%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.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 11:44:32 EDT 2023

% Result   : Theorem 0.32s 1.36s
% Output   : Proof 0.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.11  % Command  : nanocop.sh %s %d
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May 18 17:36:35 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.32/1.36  
% 0.32/1.36  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.32/1.36  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/1.36  %-----------------------------------------------------
% 0.32/1.36  ncf(matrix, plain, [(624 ^ _83769) ^ [] : [-(transfinite_sequence_of(622 ^ [], 621 ^ []))], (627 ^ _83769) ^ [] : [-(ordinal(625 ^ []))], (629 ^ _83769) ^ [] : [transfinite_sequence_of(tseq_dom_restriction(622 ^ [], 625 ^ []), 621 ^ [])], (186 ^ _83769) ^ [_89572, _89574] : [_89574 = _89572, -(relation_rng(_89574) = relation_rng(_89572))], (192 ^ _83769) ^ [_89818, _89820, _89822, _89824] : [-(relation_dom_restriction(_89824, _89820) = relation_dom_restriction(_89822, _89818)), _89824 = _89822, _89820 = _89818], (202 ^ _83769) ^ [_90149, _90151] : [_90151 = _90149, -(powerset(_90151) = powerset(_90149))], (208 ^ _83769) ^ [_90375, _90377, _90379, _90381] : [-(tseq_dom_restriction(_90381, _90377) = tseq_dom_restriction(_90379, _90375)), _90381 = _90379, _90377 = _90375], (2 ^ _83769) ^ [_83913] : [-(_83913 = _83913)], (4 ^ _83769) ^ [_84020, _84022] : [_84022 = _84020, -(_84020 = _84022)], (10 ^ _83769) ^ [_84224, _84226, _84228] : [-(_84228 = _84224), _84228 = _84226, _84226 = _84224], (20 ^ _83769) ^ [_84537, _84539] : [-(with_non_empty_elements(_84537)), _84539 = _84537, with_non_empty_elements(_84539)], (30 ^ _83769) ^ [_84832, _84834] : [-(one_to_one(_84832)), _84834 = _84832, one_to_one(_84834)], (40 ^ _83769) ^ [_85127, _85129] : [-(epsilon_transitive(_85127)), _85129 = _85127, epsilon_transitive(_85129)], (50 ^ _83769) ^ [_85422, _85424] : [-(epsilon_connected(_85422)), _85424 = _85422, epsilon_connected(_85424)], (60 ^ _83769) ^ [_85717, _85719] : [-(relation_empty_yielding(_85717)), _85719 = _85717, relation_empty_yielding(_85719)], (70 ^ _83769) ^ [_86012, _86014] : [-(relation_non_empty(_86012)), _86014 = _86012, relation_non_empty(_86014)], (80 ^ _83769) ^ [_86307, _86309] : [-(relation(_86307)), _86309 = _86307, relation(_86309)], (90 ^ _83769) ^ [_86602, _86604] : [-(function(_86602)), _86604 = _86602, function(_86604)], (100 ^ _83769) ^ [_86897, _86899] : [-(transfinite_sequence(_86897)), _86899 = _86897, transfinite_sequence(_86899)], (110 ^ _83769) ^ [_87220, _87222, _87224, _87226] : [-(subset(_87224, _87220)), subset(_87226, _87222), _87226 = _87224, _87222 = _87220], (124 ^ _83769) ^ [_87664, _87666, _87668, _87670] : [-(element(_87668, _87664)), element(_87670, _87666), _87670 = _87668, _87666 = _87664], (138 ^ _83769) ^ [_88108, _88110, _88112, _88114] : [-(in(_88112, _88108)), in(_88114, _88110), _88114 = _88112, _88110 = _88108], (152 ^ _83769) ^ [_88524, _88526] : [-(empty(_88524)), _88526 = _88524, empty(_88526)], (162 ^ _83769) ^ [_88819, _88821] : [-(ordinal(_88819)), _88821 = _88819, ordinal(_88821)], (172 ^ _83769) ^ [_89122, _89124, _89126, _89128] : [-(transfinite_sequence_of(_89126, _89122)), transfinite_sequence_of(_89128, _89124), _89128 = _89126, _89124 = _89122], (218 ^ _83769) ^ [_90752, _90754] : [in(_90754, _90752), in(_90752, _90754)], (224 ^ _83769) ^ [_90949] : [empty(_90949), -(function(_90949))], (230 ^ _83769) ^ [_91135] : [ordinal(_91135), 233 ^ _83769 : [(234 ^ _83769) ^ [] : [-(epsilon_transitive(_91135))], (236 ^ _83769) ^ [] : [-(epsilon_connected(_91135))]]], (238 ^ _83769) ^ [_91392] : [empty(_91392), -(relation(_91392))], (244 ^ _83769) ^ [_91578] : [255 ^ _83769 : [(256 ^ _83769) ^ [] : [-(relation(_91578))], (258 ^ _83769) ^ [] : [-(function(_91578))], (260 ^ _83769) ^ [] : [-(one_to_one(_91578))]], relation(_91578), empty(_91578), function(_91578)], (262 ^ _83769) ^ [_92071] : [-(ordinal(_92071)), epsilon_transitive(_92071), epsilon_connected(_92071)], (272 ^ _83769) ^ [_92340] : [empty(_92340), 275 ^ _83769 : [(276 ^ _83769) ^ [] : [-(epsilon_transitive(_92340))], (278 ^ _83769) ^ [] : [-(epsilon_connected(_92340))], (280 ^ _83769) ^ [] : [-(ordinal(_92340))]]], (282 ^ _83769) ^ [_92681, _92683] : [relation(_92681), function(_92681), transfinite_sequence(_92681), 293 ^ _83769 : [(294 ^ _83769) ^ [] : [transfinite_sequence_of(_92681, _92683), -(subset(relation_rng(_92681), _92683))], (300 ^ _83769) ^ [] : [subset(relation_rng(_92681), _92683), -(transfinite_sequence_of(_92681, _92683))]]], (306 ^ _83769) ^ [_93323, _93325] : [-(transfinite_sequence_of(tseq_dom_restriction(_93325, _93323), relation_rng(_93325))), relation(_93325), function(_93325), transfinite_sequence(_93325), ordinal(_93323)], (324 ^ _83769) ^ [_93802, _93804] : [relation(_93804), -(relation(relation_dom_restriction(_93804, _93802)))], (330 ^ _83769) ^ [_94014, _94016] : [transfinite_sequence_of(_94014, _94016), 333 ^ _83769 : [(334 ^ _83769) ^ [] : [-(relation(_94014))], (336 ^ _83769) ^ [] : [-(function(_94014))], (338 ^ _83769) ^ [] : [-(transfinite_sequence(_94014))]]], (341 ^ _83769) ^ [_94377] : [-(transfinite_sequence_of(339 ^ [_94377], _94377))], (344 ^ _83769) ^ [_94499] : [-(element(342 ^ [_94499], _94499))], (346 ^ _83769) ^ [] : [-(empty(empty_set))], (348 ^ _83769) ^ [] : [-(relation(empty_set))], (350 ^ _83769) ^ [] : [-(relation_empty_yielding(empty_set))], (352 ^ _83769) ^ [_94774, _94776] : [359 ^ _83769 : [(360 ^ _83769) ^ [] : [-(relation(relation_dom_restriction(_94776, _94774)))], (362 ^ _83769) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_94776, _94774)))]], relation(_94776), relation_empty_yielding(_94776)], (364 ^ _83769) ^ [] : [-(empty(empty_set))], (366 ^ _83769) ^ [] : [-(relation(empty_set))], (368 ^ _83769) ^ [] : [-(relation_empty_yielding(empty_set))], (370 ^ _83769) ^ [] : [-(function(empty_set))], (372 ^ _83769) ^ [] : [-(one_to_one(empty_set))], (374 ^ _83769) ^ [] : [-(empty(empty_set))], (376 ^ _83769) ^ [] : [-(epsilon_transitive(empty_set))], (378 ^ _83769) ^ [] : [-(epsilon_connected(empty_set))], (380 ^ _83769) ^ [] : [-(ordinal(empty_set))], (382 ^ _83769) ^ [_95643, _95645] : [389 ^ _83769 : [(390 ^ _83769) ^ [] : [-(relation(relation_dom_restriction(_95645, _95643)))], (392 ^ _83769) ^ [] : [-(function(relation_dom_restriction(_95645, _95643)))]], relation(_95645), function(_95645)], (394 ^ _83769) ^ [] : [-(empty(empty_set))], (396 ^ _83769) ^ [] : [-(relation(empty_set))], (398 ^ _83769) ^ [_96115] : [-(with_non_empty_elements(relation_rng(_96115))), relation(_96115), relation_non_empty(_96115), function(_96115)], (412 ^ _83769) ^ [_96471] : [empty(relation_rng(_96471)), -(empty(_96471)), relation(_96471)], (422 ^ _83769) ^ [_96748] : [empty(_96748), 425 ^ _83769 : [(426 ^ _83769) ^ [] : [-(empty(relation_rng(_96748)))], (428 ^ _83769) ^ [] : [-(relation(relation_rng(_96748)))]]], (431 ^ _83769) ^ [] : [-(relation(429 ^ []))], (433 ^ _83769) ^ [] : [-(function(429 ^ []))], (436 ^ _83769) ^ [] : [-(epsilon_transitive(434 ^ []))], (438 ^ _83769) ^ [] : [-(epsilon_connected(434 ^ []))], (440 ^ _83769) ^ [] : [-(ordinal(434 ^ []))], (443 ^ _83769) ^ [] : [-(empty(441 ^ []))], (445 ^ _83769) ^ [] : [-(relation(441 ^ []))], (448 ^ _83769) ^ [] : [-(empty(446 ^ []))], (451 ^ _83769) ^ [] : [-(relation(449 ^ []))], (453 ^ _83769) ^ [] : [-(empty(449 ^ []))], (455 ^ _83769) ^ [] : [-(function(449 ^ []))], (458 ^ _83769) ^ [] : [-(relation(456 ^ []))], (460 ^ _83769) ^ [] : [-(function(456 ^ []))], (462 ^ _83769) ^ [] : [-(one_to_one(456 ^ []))], (464 ^ _83769) ^ [] : [-(empty(456 ^ []))], (466 ^ _83769) ^ [] : [-(epsilon_transitive(456 ^ []))], (468 ^ _83769) ^ [] : [-(epsilon_connected(456 ^ []))], (470 ^ _83769) ^ [] : [-(ordinal(456 ^ []))], (473 ^ _83769) ^ [] : [empty(471 ^ [])], (475 ^ _83769) ^ [] : [-(relation(471 ^ []))], (478 ^ _83769) ^ [] : [empty(476 ^ [])], (481 ^ _83769) ^ [] : [-(relation(479 ^ []))], (483 ^ _83769) ^ [] : [-(function(479 ^ []))], (485 ^ _83769) ^ [] : [-(one_to_one(479 ^ []))], (488 ^ _83769) ^ [] : [empty(486 ^ [])], (490 ^ _83769) ^ [] : [-(epsilon_transitive(486 ^ []))], (492 ^ _83769) ^ [] : [-(epsilon_connected(486 ^ []))], (494 ^ _83769) ^ [] : [-(ordinal(486 ^ []))], (497 ^ _83769) ^ [] : [-(relation(495 ^ []))], (499 ^ _83769) ^ [] : [-(relation_empty_yielding(495 ^ []))], (502 ^ _83769) ^ [] : [-(relation(500 ^ []))], (504 ^ _83769) ^ [] : [-(relation_empty_yielding(500 ^ []))], (506 ^ _83769) ^ [] : [-(function(500 ^ []))], (509 ^ _83769) ^ [] : [-(relation(507 ^ []))], (511 ^ _83769) ^ [] : [-(function(507 ^ []))], (513 ^ _83769) ^ [] : [-(transfinite_sequence(507 ^ []))], (516 ^ _83769) ^ [] : [-(relation(514 ^ []))], (518 ^ _83769) ^ [] : [-(relation_non_empty(514 ^ []))], (520 ^ _83769) ^ [] : [-(function(514 ^ []))], (522 ^ _83769) ^ [_99776, _99778] : [-(tseq_dom_restriction(_99778, _99776) = relation_dom_restriction(_99778, _99776)), relation(_99778), function(_99778), transfinite_sequence(_99778), ordinal(_99776)], (540 ^ _83769) ^ [_100242, _100244] : [-(subset(_100244, _100244))], (542 ^ _83769) ^ [_100351, _100353] : [in(_100353, _100351), -(element(_100353, _100351))], (548 ^ _83769) ^ [_100561, _100563] : [element(_100563, _100561), -(empty(_100561)), -(in(_100563, _100561))], (558 ^ _83769) ^ [_100888, _100890] : [element(_100890, powerset(_100888)), -(subset(_100890, _100888))], (564 ^ _83769) ^ [_101054, _101056] : [subset(_101056, _101054), -(element(_101056, powerset(_101054)))], (570 ^ _83769) ^ [_101270, _101272] : [subset(_101272, _101270), 573 ^ _83769 : [(574 ^ _83769) ^ [_101407] : [transfinite_sequence_of(_101407, _101272), -(transfinite_sequence_of(_101407, _101270))]]], (580 ^ _83769) ^ [_101646, _101648, _101650] : [-(element(_101650, _101646)), in(_101650, _101648), element(_101648, powerset(_101646))], (590 ^ _83769) ^ [_101973, _101975, _101977] : [in(_101977, _101975), element(_101975, powerset(_101973)), empty(_101973)], (600 ^ _83769) ^ [_102269] : [empty(_102269), -(_102269 = empty_set)], (606 ^ _83769) ^ [_102471, _102473] : [in(_102473, _102471), empty(_102471)], (612 ^ _83769) ^ [_102658, _102660] : [empty(_102660), -(_102660 = _102658), empty(_102658)]], input).
% 0.32/1.36  ncf('1',plain,[transfinite_sequence_of(tseq_dom_restriction(622 ^ [], 625 ^ []), 621 ^ [])],start(629 ^ 0)).
% 0.32/1.36  ncf('1.1',plain,[-(transfinite_sequence_of(tseq_dom_restriction(622 ^ [], 625 ^ []), 621 ^ [])), 574 : transfinite_sequence_of(tseq_dom_restriction(622 ^ [], 625 ^ []), relation_rng(622 ^ [])), 574 : subset(relation_rng(622 ^ []), 621 ^ [])],extension(570 ^ 1,bind([[_101270, _101272, _101407], [621 ^ [], relation_rng(622 ^ []), tseq_dom_restriction(622 ^ [], 625 ^ [])]]))).
% 0.32/1.36  ncf('1.1.1',plain,[-(transfinite_sequence_of(tseq_dom_restriction(622 ^ [], 625 ^ []), relation_rng(622 ^ []))), relation(622 ^ []), function(622 ^ []), transfinite_sequence(622 ^ []), ordinal(625 ^ [])],extension(306 ^ 4,bind([[_93323, _93325], [625 ^ [], 622 ^ []]]))).
% 0.32/1.36  ncf('1.1.1.1',plain,[-(relation(622 ^ [])), transfinite_sequence_of(622 ^ [], 621 ^ [])],extension(330 ^ 5,bind([[_94014, _94016], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.1.1.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 6)).
% 0.32/1.36  ncf('1.1.1.2',plain,[-(function(622 ^ [])), transfinite_sequence_of(622 ^ [], 621 ^ [])],extension(330 ^ 5,bind([[_94014, _94016], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.1.2.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 6)).
% 0.32/1.36  ncf('1.1.1.3',plain,[-(transfinite_sequence(622 ^ [])), transfinite_sequence_of(622 ^ [], 621 ^ [])],extension(330 ^ 5,bind([[_94014, _94016], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.1.3.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 6)).
% 0.32/1.36  ncf('1.1.1.4',plain,[-(ordinal(625 ^ []))],extension(627 ^ 5)).
% 0.32/1.36  ncf('1.1.2',plain,[-(subset(relation_rng(622 ^ []), 621 ^ [])), 294 : transfinite_sequence_of(622 ^ [], 621 ^ []), 294 : relation(622 ^ []), 294 : function(622 ^ []), 294 : transfinite_sequence(622 ^ [])],extension(282 ^ 2,bind([[_92681, _92683], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.2.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 5)).
% 0.32/1.36  ncf('1.1.2.2',plain,[-(relation(622 ^ [])), transfinite_sequence_of(622 ^ [], 621 ^ [])],extension(330 ^ 3,bind([[_94014, _94016], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.2.2.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 4)).
% 0.32/1.36  ncf('1.1.2.3',plain,[-(function(622 ^ [])), transfinite_sequence_of(622 ^ [], 621 ^ [])],extension(330 ^ 3,bind([[_94014, _94016], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.2.3.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 4)).
% 0.32/1.36  ncf('1.1.2.4',plain,[-(transfinite_sequence(622 ^ [])), transfinite_sequence_of(622 ^ [], 621 ^ [])],extension(330 ^ 3,bind([[_94014, _94016], [622 ^ [], 621 ^ []]]))).
% 0.32/1.36  ncf('1.1.2.4.1',plain,[-(transfinite_sequence_of(622 ^ [], 621 ^ []))],extension(624 ^ 4)).
% 0.32/1.36  %-----------------------------------------------------
% 0.32/1.36  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------