%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n018.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 11:56:26 EDT 2023

% Result   : Theorem 0.33s 1.38s
% Output   : Proof 0.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n018.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 19:08:58 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.33/1.38  
% 0.33/1.38  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.33/1.38  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/1.38  %-----------------------------------------------------
% 0.33/1.38  ncf(matrix, plain, [(587 ^ _79855) ^ [] : [-(order(583 ^ [], 584 ^ []))], (589 ^ _79855) ^ [] : [-(least(585 ^ [], 583 ^ [], 584 ^ []))], (592 ^ _79855) ^ [] : [-(least(590 ^ [], 583 ^ [], 584 ^ []))], (594 ^ _79855) ^ [] : [585 ^ [] = 590 ^ []], (2 ^ _79855) ^ [_79979] : [-(_79979 = _79979)], (4 ^ _79855) ^ [_80086, _80088] : [_80088 = _80086, -(_80086 = _80088)], (10 ^ _79855) ^ [_80290, _80292, _80294] : [-(_80294 = _80290), _80294 = _80292, _80292 = _80290], (20 ^ _79855) ^ [_80631, _80633, _80635, _80637] : [-(total_order(_80635, _80631)), total_order(_80637, _80633), _80637 = _80635, _80633 = _80631], (34 ^ _79855) ^ [_81103, _81105, _81107, _81109, _81111, _81113] : [-(greatest(_81111, _81107, _81103)), greatest(_81113, _81109, _81105), _81113 = _81111, _81109 = _81107, _81105 = _81103], (52 ^ _79855) ^ [_81712, _81714, _81716, _81718, _81720, _81722] : [-(max(_81720, _81716, _81712)), max(_81722, _81718, _81714), _81722 = _81720, _81718 = _81716, _81714 = _81712], (70 ^ _79855) ^ [_82321, _82323, _82325, _82327, _82329, _82331] : [-(min(_82329, _82325, _82321)), min(_82331, _82327, _82323), _82331 = _82329, _82327 = _82325, _82323 = _82321], (88 ^ _79855) ^ [_82958, _82960, _82962, _82964, _82966, _82968, _82970, _82972] : [-(least_upper_bound(_82970, _82966, _82962, _82958)), least_upper_bound(_82972, _82968, _82964, _82960), _82972 = _82970, _82968 = _82966, _82964 = _82962, _82960 = _82958], (110 ^ _79855) ^ [_83720, _83722, _83724, _83726, _83728, _83730] : [-(upper_bound(_83728, _83724, _83720)), upper_bound(_83730, _83726, _83722), _83730 = _83728, _83726 = _83724, _83722 = _83720], (128 ^ _79855) ^ [_84357, _84359, _84361, _84363, _84365, _84367, _84369, _84371] : [-(greatest_lower_bound(_84369, _84365, _84361, _84357)), greatest_lower_bound(_84371, _84367, _84363, _84359), _84371 = _84369, _84367 = _84365, _84363 = _84361, _84359 = _84357], (150 ^ _79855) ^ [_85091, _85093, _85095, _85097] : [-(member(_85095, _85091)), member(_85097, _85093), _85097 = _85095, _85093 = _85091], (164 ^ _79855) ^ [_85563, _85565, _85567, _85569, _85571, _85573] : [-(lower_bound(_85571, _85567, _85563)), lower_bound(_85573, _85569, _85565), _85573 = _85571, _85569 = _85567, _85565 = _85563], (182 ^ _79855) ^ [_86172, _86174, _86176, _86178, _86180, _86182] : [-(apply(_86180, _86176, _86172)), apply(_86182, _86178, _86174), _86182 = _86180, _86178 = _86176, _86174 = _86172], (200 ^ _79855) ^ [_86753, _86755, _86757, _86759] : [-(order(_86757, _86753)), order(_86759, _86755), _86759 = _86757, _86755 = _86753], (214 ^ _79855) ^ [_87205, _87207, _87209, _87211, _87213, _87215] : [-(least(_87213, _87209, _87205)), least(_87215, _87211, _87207), _87215 = _87213, _87211 = _87209, _87207 = _87205], (282 ^ _79855) ^ [_89415, _89417] : [-(order(_89417, _89415)), 286 ^ _79855 : [(287 ^ _79855) ^ [] : [-(member(285 ^ [_89415, _89417], _89415))], (289 ^ _79855) ^ [] : [apply(_89417, 285 ^ [_89415, _89417], 285 ^ [_89415, _89417])]], 294 ^ _79855 : [(295 ^ _79855) ^ [] : [-(member(292 ^ [_89415, _89417], _89415))], (297 ^ _79855) ^ [] : [-(member(293 ^ [_89415, _89417], _89415))], (299 ^ _79855) ^ [] : [-(apply(_89417, 292 ^ [_89415, _89417], 293 ^ [_89415, _89417]))], (301 ^ _79855) ^ [] : [-(apply(_89417, 293 ^ [_89415, _89417], 292 ^ [_89415, _89417]))], (303 ^ _79855) ^ [] : [292 ^ [_89415, _89417] = 293 ^ [_89415, _89417]]], 307 ^ _79855 : [(308 ^ _79855) ^ [] : [-(member(304 ^ [_89415, _89417], _89415))], (310 ^ _79855) ^ [] : [-(member(305 ^ [_89415, _89417], _89415))], (312 ^ _79855) ^ [] : [-(member(306 ^ [_89415, _89417], _89415))], (314 ^ _79855) ^ [] : [-(apply(_89417, 304 ^ [_89415, _89417], 305 ^ [_89415, _89417]))], (316 ^ _79855) ^ [] : [-(apply(_89417, 305 ^ [_89415, _89417], 306 ^ [_89415, _89417]))], (318 ^ _79855) ^ [] : [apply(_89417, 304 ^ [_89415, _89417], 306 ^ [_89415, _89417])]]], (232 ^ _79855) ^ [_87815, _87817] : [order(_87817, _87815), 235 ^ _79855 : [(236 ^ _79855) ^ [_88069] : [member(_88069, _87815), -(apply(_87817, _88069, _88069))], (242 ^ _79855) ^ [_88291, _88293] : [member(_88293, _87815), member(_88291, _87815), -(_88293 = _88291), apply(_87817, _88293, _88291), apply(_87817, _88291, _88293)], (260 ^ _79855) ^ [_88808, _88810, _88812] : [member(_88812, _87815), member(_88810, _87815), member(_88808, _87815), -(apply(_87817, _88812, _88808)), apply(_87817, _88812, _88810), apply(_87817, _88810, _88808)]]], (342 ^ _79855) ^ [_91936, _91938] : [-(total_order(_91938, _91936)), order(_91938, _91936), 349 ^ _79855 : [(350 ^ _79855) ^ [] : [-(member(347 ^ [_91936, _91938], _91936))], (352 ^ _79855) ^ [] : [-(member(348 ^ [_91936, _91938], _91936))], (354 ^ _79855) ^ [] : [apply(_91938, 347 ^ [_91936, _91938], 348 ^ [_91936, _91938])], (356 ^ _79855) ^ [] : [apply(_91938, 348 ^ [_91936, _91938], 347 ^ [_91936, _91938])]]], (322 ^ _79855) ^ [_91308, _91310] : [total_order(_91310, _91308), 325 ^ _79855 : [(326 ^ _79855) ^ [] : [-(order(_91310, _91308))], (328 ^ _79855) ^ [_91550, _91552] : [member(_91552, _91308), member(_91550, _91308), -(apply(_91310, _91552, _91550)), -(apply(_91310, _91550, _91552))]]], (370 ^ _79855) ^ [_93047, _93049, _93051] : [372 ^ _79855 : [(373 ^ _79855) ^ [] : [-(member(371 ^ [_93047, _93049, _93051], _93049))], (375 ^ _79855) ^ [] : [apply(_93051, 371 ^ [_93047, _93049, _93051], _93047)]], -(upper_bound(_93047, _93051, _93049))], (360 ^ _79855) ^ [_92716, _92718, _92720] : [upper_bound(_92716, _92720, _92718), 363 ^ _79855 : [(364 ^ _79855) ^ [_92860] : [member(_92860, _92718), -(apply(_92720, _92860, _92716))]]], (389 ^ _79855) ^ [_93799, _93801, _93803] : [391 ^ _79855 : [(392 ^ _79855) ^ [] : [-(member(390 ^ [_93799, _93801, _93803], _93801))], (394 ^ _79855) ^ [] : [apply(_93803, _93799, 390 ^ [_93799, _93801, _93803])]], -(lower_bound(_93799, _93803, _93801))], (379 ^ _79855) ^ [_93468, _93470, _93472] : [lower_bound(_93468, _93472, _93470), 382 ^ _79855 : [(383 ^ _79855) ^ [_93612] : [member(_93612, _93470), -(apply(_93472, _93468, _93612))]]], (398 ^ _79855) ^ [_94220, _94222, _94224] : [greatest(_94220, _94224, _94222), 401 ^ _79855 : [(402 ^ _79855) ^ [] : [-(member(_94220, _94222))], (404 ^ _79855) ^ [_94438] : [member(_94438, _94222), -(apply(_94224, _94438, _94220))]]], (410 ^ _79855) ^ [_94627, _94629, _94631] : [-(greatest(_94627, _94631, _94629)), member(_94627, _94629), 416 ^ _79855 : [(417 ^ _79855) ^ [] : [-(member(415 ^ [_94627, _94629, _94631], _94629))], (419 ^ _79855) ^ [] : [apply(_94631, 415 ^ [_94627, _94629, _94631], _94627)]]], (423 ^ _79855) ^ [_95141, _95143, _95145] : [least(_95141, _95145, _95143), 426 ^ _79855 : [(427 ^ _79855) ^ [] : [-(member(_95141, _95143))], (429 ^ _79855) ^ [_95359] : [member(_95359, _95143), -(apply(_95145, _95141, _95359))]]], (435 ^ _79855) ^ [_95548, _95550, _95552] : [-(least(_95548, _95552, _95550)), member(_95548, _95550), 441 ^ _79855 : [(442 ^ _79855) ^ [] : [-(member(440 ^ [_95548, _95550, _95552], _95550))], (444 ^ _79855) ^ [] : [apply(_95552, _95548, 440 ^ [_95548, _95550, _95552])]]], (464 ^ _79855) ^ [_96572, _96574, _96576] : [-(max(_96572, _96576, _96574)), member(_96572, _96574), 470 ^ _79855 : [(471 ^ _79855) ^ [] : [-(member(469 ^ [_96572, _96574, _96576], _96574))], (473 ^ _79855) ^ [] : [-(apply(_96576, _96572, 469 ^ [_96572, _96574, _96576]))], (475 ^ _79855) ^ [] : [_96572 = 469 ^ [_96572, _96574, _96576]]]], (448 ^ _79855) ^ [_96062, _96064, _96066] : [max(_96062, _96066, _96064), 451 ^ _79855 : [(452 ^ _79855) ^ [] : [-(member(_96062, _96064))], (454 ^ _79855) ^ [_96286] : [-(_96062 = _96286), member(_96286, _96064), apply(_96066, _96062, _96286)]]], (495 ^ _79855) ^ [_97689, _97691, _97693] : [-(min(_97689, _97693, _97691)), member(_97689, _97691), 501 ^ _79855 : [(502 ^ _79855) ^ [] : [-(member(500 ^ [_97689, _97691, _97693], _97691))], (504 ^ _79855) ^ [] : [-(apply(_97693, 500 ^ [_97689, _97691, _97693], _97689))], (506 ^ _79855) ^ [] : [_97689 = 500 ^ [_97689, _97691, _97693]]]], (479 ^ _79855) ^ [_97179, _97181, _97183] : [min(_97179, _97183, _97181), 482 ^ _79855 : [(483 ^ _79855) ^ [] : [-(member(_97179, _97181))], (485 ^ _79855) ^ [_97403] : [-(_97179 = _97403), member(_97403, _97181), apply(_97183, _97403, _97179)]]], (510 ^ _79855) ^ [_98310, _98312, _98314, _98316] : [least_upper_bound(_98316, _98314, _98312, _98310), 513 ^ _79855 : [(514 ^ _79855) ^ [] : [-(member(_98316, _98314))], (516 ^ _79855) ^ [] : [-(upper_bound(_98316, _98312, _98314))], (518 ^ _79855) ^ [_98621] : [-(apply(_98312, _98316, _98621)), member(_98621, _98310), upper_bound(_98621, _98312, _98314)]]], (528 ^ _79855) ^ [_98923, _98925, _98927, _98929] : [-(least_upper_bound(_98929, _98927, _98925, _98923)), member(_98929, _98927), upper_bound(_98929, _98925, _98927), 538 ^ _79855 : [(539 ^ _79855) ^ [] : [-(member(537 ^ [_98923, _98925, _98927, _98929], _98923))], (541 ^ _79855) ^ [] : [-(upper_bound(537 ^ [_98923, _98925, _98927, _98929], _98925, _98927))], (543 ^ _79855) ^ [] : [apply(_98925, _98929, 537 ^ [_98923, _98925, _98927, _98929])]]], (547 ^ _79855) ^ [_99652, _99654, _99656, _99658] : [greatest_lower_bound(_99658, _99656, _99654, _99652), 550 ^ _79855 : [(551 ^ _79855) ^ [] : [-(member(_99658, _99656))], (553 ^ _79855) ^ [] : [-(lower_bound(_99658, _99654, _99656))], (555 ^ _79855) ^ [_99963] : [-(apply(_99654, _99963, _99658)), member(_99963, _99652), lower_bound(_99963, _99654, _99656)]]], (565 ^ _79855) ^ [_100265, _100267, _100269, _100271] : [-(greatest_lower_bound(_100271, _100269, _100267, _100265)), member(_100271, _100269), lower_bound(_100271, _100267, _100269), 575 ^ _79855 : [(576 ^ _79855) ^ [] : [-(member(574 ^ [_100265, _100267, _100269, _100271], _100265))], (578 ^ _79855) ^ [] : [-(lower_bound(574 ^ [_100265, _100267, _100269, _100271], _100267, _100269))], (580 ^ _79855) ^ [] : [apply(_100267, 574 ^ [_100265, _100267, _100269, _100271], _100271)]]]], input).
% 0.33/1.38  ncf('1',plain,[585 ^ [] = 590 ^ []],start(594 ^ 0)).
% 0.33/1.38  ncf('1.1',plain,[-(585 ^ [] = 590 ^ []), 242 : member(585 ^ [], 584 ^ []), 242 : member(590 ^ [], 584 ^ []), 242 : apply(583 ^ [], 585 ^ [], 590 ^ []), 242 : apply(583 ^ [], 590 ^ [], 585 ^ []), 242 : order(583 ^ [], 584 ^ [])],extension(232 ^ 1,bind([[_87815, _87817, _88291, _88293], [584 ^ [], 583 ^ [], 590 ^ [], 585 ^ []]]))).
% 0.33/1.38  ncf('1.1.1',plain,[-(member(585 ^ [], 584 ^ [])), member(585 ^ [], 584 ^ []), 585 ^ [] = 585 ^ [], 584 ^ [] = 584 ^ []],extension(150 ^ 4,bind([[_85091, _85093, _85095, _85097], [584 ^ [], 584 ^ [], 585 ^ [], 585 ^ []]]))).
% 0.33/1.38  ncf('1.1.1.1',plain,[-(member(585 ^ [], 584 ^ [])), least(585 ^ [], 583 ^ [], 584 ^ [])],extension(423 ^ 5,bind([[_95141, _95143, _95145], [585 ^ [], 584 ^ [], 583 ^ []]]))).
% 0.33/1.38  ncf('1.1.1.1.1',plain,[-(least(585 ^ [], 583 ^ [], 584 ^ []))],extension(589 ^ 6)).
% 0.33/1.38  ncf('1.1.1.2',plain,[-(585 ^ [] = 585 ^ [])],extension(2 ^ 5,bind([[_79979], [585 ^ []]]))).
% 0.33/1.38  ncf('1.1.1.3',plain,[-(584 ^ [] = 584 ^ [])],extension(2 ^ 5,bind([[_79979], [584 ^ []]]))).
% 0.33/1.38  ncf('1.1.2',plain,[-(member(590 ^ [], 584 ^ [])), least(590 ^ [], 583 ^ [], 584 ^ [])],extension(423 ^ 4,bind([[_95141, _95143, _95145], [590 ^ [], 584 ^ [], 583 ^ []]]))).
% 0.33/1.38  ncf('1.1.2.1',plain,[-(least(590 ^ [], 583 ^ [], 584 ^ []))],extension(592 ^ 5)).
% 0.33/1.38  ncf('1.1.3',plain,[-(apply(583 ^ [], 585 ^ [], 590 ^ [])), 429 : member(590 ^ [], 584 ^ []), 429 : least(585 ^ [], 583 ^ [], 584 ^ [])],extension(423 ^ 4,bind([[_95141, _95143, _95145, _95359], [585 ^ [], 584 ^ [], 583 ^ [], 590 ^ []]]))).
% 0.33/1.38  ncf('1.1.3.1',plain,[-(member(590 ^ [], 584 ^ [])), least(590 ^ [], 583 ^ [], 584 ^ [])],extension(423 ^ 7,bind([[_95141, _95143, _95145], [590 ^ [], 584 ^ [], 583 ^ []]]))).
% 0.33/1.38  ncf('1.1.3.1.1',plain,[-(least(590 ^ [], 583 ^ [], 584 ^ []))],extension(592 ^ 8)).
% 0.33/1.38  ncf('1.1.3.2',plain,[-(least(585 ^ [], 583 ^ [], 584 ^ []))],extension(589 ^ 5)).
% 0.33/1.38  ncf('1.1.4',plain,[-(apply(583 ^ [], 590 ^ [], 585 ^ [])), 429 : member(585 ^ [], 584 ^ []), 429 : least(590 ^ [], 583 ^ [], 584 ^ [])],extension(423 ^ 4,bind([[_95141, _95143, _95145, _95359], [590 ^ [], 584 ^ [], 583 ^ [], 585 ^ []]]))).
% 0.33/1.38  ncf('1.1.4.1',plain,[-(member(585 ^ [], 584 ^ [])), least(585 ^ [], 583 ^ [], 584 ^ [])],extension(423 ^ 7,bind([[_95141, _95143, _95145], [585 ^ [], 584 ^ [], 583 ^ []]]))).
% 0.33/1.38  ncf('1.1.4.1.1',plain,[-(least(585 ^ [], 583 ^ [], 584 ^ []))],extension(589 ^ 8)).
% 0.33/1.38  ncf('1.1.4.2',plain,[-(least(590 ^ [], 583 ^ [], 584 ^ []))],extension(592 ^ 5)).
% 0.33/1.38  ncf('1.1.5',plain,[-(order(583 ^ [], 584 ^ []))],extension(587 ^ 2)).
% 0.33/1.38  %-----------------------------------------------------
% 0.33/1.38  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------