%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.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 12:02:05 EDT 2023

% Result   : Theorem 101.52s 98.75s
% Output   : Proof 101.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n008.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 13:10:09 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 101.52/98.75  
% 101.52/98.75  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 101.52/98.75  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 101.52/98.75  %-----------------------------------------------------
% 101.52/98.75  ncf(matrix, plain, [(472 ^ _71562) ^ [] : [-(relation(470 ^ []))], (474 ^ _71562) ^ [] : [-(function(470 ^ []))], (476 ^ _71562) ^ [] : [-(one_to_one(470 ^ []))], (478 ^ _71562) ^ [] : [relation_dom(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ []), relation_rng(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ [])], (112 ^ _71562) ^ [_75137, _75139] : [_75139 = _75137, -(powerset(_75139) = powerset(_75137))], (118 ^ _71562) ^ [_75355, _75357] : [_75357 = _75355, -(relation_rng(_75357) = relation_rng(_75355))], (124 ^ _71562) ^ [_75601, _75603, _75605, _75607] : [-(relation_composition(_75607, _75603) = relation_composition(_75605, _75601)), _75607 = _75605, _75603 = _75601], (134 ^ _71562) ^ [_75932, _75934] : [_75934 = _75932, -(function_inverse(_75934) = function_inverse(_75932))], (140 ^ _71562) ^ [_76130, _76132] : [_76132 = _76130, -(relation_dom(_76132) = relation_dom(_76130))], (2 ^ _71562) ^ [_71706] : [-(_71706 = _71706)], (4 ^ _71562) ^ [_71813, _71815] : [_71815 = _71813, -(_71813 = _71815)], (10 ^ _71562) ^ [_72017, _72019, _72021] : [-(_72021 = _72017), _72021 = _72019, _72019 = _72017], (20 ^ _71562) ^ [_72330, _72332] : [-(relation_empty_yielding(_72330)), _72332 = _72330, relation_empty_yielding(_72332)], (30 ^ _71562) ^ [_72653, _72655, _72657, _72659] : [-(subset(_72657, _72653)), subset(_72659, _72655), _72659 = _72657, _72655 = _72653], (44 ^ _71562) ^ [_73097, _73099, _73101, _73103] : [-(element(_73101, _73097)), element(_73103, _73099), _73103 = _73101, _73099 = _73097], (58 ^ _71562) ^ [_73541, _73543, _73545, _73547] : [-(in(_73545, _73541)), in(_73547, _73543), _73547 = _73545, _73543 = _73541], (72 ^ _71562) ^ [_73957, _73959] : [-(empty(_73957)), _73959 = _73957, empty(_73959)], (82 ^ _71562) ^ [_74252, _74254] : [-(relation(_74252)), _74254 = _74252, relation(_74254)], (92 ^ _71562) ^ [_74547, _74549] : [-(function(_74547)), _74549 = _74547, function(_74549)], (102 ^ _71562) ^ [_74822, _74824] : [-(one_to_one(_74822)), _74824 = _74822, one_to_one(_74824)], (146 ^ _71562) ^ [_76366, _76368] : [in(_76368, _76366), in(_76366, _76368)], (152 ^ _71562) ^ [_76563] : [empty(_76563), -(function(_76563))], (158 ^ _71562) ^ [_76749] : [empty(_76749), -(relation(_76749))], (164 ^ _71562) ^ [_76935] : [175 ^ _71562 : [(176 ^ _71562) ^ [] : [-(relation(_76935))], (178 ^ _71562) ^ [] : [-(function(_76935))], (180 ^ _71562) ^ [] : [-(one_to_one(_76935))]], relation(_76935), empty(_76935), function(_76935)], (182 ^ _71562) ^ [_77428] : [189 ^ _71562 : [(190 ^ _71562) ^ [] : [-(relation(function_inverse(_77428)))], (192 ^ _71562) ^ [] : [-(function(function_inverse(_77428)))]], relation(_77428), function(_77428)], (194 ^ _71562) ^ [_77790, _77792] : [-(relation(relation_composition(_77792, _77790))), relation(_77792), relation(_77790)], (205 ^ _71562) ^ [_78099] : [-(element(203 ^ [_78099], _78099))], (207 ^ _71562) ^ [_78211, _78213] : [214 ^ _71562 : [(215 ^ _71562) ^ [] : [-(empty(relation_composition(_78211, _78213)))], (217 ^ _71562) ^ [] : [-(relation(relation_composition(_78211, _78213)))]], empty(_78213), relation(_78211)], (219 ^ _71562) ^ [] : [-(empty(empty_set))], (221 ^ _71562) ^ [] : [-(relation(empty_set))], (223 ^ _71562) ^ [] : [-(relation_empty_yielding(empty_set))], (225 ^ _71562) ^ [_78752, _78754] : [240 ^ _71562 : [(241 ^ _71562) ^ [] : [-(relation(relation_composition(_78754, _78752)))], (243 ^ _71562) ^ [] : [-(function(relation_composition(_78754, _78752)))]], relation(_78754), function(_78754), relation(_78752), function(_78752)], (245 ^ _71562) ^ [_79274] : [empty(powerset(_79274))], (247 ^ _71562) ^ [] : [-(empty(empty_set))], (249 ^ _71562) ^ [] : [-(empty(empty_set))], (251 ^ _71562) ^ [] : [-(relation(empty_set))], (253 ^ _71562) ^ [_79529] : [empty(relation_dom(_79529)), -(empty(_79529)), relation(_79529)], (263 ^ _71562) ^ [_79806] : [empty(relation_rng(_79806)), -(empty(_79806)), relation(_79806)], (273 ^ _71562) ^ [_80083] : [empty(_80083), 276 ^ _71562 : [(277 ^ _71562) ^ [] : [-(empty(relation_dom(_80083)))], (279 ^ _71562) ^ [] : [-(relation(relation_dom(_80083)))]]], (281 ^ _71562) ^ [_80348] : [empty(_80348), 284 ^ _71562 : [(285 ^ _71562) ^ [] : [-(empty(relation_rng(_80348)))], (287 ^ _71562) ^ [] : [-(relation(relation_rng(_80348)))]]], (289 ^ _71562) ^ [_80627, _80629] : [296 ^ _71562 : [(297 ^ _71562) ^ [] : [-(empty(relation_composition(_80629, _80627)))], (299 ^ _71562) ^ [] : [-(relation(relation_composition(_80629, _80627)))]], empty(_80629), relation(_80627)], (302 ^ _71562) ^ [] : [-(relation(300 ^ []))], (304 ^ _71562) ^ [] : [-(function(300 ^ []))], (307 ^ _71562) ^ [] : [-(empty(305 ^ []))], (309 ^ _71562) ^ [] : [-(relation(305 ^ []))], (311 ^ _71562) ^ [_81289] : [-(empty(_81289)), 315 ^ _71562 : [(316 ^ _71562) ^ [] : [-(element(314 ^ [_81289], powerset(_81289)))], (318 ^ _71562) ^ [] : [empty(314 ^ [_81289])]]], (321 ^ _71562) ^ [] : [-(empty(319 ^ []))], (324 ^ _71562) ^ [] : [-(relation(322 ^ []))], (326 ^ _71562) ^ [] : [-(empty(322 ^ []))], (328 ^ _71562) ^ [] : [-(function(322 ^ []))], (331 ^ _71562) ^ [] : [empty(329 ^ [])], (333 ^ _71562) ^ [] : [-(relation(329 ^ []))], (336 ^ _71562) ^ [_82120] : [-(element(334 ^ [_82120], powerset(_82120)))], (338 ^ _71562) ^ [_82171] : [-(empty(334 ^ [_82171]))], (341 ^ _71562) ^ [] : [empty(339 ^ [])], (344 ^ _71562) ^ [] : [-(relation(342 ^ []))], (346 ^ _71562) ^ [] : [-(function(342 ^ []))], (348 ^ _71562) ^ [] : [-(one_to_one(342 ^ []))], (351 ^ _71562) ^ [] : [-(relation(349 ^ []))], (353 ^ _71562) ^ [] : [-(relation_empty_yielding(349 ^ []))], (355 ^ _71562) ^ [_82717, _82719] : [-(subset(_82719, _82719))], (357 ^ _71562) ^ [_82826, _82828] : [in(_82828, _82826), -(element(_82828, _82826))], (363 ^ _71562) ^ [_83036, _83038] : [element(_83038, _83036), -(empty(_83036)), -(in(_83038, _83036))], (373 ^ _71562) ^ [_83363, _83365] : [element(_83365, powerset(_83363)), -(subset(_83365, _83363))], (379 ^ _71562) ^ [_83529, _83531] : [subset(_83531, _83529), -(element(_83531, powerset(_83529)))], (385 ^ _71562) ^ [_83731] : [relation(_83731), 388 ^ _71562 : [(389 ^ _71562) ^ [_83878] : [relation(_83878), subset(relation_rng(_83731), relation_dom(_83878)), -(relation_dom(relation_composition(_83731, _83878)) = relation_dom(_83731))]]], (399 ^ _71562) ^ [_84190] : [relation(_84190), 402 ^ _71562 : [(403 ^ _71562) ^ [_84337] : [relation(_84337), subset(relation_dom(_84190), relation_rng(_84337)), -(relation_rng(relation_composition(_84337, _84190)) = relation_rng(_84190))]]], (413 ^ _71562) ^ [_84677, _84679, _84681] : [-(element(_84681, _84677)), in(_84681, _84679), element(_84679, powerset(_84677))], (423 ^ _71562) ^ [_84976] : [relation(_84976), function(_84976), one_to_one(_84976), 434 ^ _71562 : [(435 ^ _71562) ^ [] : [-(relation_rng(_84976) = relation_dom(function_inverse(_84976)))], (437 ^ _71562) ^ [] : [-(relation_dom(_84976) = relation_rng(function_inverse(_84976)))]]], (439 ^ _71562) ^ [_85457, _85459, _85461] : [in(_85461, _85459), element(_85459, powerset(_85457)), empty(_85457)], (449 ^ _71562) ^ [_85753] : [empty(_85753), -(_85753 = empty_set)], (455 ^ _71562) ^ [_85955, _85957] : [in(_85957, _85955), empty(_85955)], (461 ^ _71562) ^ [_86142, _86144] : [empty(_86144), -(_86144 = _86142), empty(_86142)]], input).
% 101.52/98.75  ncf('1',plain,[relation_dom(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ []), relation_rng(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ [])],start(478 ^ 0)).
% 101.52/98.75  ncf('1.1',plain,[-(relation_dom(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ [])), relation_dom(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ []), relation_dom(470 ^ []) = relation_dom(470 ^ [])],extension(10 ^ 1,bind([[_72017, _72019, _72021], [relation_dom(470 ^ []), relation_dom(470 ^ []), relation_dom(relation_composition(470 ^ [], function_inverse(470 ^ [])))]]))).
% 101.52/98.75  ncf('1.1.1',plain,[-(relation_dom(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ [])), 389 : relation(function_inverse(470 ^ [])), 389 : subset(relation_rng(470 ^ []), relation_dom(function_inverse(470 ^ []))), 389 : relation(470 ^ [])],extension(385 ^ 2,bind([[_83731, _83878], [470 ^ [], function_inverse(470 ^ [])]]))).
% 101.52/98.75  ncf('1.1.1.1',plain,[-(relation(function_inverse(470 ^ []))), relation(470 ^ []), function(470 ^ [])],extension(182 ^ 5,bind([[_77428], [470 ^ []]]))).
% 101.52/98.75  ncf('1.1.1.1.1',plain,[-(relation(470 ^ []))],extension(472 ^ 6)).
% 101.52/98.75  ncf('1.1.1.1.2',plain,[-(function(470 ^ []))],extension(474 ^ 6)).
% 101.52/98.75  ncf('1.1.1.2',plain,[-(subset(relation_rng(470 ^ []), relation_dom(function_inverse(470 ^ [])))), subset(relation_rng(470 ^ []), relation_rng(470 ^ [])), relation_rng(470 ^ []) = relation_rng(470 ^ []), relation_rng(470 ^ []) = relation_dom(function_inverse(470 ^ []))],extension(30 ^ 5,bind([[_72653, _72655, _72657, _72659], [relation_dom(function_inverse(470 ^ [])), relation_rng(470 ^ []), relation_rng(470 ^ []), relation_rng(470 ^ [])]]))).
% 101.52/98.75  ncf('1.1.1.2.1',plain,[-(subset(relation_rng(470 ^ []), relation_rng(470 ^ [])))],extension(355 ^ 6,bind([[_82717, _82719], [_49897, relation_rng(470 ^ [])]]))).
% 101.52/98.75  ncf('1.1.1.2.2',plain,[-(relation_rng(470 ^ []) = relation_rng(470 ^ []))],extension(2 ^ 6,bind([[_71706], [relation_rng(470 ^ [])]]))).
% 101.52/98.75  ncf('1.1.1.2.3',plain,[-(relation_rng(470 ^ []) = relation_dom(function_inverse(470 ^ []))), relation(470 ^ []), function(470 ^ []), one_to_one(470 ^ [])],extension(423 ^ 6,bind([[_84976], [470 ^ []]]))).
% 101.52/98.75  ncf('1.1.1.2.3.1',plain,[-(relation(470 ^ []))],extension(472 ^ 7)).
% 101.52/98.75  ncf('1.1.1.2.3.2',plain,[-(function(470 ^ []))],extension(474 ^ 7)).
% 101.52/98.75  ncf('1.1.1.2.3.3',plain,[-(one_to_one(470 ^ []))],extension(476 ^ 7)).
% 101.52/98.75  ncf('1.1.1.3',plain,[-(relation(470 ^ []))],extension(472 ^ 3)).
% 101.52/98.75  ncf('1.1.2',plain,[-(relation_dom(470 ^ []) = relation_dom(470 ^ [])), 470 ^ [] = 470 ^ []],extension(140 ^ 2,bind([[_76130, _76132], [470 ^ [], 470 ^ []]]))).
% 101.52/98.75  ncf('1.1.2.1',plain,[-(470 ^ [] = 470 ^ [])],extension(2 ^ 3,bind([[_71706], [470 ^ []]]))).
% 101.52/98.75  ncf('1.2',plain,[-(relation_rng(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_dom(470 ^ [])), relation_rng(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_rng(function_inverse(470 ^ [])), relation_rng(function_inverse(470 ^ [])) = relation_dom(470 ^ [])],extension(10 ^ 1,bind([[_72017, _72019, _72021], [relation_dom(470 ^ []), relation_rng(function_inverse(470 ^ [])), relation_rng(relation_composition(470 ^ [], function_inverse(470 ^ [])))]]))).
% 101.52/98.75  ncf('1.2.1',plain,[-(relation_rng(relation_composition(470 ^ [], function_inverse(470 ^ []))) = relation_rng(function_inverse(470 ^ []))), 403 : relation(470 ^ []), 403 : subset(relation_dom(function_inverse(470 ^ [])), relation_rng(470 ^ [])), 403 : relation(function_inverse(470 ^ []))],extension(399 ^ 2,bind([[_84190, _84337], [function_inverse(470 ^ []), 470 ^ []]]))).
% 101.52/98.75  ncf('1.2.1.1',plain,[-(relation(470 ^ []))],extension(472 ^ 5)).
% 101.52/98.75  ncf('1.2.1.2',plain,[-(subset(relation_dom(function_inverse(470 ^ [])), relation_rng(470 ^ []))), subset(relation_rng(470 ^ []), relation_rng(470 ^ [])), relation_rng(470 ^ []) = relation_dom(function_inverse(470 ^ [])), relation_rng(470 ^ []) = relation_rng(470 ^ [])],extension(30 ^ 5,bind([[_72653, _72655, _72657, _72659], [relation_rng(470 ^ []), relation_rng(470 ^ []), relation_dom(function_inverse(470 ^ [])), relation_rng(470 ^ [])]]))).
% 101.52/98.75  ncf('1.2.1.2.1',plain,[-(subset(relation_rng(470 ^ []), relation_rng(470 ^ [])))],extension(355 ^ 6,bind([[_82717, _82719], [_52197, relation_rng(470 ^ [])]]))).
% 101.52/98.75  ncf('1.2.1.2.2',plain,[-(relation_rng(470 ^ []) = relation_dom(function_inverse(470 ^ []))), relation(470 ^ []), function(470 ^ []), one_to_one(470 ^ [])],extension(423 ^ 6,bind([[_84976], [470 ^ []]]))).
% 101.52/98.75  ncf('1.2.1.2.2.1',plain,[-(relation(470 ^ []))],lemmata('[2, 1].x')).
% 101.52/98.75  ncf('1.2.1.2.2.2',plain,[-(function(470 ^ []))],extension(474 ^ 7)).
% 101.52/98.75  ncf('1.2.1.2.2.3',plain,[-(one_to_one(470 ^ []))],extension(476 ^ 7)).
% 101.52/98.75  ncf('1.2.1.2.3',plain,[-(relation_rng(470 ^ []) = relation_rng(470 ^ []))],extension(2 ^ 6,bind([[_71706], [relation_rng(470 ^ [])]]))).
% 101.52/98.75  ncf('1.2.1.3',plain,[-(relation(function_inverse(470 ^ []))), relation(470 ^ []), function(470 ^ [])],extension(182 ^ 3,bind([[_77428], [470 ^ []]]))).
% 101.52/98.75  ncf('1.2.1.3.1',plain,[-(relation(470 ^ []))],extension(472 ^ 4)).
% 101.52/98.75  ncf('1.2.1.3.2',plain,[-(function(470 ^ []))],extension(474 ^ 4)).
% 101.52/98.75  ncf('1.2.2',plain,[-(relation_rng(function_inverse(470 ^ [])) = relation_dom(470 ^ [])), relation_dom(470 ^ []) = relation_rng(function_inverse(470 ^ []))],extension(4 ^ 2,bind([[_71813, _71815], [relation_rng(function_inverse(470 ^ [])), relation_dom(470 ^ [])]]))).
% 101.52/98.75  ncf('1.2.2.1',plain,[-(relation_dom(470 ^ []) = relation_rng(function_inverse(470 ^ []))), relation_dom(470 ^ []) = relation_rng(function_inverse(470 ^ [])), relation_rng(function_inverse(470 ^ [])) = relation_rng(function_inverse(470 ^ []))],extension(10 ^ 3,bind([[_72017, _72019, _72021], [relation_rng(function_inverse(470 ^ [])), relation_rng(function_inverse(470 ^ [])), relation_dom(470 ^ [])]]))).
% 101.52/98.75  ncf('1.2.2.1.1',plain,[-(relation_dom(470 ^ []) = relation_rng(function_inverse(470 ^ []))), relation(470 ^ []), function(470 ^ []), one_to_one(470 ^ [])],extension(423 ^ 4,bind([[_84976], [470 ^ []]]))).
% 101.52/98.75  ncf('1.2.2.1.1.1',plain,[-(relation(470 ^ []))],extension(472 ^ 5)).
% 101.52/98.75  ncf('1.2.2.1.1.2',plain,[-(function(470 ^ []))],extension(474 ^ 5)).
% 101.52/98.75  ncf('1.2.2.1.1.3',plain,[-(one_to_one(470 ^ []))],extension(476 ^ 5)).
% 101.52/98.75  ncf('1.2.2.1.2',plain,[-(relation_rng(function_inverse(470 ^ [])) = relation_rng(function_inverse(470 ^ [])))],extension(2 ^ 4,bind([[_71706], [relation_rng(function_inverse(470 ^ []))]]))).
% 101.52/98.75  %-----------------------------------------------------
% 101.52/98.75  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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