%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU225+3 : 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 12:02:45 EDT 2023

% Result   : Theorem 0.45s 1.38s
% Output   : Proof 0.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU225+3 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12  % 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 13:34:54 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.45/1.38  
% 0.45/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.45/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/1.38  %-----------------------------------------------------
% 0.45/1.38  ncf(matrix, plain, [(543 ^ _83223) ^ [] : [-(relation(541 ^ []))], (545 ^ _83223) ^ [] : [-(function(541 ^ []))], (547 ^ _83223) ^ [] : [-(in(540 ^ [], 539 ^ []))], (549 ^ _83223) ^ [] : [apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(541 ^ [], 540 ^ [])], (112 ^ _83223) ^ [_86826, _86828, _86830, _86832] : [-(ordered_pair(_86832, _86828) = ordered_pair(_86830, _86826)), _86832 = _86830, _86828 = _86826], (122 ^ _83223) ^ [_87157, _87159] : [_87159 = _87157, -(singleton(_87159) = singleton(_87157))], (128 ^ _83223) ^ [_87403, _87405, _87407, _87409] : [-(unordered_pair(_87409, _87405) = unordered_pair(_87407, _87403)), _87409 = _87407, _87405 = _87403], (138 ^ _83223) ^ [_87734, _87736] : [_87736 = _87734, -(powerset(_87736) = powerset(_87734))], (144 ^ _83223) ^ [_87980, _87982, _87984, _87986] : [-(set_intersection2(_87986, _87982) = set_intersection2(_87984, _87980)), _87986 = _87984, _87982 = _87980], (154 ^ _83223) ^ [_88311, _88313] : [_88313 = _88311, -(relation_dom(_88313) = relation_dom(_88311))], (160 ^ _83223) ^ [_88557, _88559, _88561, _88563] : [-(relation_dom_restriction(_88563, _88559) = relation_dom_restriction(_88561, _88557)), _88563 = _88561, _88559 = _88557], (170 ^ _83223) ^ [_88896, _88898, _88900, _88902] : [-(apply(_88902, _88898) = apply(_88900, _88896)), _88902 = _88900, _88898 = _88896], (2 ^ _83223) ^ [_83367] : [-(_83367 = _83367)], (4 ^ _83223) ^ [_83474, _83476] : [_83476 = _83474, -(_83474 = _83476)], (10 ^ _83223) ^ [_83678, _83680, _83682] : [-(_83682 = _83678), _83682 = _83680, _83680 = _83678], (20 ^ _83223) ^ [_83991, _83993] : [-(one_to_one(_83991)), _83993 = _83991, one_to_one(_83993)], (30 ^ _83223) ^ [_84286, _84288] : [-(relation_empty_yielding(_84286)), _84288 = _84286, relation_empty_yielding(_84288)], (40 ^ _83223) ^ [_84609, _84611, _84613, _84615] : [-(subset(_84613, _84609)), subset(_84615, _84611), _84615 = _84613, _84611 = _84609], (54 ^ _83223) ^ [_85053, _85055, _85057, _85059] : [-(element(_85057, _85053)), element(_85059, _85055), _85059 = _85057, _85055 = _85053], (68 ^ _83223) ^ [_85469, _85471] : [-(empty(_85469)), _85471 = _85469, empty(_85471)], (78 ^ _83223) ^ [_85764, _85766] : [-(relation(_85764)), _85766 = _85764, relation(_85766)], (88 ^ _83223) ^ [_86059, _86061] : [-(function(_86059)), _86061 = _86059, function(_86061)], (98 ^ _83223) ^ [_86362, _86364, _86366, _86368] : [-(in(_86366, _86362)), in(_86368, _86364), _86368 = _86366, _86364 = _86362], (180 ^ _83223) ^ [_89257, _89259] : [in(_89259, _89257), in(_89257, _89259)], (186 ^ _83223) ^ [_89454] : [empty(_89454), -(function(_89454))], (192 ^ _83223) ^ [_89640] : [empty(_89640), -(relation(_89640))], (198 ^ _83223) ^ [_89826] : [209 ^ _83223 : [(210 ^ _83223) ^ [] : [-(relation(_89826))], (212 ^ _83223) ^ [] : [-(function(_89826))], (214 ^ _83223) ^ [] : [-(one_to_one(_89826))]], relation(_89826), empty(_89826), function(_89826)], (216 ^ _83223) ^ [_90318, _90320] : [-(unordered_pair(_90320, _90318) = unordered_pair(_90318, _90320))], (218 ^ _83223) ^ [_90418, _90420] : [-(set_intersection2(_90420, _90418) = set_intersection2(_90418, _90420))], (220 ^ _83223) ^ [_90519] : [relation(_90519), function(_90519), 227 ^ _83223 : [(228 ^ _83223) ^ [_90811, _90813] : [in(_90813, relation_dom(_90519)), 231 ^ _83223 : [(232 ^ _83223) ^ [] : [_90811 = apply(_90519, _90813), -(in(ordered_pair(_90813, _90811), _90519))], (238 ^ _83223) ^ [] : [in(ordered_pair(_90813, _90811), _90519), -(_90811 = apply(_90519, _90813))]]], (244 ^ _83223) ^ [_91263, _91265] : [-(in(_91265, relation_dom(_90519))), 247 ^ _83223 : [(248 ^ _83223) ^ [] : [_91263 = apply(_90519, _91265), -(_91263 = empty_set)], (254 ^ _83223) ^ [] : [_91263 = empty_set, -(_91263 = apply(_90519, _91265))]]]]], (260 ^ _83223) ^ [_91751, _91753] : [-(ordered_pair(_91753, _91751) = unordered_pair(unordered_pair(_91753, _91751), singleton(_91753)))], (262 ^ _83223) ^ [_91871, _91873] : [relation(_91873), -(relation(relation_dom_restriction(_91873, _91871)))], (269 ^ _83223) ^ [_92093] : [-(element(267 ^ [_92093], _92093))], (271 ^ _83223) ^ [] : [-(empty(empty_set))], (273 ^ _83223) ^ [] : [-(relation(empty_set))], (275 ^ _83223) ^ [] : [-(relation_empty_yielding(empty_set))], (277 ^ _83223) ^ [_92368, _92370] : [284 ^ _83223 : [(285 ^ _83223) ^ [] : [-(relation(relation_dom_restriction(_92370, _92368)))], (287 ^ _83223) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_92370, _92368)))]], relation(_92370), relation_empty_yielding(_92370)], (289 ^ _83223) ^ [_92746, _92748] : [-(relation(set_intersection2(_92748, _92746))), relation(_92748), relation(_92746)], (299 ^ _83223) ^ [_93015] : [empty(powerset(_93015))], (301 ^ _83223) ^ [] : [-(empty(empty_set))], (303 ^ _83223) ^ [_93160, _93162] : [empty(ordered_pair(_93162, _93160))], (305 ^ _83223) ^ [_93241] : [empty(singleton(_93241))], (307 ^ _83223) ^ [_93333, _93335] : [empty(unordered_pair(_93335, _93333))], (309 ^ _83223) ^ [_93444, _93446] : [316 ^ _83223 : [(317 ^ _83223) ^ [] : [-(relation(relation_dom_restriction(_93446, _93444)))], (319 ^ _83223) ^ [] : [-(function(relation_dom_restriction(_93446, _93444)))]], relation(_93446), function(_93446)], (321 ^ _83223) ^ [] : [-(empty(empty_set))], (323 ^ _83223) ^ [] : [-(relation(empty_set))], (325 ^ _83223) ^ [_93916] : [empty(relation_dom(_93916)), -(empty(_93916)), relation(_93916)], (335 ^ _83223) ^ [_94193] : [empty(_94193), 338 ^ _83223 : [(339 ^ _83223) ^ [] : [-(empty(relation_dom(_94193)))], (341 ^ _83223) ^ [] : [-(relation(relation_dom(_94193)))]]], (343 ^ _83223) ^ [_94457, _94459] : [-(set_intersection2(_94459, _94459) = _94459)], (345 ^ _83223) ^ [_94583, _94585, _94587] : [relation(_94583), function(_94583), 352 ^ _83223 : [(353 ^ _83223) ^ [] : [in(_94585, relation_dom(relation_dom_restriction(_94583, _94587))), 356 ^ _83223 : [(357 ^ _83223) ^ [] : [-(in(_94585, relation_dom(_94583)))], (359 ^ _83223) ^ [] : [-(in(_94585, _94587))]]], (361 ^ _83223) ^ [] : [-(in(_94585, relation_dom(relation_dom_restriction(_94583, _94587)))), in(_94585, relation_dom(_94583)), in(_94585, _94587)]]], (372 ^ _83223) ^ [] : [-(relation(370 ^ []))], (374 ^ _83223) ^ [] : [-(function(370 ^ []))], (377 ^ _83223) ^ [] : [-(empty(375 ^ []))], (379 ^ _83223) ^ [] : [-(relation(375 ^ []))], (381 ^ _83223) ^ [_95619] : [-(empty(_95619)), 385 ^ _83223 : [(386 ^ _83223) ^ [] : [-(element(384 ^ [_95619], powerset(_95619)))], (388 ^ _83223) ^ [] : [empty(384 ^ [_95619])]]], (391 ^ _83223) ^ [] : [-(empty(389 ^ []))], (394 ^ _83223) ^ [] : [-(relation(392 ^ []))], (396 ^ _83223) ^ [] : [-(empty(392 ^ []))], (398 ^ _83223) ^ [] : [-(function(392 ^ []))], (401 ^ _83223) ^ [] : [empty(399 ^ [])], (403 ^ _83223) ^ [] : [-(relation(399 ^ []))], (406 ^ _83223) ^ [_96450] : [-(element(404 ^ [_96450], powerset(_96450)))], (408 ^ _83223) ^ [_96501] : [-(empty(404 ^ [_96501]))], (411 ^ _83223) ^ [] : [empty(409 ^ [])], (414 ^ _83223) ^ [] : [-(relation(412 ^ []))], (416 ^ _83223) ^ [] : [-(function(412 ^ []))], (418 ^ _83223) ^ [] : [-(one_to_one(412 ^ []))], (421 ^ _83223) ^ [] : [-(relation(419 ^ []))], (423 ^ _83223) ^ [] : [-(relation_empty_yielding(419 ^ []))], (425 ^ _83223) ^ [_97047, _97049] : [-(subset(_97049, _97049))], (427 ^ _83223) ^ [_97156, _97158] : [in(_97158, _97156), -(element(_97158, _97156))], (433 ^ _83223) ^ [_97337] : [-(set_intersection2(_97337, empty_set) = empty_set)], (435 ^ _83223) ^ [_97447, _97449] : [element(_97449, _97447), -(empty(_97447)), -(in(_97449, _97447))], (445 ^ _83223) ^ [_97774, _97776] : [element(_97776, powerset(_97774)), -(subset(_97776, _97774))], (451 ^ _83223) ^ [_97940, _97942] : [subset(_97942, _97940), -(element(_97942, powerset(_97940)))], (457 ^ _83223) ^ [_98170, _98172, _98174] : [-(element(_98174, _98170)), in(_98174, _98172), element(_98172, powerset(_98170))], (467 ^ _83223) ^ [_98497, _98499, _98501] : [in(_98501, _98499), element(_98499, powerset(_98497)), empty(_98497)], (518 ^ _83223) ^ [_100182] : [empty(_100182), -(_100182 = empty_set)], (524 ^ _83223) ^ [_100384, _100386] : [in(_100386, _100384), empty(_100384)], (530 ^ _83223) ^ [_100571, _100573] : [empty(_100573), -(_100573 = _100571), empty(_100571)], (477 ^ _83223) ^ [_98807, _98809] : [relation(_98807), function(_98807), 484 ^ _83223 : [(485 ^ _83223) ^ [_99074] : [relation(_99074), function(_99074), 492 ^ _83223 : [(493 ^ _83223) ^ [] : [_98807 = relation_dom_restriction(_99074, _98809), 496 ^ _83223 : [(497 ^ _83223) ^ [] : [-(relation_dom(_98807) = set_intersection2(relation_dom(_99074), _98809))], (499 ^ _83223) ^ [_99528] : [in(_99528, relation_dom(_98807)), -(apply(_98807, _99528) = apply(_99074, _99528))]]], (505 ^ _83223) ^ [] : [-(_98807 = relation_dom_restriction(_99074, _98809)), relation_dom(_98807) = set_intersection2(relation_dom(_99074), _98809), 511 ^ _83223 : [(512 ^ _83223) ^ [] : [-(in(510 ^ [_98807, _98809, _99074], relation_dom(_98807)))], (514 ^ _83223) ^ [] : [apply(_98807, 510 ^ [_98807, _98809, _99074]) = apply(_99074, 510 ^ [_98807, _98809, _99074])]]]]]]]], input).
% 0.45/1.38  ncf('1',plain,[apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(541 ^ [], 540 ^ [])],start(549 ^ 0)).
% 0.45/1.38  ncf('1.1',plain,[-(apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(541 ^ [], 540 ^ [])), 499 : in(540 ^ [], relation_dom(relation_dom_restriction(541 ^ [], 539 ^ []))), 499 : relation_dom_restriction(541 ^ [], 539 ^ []) = relation_dom_restriction(541 ^ [], 539 ^ []), 493 : relation(541 ^ []), 493 : function(541 ^ []), 485 : relation(relation_dom_restriction(541 ^ [], 539 ^ [])), 485 : function(relation_dom_restriction(541 ^ [], 539 ^ []))],extension(477 ^ 1,bind([[_98807, _98809, _99074, _99528], [relation_dom_restriction(541 ^ [], 539 ^ []), 539 ^ [], 541 ^ [], 540 ^ []]]))).
% 0.45/1.38  ncf('1.1.1',plain,[-(in(540 ^ [], relation_dom(relation_dom_restriction(541 ^ [], 539 ^ [])))), 248 : apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []), 248 : -(apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = empty_set), 244 : relation(relation_dom_restriction(541 ^ [], 539 ^ [])), 244 : function(relation_dom_restriction(541 ^ [], 539 ^ []))],extension(220 ^ 8,bind([[_90519, _91263, _91265], [relation_dom_restriction(541 ^ [], 539 ^ []), apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []), 540 ^ []]]))).
% 0.45/1.38  ncf('1.1.1.1',plain,[-(apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ [])), relation_dom_restriction(541 ^ [], 539 ^ []) = relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ [] = 540 ^ []],extension(170 ^ 13,bind([[_88896, _88898, _88900, _88902], [540 ^ [], 540 ^ [], relation_dom_restriction(541 ^ [], 539 ^ []), relation_dom_restriction(541 ^ [], 539 ^ [])]]))).
% 0.45/1.38  ncf('1.1.1.1.1',plain,[-(relation_dom_restriction(541 ^ [], 539 ^ []) = relation_dom_restriction(541 ^ [], 539 ^ []))],extension(2 ^ 14,bind([[_83367], [relation_dom_restriction(541 ^ [], 539 ^ [])]]))).
% 0.45/1.38  ncf('1.1.1.1.2',plain,[-(540 ^ [] = 540 ^ [])],extension(2 ^ 14,bind([[_83367], [540 ^ []]]))).
% 0.45/1.38  ncf('1.1.1.2',plain,[apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = empty_set, 254 : -(apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(541 ^ [], 540 ^ [])), 254 : -(in(540 ^ [], relation_dom(541 ^ []))), 244 : relation(541 ^ []), 244 : function(541 ^ [])],extension(220 ^ 13,bind([[_90519, _91263, _91265], [541 ^ [], apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []), 540 ^ []]]))).
% 0.45/1.38  ncf('1.1.1.2.1',plain,[apply(relation_dom_restriction(541 ^ [], 539 ^ []), 540 ^ []) = apply(541 ^ [], 540 ^ [])],reduction('1')).
% 0.45/1.38  ncf('1.1.1.2.2',plain,[in(540 ^ [], relation_dom(541 ^ [])), 361 : -(in(540 ^ [], relation_dom(relation_dom_restriction(541 ^ [], 539 ^ [])))), 361 : in(540 ^ [], 539 ^ []), 361 : relation(541 ^ []), 361 : function(541 ^ [])],extension(345 ^ 16,bind([[_94583, _94585, _94587], [541 ^ [], 540 ^ [], 539 ^ []]]))).
% 0.45/1.38  ncf('1.1.1.2.2.1',plain,[in(540 ^ [], relation_dom(relation_dom_restriction(541 ^ [], 539 ^ [])))],reduction('1.1')).
% 0.45/1.38  ncf('1.1.1.2.2.2',plain,[-(in(540 ^ [], 539 ^ []))],extension(547 ^ 19)).
% 0.45/1.38  ncf('1.1.1.2.2.3',plain,[-(relation(541 ^ []))],extension(543 ^ 17)).
% 0.45/1.38  ncf('1.1.1.2.2.4',plain,[-(function(541 ^ []))],extension(545 ^ 17)).
% 0.45/1.38  ncf('1.1.1.2.3',plain,[-(relation(541 ^ []))],extension(543 ^ 14)).
% 0.45/1.38  ncf('1.1.1.2.4',plain,[-(function(541 ^ []))],extension(545 ^ 14)).
% 0.45/1.38  ncf('1.1.1.3',plain,[-(relation(relation_dom_restriction(541 ^ [], 539 ^ []))), relation(541 ^ [])],extension(262 ^ 9,bind([[_91871, _91873], [539 ^ [], 541 ^ []]]))).
% 0.45/1.38  ncf('1.1.1.3.1',plain,[-(relation(541 ^ []))],extension(543 ^ 10)).
% 0.45/1.38  ncf('1.1.1.4',plain,[-(function(relation_dom_restriction(541 ^ [], 539 ^ []))), relation(541 ^ []), function(541 ^ [])],extension(309 ^ 9,bind([[_93444, _93446], [539 ^ [], 541 ^ []]]))).
% 0.45/1.38  ncf('1.1.1.4.1',plain,[-(relation(541 ^ []))],extension(543 ^ 10)).
% 0.45/1.38  ncf('1.1.1.4.2',plain,[-(function(541 ^ []))],extension(545 ^ 10)).
% 0.45/1.38  ncf('1.1.2',plain,[-(relation_dom_restriction(541 ^ [], 539 ^ []) = relation_dom_restriction(541 ^ [], 539 ^ [])), 541 ^ [] = 541 ^ [], 539 ^ [] = 539 ^ []],extension(160 ^ 6,bind([[_88557, _88559, _88561, _88563], [539 ^ [], 539 ^ [], 541 ^ [], 541 ^ []]]))).
% 0.45/1.38  ncf('1.1.2.1',plain,[-(541 ^ [] = 541 ^ [])],extension(2 ^ 7,bind([[_83367], [541 ^ []]]))).
% 0.45/1.38  ncf('1.1.2.2',plain,[-(539 ^ [] = 539 ^ [])],extension(2 ^ 7,bind([[_83367], [539 ^ []]]))).
% 0.45/1.38  ncf('1.1.3',plain,[-(relation(541 ^ []))],extension(543 ^ 4)).
% 0.45/1.38  ncf('1.1.4',plain,[-(function(541 ^ []))],extension(545 ^ 4)).
% 0.45/1.38  ncf('1.1.5',plain,[-(relation(relation_dom_restriction(541 ^ [], 539 ^ []))), relation(541 ^ [])],extension(262 ^ 2,bind([[_91871, _91873], [539 ^ [], 541 ^ []]]))).
% 0.45/1.38  ncf('1.1.5.1',plain,[-(relation(541 ^ []))],extension(543 ^ 3)).
% 0.45/1.38  ncf('1.1.6',plain,[-(function(relation_dom_restriction(541 ^ [], 539 ^ []))), relation(541 ^ []), function(541 ^ [])],extension(309 ^ 2,bind([[_93444, _93446], [539 ^ [], 541 ^ []]]))).
% 0.45/1.38  ncf('1.1.6.1',plain,[-(relation(541 ^ []))],extension(543 ^ 3)).
% 0.45/1.38  ncf('1.1.6.2',plain,[-(function(541 ^ []))],extension(545 ^ 3)).
% 0.45/1.38  %-----------------------------------------------------
% 0.45/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------