%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 12:03:06 EDT 2023

% Result   : Theorem 2.16s 2.40s
% Output   : Proof 2.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.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 13:54:48 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 2.16/2.40  
% 2.16/2.40  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 2.16/2.40  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.16/2.40  %-----------------------------------------------------
% 2.16/2.40  ncf(matrix, plain, [(671 ^ _102843) ^ [] : [-(topological_space(668 ^ []))], (673 ^ _102843) ^ [] : [-(top_str(668 ^ []))], (675 ^ _102843) ^ [] : [-(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))], (677 ^ _102843) ^ [_124994] : [element(_124994, powerset(powerset(the_carrier(668 ^ [])))), 681 ^ _102843 : [(682 ^ _102843) ^ [] : [-(element(680 ^ [_124994], powerset(the_carrier(668 ^ []))))], (684 ^ _102843) ^ [] : [685 ^ _102843 : [(686 ^ _102843) ^ [] : [-(in(680 ^ [_124994], _124994))], (688 ^ _102843) ^ [] : [in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [_124994]), 669 ^ [])]], 689 ^ _102843 : [(690 ^ _102843) ^ [] : [-(in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [_124994]), 669 ^ []))], (692 ^ _102843) ^ [] : [in(680 ^ [_124994], _124994)]]]]], (202 ^ _102843) ^ [_109091, _109093] : [_109093 = _109091, -(powerset(_109093) = powerset(_109091))], (208 ^ _102843) ^ [_109309, _109311] : [_109311 = _109309, -(the_carrier(_109311) = the_carrier(_109309))], (224 ^ _102843) ^ [_109866, _109868] : [_109868 = _109866, -(cast_as_carrier_subset(_109868) = cast_as_carrier_subset(_109866))], (214 ^ _102843) ^ [_109555, _109557, _109559, _109561] : [-(set_difference(_109561, _109557) = set_difference(_109559, _109555)), _109561 = _109559, _109557 = _109555], (2 ^ _102843) ^ [_102987] : [-(_102987 = _102987)], (4 ^ _102843) ^ [_103094, _103096] : [_103096 = _103094, -(_103094 = _103096)], (10 ^ _102843) ^ [_103298, _103300, _103302] : [-(_103302 = _103298), _103302 = _103300, _103300 = _103298], (20 ^ _102843) ^ [_103611, _103613] : [-(v1_xcmplx_0(_103611)), _103613 = _103611, v1_xcmplx_0(_103613)], (30 ^ _102843) ^ [_103906, _103908] : [-(natural(_103906)), _103908 = _103906, natural(_103908)], (40 ^ _102843) ^ [_104201, _104203] : [-(v1_xreal_0(_104201)), _104203 = _104201, v1_xreal_0(_104203)], (50 ^ _102843) ^ [_104496, _104498] : [-(v1_int_1(_104496)), _104498 = _104496, v1_int_1(_104498)], (60 ^ _102843) ^ [_104791, _104793] : [-(v1_rat_1(_104791)), _104793 = _104791, v1_rat_1(_104793)], (70 ^ _102843) ^ [_105086, _105088] : [-(v1_membered(_105086)), _105088 = _105086, v1_membered(_105088)], (80 ^ _102843) ^ [_105381, _105383] : [-(v2_membered(_105381)), _105383 = _105381, v2_membered(_105383)], (90 ^ _102843) ^ [_105676, _105678] : [-(v3_membered(_105676)), _105678 = _105676, v3_membered(_105678)], (100 ^ _102843) ^ [_105971, _105973] : [-(v4_membered(_105971)), _105973 = _105971, v4_membered(_105973)], (110 ^ _102843) ^ [_106266, _106268] : [-(v5_membered(_106266)), _106268 = _106266, v5_membered(_106268)], (120 ^ _102843) ^ [_106561, _106563] : [-(one_sorted_str(_106561)), _106563 = _106561, one_sorted_str(_106563)], (130 ^ _102843) ^ [_106884, _106886, _106888, _106890] : [-(closed_subset(_106888, _106884)), closed_subset(_106890, _106886), _106890 = _106888, _106886 = _106884], (144 ^ _102843) ^ [_107300, _107302] : [-(empty(_107300)), _107302 = _107300, empty(_107302)], (154 ^ _102843) ^ [_107595, _107597] : [-(topological_space(_107595)), _107597 = _107595, topological_space(_107597)], (164 ^ _102843) ^ [_107890, _107892] : [-(top_str(_107890)), _107892 = _107890, top_str(_107892)], (174 ^ _102843) ^ [_108213, _108215, _108217, _108219] : [-(element(_108217, _108213)), element(_108219, _108215), _108219 = _108217, _108215 = _108213], (188 ^ _102843) ^ [_108637, _108639, _108641, _108643] : [-(in(_108641, _108637)), in(_108643, _108639), _108643 = _108641, _108639 = _108637], (230 ^ _102843) ^ [_110116] : [v5_membered(_110116), -(v4_membered(_110116))], (236 ^ _102843) ^ [_110302] : [v4_membered(_110302), -(v3_membered(_110302))], (242 ^ _102843) ^ [_110488] : [v3_membered(_110488), -(v2_membered(_110488))], (248 ^ _102843) ^ [_110674] : [v2_membered(_110674), -(v1_membered(_110674))], (255 ^ _102843) ^ [] : [empty(253 ^ [])], (257 ^ _102843) ^ [] : [-(v1_membered(253 ^ []))], (259 ^ _102843) ^ [] : [-(v2_membered(253 ^ []))], (261 ^ _102843) ^ [] : [-(v3_membered(253 ^ []))], (263 ^ _102843) ^ [] : [-(v4_membered(253 ^ []))], (265 ^ _102843) ^ [] : [-(v5_membered(253 ^ []))], (267 ^ _102843) ^ [_111250] : [v1_membered(_111250), 270 ^ _102843 : [(271 ^ _102843) ^ [_111380] : [element(_111380, _111250), -(v1_xcmplx_0(_111380))]]], (277 ^ _102843) ^ [_111581] : [v2_membered(_111581), 280 ^ _102843 : [(281 ^ _102843) ^ [_111716] : [element(_111716, _111581), 284 ^ _102843 : [(285 ^ _102843) ^ [] : [-(v1_xcmplx_0(_111716))], (287 ^ _102843) ^ [] : [-(v1_xreal_0(_111716))]]]]], (289 ^ _102843) ^ [_111990] : [v3_membered(_111990), 292 ^ _102843 : [(293 ^ _102843) ^ [_112130] : [element(_112130, _111990), 296 ^ _102843 : [(297 ^ _102843) ^ [] : [-(v1_xcmplx_0(_112130))], (299 ^ _102843) ^ [] : [-(v1_xreal_0(_112130))], (301 ^ _102843) ^ [] : [-(v1_rat_1(_112130))]]]]], (303 ^ _102843) ^ [_112476] : [v4_membered(_112476), 306 ^ _102843 : [(307 ^ _102843) ^ [_112621] : [element(_112621, _112476), 310 ^ _102843 : [(311 ^ _102843) ^ [] : [-(v1_xcmplx_0(_112621))], (313 ^ _102843) ^ [] : [-(v1_xreal_0(_112621))], (315 ^ _102843) ^ [] : [-(v1_int_1(_112621))], (317 ^ _102843) ^ [] : [-(v1_rat_1(_112621))]]]]], (319 ^ _102843) ^ [_113039] : [v5_membered(_113039), 322 ^ _102843 : [(323 ^ _102843) ^ [_113189] : [element(_113189, _113039), 326 ^ _102843 : [(327 ^ _102843) ^ [] : [-(v1_xcmplx_0(_113189))], (329 ^ _102843) ^ [] : [-(natural(_113189))], (331 ^ _102843) ^ [] : [-(v1_xreal_0(_113189))], (333 ^ _102843) ^ [] : [-(v1_int_1(_113189))], (335 ^ _102843) ^ [] : [-(v1_rat_1(_113189))]]]]], (337 ^ _102843) ^ [_113679] : [v1_membered(_113679), 340 ^ _102843 : [(341 ^ _102843) ^ [_113811] : [element(_113811, powerset(_113679)), -(v1_membered(_113811))]]], (347 ^ _102843) ^ [_114016] : [v2_membered(_114016), 350 ^ _102843 : [(351 ^ _102843) ^ [_114153] : [element(_114153, powerset(_114016)), 354 ^ _102843 : [(355 ^ _102843) ^ [] : [-(v1_membered(_114153))], (357 ^ _102843) ^ [] : [-(v2_membered(_114153))]]]]], (359 ^ _102843) ^ [_114431] : [v3_membered(_114431), 362 ^ _102843 : [(363 ^ _102843) ^ [_114573] : [element(_114573, powerset(_114431)), 366 ^ _102843 : [(367 ^ _102843) ^ [] : [-(v1_membered(_114573))], (369 ^ _102843) ^ [] : [-(v2_membered(_114573))], (371 ^ _102843) ^ [] : [-(v3_membered(_114573))]]]]], (373 ^ _102843) ^ [_114923] : [v4_membered(_114923), 376 ^ _102843 : [(377 ^ _102843) ^ [_115070] : [element(_115070, powerset(_114923)), 380 ^ _102843 : [(381 ^ _102843) ^ [] : [-(v1_membered(_115070))], (383 ^ _102843) ^ [] : [-(v2_membered(_115070))], (385 ^ _102843) ^ [] : [-(v3_membered(_115070))], (387 ^ _102843) ^ [] : [-(v4_membered(_115070))]]]]], (389 ^ _102843) ^ [_115492] : [v5_membered(_115492), 392 ^ _102843 : [(393 ^ _102843) ^ [_115644] : [element(_115644, powerset(_115492)), 396 ^ _102843 : [(397 ^ _102843) ^ [] : [-(v1_membered(_115644))], (399 ^ _102843) ^ [] : [-(v2_membered(_115644))], (401 ^ _102843) ^ [] : [-(v3_membered(_115644))], (403 ^ _102843) ^ [] : [-(v4_membered(_115644))], (405 ^ _102843) ^ [] : [-(v5_membered(_115644))]]]]], (407 ^ _102843) ^ [_116152, _116154] : [v1_membered(_116154), -(v1_membered(set_difference(_116154, _116152)))], (413 ^ _102843) ^ [_116364, _116366] : [v2_membered(_116366), 416 ^ _102843 : [(417 ^ _102843) ^ [] : [-(v1_membered(set_difference(_116366, _116364)))], (419 ^ _102843) ^ [] : [-(v2_membered(set_difference(_116366, _116364)))]]], (421 ^ _102843) ^ [_116655, _116657] : [v3_membered(_116657), 424 ^ _102843 : [(425 ^ _102843) ^ [] : [-(v1_membered(set_difference(_116657, _116655)))], (427 ^ _102843) ^ [] : [-(v2_membered(set_difference(_116657, _116655)))], (429 ^ _102843) ^ [] : [-(v3_membered(set_difference(_116657, _116655)))]]], (431 ^ _102843) ^ [_117024, _117026] : [v4_membered(_117026), 434 ^ _102843 : [(435 ^ _102843) ^ [] : [-(v1_membered(set_difference(_117026, _117024)))], (437 ^ _102843) ^ [] : [-(v2_membered(set_difference(_117026, _117024)))], (439 ^ _102843) ^ [] : [-(v3_membered(set_difference(_117026, _117024)))], (441 ^ _102843) ^ [] : [-(v4_membered(set_difference(_117026, _117024)))]]], (443 ^ _102843) ^ [_117471, _117473] : [v5_membered(_117473), 446 ^ _102843 : [(447 ^ _102843) ^ [] : [-(v1_membered(set_difference(_117473, _117471)))], (449 ^ _102843) ^ [] : [-(v2_membered(set_difference(_117473, _117471)))], (451 ^ _102843) ^ [] : [-(v3_membered(set_difference(_117473, _117471)))], (453 ^ _102843) ^ [] : [-(v4_membered(set_difference(_117473, _117471)))], (455 ^ _102843) ^ [] : [-(v5_membered(set_difference(_117473, _117471)))]]], (457 ^ _102843) ^ [] : [true___, -(true___)], (463 ^ _102843) ^ [_118101] : [471 ^ _102843 : [(472 ^ _102843) ^ [] : [-(element(470 ^ [_118101], powerset(the_carrier(_118101))))], (474 ^ _102843) ^ [] : [-(closed_subset(470 ^ [_118101], _118101))]], topological_space(_118101), top_str(_118101)], (476 ^ _102843) ^ [_118519] : [-(empty(_118519)), 480 ^ _102843 : [(481 ^ _102843) ^ [] : [-(element(479 ^ [_118519], powerset(_118519)))], (483 ^ _102843) ^ [] : [empty(479 ^ [_118519])]]], (486 ^ _102843) ^ [_118902] : [-(element(484 ^ [_118902], powerset(_118902)))], (488 ^ _102843) ^ [_118953] : [-(empty(484 ^ [_118953]))], (490 ^ _102843) ^ [_119052] : [empty(_119052), 493 ^ _102843 : [(494 ^ _102843) ^ [] : [-(v1_membered(_119052))], (496 ^ _102843) ^ [] : [-(v2_membered(_119052))], (498 ^ _102843) ^ [] : [-(v3_membered(_119052))], (500 ^ _102843) ^ [] : [-(v4_membered(_119052))], (502 ^ _102843) ^ [] : [-(v5_membered(_119052))]]], (504 ^ _102843) ^ [_119533, _119535] : [in(_119535, _119533), in(_119533, _119535)], (510 ^ _102843) ^ [] : [true___, -(true___)], (516 ^ _102843) ^ [_119849] : [one_sorted_str(_119849), -(element(cast_as_carrier_subset(_119849), powerset(the_carrier(_119849))))], (522 ^ _102843) ^ [] : [true___, -(true___)], (528 ^ _102843) ^ [_120168] : [top_str(_120168), -(one_sorted_str(_120168))], (534 ^ _102843) ^ [] : [true___, -(true___)], (540 ^ _102843) ^ [] : [true___, -(true___)], (546 ^ _102843) ^ [_120592] : [-(closed_subset(cast_as_carrier_subset(_120592), _120592)), topological_space(_120592), top_str(_120592)], (556 ^ _102843) ^ [_120851] : [empty(powerset(_120851))], (558 ^ _102843) ^ [_120959, _120961] : [topological_space(_120961), top_str(_120961), element(_120959, powerset(powerset(the_carrier(_120961)))), 570 ^ _102843 : [(571 ^ _102843) ^ [_121402] : [in(_121402, 569 ^ [_120959, _120961]), 574 ^ _102843 : [(575 ^ _102843) ^ [] : [-(in(_121402, powerset(the_carrier(_120961))))], (577 ^ _102843) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_120961), _121402), _120959))]]], (579 ^ _102843) ^ [_121683] : [-(in(_121683, 569 ^ [_120959, _120961])), in(_121683, powerset(the_carrier(_120961))), in(set_difference(cast_as_carrier_subset(_120961), _121683), _120959)]]], (589 ^ _102843) ^ [_122059, _122061] : [-(empty(_122061)), 592 ^ _102843 : [(593 ^ _102843) ^ [] : [element(_122059, _122061), -(in(_122059, _122061))], (599 ^ _102843) ^ [] : [in(_122059, _122061), -(element(_122059, _122061))]]], (605 ^ _102843) ^ [_122472, _122474] : [empty(_122474), 608 ^ _102843 : [(609 ^ _102843) ^ [] : [element(_122472, _122474), -(empty(_122472))], (615 ^ _102843) ^ [] : [empty(_122472), -(element(_122472, _122474))]]], (621 ^ _102843) ^ [] : [true___, -(true___)], (628 ^ _102843) ^ [_123058] : [-(element(626 ^ [_123058], _123058))], (630 ^ _102843) ^ [] : [-(empty(empty_set))], (632 ^ _102843) ^ [_123223, _123225] : [634 ^ _102843 : [(635 ^ _102843) ^ [] : [-(in(633 ^ [_123223, _123225], _123225))], (637 ^ _102843) ^ [] : [in(633 ^ [_123223, _123225], _123223)]], -(element(_123225, powerset(_123223)))], (642 ^ _102843) ^ [] : [-(empty(640 ^ []))], (645 ^ _102843) ^ [] : [empty(643 ^ [])], (647 ^ _102843) ^ [_123747] : [empty(_123747), -(_123747 = empty_set)], (653 ^ _102843) ^ [_123949, _123951] : [in(_123951, _123949), empty(_123949)], (659 ^ _102843) ^ [_124136, _124138] : [empty(_124138), -(_124138 = _124136), empty(_124136)]], input).
% 2.16/2.40  ncf('1',plain,[in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), empty(569 ^ [669 ^ [], 668 ^ []])],start(653 ^ 0,bind([[_123949, _123951], [569 ^ [669 ^ [], 668 ^ []], 680 ^ [569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.16/2.40  ncf('1.1',plain,[-(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), 690 : -(in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [569 ^ [669 ^ [], 668 ^ []]]), 669 ^ [])), 684 : element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ []))))],extension(677 ^ 1,bind([[_124994], [569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.1.1',plain,[in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [569 ^ [669 ^ [], 668 ^ []]]), 669 ^ []), 579 : -(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), 579 : in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))), 579 : topological_space(668 ^ []), 579 : top_str(668 ^ []), 579 : element(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))],extension(558 ^ 6,bind([[_120959, _120961, _121683], [669 ^ [], 668 ^ [], 680 ^ [569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.16/2.40  ncf('1.1.1.1',plain,[in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])],reduction('1')).
% 2.16/2.40  ncf('1.1.1.2',plain,[-(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ [])))), 593 : element(680 ^ [569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))), 593 : -(empty(powerset(the_carrier(668 ^ []))))],extension(589 ^ 9,bind([[_122059, _122061], [680 ^ [569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))]]))).
% 2.16/2.40  ncf('1.1.1.2.1',plain,[-(element(680 ^ [569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))))],extension(682 ^ 12)).
% 2.16/2.40  ncf('1.1.1.2.2',plain,[empty(powerset(the_carrier(668 ^ [])))],extension(556 ^ 10,bind([[_120851], [the_carrier(668 ^ [])]]))).
% 2.16/2.40  ncf('1.1.1.3',plain,[-(topological_space(668 ^ []))],extension(671 ^ 7)).
% 2.16/2.40  ncf('1.1.1.4',plain,[-(top_str(668 ^ []))],extension(673 ^ 7)).
% 2.16/2.40  ncf('1.1.1.5',plain,[-(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))],extension(675 ^ 7)).
% 2.16/2.40  ncf('1.1.2',plain,[-(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ []))))), 615 : empty(569 ^ [669 ^ [], 668 ^ []]), 615 : empty(powerset(powerset(the_carrier(668 ^ []))))],extension(605 ^ 2,bind([[_122472, _122474], [569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))]]))).
% 2.16/2.40  ncf('1.1.2.1',plain,[-(empty(569 ^ [669 ^ [], 668 ^ []])), 593 : element(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), 593 : -(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]))],extension(589 ^ 5,bind([[_122059, _122061], [633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.1.2.1.1',plain,[-(element(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])],extension(599 ^ 8)).
% 2.16/2.40  ncf('1.1.2.1.1.1',plain,[-(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), -(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))))],extension(632 ^ 9,bind([[_123223, _123225], [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.1.2.1.1.1.1',plain,[element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ []))))],reduction('1.1')).
% 2.16/2.40  ncf('1.1.2.1.2',plain,[in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), 575 : -(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ [])))), 571 : topological_space(668 ^ []), 571 : top_str(668 ^ []), 571 : element(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))],extension(558 ^ 8,bind([[_120959, _120961, _121402], [669 ^ [], 668 ^ [], 633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.16/2.40  ncf('1.1.2.1.2.1',plain,[in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))), -(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))))],extension(632 ^ 13,bind([[_123223, _123225], [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.1.2.1.2.1.1',plain,[element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ []))))],reduction('1.1')).
% 2.16/2.40  ncf('1.1.2.1.2.2',plain,[-(topological_space(668 ^ []))],extension(671 ^ 9)).
% 2.16/2.40  ncf('1.1.2.1.2.3',plain,[-(top_str(668 ^ []))],extension(673 ^ 9)).
% 2.16/2.40  ncf('1.1.2.1.2.4',plain,[-(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))],extension(675 ^ 9)).
% 2.16/2.40  ncf('1.1.2.2',plain,[-(empty(powerset(powerset(the_carrier(668 ^ []))))), 599 : in(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))), 599 : -(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))],extension(589 ^ 3,bind([[_122059, _122061], [669 ^ [], powerset(powerset(the_carrier(668 ^ [])))]]))).
% 2.16/2.40  ncf('1.1.2.2.1',plain,[-(in(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))), in(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))), 669 ^ [] = 669 ^ [], powerset(powerset(the_carrier(668 ^ []))) = powerset(powerset(the_carrier(668 ^ [])))],extension(188 ^ 6,bind([[_108637, _108639, _108641, _108643], [powerset(powerset(the_carrier(668 ^ []))), powerset(powerset(the_carrier(668 ^ []))), 669 ^ [], 669 ^ []]]))).
% 2.16/2.40  ncf('1.1.2.2.1.1',plain,[-(in(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))), element(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))],extension(593 ^ 7)).
% 2.16/2.40  ncf('1.1.2.2.1.1.1',plain,[-(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))],extension(675 ^ 8)).
% 2.16/2.40  ncf('1.1.2.2.1.2',plain,[-(669 ^ [] = 669 ^ [])],extension(2 ^ 7,bind([[_102987], [669 ^ []]]))).
% 2.16/2.40  ncf('1.1.2.2.1.3',plain,[-(powerset(powerset(the_carrier(668 ^ []))) = powerset(powerset(the_carrier(668 ^ []))))],extension(2 ^ 7,bind([[_102987], [powerset(powerset(the_carrier(668 ^ [])))]]))).
% 2.16/2.40  ncf('1.1.2.2.2',plain,[element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))), topological_space(668 ^ []), top_str(668 ^ []), 571 : in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), 575 : -(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))))],extension(558 ^ 6,bind([[_120959, _120961, _121402], [669 ^ [], 668 ^ [], 633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.16/2.40  ncf('1.1.2.2.2.1',plain,[-(topological_space(668 ^ []))],extension(671 ^ 7)).
% 2.16/2.40  ncf('1.1.2.2.2.2',plain,[-(top_str(668 ^ []))],extension(673 ^ 7)).
% 2.16/2.40  ncf('1.1.2.2.2.3',plain,[-(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), -(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))))],extension(632 ^ 9,bind([[_123223, _123225], [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.1.2.2.2.3.1',plain,[element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ []))))],reduction('1.1')).
% 2.16/2.40  ncf('1.1.2.2.2.4',plain,[in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))), -(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))))],extension(632 ^ 11,bind([[_123223, _123225], [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.1.2.2.2.4.1',plain,[element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ []))))],reduction('1.1')).
% 2.16/2.40  ncf('1.2',plain,[-(empty(569 ^ [669 ^ [], 668 ^ []])), 593 : element(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), 593 : -(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]))],extension(589 ^ 1,bind([[_122059, _122061], [633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.16/2.40  ncf('1.2.1',plain,[-(element(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])],extension(599 ^ 4)).
% 2.16/2.40  ncf('1.2.1.1',plain,[-(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])), -(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))))],extension(632 ^ 5,bind([[_123223, _123225], [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.19/2.40  ncf('1.2.1.1.1',plain,[element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))), 688 : in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [569 ^ [669 ^ [], 668 ^ []]]), 669 ^ []), 692 : in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])],extension(677 ^ 6,bind([[_124994], [569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.19/2.40  ncf('1.2.1.1.1.1',plain,[-(in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [569 ^ [669 ^ [], 668 ^ []]]), 669 ^ [])), 571 : in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), 571 : topological_space(668 ^ []), 571 : top_str(668 ^ []), 571 : element(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))],extension(558 ^ 11,bind([[_120959, _120961, _121402], [669 ^ [], 668 ^ [], 680 ^ [569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.19/2.40  ncf('1.2.1.1.1.1.1',plain,[-(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]))],lemmata('x')).
% 2.19/2.40  ncf('1.2.1.1.1.1.2',plain,[-(topological_space(668 ^ []))],extension(671 ^ 12)).
% 2.19/2.40  ncf('1.2.1.1.1.1.3',plain,[-(top_str(668 ^ []))],extension(673 ^ 12)).
% 2.19/2.40  ncf('1.2.1.1.1.1.4',plain,[-(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))],extension(675 ^ 12)).
% 2.19/2.40  ncf('1.2.1.1.1.2',plain,[-(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]))],lemmata('x')).
% 2.19/2.40  ncf('1.2.2',plain,[in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]), 575 : -(in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ [])))), 571 : topological_space(668 ^ []), 571 : top_str(668 ^ []), 571 : element(669 ^ [], powerset(powerset(the_carrier(668 ^ []))))],extension(558 ^ 4,bind([[_120959, _120961, _121402], [669 ^ [], 668 ^ [], 633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.19/2.40  ncf('1.2.2.1',plain,[in(633 ^ [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]], powerset(the_carrier(668 ^ []))), -(element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))))],extension(632 ^ 9,bind([[_123223, _123225], [powerset(the_carrier(668 ^ [])), 569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.19/2.40  ncf('1.2.2.1.1',plain,[element(569 ^ [669 ^ [], 668 ^ []], powerset(powerset(the_carrier(668 ^ [])))), 688 : in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [569 ^ [669 ^ [], 668 ^ []]]), 669 ^ []), 692 : in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])],extension(677 ^ 10,bind([[_124994], [569 ^ [669 ^ [], 668 ^ []]]]))).
% 2.19/2.40  ncf('1.2.2.1.1.1',plain,[-(in(set_difference(cast_as_carrier_subset(668 ^ []), 680 ^ [569 ^ [669 ^ [], 668 ^ []]]), 669 ^ [])), in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []])],extension(571 ^ 15,bind([[_121402], [680 ^ [569 ^ [669 ^ [], 668 ^ []]]]]))).
% 2.19/2.40  ncf('1.2.2.1.1.1.1',plain,[-(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]))],lemmata('x')).
% 2.19/2.40  ncf('1.2.2.1.1.2',plain,[-(in(680 ^ [569 ^ [669 ^ [], 668 ^ []]], 569 ^ [669 ^ [], 668 ^ []]))],lemmata('x')).
% 2.19/2.40  ncf('1.2.2.2',plain,[-(topological_space(668 ^ []))],extension(671 ^ 5)).
% 2.19/2.40  ncf('1.2.2.3',plain,[-(top_str(668 ^ []))],extension(673 ^ 5)).
% 2.19/2.40  ncf('1.2.2.4',plain,[-(element(669 ^ [], powerset(powerset(the_carrier(668 ^ [])))))],extension(675 ^ 5)).
% 2.19/2.40  %-----------------------------------------------------
% 2.19/2.40  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------