%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n006.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 43.20s 42.68s
% Output   : Proof 43.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n006.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 12:30:51 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 43.20/42.68  
% 43.20/42.68  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 43.20/42.68  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.20/42.68  %-----------------------------------------------------
% 43.20/42.68  ncf(matrix, plain, [(515 ^ _98305) ^ [] : [-(relation(513 ^ []))], (521 ^ _98305) ^ [] : [-(relation_rng(508 ^ []) = relation_dom(513 ^ []))], (510 ^ _98305) ^ [] : [-(relation(508 ^ []))], (523 ^ _98305) ^ [] : [-(relation_composition(508 ^ [], 513 ^ []) = identity_relation(relation_dom(508 ^ [])))], (517 ^ _98305) ^ [] : [-(function(513 ^ []))], (519 ^ _98305) ^ [] : [-(one_to_one(508 ^ []))], (525 ^ _98305) ^ [] : [513 ^ [] = function_inverse(508 ^ [])], (512 ^ _98305) ^ [] : [-(function(508 ^ []))], !, (188 ^ _82056) ^ [_88124] : [195 ^ _82056 : [(198 ^ _82056) ^ [] : [-(function(function_inverse(_88124)))], (196 ^ _82056) ^ [] : [-(relation(function_inverse(_88124)))]], relation(_88124), function(_88124)], (401 ^ _82056) ^ [] : [-(relation(399 ^ []))], (386 ^ _82056) ^ [_94240] : [-(element(384 ^ [_94240], powerset(_94240)))], (227 ^ _82056) ^ [] : [-(empty(empty_set))], (499 ^ _82056) ^ [_97809, _97811] : [empty(_97811), -(_97811 = _97809), empty(_97809)], (4 ^ _82056) ^ [_82287, _82289] : [_82289 = _82287, -(_82287 = _82289)], (58 ^ _82056) ^ [_84015, _84017, _84019, _84021] : [-(in(_84019, _84015)), in(_84021, _84017), _84021 = _84019, _84017 = _84015], (378 ^ _82056) ^ [] : [-(function(372 ^ []))], (213 ^ _82056) ^ [_88874] : [-(element(211 ^ [_88874], _88874))], (72 ^ _82056) ^ [_84431, _84433] : [-(empty(_84431)), _84433 = _84431, empty(_84433)], (210 ^ _82056) ^ [_88756] : [-(relation(identity_relation(_88756)))], (20 ^ _82056) ^ [_82804, _82806] : [-(relation_empty_yielding(_82804)), _82806 = _82804, relation_empty_yielding(_82806)], (265 ^ _82056) ^ [_90450] : [empty(relation_dom(_90450)), -(empty(_90450)), relation(_90450)], (354 ^ _82056) ^ [] : [-(function(350 ^ []))], (361 ^ _82056) ^ [_93409] : [-(empty(_93409)), 365 ^ _82056 : [(368 ^ _82056) ^ [] : [empty(364 ^ [_93409])], (366 ^ _82056) ^ [] : [-(element(364 ^ [_93409], powerset(_93409)))]]], (275 ^ _82056) ^ [_90727] : [empty(relation_rng(_90727)), -(empty(_90727)), relation(_90727)], (146 ^ _82056) ^ [_86822, _86824] : [_86824 = _86822, -(function_inverse(_86824) = function_inverse(_86822))], (44 ^ _82056) ^ [_83571, _83573, _83575, _83577] : [-(element(_83575, _83571)), element(_83577, _83573), _83577 = _83575, _83573 = _83571], (487 ^ _82056) ^ [_97420] : [empty(_97420), -(_97420 = empty_set)], (255 ^ _82056) ^ [] : [-(empty(empty_set))], (92 ^ _82056) ^ [_85021, _85023] : [-(function(_85021)), _85023 = _85021, function(_85023)], (376 ^ _82056) ^ [] : [-(empty(372 ^ []))], (394 ^ _82056) ^ [] : [-(relation(392 ^ []))], (301 ^ _82056) ^ [_91548, _91550] : [308 ^ _82056 : [(311 ^ _82056) ^ [] : [-(relation(relation_composition(_91550, _91548)))], (309 ^ _82056) ^ [] : [-(empty(relation_composition(_91550, _91548)))]], empty(_91550), relation(_91548)], (231 ^ _82056) ^ [] : [-(relation_empty_yielding(empty_set))], (471 ^ _82056) ^ [_96955] : [relation(_96955), function(_96955), one_to_one(_96955), 482 ^ _82056 : [(485 ^ _82056) ^ [] : [-(relation_composition(function_inverse(_96955), _96955) = identity_relation(relation_rng(_96955)))], (483 ^ _82056) ^ [] : [-(relation_composition(_96955, function_inverse(_96955)) = identity_relation(relation_dom(_96955)))]]], (124 ^ _82056) ^ [_86075, _86077, _86079, _86081] : [-(relation_composition(_86081, _86077) = relation_composition(_86079, _86075)), _86081 = _86079, _86077 = _86075], (82 ^ _82056) ^ [_84726, _84728] : [-(relation(_84726)), _84728 = _84726, relation(_84728)], (396 ^ _82056) ^ [] : [-(function(392 ^ []))], (200 ^ _82056) ^ [_88486, _88488] : [-(relation(relation_composition(_88488, _88486))), relation(_88488), relation(_88486)], (445 ^ _82056) ^ [_96178] : [relation(_96178), function(_96178), one_to_one(_96178), 456 ^ _82056 : [(459 ^ _82056) ^ [] : [-(relation_dom(_96178) = relation_rng(function_inverse(_96178)))], (457 ^ _82056) ^ [] : [-(relation_rng(_96178) = relation_dom(function_inverse(_96178)))]]], (118 ^ _82056) ^ [_85829, _85831] : [_85831 = _85829, -(relation_rng(_85831) = relation_rng(_85829))], (405 ^ _82056) ^ [_94837, _94839] : [-(subset(_94839, _94839))], (10 ^ _82056) ^ [_82491, _82493, _82495] : [-(_82495 = _82491), _82495 = _82493, _82493 = _82491], (407 ^ _82056) ^ [_94946, _94948] : [in(_94948, _94946), -(element(_94948, _94946))], (398 ^ _82056) ^ [] : [-(one_to_one(392 ^ []))], (233 ^ _82056) ^ [_89527, _89529] : [248 ^ _82056 : [(251 ^ _82056) ^ [] : [-(function(relation_composition(_89529, _89527)))], (249 ^ _82056) ^ [] : [-(relation(relation_composition(_89529, _89527)))]], relation(_89529), function(_89529), relation(_89527), function(_89527)], (170 ^ _82056) ^ [_87631] : [181 ^ _82056 : [(186 ^ _82056) ^ [] : [-(one_to_one(_87631))], (184 ^ _82056) ^ [] : [-(function(_87631))], (182 ^ _82056) ^ [] : [-(relation(_87631))]], relation(_87631), empty(_87631), function(_87631)], (403 ^ _82056) ^ [] : [-(relation_empty_yielding(399 ^ []))], (383 ^ _82056) ^ [] : [-(relation(379 ^ []))], (435 ^ _82056) ^ [_95879, _95881, _95883] : [-(element(_95883, _95879)), in(_95883, _95881), element(_95881, powerset(_95879))], (112 ^ _82056) ^ [_85611, _85613] : [_85613 = _85611, -(powerset(_85613) = powerset(_85611))], (263 ^ _82056) ^ [] : [-(relation(empty_set))], (158 ^ _82056) ^ [_87259] : [empty(_87259), -(function(_87259))], (285 ^ _82056) ^ [_91004] : [empty(_91004), 288 ^ _82056 : [(291 ^ _82056) ^ [] : [-(relation(relation_dom(_91004)))], (289 ^ _82056) ^ [] : [-(empty(relation_dom(_91004)))]]], (259 ^ _82056) ^ [_90246] : [-(function(identity_relation(_90246)))], (152 ^ _82056) ^ [_87062, _87064] : [in(_87064, _87062), in(_87062, _87064)], (374 ^ _82056) ^ [] : [-(relation(372 ^ []))], (423 ^ _82056) ^ [_95483, _95485] : [element(_95485, powerset(_95483)), -(subset(_95485, _95483))], (140 ^ _82056) ^ [_86624, _86626] : [_86626 = _86624, -(relation_dom(_86626) = relation_dom(_86624))], (352 ^ _82056) ^ [] : [-(relation(350 ^ []))], (261 ^ _82056) ^ [] : [-(empty(empty_set))], (229 ^ _82056) ^ [] : [-(relation(empty_set))], (215 ^ _82056) ^ [_88986, _88988] : [222 ^ _82056 : [(225 ^ _82056) ^ [] : [-(relation(relation_composition(_88986, _88988)))], (223 ^ _82056) ^ [] : [-(empty(relation_composition(_88986, _88988)))]], empty(_88988), relation(_88986)], (359 ^ _82056) ^ [] : [-(relation(355 ^ []))], (388 ^ _82056) ^ [_94291] : [-(empty(384 ^ [_94291]))], (134 ^ _82056) ^ [_86406, _86408] : [_86408 = _86406, -(identity_relation(_86408) = identity_relation(_86406))], (461 ^ _82056) ^ [_96659, _96661, _96663] : [in(_96663, _96661), element(_96661, powerset(_96659)), empty(_96659)], (381 ^ _82056) ^ [] : [empty(379 ^ [])], (257 ^ _82056) ^ [_90201] : [-(relation(identity_relation(_90201)))], (357 ^ _82056) ^ [] : [-(empty(355 ^ []))], (30 ^ _82056) ^ [_83127, _83129, _83131, _83133] : [-(subset(_83131, _83127)), subset(_83133, _83129), _83133 = _83131, _83129 = _83127], (391 ^ _82056) ^ [] : [empty(389 ^ [])], (493 ^ _82056) ^ [_97622, _97624] : [in(_97624, _97622), empty(_97622)], (293 ^ _82056) ^ [_91269] : [empty(_91269), 296 ^ _82056 : [(299 ^ _82056) ^ [] : [-(relation(relation_rng(_91269)))], (297 ^ _82056) ^ [] : [-(empty(relation_rng(_91269)))]]], (102 ^ _82056) ^ [_85296, _85298] : [-(one_to_one(_85296)), _85298 = _85296, one_to_one(_85298)], (253 ^ _82056) ^ [_90049] : [empty(powerset(_90049))], (429 ^ _82056) ^ [_95649, _95651] : [subset(_95651, _95649), -(element(_95651, powerset(_95649)))], (413 ^ _82056) ^ [_95156, _95158] : [element(_95158, _95156), -(empty(_95156)), -(in(_95158, _95156))], (313 ^ _82056) ^ [_91926, _91928] : [relation(_91926), function(_91926), 320 ^ _82056 : [(321 ^ _82056) ^ [_92199] : [relation(_92199), function(_92199), 328 ^ _82056 : [(329 ^ _82056) ^ [_92469] : [relation(_92469), function(_92469), -(_92469 = _91926), relation_rng(_91926) = _91928, relation_composition(_91926, _92199) = identity_relation(relation_dom(_92469)), relation_composition(_92199, _92469) = identity_relation(_91928)]]]]], (2 ^ _82056) ^ [_82180] : [-(_82180 = _82180)], (164 ^ _82056) ^ [_87445] : [empty(_87445), -(relation(_87445))], (371 ^ _82056) ^ [] : [-(empty(369 ^ []))]], input).
% 43.20/42.68  ncf('1',plain,[-(relation(513 ^ []))],start(515 ^ 0)).
% 43.20/42.68  ncf('1.1',plain,[relation(513 ^ []), 329 : function(513 ^ []), 329 : -(513 ^ [] = function_inverse(508 ^ [])), 329 : relation_rng(function_inverse(508 ^ [])) = relation_dom(508 ^ []), 329 : relation_composition(function_inverse(508 ^ []), 508 ^ []) = identity_relation(relation_dom(513 ^ [])), 329 : relation_composition(508 ^ [], 513 ^ []) = identity_relation(relation_dom(508 ^ [])), 329 : relation(508 ^ []), 329 : function(508 ^ []), 321 : relation(function_inverse(508 ^ [])), 321 : function(function_inverse(508 ^ []))],extension(313 ^ 1,bind([[_91926, _91928, _92199, _92469], [function_inverse(508 ^ []), relation_dom(508 ^ []), 508 ^ [], 513 ^ []]]))).
% 43.20/42.68  ncf('1.1.1',plain,[-(function(513 ^ []))],extension(517 ^ 6)).
% 43.20/42.68  ncf('1.1.2',plain,[513 ^ [] = function_inverse(508 ^ [])],extension(525 ^ 6)).
% 43.20/42.68  ncf('1.1.3',plain,[-(relation_rng(function_inverse(508 ^ [])) = relation_dom(508 ^ [])), relation_dom(508 ^ []) = relation_rng(function_inverse(508 ^ []))],extension(4 ^ 6,bind([[_82287, _82289], [relation_rng(function_inverse(508 ^ [])), relation_dom(508 ^ [])]]))).
% 43.20/42.68  ncf('1.1.3.1',plain,[-(relation_dom(508 ^ []) = relation_rng(function_inverse(508 ^ []))), relation(508 ^ []), function(508 ^ []), one_to_one(508 ^ [])],extension(445 ^ 7,bind([[_96178], [508 ^ []]]))).
% 43.20/42.68  ncf('1.1.3.1.1',plain,[-(relation(508 ^ []))],extension(510 ^ 8)).
% 43.20/42.68  ncf('1.1.3.1.2',plain,[-(function(508 ^ []))],extension(512 ^ 8)).
% 43.20/42.68  ncf('1.1.3.1.3',plain,[-(one_to_one(508 ^ []))],extension(519 ^ 8)).
% 43.20/42.68  ncf('1.1.4',plain,[-(relation_composition(function_inverse(508 ^ []), 508 ^ []) = identity_relation(relation_dom(513 ^ []))), relation_composition(function_inverse(508 ^ []), 508 ^ []) = identity_relation(relation_rng(508 ^ [])), identity_relation(relation_rng(508 ^ [])) = identity_relation(relation_dom(513 ^ []))],extension(10 ^ 6,bind([[_82491, _82493, _82495], [identity_relation(relation_dom(513 ^ [])), identity_relation(relation_rng(508 ^ [])), relation_composition(function_inverse(508 ^ []), 508 ^ [])]]))).
% 43.20/42.68  ncf('1.1.4.1',plain,[-(relation_composition(function_inverse(508 ^ []), 508 ^ []) = identity_relation(relation_rng(508 ^ []))), relation(508 ^ []), function(508 ^ []), one_to_one(508 ^ [])],extension(471 ^ 7,bind([[_96955], [508 ^ []]]))).
% 43.20/42.68  ncf('1.1.4.1.1',plain,[-(relation(508 ^ []))],extension(510 ^ 8)).
% 43.20/42.68  ncf('1.1.4.1.2',plain,[-(function(508 ^ []))],extension(512 ^ 8)).
% 43.20/42.68  ncf('1.1.4.1.3',plain,[-(one_to_one(508 ^ []))],extension(519 ^ 8)).
% 43.20/42.68  ncf('1.1.4.2',plain,[-(identity_relation(relation_rng(508 ^ [])) = identity_relation(relation_dom(513 ^ []))), relation_rng(508 ^ []) = relation_dom(513 ^ [])],extension(134 ^ 7,bind([[_86406, _86408], [relation_dom(513 ^ []), relation_rng(508 ^ [])]]))).
% 43.20/42.68  ncf('1.1.4.2.1',plain,[-(relation_rng(508 ^ []) = relation_dom(513 ^ []))],extension(521 ^ 8)).
% 43.20/42.68  ncf('1.1.5',plain,[-(relation_composition(508 ^ [], 513 ^ []) = identity_relation(relation_dom(508 ^ [])))],extension(523 ^ 6)).
% 43.20/42.68  ncf('1.1.6',plain,[-(relation(508 ^ []))],extension(510 ^ 4)).
% 43.20/42.68  ncf('1.1.7',plain,[-(function(508 ^ []))],extension(512 ^ 4)).
% 43.20/42.68  ncf('1.1.8',plain,[-(relation(function_inverse(508 ^ []))), relation(508 ^ []), function(508 ^ [])],extension(188 ^ 2,bind([[_88124], [508 ^ []]]))).
% 43.20/42.68  ncf('1.1.8.1',plain,[-(relation(508 ^ []))],extension(510 ^ 3)).
% 43.20/42.68  ncf('1.1.8.2',plain,[-(function(508 ^ []))],extension(512 ^ 3)).
% 43.20/42.68  ncf('1.1.9',plain,[-(function(function_inverse(508 ^ []))), relation(508 ^ []), function(508 ^ [])],extension(188 ^ 2,bind([[_88124], [508 ^ []]]))).
% 43.20/42.68  ncf('1.1.9.1',plain,[-(relation(508 ^ []))],extension(510 ^ 3)).
% 43.20/42.68  ncf('1.1.9.2',plain,[-(function(508 ^ []))],extension(512 ^ 3)).
% 43.20/42.68  %-----------------------------------------------------
% 43.20/42.68  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------