%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n032.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 64.00s 62.99s
% Output   : Proof 64.00s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09  % Command  : nanocop.sh %s %d
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit : 300
% 0.08/0.27  % WCLimit  : 300
% 0.08/0.27  % DateTime : Thu May 18 12:28:19 EDT 2023
% 0.08/0.27  % CPUTime  : 
% 64.00/62.99  
% 64.00/62.99  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 64.00/62.99  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.00/62.99  %-----------------------------------------------------
% 64.00/62.99  ncf(matrix, plain, [(518 ^ _96591) ^ [] : [-(function(514 ^ []))], (520 ^ _96591) ^ [] : [-(one_to_one(514 ^ []))], (522 ^ _96591) ^ [] : [function_inverse(function_inverse(514 ^ [])) = 514 ^ []], (516 ^ _96591) ^ [] : [-(relation(514 ^ []))], !, (350 ^ _80374) ^ [_91410] : [-(empty(346 ^ [_91410]))], (391 ^ _80374) ^ [_92768, _92770] : [subset(_92770, _92768), -(element(_92770, powerset(_92768)))], (261 ^ _80374) ^ [] : [-(empty(empty_set))], (338 ^ _80374) ^ [] : [-(empty(334 ^ []))], (259 ^ _80374) ^ [_88564] : [-(function(identity_relation(_88564)))], (2 ^ _80374) ^ [_80498] : [-(_80498 = _80498)], (375 ^ _80374) ^ [_92275, _92277] : [element(_92277, _92275), -(empty(_92275)), -(in(_92277, _92275))], (188 ^ _80374) ^ [_86442] : [195 ^ _80374 : [(198 ^ _80374) ^ [] : [-(function(function_inverse(_86442)))], (196 ^ _80374) ^ [] : [-(relation(function_inverse(_86442)))]], relation(_86442), function(_86442)], (233 ^ _80374) ^ [_87845, _87847] : [248 ^ _80374 : [(251 ^ _80374) ^ [] : [-(function(relation_composition(_87847, _87845)))], (249 ^ _80374) ^ [] : [-(relation(relation_composition(_87847, _87845)))]], relation(_87847), function(_87847), relation(_87845), function(_87845)], (369 ^ _80374) ^ [_92065, _92067] : [in(_92067, _92065), -(element(_92067, _92065))], (263 ^ _80374) ^ [] : [-(relation(empty_set))], (499 ^ _80374) ^ [_95930, _95932] : [in(_95932, _95930), empty(_95930)], (314 ^ _80374) ^ [] : [-(relation(312 ^ []))], (363 ^ _80374) ^ [] : [-(relation(361 ^ []))], (158 ^ _80374) ^ [_85577] : [empty(_85577), -(function(_85577))], (340 ^ _80374) ^ [] : [-(function(334 ^ []))], (319 ^ _80374) ^ [] : [-(empty(317 ^ []))], (285 ^ _80374) ^ [_89322] : [empty(_89322), 288 ^ _80374 : [(291 ^ _80374) ^ [] : [-(relation(relation_dom(_89322)))], (289 ^ _80374) ^ [] : [-(empty(relation_dom(_89322)))]]], (385 ^ _80374) ^ [_92602, _92604] : [element(_92604, powerset(_92602)), -(subset(_92604, _92602))], (323 ^ _80374) ^ [_90528] : [-(empty(_90528)), 327 ^ _80374 : [(330 ^ _80374) ^ [] : [empty(326 ^ [_90528])], (328 ^ _80374) ^ [] : [-(element(326 ^ [_90528], powerset(_90528)))]]], (170 ^ _80374) ^ [_85949] : [181 ^ _80374 : [(186 ^ _80374) ^ [] : [-(one_to_one(_85949))], (184 ^ _80374) ^ [] : [-(function(_85949))], (182 ^ _80374) ^ [] : [-(relation(_85949))]], relation(_85949), empty(_85949), function(_85949)], (423 ^ _80374) ^ [_93778, _93780, _93782] : [in(_93782, _93780), element(_93780, powerset(_93778)), empty(_93778)], (231 ^ _80374) ^ [] : [-(relation_empty_yielding(empty_set))], (227 ^ _80374) ^ [] : [-(empty(empty_set))], (463 ^ _80374) ^ [_94897] : [relation(_94897), function(_94897), 470 ^ _80374 : [(471 ^ _80374) ^ [_95145] : [relation(_95145), function(_95145), -(_95145 = function_inverse(_94897)), one_to_one(_94897), relation_rng(_94897) = relation_dom(_95145), relation_composition(_94897, _95145) = identity_relation(relation_dom(_94897))]]], (10 ^ _80374) ^ [_80809, _80811, _80813] : [-(_80813 = _80809), _80813 = _80811, _80811 = _80809], (213 ^ _80374) ^ [_87192] : [-(element(211 ^ [_87192], _87192))], (356 ^ _80374) ^ [] : [-(relation(354 ^ []))], (20 ^ _80374) ^ [_81122, _81124] : [-(relation_empty_yielding(_81122)), _81124 = _81122, relation_empty_yielding(_81124)], (360 ^ _80374) ^ [] : [-(one_to_one(354 ^ []))], (333 ^ _80374) ^ [] : [-(empty(331 ^ []))], (493 ^ _80374) ^ [_95728] : [empty(_95728), -(_95728 = empty_set)], (82 ^ _80374) ^ [_83044, _83046] : [-(relation(_83044)), _83046 = _83044, relation(_83046)], (407 ^ _80374) ^ [_93297] : [relation(_93297), function(_93297), one_to_one(_93297), 418 ^ _80374 : [(421 ^ _80374) ^ [] : [-(relation_dom(_93297) = relation_rng(function_inverse(_93297)))], (419 ^ _80374) ^ [] : [-(relation_rng(_93297) = relation_dom(function_inverse(_93297)))]]], (140 ^ _80374) ^ [_84942, _84944] : [_84944 = _84942, -(relation_dom(_84944) = relation_dom(_84942))], (316 ^ _80374) ^ [] : [-(function(312 ^ []))], (146 ^ _80374) ^ [_85140, _85142] : [_85142 = _85140, -(function_inverse(_85142) = function_inverse(_85140))], (30 ^ _80374) ^ [_81445, _81447, _81449, _81451] : [-(subset(_81449, _81445)), subset(_81451, _81447), _81451 = _81449, _81447 = _81445], (44 ^ _80374) ^ [_81889, _81891, _81893, _81895] : [-(element(_81893, _81889)), element(_81895, _81891), _81895 = _81893, _81891 = _81889], (367 ^ _80374) ^ [_91956, _91958] : [-(subset(_91958, _91958))], (301 ^ _80374) ^ [_89866, _89868] : [308 ^ _80374 : [(311 ^ _80374) ^ [] : [-(relation(relation_composition(_89868, _89866)))], (309 ^ _80374) ^ [] : [-(empty(relation_composition(_89868, _89866)))]], empty(_89868), relation(_89866)], (348 ^ _80374) ^ [_91359] : [-(element(346 ^ [_91359], powerset(_91359)))], (92 ^ _80374) ^ [_83339, _83341] : [-(function(_83339)), _83341 = _83339, function(_83341)], (321 ^ _80374) ^ [] : [-(relation(317 ^ []))], (358 ^ _80374) ^ [] : [-(function(354 ^ []))], (397 ^ _80374) ^ [_92998, _93000, _93002] : [-(element(_93002, _92998)), in(_93002, _93000), element(_93000, powerset(_92998))], (275 ^ _80374) ^ [_89045] : [empty(relation_rng(_89045)), -(empty(_89045)), relation(_89045)], (433 ^ _80374) ^ [_94074] : [relation(_94074), function(_94074), one_to_one(_94074), 444 ^ _80374 : [(447 ^ _80374) ^ [] : [-(relation_composition(function_inverse(_94074), _94074) = identity_relation(relation_rng(_94074)))], (445 ^ _80374) ^ [] : [-(relation_composition(_94074, function_inverse(_94074)) = identity_relation(relation_dom(_94074)))]]], (353 ^ _80374) ^ [] : [empty(351 ^ [])], (72 ^ _80374) ^ [_82749, _82751] : [-(empty(_82749)), _82751 = _82749, empty(_82751)], (164 ^ _80374) ^ [_85763] : [empty(_85763), -(relation(_85763))], (102 ^ _80374) ^ [_83614, _83616] : [-(one_to_one(_83614)), _83616 = _83614, one_to_one(_83616)], (257 ^ _80374) ^ [_88519] : [-(relation(identity_relation(_88519)))], (265 ^ _80374) ^ [_88768] : [empty(relation_dom(_88768)), -(empty(_88768)), relation(_88768)], (58 ^ _80374) ^ [_82333, _82335, _82337, _82339] : [-(in(_82337, _82333)), in(_82339, _82335), _82339 = _82337, _82335 = _82333], (124 ^ _80374) ^ [_84393, _84395, _84397, _84399] : [-(relation_composition(_84399, _84395) = relation_composition(_84397, _84393)), _84399 = _84397, _84395 = _84393], (215 ^ _80374) ^ [_87304, _87306] : [222 ^ _80374 : [(225 ^ _80374) ^ [] : [-(relation(relation_composition(_87304, _87306)))], (223 ^ _80374) ^ [] : [-(empty(relation_composition(_87304, _87306)))]], empty(_87306), relation(_87304)], (118 ^ _80374) ^ [_84147, _84149] : [_84149 = _84147, -(relation_rng(_84149) = relation_rng(_84147))], (505 ^ _80374) ^ [_96117, _96119] : [empty(_96119), -(_96119 = _96117), empty(_96117)], (152 ^ _80374) ^ [_85380, _85382] : [in(_85382, _85380), in(_85380, _85382)], (229 ^ _80374) ^ [] : [-(relation(empty_set))], (210 ^ _80374) ^ [_87074] : [-(relation(identity_relation(_87074)))], (345 ^ _80374) ^ [] : [-(relation(341 ^ []))], (200 ^ _80374) ^ [_86804, _86806] : [-(relation(relation_composition(_86806, _86804))), relation(_86806), relation(_86804)], (336 ^ _80374) ^ [] : [-(relation(334 ^ []))], (112 ^ _80374) ^ [_83929, _83931] : [_83931 = _83929, -(powerset(_83931) = powerset(_83929))], (255 ^ _80374) ^ [] : [-(empty(empty_set))], (4 ^ _80374) ^ [_80605, _80607] : [_80607 = _80605, -(_80605 = _80607)], (449 ^ _80374) ^ [_94539] : [relation(_94539), function(_94539), one_to_one(_94539), -(one_to_one(function_inverse(_94539)))], (293 ^ _80374) ^ [_89587] : [empty(_89587), 296 ^ _80374 : [(299 ^ _80374) ^ [] : [-(relation(relation_rng(_89587)))], (297 ^ _80374) ^ [] : [-(empty(relation_rng(_89587)))]]], (134 ^ _80374) ^ [_84724, _84726] : [_84726 = _84724, -(identity_relation(_84726) = identity_relation(_84724))], (343 ^ _80374) ^ [] : [empty(341 ^ [])], (253 ^ _80374) ^ [_88367] : [empty(powerset(_88367))], (365 ^ _80374) ^ [] : [-(relation_empty_yielding(361 ^ []))]], input).
% 64.00/62.99  ncf('1',plain,[-(function(514 ^ []))],start(518 ^ 0)).
% 64.00/62.99  ncf('1.1',plain,[function(514 ^ []), relation(514 ^ []), one_to_one(514 ^ []), 447 : -(relation_composition(function_inverse(514 ^ []), 514 ^ []) = identity_relation(relation_rng(514 ^ [])))],extension(433 ^ 1,bind([[_94074], [514 ^ []]]))).
% 64.00/62.99  ncf('1.1.1',plain,[-(relation(514 ^ []))],extension(516 ^ 2)).
% 64.00/62.99  ncf('1.1.2',plain,[-(one_to_one(514 ^ []))],extension(520 ^ 2)).
% 64.00/62.99  ncf('1.1.3',plain,[relation_composition(function_inverse(514 ^ []), 514 ^ []) = identity_relation(relation_rng(514 ^ [])), -(relation_composition(function_inverse(514 ^ []), 514 ^ []) = identity_relation(relation_dom(function_inverse(514 ^ [])))), identity_relation(relation_rng(514 ^ [])) = identity_relation(relation_dom(function_inverse(514 ^ [])))],extension(10 ^ 4,bind([[_80809, _80811, _80813], [identity_relation(relation_dom(function_inverse(514 ^ []))), identity_relation(relation_rng(514 ^ [])), relation_composition(function_inverse(514 ^ []), 514 ^ [])]]))).
% 64.00/62.99  ncf('1.1.3.1',plain,[relation_composition(function_inverse(514 ^ []), 514 ^ []) = identity_relation(relation_dom(function_inverse(514 ^ []))), 471 : relation(514 ^ []), 471 : function(514 ^ []), 471 : -(514 ^ [] = function_inverse(function_inverse(514 ^ []))), 471 : one_to_one(function_inverse(514 ^ [])), 471 : relation_rng(function_inverse(514 ^ [])) = relation_dom(514 ^ []), 471 : relation(function_inverse(514 ^ [])), 471 : function(function_inverse(514 ^ []))],extension(463 ^ 5,bind([[_94897, _95145], [function_inverse(514 ^ []), 514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.1',plain,[-(relation(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  ncf('1.1.3.1.2',plain,[-(function(514 ^ []))],reduction('1')).
% 64.00/62.99  ncf('1.1.3.1.3',plain,[514 ^ [] = function_inverse(function_inverse(514 ^ [])), -(514 ^ [] = function_inverse(function_inverse(514 ^ []))), function_inverse(function_inverse(514 ^ [])) = function_inverse(function_inverse(514 ^ []))],extension(10 ^ 8,bind([[_80809, _80811, _80813], [function_inverse(function_inverse(514 ^ [])), function_inverse(function_inverse(514 ^ [])), 514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.3.1',plain,[514 ^ [] = function_inverse(function_inverse(514 ^ [])), -(function_inverse(function_inverse(514 ^ [])) = 514 ^ [])],extension(4 ^ 9,bind([[_80605, _80607], [function_inverse(function_inverse(514 ^ [])), 514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.3.1.1',plain,[function_inverse(function_inverse(514 ^ [])) = 514 ^ []],extension(522 ^ 10)).
% 64.00/62.99  ncf('1.1.3.1.3.2',plain,[-(function_inverse(function_inverse(514 ^ [])) = function_inverse(function_inverse(514 ^ [])))],extension(2 ^ 9,bind([[_80498], [function_inverse(function_inverse(514 ^ []))]]))).
% 64.00/62.99  ncf('1.1.3.1.4',plain,[-(one_to_one(function_inverse(514 ^ []))), relation(514 ^ []), function(514 ^ []), one_to_one(514 ^ [])],extension(449 ^ 8,bind([[_94539], [514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.4.1',plain,[-(relation(514 ^ []))],lemmata('[3, 1, 1].x')).
% 64.00/62.99  ncf('1.1.3.1.4.2',plain,[-(function(514 ^ []))],lemmata('[3, 1, 1].x')).
% 64.00/62.99  ncf('1.1.3.1.4.3',plain,[-(one_to_one(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  ncf('1.1.3.1.5',plain,[-(relation_rng(function_inverse(514 ^ [])) = relation_dom(514 ^ [])), relation_dom(514 ^ []) = relation_rng(function_inverse(514 ^ []))],extension(4 ^ 8,bind([[_80605, _80607], [relation_rng(function_inverse(514 ^ [])), relation_dom(514 ^ [])]]))).
% 64.00/62.99  ncf('1.1.3.1.5.1',plain,[-(relation_dom(514 ^ []) = relation_rng(function_inverse(514 ^ []))), relation(514 ^ []), function(514 ^ []), one_to_one(514 ^ [])],extension(407 ^ 9,bind([[_93297], [514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.5.1.1',plain,[-(relation(514 ^ []))],lemmata('[3, 1, 1].x')).
% 64.00/62.99  ncf('1.1.3.1.5.1.2',plain,[-(function(514 ^ []))],lemmata('[3, 1, 1].x')).
% 64.00/62.99  ncf('1.1.3.1.5.1.3',plain,[-(one_to_one(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  ncf('1.1.3.1.6',plain,[-(relation(function_inverse(514 ^ []))), relation(514 ^ []), function(514 ^ [])],extension(188 ^ 6,bind([[_86442], [514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.6.1',plain,[-(relation(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  ncf('1.1.3.1.6.2',plain,[-(function(514 ^ []))],reduction('1')).
% 64.00/62.99  ncf('1.1.3.1.7',plain,[-(function(function_inverse(514 ^ []))), relation(514 ^ []), function(514 ^ [])],extension(188 ^ 6,bind([[_86442], [514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.1.7.1',plain,[-(relation(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  ncf('1.1.3.1.7.2',plain,[-(function(514 ^ []))],reduction('1')).
% 64.00/62.99  ncf('1.1.3.2',plain,[-(identity_relation(relation_rng(514 ^ [])) = identity_relation(relation_dom(function_inverse(514 ^ [])))), relation_rng(514 ^ []) = relation_dom(function_inverse(514 ^ []))],extension(134 ^ 5,bind([[_84724, _84726], [relation_dom(function_inverse(514 ^ [])), relation_rng(514 ^ [])]]))).
% 64.00/62.99  ncf('1.1.3.2.1',plain,[-(relation_rng(514 ^ []) = relation_dom(function_inverse(514 ^ []))), relation(514 ^ []), function(514 ^ []), one_to_one(514 ^ [])],extension(407 ^ 6,bind([[_93297], [514 ^ []]]))).
% 64.00/62.99  ncf('1.1.3.2.1.1',plain,[-(relation(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  ncf('1.1.3.2.1.2',plain,[-(function(514 ^ []))],reduction('1')).
% 64.00/62.99  ncf('1.1.3.2.1.3',plain,[-(one_to_one(514 ^ []))],lemmata('[1].x')).
% 64.00/62.99  %-----------------------------------------------------
% 64.00/62.99  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------