%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n012.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 12:03:01 EDT 2023

% Result   : Theorem 98.85s 95.62s
% Output   : Proof 98.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n012.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 13:19:46 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 98.85/95.62  
% 98.85/95.62  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 98.85/95.62  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.85/95.62  %-----------------------------------------------------
% 98.85/95.62  ncf(matrix, plain, [(671 ^ _133422) ^ [] : [-(relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ []))], (678 ^ _133422) ^ [] : [-(in(664 ^ [], 662 ^ []))], (667 ^ _133422) ^ [] : [-(function(665 ^ []))], (680 ^ _133422) ^ [] : [663 ^ [] = empty_set], (674 ^ _133422) ^ [] : [-(relation(672 ^ []))], (676 ^ _133422) ^ [] : [-(function(672 ^ []))], (682 ^ _133422) ^ [] : [apply(relation_composition(665 ^ [], 672 ^ []), 664 ^ []) = apply(672 ^ [], apply(665 ^ [], 664 ^ []))], (669 ^ _133422) ^ [] : [-(quasi_total(665 ^ [], 662 ^ [], 663 ^ []))], !, (563 ^ _111686) ^ [_129592, _129594, _129596] : [relation_of2(_129592, _129596, _129594), -(relation_of2_as_subset(_129592, _129596, _129594))], (58 ^ _111686) ^ [_113661, _113663, _113665, _113667] : [-(subset(_113665, _113661)), subset(_113667, _113663), _113667 = _113665, _113663 = _113661], (631 ^ _111686) ^ [_131853, _131855, _131857] : [in(_131857, _131855), element(_131855, powerset(_131853)), empty(_131853)], (547 ^ _111686) ^ [] : [-(relation_empty_yielding(543 ^ []))], (336 ^ _111686) ^ [_122264, _122266, _122268] : [relation_of2(_122264, _122268, _122266), -(element(relation_dom_as_subset(_122268, _122266, _122264), powerset(_122268)))], (571 ^ _111686) ^ [_129908, _129910] : [in(_129910, _129908), -(element(_129910, _129908))], (397 ^ _111686) ^ [_124224, _124226] : [412 ^ _111686 : [(415 ^ _111686) ^ [] : [-(function(relation_composition(_124226, _124224)))], (413 ^ _111686) ^ [] : [-(relation(relation_composition(_124226, _124224)))]], relation(_124226), function(_124226), relation(_124224), function(_124224)], (484 ^ _111686) ^ [] : [-(one_to_one(478 ^ []))], (374 ^ _111686) ^ [_123427] : [-(element(372 ^ [_123427], _123427))], (533 ^ _111686) ^ [] : [-(relation(531 ^ []))], (542 ^ _111686) ^ [] : [-(relation_empty_yielding(538 ^ []))], (425 ^ _111686) ^ [_125015, _125017] : [empty(cartesian_product2(_125017, _125015)), -(empty(_125017)), -(empty(_125015))], (549 ^ _111686) ^ [] : [-(function(543 ^ []))], (352 ^ _111686) ^ [] : [true___, -(true___)], (609 ^ _111686) ^ [_131130, _131132] : [element(_131132, powerset(_131130)), -(subset(_131132, _131130))], (212 ^ _111686) ^ [_118752, _118754, _118756, _118758] : [-(apply(_118758, _118754) = apply(_118756, _118752)), _118758 = _118756, _118754 = _118752], (4 ^ _111686) ^ [_111917, _111919] : [_111919 = _111917, -(_111917 = _111919)], (445 ^ _111686) ^ [_125584] : [empty(_125584), 448 ^ _111686 : [(451 ^ _111686) ^ [] : [-(relation(relation_dom(_125584)))], (449 ^ _111686) ^ [] : [-(empty(relation_dom(_125584)))]]], (176 ^ _111686) ^ [_117489, _117491, _117493, _117495, _117497, _117499] : [-(relation_dom_as_subset(_117499, _117495, _117491) = relation_dom_as_subset(_117497, _117493, _117489)), _117499 = _117497, _117495 = _117493, _117491 = _117489], (72 ^ _111686) ^ [_114105, _114107, _114109, _114111] : [-(element(_114109, _114105)), element(_114111, _114107), _114111 = _114109, _114107 = _114105], (537 ^ _111686) ^ [] : [-(one_to_one(531 ^ []))], (228 ^ _111686) ^ [_119334] : [empty(_119334), -(function(_119334))], (475 ^ _111686) ^ [_126600, _126602] : [-(function(469 ^ [_126600, _126602]))], (377 ^ _111686) ^ [_123566, _123568] : [-(relation_of2_as_subset(375 ^ [_123566, _123568], _123568, _123566))], (190 ^ _111686) ^ [_117949, _117951] : [_117951 = _117949, -(relation_dom(_117951) = relation_dom(_117949))], (330 ^ _111686) ^ [] : [true___, -(true___)], (569 ^ _111686) ^ [_129799, _129801] : [-(subset(_129801, _129801))], (545 ^ _111686) ^ [] : [-(relation(543 ^ []))], (393 ^ _111686) ^ [] : [-(relation(empty_set))], (621 ^ _111686) ^ [_131526, _131528, _131530] : [-(element(_131530, _131526)), in(_131530, _131528), element(_131528, powerset(_131526))], (525 ^ _111686) ^ [_128312] : [-(element(523 ^ [_128312], powerset(_128312)))], (599 ^ _111686) ^ [_130803, _130805] : [element(_130805, _130803), -(empty(_130803)), -(in(_130805, _130803))], (557 ^ _111686) ^ [_129420, _129422, _129424] : [relation_of2_as_subset(_129420, _129424, _129422), -(relation_of2(_129420, _129424, _129422))], (489 ^ _111686) ^ [] : [-(empty(487 ^ []))], (395 ^ _111686) ^ [] : [-(relation_empty_yielding(empty_set))], (342 ^ _111686) ^ [_122494, _122496] : [-(relation(relation_composition(_122496, _122494))), relation(_122496), relation(_122494)], (473 ^ _111686) ^ [_126528, _126530] : [-(relation(469 ^ [_126528, _126530]))], (522 ^ _111686) ^ [] : [-(relation(518 ^ []))], (30 ^ _111686) ^ [_112729, _112731] : [-(relation_empty_yielding(_112729)), _112731 = _112729, relation_empty_yielding(_112731)], (530 ^ _111686) ^ [] : [empty(528 ^ [])], (577 ^ _111686) ^ [_130118, _130120] : [relation(_130118), function(_130118), 584 ^ _111686 : [(585 ^ _111686) ^ [_130364] : [relation(_130364), function(_130364), in(_130120, relation_dom(_130118)), -(apply(relation_composition(_130118, _130364), _130120) = apply(_130364, apply(_130118, _130120)))]]], (520 ^ _111686) ^ [] : [empty(518 ^ [])], (318 ^ _111686) ^ [] : [true___, -(true___)], (358 ^ _111686) ^ [] : [true___, -(true___)], (453 ^ _111686) ^ [_125863, _125865] : [460 ^ _111686 : [(463 ^ _111686) ^ [] : [-(relation(relation_composition(_125865, _125863)))], (461 ^ _111686) ^ [] : [-(empty(relation_composition(_125865, _125863)))]], empty(_125865), relation(_125863)], (480 ^ _111686) ^ [] : [-(relation(478 ^ []))], (222 ^ _111686) ^ [_119137, _119139] : [in(_119139, _119137), in(_119137, _119139)], (477 ^ _111686) ^ [_126652, _126654] : [-(quasi_total(469 ^ [_126652, _126654], _126654, _126652))], (647 ^ _111686) ^ [_132351, _132353] : [in(_132353, _132351), empty(_132351)], (10 ^ _111686) ^ [_112121, _112123, _112125] : [-(_112125 = _112121), _112125 = _112123, _112123 = _112121], (132 ^ _111686) ^ [_116034, _116036] : [-(relation(_116034)), _116036 = _116034, relation(_116036)], (551 ^ _111686) ^ [_129147, _129149, _129151] : [relation_of2(_129147, _129151, _129149), -(relation_dom_as_subset(_129151, _129149, _129147) = relation_dom(_129147))], (466 ^ _111686) ^ [] : [-(relation(464 ^ []))], (508 ^ _111686) ^ [] : [-(empty(504 ^ []))], (506 ^ _111686) ^ [] : [-(relation(504 ^ []))], (114 ^ _111686) ^ [_115481, _115483, _115485, _115487, _115489, _115491] : [-(relation_of2_as_subset(_115489, _115485, _115481)), relation_of2_as_subset(_115491, _115487, _115483), _115491 = _115489, _115487 = _115485, _115483 = _115481], (615 ^ _111686) ^ [_131296, _131298] : [subset(_131298, _131296), -(element(_131298, powerset(_131296)))], (96 ^ _111686) ^ [_114872, _114874, _114876, _114878, _114880, _114882] : [-(quasi_total(_114880, _114876, _114872)), quasi_total(_114882, _114878, _114874), _114882 = _114880, _114878 = _114876, _114874 = _114872], (86 ^ _111686) ^ [_114521, _114523] : [-(empty(_114521)), _114523 = _114521, empty(_114523)], (371 ^ _111686) ^ [_123300, _123302] : [-(relation_of2(369 ^ [_123300, _123302], _123302, _123300))], (540 ^ _111686) ^ [] : [-(relation(538 ^ []))], (240 ^ _111686) ^ [_119734, _119736, _119738] : [element(_119734, powerset(cartesian_product2(_119738, _119736))), -(relation(_119734))], (471 ^ _111686) ^ [_126454, _126456] : [-(relation_of2(469 ^ [_126454, _126456], _126456, _126454))], (20 ^ _111686) ^ [_112434, _112436] : [-(one_to_one(_112434)), _112436 = _112434, one_to_one(_112436)], (264 ^ _111686) ^ [_120465, _120467, _120469] : [relation_of2_as_subset(_120465, _120469, _120467), 267 ^ _111686 : [(286 ^ _111686) ^ [] : [_120467 = empty_set, -(_120469 = empty_set), 293 ^ _111686 : [(300 ^ _111686) ^ [] : [_120465 = empty_set, -(quasi_total(_120465, _120469, _120467))], (294 ^ _111686) ^ [] : [quasi_total(_120465, _120469, _120467), -(_120465 = empty_set)]]], (268 ^ _111686) ^ [] : [269 ^ _111686 : [(272 ^ _111686) ^ [] : [_120469 = empty_set], (270 ^ _111686) ^ [] : [-(_120467 = empty_set)]], 273 ^ _111686 : [(280 ^ _111686) ^ [] : [_120469 = relation_dom_as_subset(_120469, _120467, _120465), -(quasi_total(_120465, _120469, _120467))], (274 ^ _111686) ^ [] : [quasi_total(_120465, _120469, _120467), -(_120469 = relation_dom_as_subset(_120469, _120467, _120465))]]]]], (423 ^ _111686) ^ [] : [-(relation(empty_set))], (491 ^ _111686) ^ [] : [-(relation(487 ^ []))], (513 ^ _111686) ^ [_127880, _127882] : [-(relation_of2(511 ^ [_127880, _127882], _127882, _127880))], (417 ^ _111686) ^ [_124746] : [empty(powerset(_124746))], (535 ^ _111686) ^ [] : [-(function(531 ^ []))], (435 ^ _111686) ^ [_125307] : [empty(relation_dom(_125307)), -(empty(_125307)), relation(_125307)], (482 ^ _111686) ^ [] : [-(function(478 ^ []))], (421 ^ _111686) ^ [] : [-(empty(empty_set))], (324 ^ _111686) ^ [] : [true___, -(true___)], (196 ^ _111686) ^ [_118167, _118169] : [_118169 = _118167, -(powerset(_118169) = powerset(_118167))], (515 ^ _111686) ^ [_127954, _127956] : [-(relation(511 ^ [_127954, _127956]))], (503 ^ _111686) ^ [] : [-(empty(501 ^ []))], (234 ^ _111686) ^ [_119520] : [empty(_119520), -(relation(_119520))], (166 ^ _111686) ^ [_117102, _117104, _117106, _117108] : [-(cartesian_product2(_117108, _117104) = cartesian_product2(_117106, _117102)), _117108 = _117106, _117104 = _117102], (202 ^ _111686) ^ [_118413, _118415, _118417, _118419] : [-(relation_composition(_118419, _118415) = relation_composition(_118417, _118413)), _118419 = _118417, _118415 = _118413], (419 ^ _111686) ^ [] : [-(empty(empty_set))], (517 ^ _111686) ^ [_128006, _128008] : [-(function(511 ^ [_128006, _128008]))], (364 ^ _111686) ^ [_123045, _123047, _123049] : [relation_of2_as_subset(_123045, _123049, _123047), -(element(_123045, powerset(cartesian_product2(_123049, _123047))))], (306 ^ _111686) ^ [] : [true___, -(true___)], (40 ^ _111686) ^ [_113080, _113082, _113084, _113086, _113088, _113090] : [-(relation_of2(_113088, _113084, _113080)), relation_of2(_113090, _113086, _113082), _113090 = _113088, _113086 = _113084, _113082 = _113080], (493 ^ _111686) ^ [_127179] : [-(empty(_127179)), 497 ^ _111686 : [(500 ^ _111686) ^ [] : [empty(496 ^ [_127179])], (498 ^ _111686) ^ [] : [-(element(496 ^ [_127179], powerset(_127179)))]]], (142 ^ _111686) ^ [_116329, _116331] : [-(function(_116329)), _116331 = _116329, function(_116331)], (2 ^ _111686) ^ [_111810] : [-(_111810 = _111810)], (312 ^ _111686) ^ [] : [true___, -(true___)], (653 ^ _111686) ^ [_132538, _132540] : [empty(_132540), -(_132540 = _132538), empty(_132538)], (641 ^ _111686) ^ [_132149] : [empty(_132149), -(_132149 = empty_set)], (510 ^ _111686) ^ [] : [-(function(504 ^ []))], (391 ^ _111686) ^ [] : [-(empty(empty_set))], (379 ^ _111686) ^ [_123683, _123685] : [386 ^ _111686 : [(389 ^ _111686) ^ [] : [-(relation(relation_composition(_123683, _123685)))], (387 ^ _111686) ^ [] : [-(empty(relation_composition(_123683, _123685)))]], empty(_123685), relation(_123683)], (152 ^ _111686) ^ [_116632, _116634, _116636, _116638] : [-(in(_116636, _116632)), in(_116638, _116634), _116638 = _116636, _116634 = _116632], (468 ^ _111686) ^ [] : [-(function(464 ^ []))], (486 ^ _111686) ^ [] : [-(empty(478 ^ []))], (527 ^ _111686) ^ [_128363] : [-(empty(523 ^ [_128363]))], (246 ^ _111686) ^ [_119944] : [257 ^ _111686 : [(262 ^ _111686) ^ [] : [-(one_to_one(_119944))], (260 ^ _111686) ^ [] : [-(function(_119944))], (258 ^ _111686) ^ [] : [-(relation(_119944))]], relation(_119944), empty(_119944), function(_119944)]], input).
% 98.85/95.62  ncf('1',plain,[-(relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ []))],start(671 ^ 0)).
% 98.85/95.62  ncf('1.1',plain,[relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ []), -(relation_of2(665 ^ [], 662 ^ [], 663 ^ []))],extension(557 ^ 1,bind([[_129420, _129422, _129424], [665 ^ [], 663 ^ [], 662 ^ []]]))).
% 98.85/95.62  ncf('1.1.1',plain,[relation_of2(665 ^ [], 662 ^ [], 663 ^ []), -(relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []) = relation_dom(665 ^ []))],extension(551 ^ 2,bind([[_129147, _129149, _129151], [665 ^ [], 663 ^ [], 662 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1',plain,[relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []) = relation_dom(665 ^ []), -(in(664 ^ [], relation_dom(665 ^ []))), in(664 ^ [], relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ [])), 664 ^ [] = 664 ^ []],extension(152 ^ 3,bind([[_116632, _116634, _116636, _116638], [relation_dom(665 ^ []), relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []), 664 ^ [], 664 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.1',plain,[in(664 ^ [], relation_dom(665 ^ [])), 585 : relation(672 ^ []), 585 : function(672 ^ []), 585 : -(apply(relation_composition(665 ^ [], 672 ^ []), 664 ^ []) = apply(672 ^ [], apply(665 ^ [], 664 ^ []))), 585 : relation(665 ^ []), 585 : function(665 ^ [])],extension(577 ^ 4,bind([[_130118, _130120, _130364], [665 ^ [], 664 ^ [], 672 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.1.1',plain,[-(relation(672 ^ []))],extension(674 ^ 7)).
% 98.85/95.62  ncf('1.1.1.1.1.2',plain,[-(function(672 ^ []))],extension(676 ^ 7)).
% 98.85/95.62  ncf('1.1.1.1.1.3',plain,[apply(relation_composition(665 ^ [], 672 ^ []), 664 ^ []) = apply(672 ^ [], apply(665 ^ [], 664 ^ []))],extension(682 ^ 7)).
% 98.85/95.62  ncf('1.1.1.1.1.4',plain,[-(relation(665 ^ [])), element(665 ^ [], powerset(cartesian_product2(662 ^ [], 663 ^ [])))],extension(240 ^ 5,bind([[_119734, _119736, _119738], [665 ^ [], 663 ^ [], 662 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.1.4.1',plain,[-(element(665 ^ [], powerset(cartesian_product2(662 ^ [], 663 ^ [])))), relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ [])],extension(364 ^ 6,bind([[_123045, _123047, _123049], [665 ^ [], 663 ^ [], 662 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.1.4.1.1',plain,[-(relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ []))],reduction('1')).
% 98.85/95.62  ncf('1.1.1.1.1.5',plain,[-(function(665 ^ []))],extension(667 ^ 5)).
% 98.85/95.62  ncf('1.1.1.1.2',plain,[-(in(664 ^ [], relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []))), in(664 ^ [], 662 ^ []), 664 ^ [] = 664 ^ [], 662 ^ [] = relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ [])],extension(152 ^ 4,bind([[_116632, _116634, _116636, _116638], [relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []), 662 ^ [], 664 ^ [], 664 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.2.1',plain,[-(in(664 ^ [], 662 ^ []))],extension(678 ^ 5)).
% 98.85/95.62  ncf('1.1.1.1.2.2',plain,[-(664 ^ [] = 664 ^ []), 664 ^ [] = 664 ^ []],extension(4 ^ 5,bind([[_111917, _111919], [664 ^ [], 664 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.2.2.1',plain,[-(664 ^ [] = 664 ^ [])],extension(2 ^ 6,bind([[_111810], [664 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.2.3',plain,[-(662 ^ [] = relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ [])), 662 ^ [] = relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []), relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []) = relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ [])],extension(10 ^ 5,bind([[_112121, _112123, _112125], [relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []), relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []), 662 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.2.3.1',plain,[-(662 ^ [] = relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ [])), 274 : quasi_total(665 ^ [], 662 ^ [], 663 ^ []), 270 : -(663 ^ [] = empty_set), 268 : relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ [])],extension(264 ^ 6,bind([[_120465, _120467, _120469], [665 ^ [], 663 ^ [], 662 ^ []]]))).
% 98.85/95.62  ncf('1.1.1.1.2.3.1.1',plain,[-(quasi_total(665 ^ [], 662 ^ [], 663 ^ []))],extension(669 ^ 11)).
% 98.85/95.62  ncf('1.1.1.1.2.3.1.2',plain,[663 ^ [] = empty_set],extension(680 ^ 11)).
% 98.85/95.62  ncf('1.1.1.1.2.3.1.3',plain,[-(relation_of2_as_subset(665 ^ [], 662 ^ [], 663 ^ []))],reduction('1')).
% 98.85/95.62  ncf('1.1.1.1.2.3.2',plain,[-(relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []) = relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ []))],extension(2 ^ 6,bind([[_111810], [relation_dom_as_subset(662 ^ [], 663 ^ [], 665 ^ [])]]))).
% 98.85/95.62  ncf('1.1.1.1.3',plain,[-(664 ^ [] = 664 ^ [])],extension(2 ^ 4,bind([[_111810], [664 ^ []]]))).
% 98.85/95.62  %-----------------------------------------------------
% 98.85/95.62  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------