%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n013.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 15.03s 14.80s
% Output   : Proof 15.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n013.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 12:45:20 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 15.03/14.80  
% 15.03/14.80  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 15.03/14.80  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.03/14.80  %-----------------------------------------------------
% 15.03/14.80  ncf(matrix, plain, [(618 ^ _102462) ^ [] : [-(topological_space(615 ^ []))], (620 ^ _102462) ^ [] : [-(top_str(615 ^ []))], (622 ^ _102462) ^ [] : [-(element(616 ^ [], powerset(the_carrier(615 ^ []))))], (624 ^ _102462) ^ [_122873] : [element(_122873, powerset(powerset(the_carrier(615 ^ [])))), 628 ^ _102462 : [(629 ^ _102462) ^ [] : [-(element(627 ^ [_122873], powerset(the_carrier(615 ^ []))))], (631 ^ _102462) ^ [] : [649 ^ _102462 : [(650 ^ _102462) ^ [] : [-(element(648 ^ [_122873], powerset(the_carrier(615 ^ []))))], (652 ^ _102462) ^ [] : [-(648 ^ [_122873] = 627 ^ [_122873])], (654 ^ _102462) ^ [] : [-(closed_subset(648 ^ [_122873], 615 ^ []))], (656 ^ _102462) ^ [] : [-(subset(616 ^ [], 627 ^ [_122873]))], (658 ^ _102462) ^ [] : [in(627 ^ [_122873], _122873)]], 632 ^ _102462 : [(633 ^ _102462) ^ [] : [-(in(627 ^ [_122873], _122873))], (635 ^ _102462) ^ [_123290] : [element(_123290, powerset(the_carrier(615 ^ []))), _123290 = 627 ^ [_122873], closed_subset(_123290, 615 ^ []), subset(616 ^ [], 627 ^ [_122873])]]]]], (216 ^ _102462) ^ [_109188, _109190] : [_109190 = _109188, -(powerset(_109190) = powerset(_109188))], (222 ^ _102462) ^ [_109386, _109388] : [_109388 = _109386, -(the_carrier(_109388) = the_carrier(_109386))], (2 ^ _102462) ^ [_102606] : [-(_102606 = _102606)], (4 ^ _102462) ^ [_102713, _102715] : [_102715 = _102713, -(_102713 = _102715)], (10 ^ _102462) ^ [_102917, _102919, _102921] : [-(_102921 = _102917), _102921 = _102919, _102919 = _102917], (20 ^ _102462) ^ [_103230, _103232] : [-(v1_xcmplx_0(_103230)), _103232 = _103230, v1_xcmplx_0(_103232)], (30 ^ _102462) ^ [_103525, _103527] : [-(natural(_103525)), _103527 = _103525, natural(_103527)], (40 ^ _102462) ^ [_103820, _103822] : [-(v1_xreal_0(_103820)), _103822 = _103820, v1_xreal_0(_103822)], (50 ^ _102462) ^ [_104115, _104117] : [-(v1_int_1(_104115)), _104117 = _104115, v1_int_1(_104117)], (60 ^ _102462) ^ [_104410, _104412] : [-(v1_rat_1(_104410)), _104412 = _104410, v1_rat_1(_104412)], (70 ^ _102462) ^ [_104705, _104707] : [-(v1_membered(_104705)), _104707 = _104705, v1_membered(_104707)], (80 ^ _102462) ^ [_105000, _105002] : [-(v2_membered(_105000)), _105002 = _105000, v2_membered(_105002)], (90 ^ _102462) ^ [_105295, _105297] : [-(v3_membered(_105295)), _105297 = _105295, v3_membered(_105297)], (100 ^ _102462) ^ [_105590, _105592] : [-(v4_membered(_105590)), _105592 = _105590, v4_membered(_105592)], (110 ^ _102462) ^ [_105885, _105887] : [-(v5_membered(_105885)), _105887 = _105885, v5_membered(_105887)], (120 ^ _102462) ^ [_106180, _106182] : [-(one_sorted_str(_106180)), _106182 = _106180, one_sorted_str(_106182)], (130 ^ _102462) ^ [_106475, _106477] : [-(empty(_106475)), _106477 = _106475, empty(_106477)], (140 ^ _102462) ^ [_106770, _106772] : [-(topological_space(_106770)), _106772 = _106770, topological_space(_106772)], (150 ^ _102462) ^ [_107065, _107067] : [-(top_str(_107065)), _107067 = _107065, top_str(_107067)], (160 ^ _102462) ^ [_107388, _107390, _107392, _107394] : [-(in(_107392, _107388)), in(_107394, _107390), _107394 = _107392, _107390 = _107388], (174 ^ _102462) ^ [_107832, _107834, _107836, _107838] : [-(element(_107836, _107832)), element(_107838, _107834), _107838 = _107836, _107834 = _107832], (188 ^ _102462) ^ [_108276, _108278, _108280, _108282] : [-(closed_subset(_108280, _108276)), closed_subset(_108282, _108278), _108282 = _108280, _108278 = _108276], (202 ^ _102462) ^ [_108700, _108702, _108704, _108706] : [-(subset(_108704, _108700)), subset(_108706, _108702), _108706 = _108704, _108702 = _108700], (228 ^ _102462) ^ [_109600] : [v5_membered(_109600), -(v4_membered(_109600))], (234 ^ _102462) ^ [_109786] : [v4_membered(_109786), -(v3_membered(_109786))], (240 ^ _102462) ^ [_109972] : [v3_membered(_109972), -(v2_membered(_109972))], (246 ^ _102462) ^ [_110158] : [v2_membered(_110158), -(v1_membered(_110158))], (253 ^ _102462) ^ [] : [empty(251 ^ [])], (255 ^ _102462) ^ [] : [-(v1_membered(251 ^ []))], (257 ^ _102462) ^ [] : [-(v2_membered(251 ^ []))], (259 ^ _102462) ^ [] : [-(v3_membered(251 ^ []))], (261 ^ _102462) ^ [] : [-(v4_membered(251 ^ []))], (263 ^ _102462) ^ [] : [-(v5_membered(251 ^ []))], (265 ^ _102462) ^ [_110734] : [v1_membered(_110734), 268 ^ _102462 : [(269 ^ _102462) ^ [_110864] : [element(_110864, _110734), -(v1_xcmplx_0(_110864))]]], (275 ^ _102462) ^ [_111065] : [v2_membered(_111065), 278 ^ _102462 : [(279 ^ _102462) ^ [_111200] : [element(_111200, _111065), 282 ^ _102462 : [(283 ^ _102462) ^ [] : [-(v1_xcmplx_0(_111200))], (285 ^ _102462) ^ [] : [-(v1_xreal_0(_111200))]]]]], (287 ^ _102462) ^ [_111474] : [v3_membered(_111474), 290 ^ _102462 : [(291 ^ _102462) ^ [_111614] : [element(_111614, _111474), 294 ^ _102462 : [(295 ^ _102462) ^ [] : [-(v1_xcmplx_0(_111614))], (297 ^ _102462) ^ [] : [-(v1_xreal_0(_111614))], (299 ^ _102462) ^ [] : [-(v1_rat_1(_111614))]]]]], (301 ^ _102462) ^ [_111960] : [v4_membered(_111960), 304 ^ _102462 : [(305 ^ _102462) ^ [_112105] : [element(_112105, _111960), 308 ^ _102462 : [(309 ^ _102462) ^ [] : [-(v1_xcmplx_0(_112105))], (311 ^ _102462) ^ [] : [-(v1_xreal_0(_112105))], (313 ^ _102462) ^ [] : [-(v1_int_1(_112105))], (315 ^ _102462) ^ [] : [-(v1_rat_1(_112105))]]]]], (317 ^ _102462) ^ [_112523] : [v5_membered(_112523), 320 ^ _102462 : [(321 ^ _102462) ^ [_112673] : [element(_112673, _112523), 324 ^ _102462 : [(325 ^ _102462) ^ [] : [-(v1_xcmplx_0(_112673))], (327 ^ _102462) ^ [] : [-(natural(_112673))], (329 ^ _102462) ^ [] : [-(v1_xreal_0(_112673))], (331 ^ _102462) ^ [] : [-(v1_int_1(_112673))], (333 ^ _102462) ^ [] : [-(v1_rat_1(_112673))]]]]], (335 ^ _102462) ^ [_113163] : [v1_membered(_113163), 338 ^ _102462 : [(339 ^ _102462) ^ [_113295] : [element(_113295, powerset(_113163)), -(v1_membered(_113295))]]], (345 ^ _102462) ^ [_113500] : [v2_membered(_113500), 348 ^ _102462 : [(349 ^ _102462) ^ [_113637] : [element(_113637, powerset(_113500)), 352 ^ _102462 : [(353 ^ _102462) ^ [] : [-(v1_membered(_113637))], (355 ^ _102462) ^ [] : [-(v2_membered(_113637))]]]]], (357 ^ _102462) ^ [_113915] : [v3_membered(_113915), 360 ^ _102462 : [(361 ^ _102462) ^ [_114057] : [element(_114057, powerset(_113915)), 364 ^ _102462 : [(365 ^ _102462) ^ [] : [-(v1_membered(_114057))], (367 ^ _102462) ^ [] : [-(v2_membered(_114057))], (369 ^ _102462) ^ [] : [-(v3_membered(_114057))]]]]], (371 ^ _102462) ^ [_114407] : [v4_membered(_114407), 374 ^ _102462 : [(375 ^ _102462) ^ [_114554] : [element(_114554, powerset(_114407)), 378 ^ _102462 : [(379 ^ _102462) ^ [] : [-(v1_membered(_114554))], (381 ^ _102462) ^ [] : [-(v2_membered(_114554))], (383 ^ _102462) ^ [] : [-(v3_membered(_114554))], (385 ^ _102462) ^ [] : [-(v4_membered(_114554))]]]]], (387 ^ _102462) ^ [_114976] : [v5_membered(_114976), 390 ^ _102462 : [(391 ^ _102462) ^ [_115128] : [element(_115128, powerset(_114976)), 394 ^ _102462 : [(395 ^ _102462) ^ [] : [-(v1_membered(_115128))], (397 ^ _102462) ^ [] : [-(v2_membered(_115128))], (399 ^ _102462) ^ [] : [-(v3_membered(_115128))], (401 ^ _102462) ^ [] : [-(v4_membered(_115128))], (403 ^ _102462) ^ [] : [-(v5_membered(_115128))]]]]], (405 ^ _102462) ^ [] : [true___, -(true___)], (411 ^ _102462) ^ [_115741] : [-(empty(_115741)), 415 ^ _102462 : [(416 ^ _102462) ^ [] : [-(element(414 ^ [_115741], powerset(_115741)))], (418 ^ _102462) ^ [] : [empty(414 ^ [_115741])]]], (421 ^ _102462) ^ [_116124] : [-(element(419 ^ [_116124], powerset(_116124)))], (423 ^ _102462) ^ [_116175] : [-(empty(419 ^ [_116175]))], (425 ^ _102462) ^ [_116274] : [empty(_116274), 428 ^ _102462 : [(429 ^ _102462) ^ [] : [-(v1_membered(_116274))], (431 ^ _102462) ^ [] : [-(v2_membered(_116274))], (433 ^ _102462) ^ [] : [-(v3_membered(_116274))], (435 ^ _102462) ^ [] : [-(v4_membered(_116274))], (437 ^ _102462) ^ [] : [-(v5_membered(_116274))]]], (439 ^ _102462) ^ [_116740, _116742] : [-(subset(_116742, _116742))], (441 ^ _102462) ^ [_116849, _116851] : [in(_116851, _116849), in(_116849, _116851)], (447 ^ _102462) ^ [] : [true___, -(true___)], (453 ^ _102462) ^ [_117165] : [top_str(_117165), -(one_sorted_str(_117165))], (459 ^ _102462) ^ [] : [true___, -(true___)], (465 ^ _102462) ^ [] : [true___, -(true___)], (471 ^ _102462) ^ [_117589] : [479 ^ _102462 : [(480 ^ _102462) ^ [] : [-(element(478 ^ [_117589], powerset(the_carrier(_117589))))], (482 ^ _102462) ^ [] : [-(closed_subset(478 ^ [_117589], _117589))]], topological_space(_117589), top_str(_117589)], (484 ^ _102462) ^ [_117991] : [empty(powerset(_117991))], (486 ^ _102462) ^ [_118099, _118101] : [topological_space(_118101), top_str(_118101), element(_118099, powerset(the_carrier(_118101))), 498 ^ _102462 : [(499 ^ _102462) ^ [_118582] : [in(_118582, 497 ^ [_118099, _118101]), 502 ^ _102462 : [(503 ^ _102462) ^ [] : [-(in(_118582, powerset(the_carrier(_118101))))], (506 ^ _102462) ^ [] : [-(element(504 ^ [_118099, _118101, _118582], powerset(the_carrier(_118101))))], (508 ^ _102462) ^ [] : [-(504 ^ [_118099, _118101, _118582] = _118582)], (510 ^ _102462) ^ [] : [-(closed_subset(504 ^ [_118099, _118101, _118582], _118101))], (512 ^ _102462) ^ [] : [-(subset(_118099, _118582))]]], (514 ^ _102462) ^ [_119192] : [-(in(_119192, 497 ^ [_118099, _118101])), in(_119192, powerset(the_carrier(_118101))), 519 ^ _102462 : [(520 ^ _102462) ^ [_119410] : [element(_119410, powerset(the_carrier(_118101))), _119410 = _119192, closed_subset(_119410, _118101), subset(_118099, _119192)]]]]], (536 ^ _102462) ^ [_119934, _119936] : [-(empty(_119936)), 539 ^ _102462 : [(540 ^ _102462) ^ [] : [element(_119934, _119936), -(in(_119934, _119936))], (546 ^ _102462) ^ [] : [in(_119934, _119936), -(element(_119934, _119936))]]], (552 ^ _102462) ^ [_120347, _120349] : [empty(_120349), 555 ^ _102462 : [(556 ^ _102462) ^ [] : [element(_120347, _120349), -(empty(_120347))], (562 ^ _102462) ^ [] : [empty(_120347), -(element(_120347, _120349))]]], (568 ^ _102462) ^ [] : [true___, -(true___)], (575 ^ _102462) ^ [_120933] : [-(element(573 ^ [_120933], _120933))], (577 ^ _102462) ^ [] : [-(empty(empty_set))], (579 ^ _102462) ^ [_121098, _121100] : [581 ^ _102462 : [(582 ^ _102462) ^ [] : [-(in(580 ^ [_121098, _121100], _121100))], (584 ^ _102462) ^ [] : [in(580 ^ [_121098, _121100], _121098)]], -(element(_121100, powerset(_121098)))], (589 ^ _102462) ^ [] : [-(empty(587 ^ []))], (592 ^ _102462) ^ [] : [empty(590 ^ [])], (594 ^ _102462) ^ [_121622] : [empty(_121622), -(_121622 = empty_set)], (600 ^ _102462) ^ [_121824, _121826] : [in(_121826, _121824), empty(_121824)], (606 ^ _102462) ^ [_122011, _122013] : [empty(_122013), -(_122013 = _122011), empty(_122011)]], input).
% 15.03/14.80  ncf('1',plain,[in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), empty(497 ^ [616 ^ [], 615 ^ []])],start(600 ^ 0,bind([[_121824, _121826], [497 ^ [616 ^ [], 615 ^ []], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.1',plain,[-(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])), 650 : -(element(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), 631 : element(497 ^ [616 ^ [], 615 ^ []], powerset(powerset(the_carrier(615 ^ []))))],extension(624 ^ 1,bind([[_122873], [497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.1.1',plain,[element(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 520 : 648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 520 : closed_subset(648 ^ [497 ^ [616 ^ [], 615 ^ []]], 615 ^ []), 520 : subset(616 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]), 520 : -(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])), 520 : in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 514 : topological_space(615 ^ []), 514 : top_str(615 ^ []), 514 : element(616 ^ [], powerset(the_carrier(615 ^ [])))],extension(486 ^ 6,bind([[_118099, _118101, _119192, _119410], [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 648 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.1.1.1',plain,[-(648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]])],extension(652 ^ 11)).
% 15.03/14.80  ncf('1.1.1.2',plain,[-(closed_subset(648 ^ [497 ^ [616 ^ [], 615 ^ []]], 615 ^ []))],extension(654 ^ 11)).
% 15.03/14.80  ncf('1.1.1.3',plain,[-(subset(616 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]))],extension(656 ^ 11)).
% 15.03/14.80  ncf('1.1.1.4',plain,[in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])],reduction('1')).
% 15.03/14.80  ncf('1.1.1.5',plain,[-(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 627 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])) = powerset(the_carrier(615 ^ []))],extension(160 ^ 9,bind([[_107388, _107390, _107392, _107394], [powerset(the_carrier(615 ^ [])), powerset(the_carrier(615 ^ [])), 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.1.1.5.1',plain,[-(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), in(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])) = powerset(the_carrier(615 ^ []))],extension(160 ^ 10,bind([[_107388, _107390, _107392, _107394], [powerset(the_carrier(615 ^ [])), powerset(the_carrier(615 ^ [])), 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 648 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.1.1.5.1.1',plain,[-(in(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), 540 : element(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 540 : -(empty(powerset(the_carrier(615 ^ []))))],extension(536 ^ 11,bind([[_119934, _119936], [648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))]]))).
% 15.03/14.80  ncf('1.1.1.5.1.1.1',plain,[-(element(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))))],reduction('1.1')).
% 15.03/14.80  ncf('1.1.1.5.1.1.2',plain,[empty(powerset(the_carrier(615 ^ [])))],extension(484 ^ 12,bind([[_117991], [the_carrier(615 ^ [])]]))).
% 15.03/14.80  ncf('1.1.1.5.1.2',plain,[-(648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]])],extension(652 ^ 11)).
% 15.03/14.80  ncf('1.1.1.5.1.3',plain,[-(powerset(the_carrier(615 ^ [])) = powerset(the_carrier(615 ^ []))), the_carrier(615 ^ []) = the_carrier(615 ^ [])],extension(216 ^ 11,bind([[_109188, _109190], [the_carrier(615 ^ []), the_carrier(615 ^ [])]]))).
% 15.03/14.80  ncf('1.1.1.5.1.3.1',plain,[-(the_carrier(615 ^ []) = the_carrier(615 ^ []))],extension(2 ^ 12,bind([[_102606], [the_carrier(615 ^ [])]]))).
% 15.03/14.80  ncf('1.1.1.5.2',plain,[-(627 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]])],extension(2 ^ 10,bind([[_102606], [627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.1.1.5.3',plain,[-(powerset(the_carrier(615 ^ [])) = powerset(the_carrier(615 ^ []))), the_carrier(615 ^ []) = the_carrier(615 ^ [])],extension(216 ^ 10,bind([[_109188, _109190], [the_carrier(615 ^ []), the_carrier(615 ^ [])]]))).
% 15.03/14.80  ncf('1.1.1.5.3.1',plain,[-(the_carrier(615 ^ []) = the_carrier(615 ^ [])), 615 ^ [] = 615 ^ []],extension(222 ^ 11,bind([[_109386, _109388], [615 ^ [], 615 ^ []]]))).
% 15.03/14.80  ncf('1.1.1.5.3.1.1',plain,[-(615 ^ [] = 615 ^ [])],extension(2 ^ 12,bind([[_102606], [615 ^ []]]))).
% 15.03/14.80  ncf('1.1.1.6',plain,[-(topological_space(615 ^ []))],extension(618 ^ 7)).
% 15.03/14.80  ncf('1.1.1.7',plain,[-(top_str(615 ^ []))],extension(620 ^ 7)).
% 15.03/14.80  ncf('1.1.1.8',plain,[-(element(616 ^ [], powerset(the_carrier(615 ^ []))))],extension(622 ^ 7)).
% 15.03/14.80  ncf('1.1.2',plain,[-(element(497 ^ [616 ^ [], 615 ^ []], powerset(powerset(the_carrier(615 ^ []))))), 582 : -(in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]))],extension(579 ^ 2,bind([[_121098, _121100], [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.1.2.1',plain,[in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), 503 : -(in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), 499 : topological_space(615 ^ []), 499 : top_str(615 ^ []), 499 : element(616 ^ [], powerset(the_carrier(615 ^ [])))],extension(486 ^ 5,bind([[_118099, _118101, _118582], [616 ^ [], 615 ^ [], 580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.1.2.1.1',plain,[in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))],extension(584 ^ 10)).
% 15.03/14.80  ncf('1.1.2.1.2',plain,[-(topological_space(615 ^ []))],extension(618 ^ 6)).
% 15.03/14.80  ncf('1.1.2.1.3',plain,[-(top_str(615 ^ []))],extension(620 ^ 6)).
% 15.03/14.80  ncf('1.1.2.1.4',plain,[-(element(616 ^ [], powerset(the_carrier(615 ^ []))))],extension(622 ^ 6)).
% 15.03/14.80  ncf('1.2',plain,[-(empty(497 ^ [616 ^ [], 615 ^ []])), 540 : element(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), 540 : -(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]))],extension(536 ^ 1,bind([[_119934, _119936], [627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.2.1',plain,[-(element(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])), in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])],extension(546 ^ 4)).
% 15.03/14.80  ncf('1.2.1.1',plain,[-(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])), 650 : -(element(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), 631 : element(497 ^ [616 ^ [], 615 ^ []], powerset(powerset(the_carrier(615 ^ []))))],extension(624 ^ 5,bind([[_122873], [497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.2.1.1.1',plain,[element(648 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 520 : 648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 520 : closed_subset(648 ^ [497 ^ [616 ^ [], 615 ^ []]], 615 ^ []), 520 : subset(616 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]), 520 : -(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])), 520 : in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 514 : topological_space(615 ^ []), 514 : top_str(615 ^ []), 514 : element(616 ^ [], powerset(the_carrier(615 ^ [])))],extension(486 ^ 10,bind([[_118099, _118101, _119192, _119410], [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 648 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.1.1.1.1',plain,[-(648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]])],extension(652 ^ 15)).
% 15.03/14.80  ncf('1.2.1.1.1.2',plain,[-(closed_subset(648 ^ [497 ^ [616 ^ [], 615 ^ []]], 615 ^ []))],extension(654 ^ 15)).
% 15.03/14.80  ncf('1.2.1.1.1.3',plain,[-(subset(616 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]))],extension(656 ^ 15)).
% 15.03/14.80  ncf('1.2.1.1.1.4',plain,[in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])],reduction('1.2.1')).
% 15.03/14.80  ncf('1.2.1.1.1.5',plain,[-(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), 540 : element(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))), 540 : -(empty(powerset(the_carrier(615 ^ []))))],extension(536 ^ 13,bind([[_119934, _119936], [627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))]]))).
% 15.03/14.80  ncf('1.2.1.1.1.5.1',plain,[-(element(627 ^ [497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))))],extension(629 ^ 16)).
% 15.03/14.80  ncf('1.2.1.1.1.5.2',plain,[empty(powerset(the_carrier(615 ^ [])))],extension(484 ^ 14,bind([[_117991], [the_carrier(615 ^ [])]]))).
% 15.03/14.80  ncf('1.2.1.1.1.6',plain,[-(topological_space(615 ^ []))],extension(618 ^ 11)).
% 15.03/14.80  ncf('1.2.1.1.1.7',plain,[-(top_str(615 ^ []))],extension(620 ^ 11)).
% 15.03/14.80  ncf('1.2.1.1.1.8',plain,[-(element(616 ^ [], powerset(the_carrier(615 ^ []))))],extension(622 ^ 11)).
% 15.03/14.80  ncf('1.2.1.1.2',plain,[-(element(497 ^ [616 ^ [], 615 ^ []], powerset(powerset(the_carrier(615 ^ []))))), 582 : -(in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]))],extension(579 ^ 6,bind([[_121098, _121100], [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.2.1.1.2.1',plain,[in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), 503 : -(in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))), 499 : topological_space(615 ^ []), 499 : top_str(615 ^ []), 499 : element(616 ^ [], powerset(the_carrier(615 ^ [])))],extension(486 ^ 9,bind([[_118099, _118101, _118582], [616 ^ [], 615 ^ [], 580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.1.1.2.1.1',plain,[in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))],extension(584 ^ 14)).
% 15.03/14.80  ncf('1.2.1.1.2.1.2',plain,[-(topological_space(615 ^ []))],extension(618 ^ 10)).
% 15.03/14.80  ncf('1.2.1.1.2.1.3',plain,[-(top_str(615 ^ []))],extension(620 ^ 10)).
% 15.03/14.80  ncf('1.2.1.1.2.1.4',plain,[-(element(616 ^ [], powerset(the_carrier(615 ^ []))))],extension(622 ^ 10)).
% 15.03/14.80  ncf('1.2.2',plain,[in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), 506 : -(element(504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]], powerset(the_carrier(615 ^ [])))), 499 : topological_space(615 ^ []), 499 : top_str(615 ^ []), 499 : element(616 ^ [], powerset(the_carrier(615 ^ [])))],extension(486 ^ 4,bind([[_118099, _118101, _118582], [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.2.1',plain,[element(504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]], powerset(the_carrier(615 ^ []))), 635 : 504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 635 : closed_subset(504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]], 615 ^ []), 635 : subset(616 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]), 652 : -(648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]]), 631 : element(497 ^ [616 ^ [], 615 ^ []], powerset(powerset(the_carrier(615 ^ []))))],extension(624 ^ 9,bind([[_122873, _123290], [497 ^ [616 ^ [], 615 ^ []], 504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]]))).
% 15.03/14.80  ncf('1.2.2.1.1',plain,[-(504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]])],extension(508 ^ 14)).
% 15.03/14.80  ncf('1.2.2.1.2',plain,[-(closed_subset(504 ^ [616 ^ [], 615 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]], 615 ^ []))],extension(510 ^ 14)).
% 15.03/14.80  ncf('1.2.2.1.3',plain,[-(subset(616 ^ [], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]))],extension(512 ^ 14)).
% 15.03/14.80  ncf('1.2.2.1.4',plain,[648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], -(627 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]]), 627 ^ [497 ^ [616 ^ [], 615 ^ []]] = 648 ^ [497 ^ [616 ^ [], 615 ^ []]]],extension(10 ^ 14,bind([[_102917, _102919, _102921], [627 ^ [497 ^ [616 ^ [], 615 ^ []]], 648 ^ [497 ^ [616 ^ [], 615 ^ []]], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.2.1.4.1',plain,[627 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]], -(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])), in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), 497 ^ [616 ^ [], 615 ^ []] = 497 ^ [616 ^ [], 615 ^ []]],extension(160 ^ 15,bind([[_107388, _107390, _107392, _107394], [497 ^ [616 ^ [], 615 ^ []], 497 ^ [616 ^ [], 615 ^ []], 627 ^ [497 ^ [616 ^ [], 615 ^ []]], 627 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.2.1.4.1.1',plain,[in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []])],extension(658 ^ 16)).
% 15.03/14.80  ncf('1.2.2.1.4.1.2',plain,[-(in(627 ^ [497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]))],reduction('1.2')).
% 15.03/14.80  ncf('1.2.2.1.4.1.3',plain,[-(497 ^ [616 ^ [], 615 ^ []] = 497 ^ [616 ^ [], 615 ^ []])],extension(2 ^ 16,bind([[_102606], [497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.2.2.1.4.2',plain,[-(627 ^ [497 ^ [616 ^ [], 615 ^ []]] = 648 ^ [497 ^ [616 ^ [], 615 ^ []]]), 648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]]],extension(4 ^ 15,bind([[_102713, _102715], [627 ^ [497 ^ [616 ^ [], 615 ^ []]], 648 ^ [497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.2.1.4.2.1',plain,[-(648 ^ [497 ^ [616 ^ [], 615 ^ []]] = 627 ^ [497 ^ [616 ^ [], 615 ^ []]])],reduction('1.2.2.1')).
% 15.03/14.80  ncf('1.2.2.1.5',plain,[-(element(497 ^ [616 ^ [], 615 ^ []], powerset(powerset(the_carrier(615 ^ []))))), 582 : -(in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]))],extension(579 ^ 10,bind([[_121098, _121100], [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]]]))).
% 15.03/14.80  ncf('1.2.2.1.5.1',plain,[in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], 497 ^ [616 ^ [], 615 ^ []]), 503 : -(in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ []))))],extension(499 ^ 13,bind([[_118582], [580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]]]]))).
% 15.03/14.80  ncf('1.2.2.1.5.1.1',plain,[in(580 ^ [powerset(the_carrier(615 ^ [])), 497 ^ [616 ^ [], 615 ^ []]], powerset(the_carrier(615 ^ [])))],extension(584 ^ 16)).
% 15.03/14.80  ncf('1.2.2.2',plain,[-(topological_space(615 ^ []))],extension(618 ^ 5)).
% 15.03/14.80  ncf('1.2.2.3',plain,[-(top_str(615 ^ []))],extension(620 ^ 5)).
% 15.03/14.80  ncf('1.2.2.4',plain,[-(element(616 ^ [], powerset(the_carrier(615 ^ []))))],extension(622 ^ 5)).
% 15.03/14.80  %-----------------------------------------------------
% 15.03/14.80  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------