%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU023+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.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 46.60s 45.85s
% Output   : Proof 46.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU023+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n020.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 12:30:47 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 46.60/45.85  
% 46.60/45.85  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 46.60/45.85  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.60/45.85  %-----------------------------------------------------
% 46.60/45.85  ncf(matrix, plain, [(543 ^ _101698) ^ [] : [-(relation(541 ^ []))], (547 ^ _101698) ^ [] : [-(one_to_one(541 ^ []))], (551 ^ _101698) ^ [] : [540 ^ [] = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])), 540 ^ [] = apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ [])], (549 ^ _101698) ^ [] : [-(in(540 ^ [], relation_dom(541 ^ [])))], (545 ^ _101698) ^ [] : [-(function(541 ^ []))], !, (263 ^ _84057) ^ [_92367] : [empty(relation_dom(_92367)), -(empty(_92367)), relation(_92367)], (235 ^ _84057) ^ [_91590, _91592] : [250 ^ _84057 : [(253 ^ _84057) ^ [] : [-(function(relation_composition(_91592, _91590)))], (251 ^ _84057) ^ [] : [-(relation(relation_composition(_91592, _91590)))]], relation(_91592), function(_91592), relation(_91590), function(_91590)], (331 ^ _84057) ^ [] : [-(empty(329 ^ []))], (338 ^ _84057) ^ [] : [-(function(332 ^ []))], (229 ^ _84057) ^ [] : [-(empty(empty_set))], (88 ^ _84057) ^ [_86873, _86875] : [-(one_to_one(_86873)), _86875 = _86873, one_to_one(_86875)], (78 ^ _84057) ^ [_86578, _86580] : [-(function(_86578)), _86580 = _86578, function(_86580)], (373 ^ _84057) ^ [_95874, _95876] : [relation(_95874), function(_95874), 380 ^ _84057 : [(381 ^ _84057) ^ [_96120] : [relation(_96120), function(_96120), in(_95876, relation_dom(_95874)), -(apply(relation_composition(_95874, _96120), _95876) = apply(_96120, apply(_95874, _95876)))]]], (192 ^ _84057) ^ [_90266] : [199 ^ _84057 : [(202 ^ _84057) ^ [] : [-(function(function_inverse(_90266)))], (200 ^ _84057) ^ [] : [-(relation(function_inverse(_90266)))]], relation(_90266), function(_90266)], (98 ^ _84057) ^ [_87176, _87178, _87180, _87182] : [-(in(_87180, _87176)), in(_87182, _87178), _87182 = _87180, _87178 = _87176], (312 ^ _84057) ^ [] : [-(relation(310 ^ []))], (334 ^ _84057) ^ [] : [-(relation(332 ^ []))], (354 ^ _84057) ^ [] : [-(relation(352 ^ []))], (58 ^ _84057) ^ [_85988, _85990] : [-(empty(_85988)), _85990 = _85988, empty(_85990)], (257 ^ _84057) ^ [] : [-(empty(empty_set))], (365 ^ _84057) ^ [_95555, _95557] : [-(subset(_95557, _95557))], (124 ^ _84057) ^ [_88048, _88050] : [_88050 = _88048, -(relation_dom(_88050) = relation_dom(_88048))], (321 ^ _84057) ^ [_94127] : [-(empty(_94127)), 325 ^ _84057 : [(328 ^ _84057) ^ [] : [empty(324 ^ [_94127])], (326 ^ _84057) ^ [] : [-(element(324 ^ [_94127], powerset(_94127)))]]], (417 ^ _84057) ^ [_97282, _97284, _97286] : [-(element(_97286, _97282)), in(_97286, _97284), element(_97284, powerset(_97282))], (215 ^ _84057) ^ [_90937] : [-(element(213 ^ [_90937], _90937))], (361 ^ _84057) ^ [] : [-(relation(359 ^ []))], (314 ^ _84057) ^ [] : [-(function(310 ^ []))], (319 ^ _84057) ^ [] : [-(relation(315 ^ []))], (405 ^ _84057) ^ [_96886, _96888] : [element(_96888, powerset(_96886)), -(subset(_96888, _96886))], (531 ^ _84057) ^ [_101119, _101121] : [empty(_101121), -(_101121 = _101119), empty(_101119)], (351 ^ _84057) ^ [] : [empty(349 ^ [])], (341 ^ _84057) ^ [] : [empty(339 ^ [])], (525 ^ _84057) ^ [_100932, _100934] : [in(_100934, _100932), empty(_100932)], (259 ^ _84057) ^ [] : [-(empty(empty_set))], (168 ^ _84057) ^ [_89587] : [empty(_89587), -(relation(_89587))], (44 ^ _84057) ^ [_85572, _85574, _85576, _85578] : [-(element(_85576, _85572)), element(_85578, _85574), _85578 = _85576, _85574 = _85572], (411 ^ _84057) ^ [_97052, _97054] : [subset(_97054, _97052), -(element(_97054, powerset(_97052)))], (10 ^ _84057) ^ [_84492, _84494, _84496] : [-(_84496 = _84492), _84496 = _84494, _84494 = _84492], (283 ^ _84057) ^ [_92921] : [empty(_92921), 286 ^ _84057 : [(289 ^ _84057) ^ [] : [-(relation(relation_dom(_92921)))], (287 ^ _84057) ^ [] : [-(empty(relation_dom(_92921)))]]], (255 ^ _84057) ^ [_92112] : [empty(powerset(_92112))], (140 ^ _84057) ^ [_88653, _88655, _88657, _88659] : [-(relation_composition(_88659, _88655) = relation_composition(_88657, _88653)), _88659 = _88657, _88655 = _88653], (367 ^ _84057) ^ [_95664, _95666] : [in(_95666, _95664), -(element(_95666, _95664))], (358 ^ _84057) ^ [] : [-(one_to_one(352 ^ []))], (2 ^ _84057) ^ [_84181] : [-(_84181 = _84181)], (343 ^ _84057) ^ [] : [-(relation(339 ^ []))], (299 ^ _84057) ^ [_93465, _93467] : [306 ^ _84057 : [(309 ^ _84057) ^ [] : [-(relation(relation_composition(_93467, _93465)))], (307 ^ _84057) ^ [] : [-(empty(relation_composition(_93467, _93465)))]], empty(_93467), relation(_93465)], (427 ^ _84057) ^ [_97581] : [relation(_97581), function(_97581), one_to_one(_97581), 438 ^ _84057 : [(439 ^ _84057) ^ [_97968] : [relation(_97968), function(_97968), 446 ^ _84057 : [(447 ^ _84057) ^ [] : [_97968 = function_inverse(_97581), 450 ^ _84057 : [(465 ^ _84057) ^ [_98859, _98861] : [472 ^ _84057 : [(475 ^ _84057) ^ [] : [-(_98859 = apply(_97968, _98861))], (473 ^ _84057) ^ [] : [-(in(_98861, relation_rng(_97581)))]], in(_98859, relation_dom(_97581)), _98861 = apply(_97581, _98859)], (453 ^ _84057) ^ [_98485, _98487] : [460 ^ _84057 : [(463 ^ _84057) ^ [] : [-(_98487 = apply(_97581, _98485))], (461 ^ _84057) ^ [] : [-(in(_98485, relation_dom(_97581)))]], in(_98487, relation_rng(_97581)), _98485 = apply(_97968, _98487)], (451 ^ _84057) ^ [] : [-(relation_dom(_97968) = relation_rng(_97581))]]], (477 ^ _84057) ^ [] : [-(_97968 = function_inverse(_97581)), relation_dom(_97968) = relation_rng(_97581), 486 ^ _84057 : [(491 ^ _84057) ^ [] : [in(483 ^ [_97581, _97968], relation_dom(_97581)), 482 ^ [_97581, _97968] = apply(_97581, 483 ^ [_97581, _97968])], (489 ^ _84057) ^ [] : [-(483 ^ [_97581, _97968] = apply(_97968, 482 ^ [_97581, _97968]))], (487 ^ _84057) ^ [] : [-(in(482 ^ [_97581, _97968], relation_rng(_97581)))]], 496 ^ _84057 : [(501 ^ _84057) ^ [] : [in(482 ^ [_97581, _97968], relation_rng(_97581)), 483 ^ [_97581, _97968] = apply(_97968, 482 ^ [_97581, _97968])], (499 ^ _84057) ^ [] : [-(482 ^ [_97581, _97968] = apply(_97581, 483 ^ [_97581, _97968]))], (497 ^ _84057) ^ [] : [-(in(483 ^ [_97581, _97968], relation_dom(_97581)))]]]]]]], (346 ^ _84057) ^ [_94958] : [-(element(344 ^ [_94958], powerset(_94958)))], (156 ^ _84057) ^ [_89204, _89206] : [in(_89206, _89204), in(_89204, _89206)], (217 ^ _84057) ^ [_91049, _91051] : [224 ^ _84057 : [(227 ^ _84057) ^ [] : [-(relation(relation_composition(_91049, _91051)))], (225 ^ _84057) ^ [] : [-(empty(relation_composition(_91049, _91051)))]], empty(_91051), relation(_91049)], (356 ^ _84057) ^ [] : [-(function(352 ^ []))], (130 ^ _84057) ^ [_88294, _88296, _88298, _88300] : [-(apply(_88300, _88296) = apply(_88298, _88294)), _88300 = _88298, _88296 = _88294], (348 ^ _84057) ^ [_95009] : [-(empty(344 ^ [_95009]))], (395 ^ _84057) ^ [_96559, _96561] : [element(_96561, _96559), -(empty(_96559)), -(in(_96561, _96559))], (150 ^ _84057) ^ [_88964, _88966] : [_88966 = _88964, -(function_inverse(_88966) = function_inverse(_88964))], (509 ^ _84057) ^ [_100434, _100436, _100438] : [in(_100438, _100436), element(_100436, powerset(_100434)), empty(_100434)], (174 ^ _84057) ^ [_89773] : [185 ^ _84057 : [(190 ^ _84057) ^ [] : [-(one_to_one(_89773))], (188 ^ _84057) ^ [] : [-(function(_89773))], (186 ^ _84057) ^ [] : [-(relation(_89773))]], relation(_89773), empty(_89773), function(_89773)], (112 ^ _84057) ^ [_87612, _87614] : [_87614 = _87612, -(relation_rng(_87614) = relation_rng(_87612))], (20 ^ _84057) ^ [_84805, _84807] : [-(relation_empty_yielding(_84805)), _84807 = _84805, relation_empty_yielding(_84807)], (162 ^ _84057) ^ [_89401] : [empty(_89401), -(function(_89401))], (336 ^ _84057) ^ [] : [-(empty(332 ^ []))], (233 ^ _84057) ^ [] : [-(relation_empty_yielding(empty_set))], (68 ^ _84057) ^ [_86283, _86285] : [-(relation(_86283)), _86285 = _86283, relation(_86285)], (231 ^ _84057) ^ [] : [-(relation(empty_set))], (317 ^ _84057) ^ [] : [-(empty(315 ^ []))], (30 ^ _84057) ^ [_85128, _85130, _85132, _85134] : [-(subset(_85132, _85128)), subset(_85134, _85130), _85134 = _85132, _85130 = _85128], (273 ^ _84057) ^ [_92644] : [empty(relation_rng(_92644)), -(empty(_92644)), relation(_92644)], (118 ^ _84057) ^ [_87830, _87832] : [_87832 = _87830, -(powerset(_87832) = powerset(_87830))], (291 ^ _84057) ^ [_93186] : [empty(_93186), 294 ^ _84057 : [(297 ^ _84057) ^ [] : [-(relation(relation_rng(_93186)))], (295 ^ _84057) ^ [] : [-(empty(relation_rng(_93186)))]]], (204 ^ _84057) ^ [_90628, _90630] : [-(relation(relation_composition(_90630, _90628))), relation(_90630), relation(_90628)], (4 ^ _84057) ^ [_84288, _84290] : [_84290 = _84288, -(_84288 = _84290)], (519 ^ _84057) ^ [_100730] : [empty(_100730), -(_100730 = empty_set)], (261 ^ _84057) ^ [] : [-(relation(empty_set))], (363 ^ _84057) ^ [] : [-(relation_empty_yielding(359 ^ []))]], input).
% 46.60/45.85  ncf('1',plain,[540 ^ [] = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])), 540 ^ [] = apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ [])],start(551 ^ 0)).
% 46.60/45.85  ncf('1.1',plain,[-(540 ^ [] = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ []))), 465 : in(540 ^ [], relation_dom(541 ^ [])), 465 : apply(541 ^ [], 540 ^ []) = apply(541 ^ [], 540 ^ []), 465 : function_inverse(541 ^ []) = function_inverse(541 ^ []), 447 : relation(function_inverse(541 ^ [])), 447 : function(function_inverse(541 ^ [])), 439 : relation(541 ^ []), 439 : function(541 ^ []), 439 : one_to_one(541 ^ [])],extension(427 ^ 1,bind([[_97581, _97968, _98859, _98861], [541 ^ [], function_inverse(541 ^ []), 540 ^ [], apply(541 ^ [], 540 ^ [])]]))).
% 46.60/45.85  ncf('1.1.1',plain,[-(in(540 ^ [], relation_dom(541 ^ [])))],extension(549 ^ 8)).
% 46.60/45.85  ncf('1.1.2',plain,[-(apply(541 ^ [], 540 ^ []) = apply(541 ^ [], 540 ^ []))],extension(2 ^ 8,bind([[_84181], [apply(541 ^ [], 540 ^ [])]]))).
% 46.60/45.85  ncf('1.1.3',plain,[-(function_inverse(541 ^ []) = function_inverse(541 ^ []))],extension(2 ^ 6,bind([[_84181], [function_inverse(541 ^ [])]]))).
% 46.60/45.85  ncf('1.1.4',plain,[-(relation(function_inverse(541 ^ []))), relation(541 ^ []), function(541 ^ [])],extension(192 ^ 4,bind([[_90266], [541 ^ []]]))).
% 46.60/45.85  ncf('1.1.4.1',plain,[-(relation(541 ^ []))],extension(543 ^ 5)).
% 46.60/45.85  ncf('1.1.4.2',plain,[-(function(541 ^ []))],extension(545 ^ 5)).
% 46.60/45.85  ncf('1.1.5',plain,[-(function(function_inverse(541 ^ []))), relation(541 ^ []), function(541 ^ [])],extension(192 ^ 4,bind([[_90266], [541 ^ []]]))).
% 46.60/45.85  ncf('1.1.5.1',plain,[-(relation(541 ^ []))],extension(543 ^ 5)).
% 46.60/45.85  ncf('1.1.5.2',plain,[-(function(541 ^ []))],extension(545 ^ 5)).
% 46.60/45.85  ncf('1.1.6',plain,[-(relation(541 ^ []))],extension(543 ^ 2)).
% 46.60/45.85  ncf('1.1.7',plain,[-(function(541 ^ []))],extension(545 ^ 2)).
% 46.60/45.85  ncf('1.1.8',plain,[-(one_to_one(541 ^ []))],extension(547 ^ 2)).
% 46.60/45.85  ncf('1.2',plain,[-(540 ^ [] = apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ [])), apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ []) = 540 ^ []],extension(4 ^ 1,bind([[_84288, _84290], [540 ^ [], apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ [])]]))).
% 46.60/45.85  ncf('1.2.1',plain,[-(apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ []) = 540 ^ []), apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ []) = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])), apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])) = 540 ^ []],extension(10 ^ 2,bind([[_84492, _84494, _84496], [540 ^ [], apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])), apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ [])]]))).
% 46.60/45.85  ncf('1.2.1.1',plain,[-(apply(relation_composition(541 ^ [], function_inverse(541 ^ [])), 540 ^ []) = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ []))), 381 : relation(function_inverse(541 ^ [])), 381 : function(function_inverse(541 ^ [])), 381 : in(540 ^ [], relation_dom(541 ^ [])), 381 : relation(541 ^ []), 381 : function(541 ^ [])],extension(373 ^ 3,bind([[_95874, _95876, _96120], [541 ^ [], 540 ^ [], function_inverse(541 ^ [])]]))).
% 46.60/45.85  ncf('1.2.1.1.1',plain,[-(relation(function_inverse(541 ^ []))), relation(541 ^ []), function(541 ^ [])],extension(192 ^ 6,bind([[_90266], [541 ^ []]]))).
% 46.60/45.85  ncf('1.2.1.1.1.1',plain,[-(relation(541 ^ []))],extension(543 ^ 7)).
% 46.60/45.85  ncf('1.2.1.1.1.2',plain,[-(function(541 ^ []))],extension(545 ^ 7)).
% 46.60/45.85  ncf('1.2.1.1.2',plain,[-(function(function_inverse(541 ^ []))), relation(541 ^ []), function(541 ^ [])],extension(192 ^ 6,bind([[_90266], [541 ^ []]]))).
% 46.60/45.85  ncf('1.2.1.1.2.1',plain,[-(relation(541 ^ []))],extension(543 ^ 7)).
% 46.60/45.85  ncf('1.2.1.1.2.2',plain,[-(function(541 ^ []))],extension(545 ^ 7)).
% 46.60/45.85  ncf('1.2.1.1.3',plain,[-(in(540 ^ [], relation_dom(541 ^ [])))],extension(549 ^ 6)).
% 46.60/45.85  ncf('1.2.1.1.4',plain,[-(relation(541 ^ []))],extension(543 ^ 4)).
% 46.60/45.85  ncf('1.2.1.1.5',plain,[-(function(541 ^ []))],extension(545 ^ 4)).
% 46.60/45.85  ncf('1.2.1.2',plain,[-(apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])) = 540 ^ []), 540 ^ [] = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ []))],extension(4 ^ 3,bind([[_84288, _84290], [apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])), 540 ^ []]]))).
% 46.60/45.85  ncf('1.2.1.2.1',plain,[-(540 ^ [] = apply(function_inverse(541 ^ []), apply(541 ^ [], 540 ^ [])))],lemmata('x')).
% 46.60/45.85  %-----------------------------------------------------
% 46.60/45.85  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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