ^ [], 419 ^ []))), 181 : in(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], relation_rng(420 ^ []))],extension(170 ^ 11,bind([[_74584, _74586], [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]))).
% 46.97/45.83  ncf('1.1.4.1.1.1.1',plain,[relation_rng(420 ^ []) = singleton(apply(420 ^ [], 419 ^ []))],extension(428 ^ 12)).
% 46.97/45.83  ncf('1.1.4.1.1.1.2',plain,[-(in(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])], relation_rng(420 ^ [])))],lemmata('[1].x')).
% 46.97/45.83  ncf('1.1.4.1.1.2',plain,[-(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ []))],reduction('1.1.4')).
% 46.97/45.83  ncf('1.1.4.1.2',plain,[-(apply(420 ^ [], 419 ^ []) = 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ [])],extension(4 ^ 10,bind([[_69195, _69197], [apply(420 ^ [], 419 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]]))).
% 46.97/45.83  ncf('1.1.4.1.2.1',plain,[-(171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])] = apply(420 ^ [], 419 ^ []))],reduction('1.1.4')).
% 46.97/45.83  ncf('1.1.4.2',plain,[-(apply(420 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]) = apply(420 ^ [], 419 ^ [])), 420 ^ [] = 420 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]] = 419 ^ []],extension(126 ^ 9,bind([[_73102, _73104, _73106, _73108], [419 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]], 420 ^ [], 420 ^ []]]))).
% 46.97/45.83  ncf('1.1.4.2.1',plain,[-(420 ^ [] = 420 ^ []), 358 : in(352 ^ [420 ^ [], 420 ^ []], 420 ^ []), 362 : in(352 ^ [420 ^ [], 420 ^ []], 420 ^ [])],extension(351 ^ 10,bind([[_80743, _80745], [420 ^ [], 420 ^ []]]))).
% 46.97/45.83  ncf('1.1.4.2.1.1',plain,[-(in(352 ^ [420 ^ [], 420 ^ []], 420 ^ []))],extension(356 ^ 13)).
% 46.97/45.83  ncf('1.1.4.2.1.2',plain,[-(in(352 ^ [420 ^ [], 420 ^ []], 420 ^ []))],extension(360 ^ 13)).
% 46.97/45.83  ncf('1.1.4.2.2',plain,[-(200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]] = 419 ^ []), 158 : in(200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]], relation_dom(420 ^ [])), 158 : relation_dom(420 ^ []) = singleton(419 ^ [])],extension(154 ^ 10,bind([[_74063, _74065, _74233], [relation_dom(420 ^ []), 419 ^ [], 200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]]]]))).
% 46.97/45.83  ncf('1.1.4.2.2.1',plain,[-(in(200 ^ [420 ^ [], relation_rng(420 ^ []), 171 ^ [relation_rng(420 ^ []), apply(420 ^ [], 419 ^ [])]], relation_dom(420 ^ [])))],extension(202 ^ 13)).
% 46.97/45.83  ncf('1.1.4.2.2.2',plain,[-(relation_dom(420 ^ []) = singleton(419 ^ []))],extension(426 ^ 11)).
% 46.97/45.83  %-----------------------------------------------------
% 46.97/45.83  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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