%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n015.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 12:02:06 EDT 2023

% Result   : Theorem 8.93s 9.64s
% Output   : Proof 8.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n015.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 13:58:22 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 8.93/9.64  
% 8.93/9.64  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 8.93/9.64  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.93/9.64  %-----------------------------------------------------
% 8.93/9.64  ncf(matrix, plain, [(538 ^ _92607) ^ [] : [-(relation(536 ^ []))], (540 ^ _92607) ^ [] : [-(function(536 ^ []))], (543 ^ _92607) ^ [] : [-(relation(541 ^ []))], (545 ^ _92607) ^ [] : [-(function(541 ^ []))], (573 ^ _92607) ^ [] : [541 ^ [] = function_inverse(536 ^ [])], (547 ^ _92607) ^ [] : [-(one_to_one(536 ^ []))], (549 ^ _92607) ^ [] : [-(relation_dom(536 ^ []) = relation_rng(541 ^ []))], (551 ^ _92607) ^ [] : [-(relation_rng(536 ^ []) = relation_dom(541 ^ []))], (553 ^ _92607) ^ [_111060, _111062] : [in(_111062, relation_dom(536 ^ [])), in(_111060, relation_dom(541 ^ [])), 560 ^ _92607 : [(561 ^ _92607) ^ [] : [apply(536 ^ [], _111062) = _111060, -(apply(541 ^ [], _111060) = _111062)], (567 ^ _92607) ^ [] : [apply(541 ^ [], _111060) = _111062, -(apply(536 ^ [], _111062) = _111060)]]], (112 ^ _92607) ^ [_96182, _96184] : [_96184 = _96182, -(powerset(_96184) = powerset(_96182))], (118 ^ _92607) ^ [_96400, _96402] : [_96402 = _96400, -(relation_rng(_96402) = relation_rng(_96400))], (124 ^ _92607) ^ [_96618, _96620] : [_96620 = _96618, -(relation_dom(_96620) = relation_dom(_96618))], (140 ^ _92607) ^ [_97175, _97177] : [_97177 = _97175, -(function_inverse(_97177) = function_inverse(_97175))], (130 ^ _92607) ^ [_96864, _96866, _96868, _96870] : [-(apply(_96870, _96866) = apply(_96868, _96864)), _96870 = _96868, _96866 = _96864], (2 ^ _92607) ^ [_92751] : [-(_92751 = _92751)], (4 ^ _92607) ^ [_92858, _92860] : [_92860 = _92858, -(_92858 = _92860)], (10 ^ _92607) ^ [_93062, _93064, _93066] : [-(_93066 = _93062), _93066 = _93064, _93064 = _93062], (20 ^ _92607) ^ [_93375, _93377] : [-(relation_empty_yielding(_93375)), _93377 = _93375, relation_empty_yielding(_93377)], (30 ^ _92607) ^ [_93698, _93700, _93702, _93704] : [-(subset(_93702, _93698)), subset(_93704, _93700), _93704 = _93702, _93700 = _93698], (44 ^ _92607) ^ [_94142, _94144, _94146, _94148] : [-(element(_94146, _94142)), element(_94148, _94144), _94148 = _94146, _94144 = _94142], (58 ^ _92607) ^ [_94558, _94560] : [-(empty(_94558)), _94560 = _94558, empty(_94560)], (68 ^ _92607) ^ [_94853, _94855] : [-(relation(_94853)), _94855 = _94853, relation(_94855)], (78 ^ _92607) ^ [_95148, _95150] : [-(function(_95148)), _95150 = _95148, function(_95150)], (88 ^ _92607) ^ [_95443, _95445] : [-(one_to_one(_95443)), _95445 = _95443, one_to_one(_95445)], (98 ^ _92607) ^ [_95746, _95748, _95750, _95752] : [-(in(_95750, _95746)), in(_95752, _95748), _95752 = _95750, _95748 = _95746], (146 ^ _92607) ^ [_97411, _97413] : [in(_97413, _97411), in(_97411, _97413)], (152 ^ _92607) ^ [_97608] : [empty(_97608), -(function(_97608))], (158 ^ _92607) ^ [_97794] : [empty(_97794), -(relation(_97794))], (164 ^ _92607) ^ [_97980] : [175 ^ _92607 : [(176 ^ _92607) ^ [] : [-(relation(_97980))], (178 ^ _92607) ^ [] : [-(function(_97980))], (180 ^ _92607) ^ [] : [-(one_to_one(_97980))]], relation(_97980), empty(_97980), function(_97980)], (182 ^ _92607) ^ [_98473] : [relation(_98473), function(_98473), 189 ^ _92607 : [(213 ^ _92607) ^ [_99627] : [-(_99627 = relation_rng(_98473)), 226 ^ _92607 : [(227 ^ _92607) ^ [] : [-(in(225 ^ [_98473, _99627], relation_dom(_98473)))], (229 ^ _92607) ^ [] : [-(214 ^ [_98473, _99627] = apply(_98473, 225 ^ [_98473, _99627]))], (231 ^ _92607) ^ [] : [in(214 ^ [_98473, _99627], _99627)]], 217 ^ _92607 : [(218 ^ _92607) ^ [] : [-(in(214 ^ [_98473, _99627], _99627))], (220 ^ _92607) ^ [_99922] : [in(_99922, relation_dom(_98473)), 214 ^ [_98473, _99627] = apply(_98473, _99922)]]], (190 ^ _92607) ^ [_98745] : [_98745 = relation_rng(_98473), 193 ^ _92607 : [(194 ^ _92607) ^ [_98933] : [in(_98933, _98745), 198 ^ _92607 : [(199 ^ _92607) ^ [] : [-(in(197 ^ [_98473, _98745, _98933], relation_dom(_98473)))], (201 ^ _92607) ^ [] : [-(_98933 = apply(_98473, 197 ^ [_98473, _98745, _98933]))]]], (203 ^ _92607) ^ [_99275] : [-(in(_99275, _98745)), 204 ^ _92607 : [(205 ^ _92607) ^ [_99378] : [in(_99378, relation_dom(_98473)), _99275 = apply(_98473, _99378)]]]]]]], (235 ^ _92607) ^ [_100499] : [242 ^ _92607 : [(243 ^ _92607) ^ [] : [-(relation(function_inverse(_100499)))], (245 ^ _92607) ^ [] : [-(function(function_inverse(_100499)))]], relation(_100499), function(_100499)], (248 ^ _92607) ^ [_100871] : [-(element(246 ^ [_100871], _100871))], (250 ^ _92607) ^ [] : [-(empty(empty_set))], (252 ^ _92607) ^ [] : [-(relation(empty_set))], (254 ^ _92607) ^ [] : [-(relation_empty_yielding(empty_set))], (256 ^ _92607) ^ [_101116] : [empty(powerset(_101116))], (258 ^ _92607) ^ [] : [-(empty(empty_set))], (260 ^ _92607) ^ [] : [-(empty(empty_set))], (262 ^ _92607) ^ [] : [-(relation(empty_set))], (264 ^ _92607) ^ [_101371] : [empty(relation_dom(_101371)), -(empty(_101371)), relation(_101371)], (274 ^ _92607) ^ [_101648] : [empty(relation_rng(_101648)), -(empty(_101648)), relation(_101648)], (284 ^ _92607) ^ [_101925] : [empty(_101925), 287 ^ _92607 : [(288 ^ _92607) ^ [] : [-(empty(relation_dom(_101925)))], (290 ^ _92607) ^ [] : [-(relation(relation_dom(_101925)))]]], (292 ^ _92607) ^ [_102190] : [empty(_102190), 295 ^ _92607 : [(296 ^ _92607) ^ [] : [-(empty(relation_rng(_102190)))], (298 ^ _92607) ^ [] : [-(relation(relation_rng(_102190)))]]], (301 ^ _92607) ^ [] : [-(relation(299 ^ []))], (303 ^ _92607) ^ [] : [-(function(299 ^ []))], (306 ^ _92607) ^ [] : [-(empty(304 ^ []))], (308 ^ _92607) ^ [] : [-(relation(304 ^ []))], (310 ^ _92607) ^ [_102753] : [-(empty(_102753)), 314 ^ _92607 : [(315 ^ _92607) ^ [] : [-(element(313 ^ [_102753], powerset(_102753)))], (317 ^ _92607) ^ [] : [empty(313 ^ [_102753])]]], (320 ^ _92607) ^ [] : [-(empty(318 ^ []))], (323 ^ _92607) ^ [] : [-(relation(321 ^ []))], (325 ^ _92607) ^ [] : [-(empty(321 ^ []))], (327 ^ _92607) ^ [] : [-(function(321 ^ []))], (330 ^ _92607) ^ [] : [empty(328 ^ [])], (332 ^ _92607) ^ [] : [-(relation(328 ^ []))], (335 ^ _92607) ^ [_103584] : [-(element(333 ^ [_103584], powerset(_103584)))], (337 ^ _92607) ^ [_103635] : [-(empty(333 ^ [_103635]))], (340 ^ _92607) ^ [] : [empty(338 ^ [])], (343 ^ _92607) ^ [] : [-(relation(341 ^ []))], (345 ^ _92607) ^ [] : [-(function(341 ^ []))], (347 ^ _92607) ^ [] : [-(one_to_one(341 ^ []))], (350 ^ _92607) ^ [] : [-(relation(348 ^ []))], (352 ^ _92607) ^ [] : [-(relation_empty_yielding(348 ^ []))], (354 ^ _92607) ^ [_104181, _104183] : [-(subset(_104183, _104183))], (356 ^ _92607) ^ [_104290, _104292] : [in(_104292, _104290), -(element(_104292, _104290))], (362 ^ _92607) ^ [_104500, _104502] : [element(_104502, _104500), -(empty(_104500)), -(in(_104502, _104500))], (372 ^ _92607) ^ [_104827, _104829] : [element(_104829, powerset(_104827)), -(subset(_104829, _104827))], (378 ^ _92607) ^ [_104993, _104995] : [subset(_104995, _104993), -(element(_104995, powerset(_104993)))], (384 ^ _92607) ^ [_105223, _105225, _105227] : [-(element(_105227, _105223)), in(_105227, _105225), element(_105225, powerset(_105223))], (394 ^ _92607) ^ [_105522] : [relation(_105522), function(_105522), one_to_one(_105522), 405 ^ _92607 : [(406 ^ _92607) ^ [_105909] : [relation(_105909), function(_105909), 413 ^ _92607 : [(444 ^ _92607) ^ [] : [-(_105909 = function_inverse(_105522)), relation_dom(_105909) = relation_rng(_105522), 453 ^ _92607 : [(454 ^ _92607) ^ [] : [-(in(449 ^ [_105522, _105909], relation_rng(_105522)))], (456 ^ _92607) ^ [] : [-(450 ^ [_105522, _105909] = apply(_105909, 449 ^ [_105522, _105909]))], (458 ^ _92607) ^ [] : [in(450 ^ [_105522, _105909], relation_dom(_105522)), 449 ^ [_105522, _105909] = apply(_105522, 450 ^ [_105522, _105909])]], 463 ^ _92607 : [(464 ^ _92607) ^ [] : [-(in(450 ^ [_105522, _105909], relation_dom(_105522)))], (466 ^ _92607) ^ [] : [-(449 ^ [_105522, _105909] = apply(_105522, 450 ^ [_105522, _105909]))], (468 ^ _92607) ^ [] : [in(449 ^ [_105522, _105909], relation_rng(_105522)), 450 ^ [_105522, _105909] = apply(_105909, 449 ^ [_105522, _105909])]]], (414 ^ _92607) ^ [] : [_105909 = function_inverse(_105522), 417 ^ _92607 : [(418 ^ _92607) ^ [] : [-(relation_dom(_105909) = relation_rng(_105522))], (420 ^ _92607) ^ [_106426, _106428] : [427 ^ _92607 : [(428 ^ _92607) ^ [] : [-(in(_106426, relation_dom(_105522)))], (430 ^ _92607) ^ [] : [-(_106428 = apply(_105522, _106426))]], in(_106428, relation_rng(_105522)), _106426 = apply(_105909, _106428)], (432 ^ _92607) ^ [_106800, _106802] : [439 ^ _92607 : [(440 ^ _92607) ^ [] : [-(in(_106802, relation_rng(_105522)))], (442 ^ _92607) ^ [] : [-(_106800 = apply(_105909, _106802))]], in(_106800, relation_dom(_105522)), _106802 = apply(_105522, _106800)]]]]]]], (476 ^ _92607) ^ [_108375, _108377, _108379] : [in(_108379, _108377), element(_108377, powerset(_108375)), empty(_108375)], (486 ^ _92607) ^ [_108671] : [empty(_108671), -(_108671 = empty_set)], (492 ^ _92607) ^ [_108873, _108875] : [in(_108875, _108873), empty(_108873)], (498 ^ _92607) ^ [_109080, _109082] : [empty(_109082), -(_109082 = _109080), empty(_109080)], (508 ^ _92607) ^ [_109343] : [relation(_109343), function(_109343), 515 ^ _92607 : [(516 ^ _92607) ^ [_109596] : [relation(_109596), function(_109596), -(_109343 = _109596), relation_dom(_109343) = relation_dom(_109596), 530 ^ _92607 : [(531 ^ _92607) ^ [] : [-(in(529 ^ [_109343, _109596], relation_dom(_109343)))], (533 ^ _92607) ^ [] : [apply(_109343, 529 ^ [_109343, _109596]) = apply(_109596, 529 ^ [_109343, _109596])]]]]]], input).
% 8.93/9.64  ncf('1',plain,[541 ^ [] = function_inverse(536 ^ [])],start(573 ^ 0)).
% 8.93/9.64  ncf('1.1',plain,[-(541 ^ [] = function_inverse(536 ^ [])), 444 : relation_dom(541 ^ []) = relation_rng(536 ^ []), 458 : in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])), 458 : 449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]), 468 : in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ [])), 468 : 450 ^ [536 ^ [], 541 ^ []] = apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]), 444 : relation(541 ^ []), 444 : function(541 ^ []), 406 : relation(536 ^ []), 406 : function(536 ^ []), 406 : one_to_one(536 ^ [])],extension(394 ^ 1,bind([[_105522, _105909], [536 ^ [], 541 ^ []]]))).
% 8.93/9.64  ncf('1.1.1',plain,[-(relation_dom(541 ^ []) = relation_rng(536 ^ [])), relation_rng(536 ^ []) = relation_dom(541 ^ [])],extension(4 ^ 6,bind([[_92858, _92860], [relation_dom(541 ^ []), relation_rng(536 ^ [])]]))).
% 8.93/9.64  ncf('1.1.1.1',plain,[-(relation_rng(536 ^ []) = relation_dom(541 ^ []))],extension(551 ^ 7)).
% 8.93/9.64  ncf('1.1.2',plain,[-(in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ []))), 205 : in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ [])), 205 : 450 ^ [536 ^ [], 541 ^ []] = apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]), 203 : relation_dom(536 ^ []) = relation_rng(541 ^ []), 190 : relation(541 ^ []), 190 : function(541 ^ [])],extension(182 ^ 8,bind([[_98473, _98745, _99275, _99378], [541 ^ [], relation_dom(536 ^ []), 450 ^ [536 ^ [], 541 ^ []], 449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.2.1',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []))), in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ [])), 449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []) = relation_dom(541 ^ [])],extension(98 ^ 15,bind([[_95746, _95748, _95750, _95752], [relation_dom(541 ^ []), relation_dom(541 ^ []), 449 ^ [536 ^ [], 541 ^ []], 449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.2.1.1',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []))), in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ [])), 449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []) = relation_dom(541 ^ [])],extension(98 ^ 16,bind([[_95746, _95748, _95750, _95752], [relation_dom(541 ^ []), relation_rng(536 ^ []), 449 ^ [536 ^ [], 541 ^ []], 449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.2.1.1.1',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ [])))],extension(454 ^ 17)).
% 8.93/9.64  ncf('1.1.2.1.1.2',plain,[-(449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []])],extension(2 ^ 17,bind([[_92751], [449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.2.1.1.3',plain,[-(relation_rng(536 ^ []) = relation_dom(541 ^ []))],extension(551 ^ 17)).
% 8.93/9.64  ncf('1.1.2.1.2',plain,[-(449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []])],extension(2 ^ 16,bind([[_92751], [449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.2.1.3',plain,[-(relation_dom(541 ^ []) = relation_dom(541 ^ [])), 541 ^ [] = 541 ^ []],extension(124 ^ 16,bind([[_96618, _96620], [541 ^ [], 541 ^ []]]))).
% 8.93/9.64  ncf('1.1.2.1.3.1',plain,[-(541 ^ [] = 541 ^ [])],extension(2 ^ 17,bind([[_92751], [541 ^ []]]))).
% 8.93/9.64  ncf('1.1.2.2',plain,[-(450 ^ [536 ^ [], 541 ^ []] = apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]))],extension(456 ^ 15)).
% 8.93/9.64  ncf('1.1.2.3',plain,[-(relation_dom(536 ^ []) = relation_rng(541 ^ []))],extension(549 ^ 11)).
% 8.93/9.64  ncf('1.1.2.4',plain,[-(relation(541 ^ []))],extension(543 ^ 9)).
% 8.93/9.64  ncf('1.1.2.5',plain,[-(function(541 ^ []))],extension(545 ^ 9)).
% 8.93/9.64  ncf('1.1.3',plain,[-(449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []])), apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]) = 449 ^ [536 ^ [], 541 ^ []]],extension(4 ^ 8,bind([[_92858, _92860], [449 ^ [536 ^ [], 541 ^ []], apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []])]]))).
% 8.93/9.64  ncf('1.1.3.1',plain,[-(apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]) = 449 ^ [536 ^ [], 541 ^ []]), 567 : apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]) = 450 ^ [536 ^ [], 541 ^ []], 567 : in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])), 567 : in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []))],extension(553 ^ 9,bind([[_111060, _111062], [449 ^ [536 ^ [], 541 ^ []], 450 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.3.1.1',plain,[-(apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]) = 450 ^ [536 ^ [], 541 ^ []]), 450 ^ [536 ^ [], 541 ^ []] = apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []])],extension(4 ^ 12,bind([[_92858, _92860], [apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]), 450 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.3.1.1.1',plain,[-(450 ^ [536 ^ [], 541 ^ []] = apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]))],extension(456 ^ 13)).
% 8.93/9.64  ncf('1.1.3.1.2',plain,[-(in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])))],lemmata('[1].x')).
% 8.93/9.64  ncf('1.1.3.1.3',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []))), in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ [])), 449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []) = relation_dom(541 ^ [])],extension(98 ^ 10,bind([[_95746, _95748, _95750, _95752], [relation_dom(541 ^ []), relation_rng(536 ^ []), 449 ^ [536 ^ [], 541 ^ []], 449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.3.1.3.1',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ [])))],extension(454 ^ 11)).
% 8.93/9.64  ncf('1.1.3.1.3.2',plain,[-(449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []])],extension(2 ^ 11,bind([[_92751], [449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.3.1.3.3',plain,[-(relation_rng(536 ^ []) = relation_dom(541 ^ []))],extension(551 ^ 11)).
% 8.93/9.64  ncf('1.1.4',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []))), in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ [])), 449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []) = relation_rng(536 ^ [])],extension(98 ^ 8,bind([[_95746, _95748, _95750, _95752], [relation_rng(536 ^ []), relation_rng(536 ^ []), 449 ^ [536 ^ [], 541 ^ []], 449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.4.1',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []))), 444 : -(541 ^ [] = function_inverse(536 ^ [])), 444 : relation_dom(541 ^ []) = relation_rng(536 ^ []), 466 : -(449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []])), 444 : relation(541 ^ []), 444 : function(541 ^ [])],extension(406 ^ 9,bind([[_105909], [541 ^ []]]))).
% 8.93/9.64  ncf('1.1.4.1.1',plain,[541 ^ [] = function_inverse(536 ^ [])],reduction('1')).
% 8.93/9.64  ncf('1.1.4.1.2',plain,[-(relation_dom(541 ^ []) = relation_rng(536 ^ []))],lemmata('[1].x')).
% 8.93/9.64  ncf('1.1.4.1.3',plain,[449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]), 205 : in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])), 205 : -(in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []))), 203 : relation_rng(536 ^ []) = relation_rng(536 ^ []), 190 : relation(536 ^ []), 190 : function(536 ^ [])],extension(182 ^ 14,bind([[_98473, _98745, _99275, _99378], [536 ^ [], relation_rng(536 ^ []), 449 ^ [536 ^ [], 541 ^ []], 450 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.4.1.3.1',plain,[-(in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])))],extension(464 ^ 21)).
% 8.93/9.64  ncf('1.1.4.1.3.2',plain,[in(449 ^ [536 ^ [], 541 ^ []], relation_rng(536 ^ []))],reduction('1.1.4')).
% 8.93/9.64  ncf('1.1.4.1.3.3',plain,[-(relation_rng(536 ^ []) = relation_rng(536 ^ []))],extension(2 ^ 17,bind([[_92751], [relation_rng(536 ^ [])]]))).
% 8.93/9.64  ncf('1.1.4.1.3.4',plain,[-(relation(536 ^ []))],extension(538 ^ 15)).
% 8.93/9.64  ncf('1.1.4.1.3.5',plain,[-(function(536 ^ []))],extension(540 ^ 15)).
% 8.93/9.64  ncf('1.1.4.1.4',plain,[-(relation(541 ^ []))],extension(543 ^ 10)).
% 8.93/9.64  ncf('1.1.4.1.5',plain,[-(function(541 ^ []))],extension(545 ^ 10)).
% 8.93/9.64  ncf('1.1.4.2',plain,[-(449 ^ [536 ^ [], 541 ^ []] = 449 ^ [536 ^ [], 541 ^ []])],extension(2 ^ 9,bind([[_92751], [449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.4.3',plain,[-(relation_rng(536 ^ []) = relation_rng(536 ^ [])), 536 ^ [] = 536 ^ []],extension(118 ^ 9,bind([[_96400, _96402], [536 ^ [], 536 ^ []]]))).
% 8.93/9.64  ncf('1.1.4.3.1',plain,[-(536 ^ [] = 536 ^ [])],extension(2 ^ 10,bind([[_92751], [536 ^ []]]))).
% 8.93/9.64  ncf('1.1.5',plain,[-(450 ^ [536 ^ [], 541 ^ []] = apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []])), apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]) = 450 ^ [536 ^ [], 541 ^ []]],extension(4 ^ 8,bind([[_92858, _92860], [450 ^ [536 ^ [], 541 ^ []], apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []])]]))).
% 8.93/9.64  ncf('1.1.5.1',plain,[-(apply(541 ^ [], 449 ^ [536 ^ [], 541 ^ []]) = 450 ^ [536 ^ [], 541 ^ []]), 561 : apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]) = 449 ^ [536 ^ [], 541 ^ []], 561 : in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])), 561 : in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []))],extension(553 ^ 9,bind([[_111060, _111062], [449 ^ [536 ^ [], 541 ^ []], 450 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.5.1.1',plain,[-(apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]) = 449 ^ [536 ^ [], 541 ^ []]), 449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []])],extension(4 ^ 12,bind([[_92858, _92860], [apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]), 449 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.5.1.1.1',plain,[-(449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]))],extension(466 ^ 13)).
% 8.93/9.64  ncf('1.1.5.1.2',plain,[-(in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])))],extension(464 ^ 10)).
% 8.93/9.64  ncf('1.1.5.1.3',plain,[-(in(449 ^ [536 ^ [], 541 ^ []], relation_dom(541 ^ []))), 205 : in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])), 205 : 449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]), 203 : relation_dom(541 ^ []) = relation_rng(536 ^ []), 190 : relation(536 ^ []), 190 : function(536 ^ [])],extension(182 ^ 10,bind([[_98473, _98745, _99275, _99378], [536 ^ [], relation_dom(541 ^ []), 449 ^ [536 ^ [], 541 ^ []], 450 ^ [536 ^ [], 541 ^ []]]]))).
% 8.93/9.64  ncf('1.1.5.1.3.1',plain,[-(in(450 ^ [536 ^ [], 541 ^ []], relation_dom(536 ^ [])))],extension(464 ^ 17)).
% 8.93/9.64  ncf('1.1.5.1.3.2',plain,[-(449 ^ [536 ^ [], 541 ^ []] = apply(536 ^ [], 450 ^ [536 ^ [], 541 ^ []]))],extension(466 ^ 17)).
% 8.93/9.64  ncf('1.1.5.1.3.3',plain,[-(relation_dom(541 ^ []) = relation_rng(536 ^ []))],lemmata('[1].x')).
% 8.93/9.64  ncf('1.1.5.1.3.4',plain,[-(relation(536 ^ []))],extension(538 ^ 11)).
% 8.93/9.64  ncf('1.1.5.1.3.5',plain,[-(function(536 ^ []))],extension(540 ^ 11)).
% 8.93/9.64  ncf('1.1.6',plain,[-(relation(541 ^ []))],extension(543 ^ 4)).
% 8.93/9.64  ncf('1.1.7',plain,[-(function(541 ^ []))],extension(545 ^ 4)).
% 8.93/9.64  ncf('1.1.8',plain,[-(relation(536 ^ []))],extension(538 ^ 2)).
% 8.93/9.64  ncf('1.1.9',plain,[-(function(536 ^ []))],extension(540 ^ 2)).
% 8.93/9.64  ncf('1.1.10',plain,[-(one_to_one(536 ^ []))],extension(547 ^ 2)).
% 8.93/9.64  %-----------------------------------------------------
% 8.93/9.64  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------