%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 12:02:30 EDT 2023

% Result   : Theorem 12.31s 12.78s
% Output   : Proof 12.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.14/0.34  % Computer : n002.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May 18 13:02:34 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 12.31/12.78  
% 12.31/12.78  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 12.31/12.78  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.31/12.78  %-----------------------------------------------------
% 12.31/12.78  ncf(matrix, plain, [(1288 ^ _173442) ^ [] : [-(element(1286 ^ [], powerset(1285 ^ [])))], (1291 ^ _173442) ^ [] : [-(in(1289 ^ [], 1286 ^ []))], (1293 ^ _173442) ^ [] : [in(1289 ^ [], 1285 ^ [])], (114 ^ _173442) ^ [_177195, _177197, _177199, _177201] : [-(cartesian_product2(_177201, _177197) = cartesian_product2(_177199, _177195)), _177201 = _177199, _177197 = _177195], (124 ^ _173442) ^ [_177554, _177556, _177558, _177560] : [-(ordered_pair(_177560, _177556) = ordered_pair(_177558, _177554)), _177560 = _177558, _177556 = _177554], (134 ^ _173442) ^ [_177913, _177915, _177917, _177919] : [-(set_intersection2(_177919, _177915) = set_intersection2(_177917, _177913)), _177919 = _177917, _177915 = _177913], (144 ^ _173442) ^ [_178272, _178274, _178276, _178278] : [-(set_difference(_178278, _178274) = set_difference(_178276, _178272)), _178278 = _178276, _178274 = _178272], (154 ^ _173442) ^ [_178631, _178633, _178635, _178637] : [-(set_union2(_178637, _178633) = set_union2(_178635, _178631)), _178637 = _178635, _178633 = _178631], (164 ^ _173442) ^ [_178962, _178964] : [_178964 = _178962, -(union(_178964) = union(_178962))], (170 ^ _173442) ^ [_179180, _179182] : [_179182 = _179180, -(singleton(_179182) = singleton(_179180))], (186 ^ _173442) ^ [_179737, _179739] : [_179739 = _179737, -(powerset(_179739) = powerset(_179737))], (176 ^ _173442) ^ [_179426, _179428, _179430, _179432] : [-(unordered_pair(_179432, _179428) = unordered_pair(_179430, _179426)), _179432 = _179430, _179428 = _179426], (2 ^ _173442) ^ [_173586] : [-(_173586 = _173586)], (4 ^ _173442) ^ [_173693, _173695] : [_173695 = _173693, -(_173693 = _173695)], (10 ^ _173442) ^ [_173897, _173899, _173901] : [-(_173901 = _173897), _173901 = _173899, _173899 = _173897], (20 ^ _173442) ^ [_174238, _174240, _174242, _174244] : [-(proper_subset(_174242, _174238)), proper_subset(_174244, _174240), _174244 = _174242, _174240 = _174238], (34 ^ _173442) ^ [_174682, _174684, _174686, _174688] : [-(disjoint(_174686, _174682)), disjoint(_174688, _174684), _174688 = _174686, _174684 = _174682], (48 ^ _173442) ^ [_175098, _175100] : [-(empty(_175098)), _175100 = _175098, empty(_175100)], (58 ^ _173442) ^ [_175421, _175423, _175425, _175427] : [-(subset(_175425, _175421)), subset(_175427, _175423), _175427 = _175425, _175423 = _175421], (72 ^ _173442) ^ [_175865, _175867, _175869, _175871] : [-(are_equipotent(_175869, _175865)), are_equipotent(_175871, _175867), _175871 = _175869, _175867 = _175865], (86 ^ _173442) ^ [_176309, _176311, _176313, _176315] : [-(element(_176313, _176309)), element(_176315, _176311), _176315 = _176313, _176311 = _176309], (100 ^ _173442) ^ [_176733, _176735, _176737, _176739] : [-(in(_176737, _176733)), in(_176739, _176735), _176739 = _176737, _176735 = _176733], (192 ^ _173442) ^ [_179989, _179991] : [in(_179991, _179989), in(_179989, _179991)], (198 ^ _173442) ^ [_180200, _180202] : [proper_subset(_180202, _180200), proper_subset(_180200, _180202)], (204 ^ _173442) ^ [_180396, _180398] : [-(unordered_pair(_180398, _180396) = unordered_pair(_180396, _180398))], (206 ^ _173442) ^ [_180496, _180498] : [-(set_union2(_180498, _180496) = set_union2(_180496, _180498))], (208 ^ _173442) ^ [_180596, _180598] : [-(set_intersection2(_180598, _180596) = set_intersection2(_180596, _180598))], (210 ^ _173442) ^ [_180740, _180742] : [_180742 = _180740, 213 ^ _173442 : [(214 ^ _173442) ^ [] : [-(subset(_180742, _180740))], (216 ^ _173442) ^ [] : [-(subset(_180740, _180742))]]], (218 ^ _173442) ^ [_180977, _180979] : [-(_180979 = _180977), subset(_180979, _180977), subset(_180977, _180979)], (244 ^ _173442) ^ [_181828, _181830] : [-(_181828 = singleton(_181830)), 248 ^ _173442 : [(249 ^ _173442) ^ [] : [-(in(245 ^ [_181828, _181830], _181828))], (251 ^ _173442) ^ [] : [245 ^ [_181828, _181830] = _181830]], 252 ^ _173442 : [(253 ^ _173442) ^ [] : [-(245 ^ [_181828, _181830] = _181830)], (255 ^ _173442) ^ [] : [in(245 ^ [_181828, _181830], _181828)]]], (228 ^ _173442) ^ [_181307, _181309] : [_181307 = singleton(_181309), 231 ^ _173442 : [(232 ^ _173442) ^ [_181477] : [in(_181477, _181307), -(_181477 = _181309)], (238 ^ _173442) ^ [_181649] : [_181649 = _181309, -(in(_181649, _181307))]]], (259 ^ _173442) ^ [_182379] : [_182379 = empty_set, 262 ^ _173442 : [(263 ^ _173442) ^ [_182492] : [in(_182492, _182379)]]], (265 ^ _173442) ^ [_182558] : [-(in(266 ^ [_182558], _182558)), -(_182558 = empty_set)], (288 ^ _173442) ^ [_183370, _183372] : [-(_183370 = powerset(_183372)), 292 ^ _173442 : [(293 ^ _173442) ^ [] : [-(in(289 ^ [_183370, _183372], _183370))], (295 ^ _173442) ^ [] : [subset(289 ^ [_183370, _183372], _183372)]], 296 ^ _173442 : [(297 ^ _173442) ^ [] : [-(subset(289 ^ [_183370, _183372], _183372))], (299 ^ _173442) ^ [] : [in(289 ^ [_183370, _183372], _183370)]]], (272 ^ _173442) ^ [_182849, _182851] : [_182849 = powerset(_182851), 275 ^ _173442 : [(276 ^ _173442) ^ [_183019] : [in(_183019, _182849), -(subset(_183019, _182851))], (282 ^ _173442) ^ [_183191] : [subset(_183191, _182851), -(in(_183191, _182849))]]], (303 ^ _173442) ^ [_183926, _183928] : [-(empty(_183928)), 306 ^ _173442 : [(307 ^ _173442) ^ [] : [element(_183926, _183928), -(in(_183926, _183928))], (313 ^ _173442) ^ [] : [in(_183926, _183928), -(element(_183926, _183928))]]], (319 ^ _173442) ^ [_184339, _184341] : [empty(_184341), 322 ^ _173442 : [(323 ^ _173442) ^ [] : [element(_184339, _184341), -(empty(_184339))], (329 ^ _173442) ^ [] : [empty(_184339), -(element(_184339, _184341))]]], (357 ^ _173442) ^ [_185564, _185566, _185568] : [-(_185564 = unordered_pair(_185568, _185566)), 361 ^ _173442 : [(362 ^ _173442) ^ [] : [-(in(358 ^ [_185564, _185566, _185568], _185564))], (364 ^ _173442) ^ [] : [358 ^ [_185564, _185566, _185568] = _185568], (366 ^ _173442) ^ [] : [358 ^ [_185564, _185566, _185568] = _185566]], 367 ^ _173442 : [(374 ^ _173442) ^ [] : [in(358 ^ [_185564, _185566, _185568], _185564)], (368 ^ _173442) ^ [] : [-(358 ^ [_185564, _185566, _185568] = _185568), -(358 ^ [_185564, _185566, _185568] = _185566)]]], (335 ^ _173442) ^ [_184839, _184841, _184843] : [_184839 = unordered_pair(_184843, _184841), 338 ^ _173442 : [(349 ^ _173442) ^ [_185299] : [350 ^ _173442 : [(351 ^ _173442) ^ [] : [_185299 = _184843], (353 ^ _173442) ^ [] : [_185299 = _184841]], -(in(_185299, _184839))], (339 ^ _173442) ^ [_185021] : [in(_185021, _184839), -(_185021 = _184843), -(_185021 = _184841)]]], (400 ^ _173442) ^ [_187083, _187085, _187087] : [-(_187083 = set_union2(_187087, _187085)), 404 ^ _173442 : [(405 ^ _173442) ^ [] : [-(in(401 ^ [_187083, _187085, _187087], _187083))], (407 ^ _173442) ^ [] : [in(401 ^ [_187083, _187085, _187087], _187087)], (409 ^ _173442) ^ [] : [in(401 ^ [_187083, _187085, _187087], _187085)]], 410 ^ _173442 : [(417 ^ _173442) ^ [] : [in(401 ^ [_187083, _187085, _187087], _187083)], (411 ^ _173442) ^ [] : [-(in(401 ^ [_187083, _187085, _187087], _187087)), -(in(401 ^ [_187083, _187085, _187087], _187085))]]], (378 ^ _173442) ^ [_186358, _186360, _186362] : [_186358 = set_union2(_186362, _186360), 381 ^ _173442 : [(392 ^ _173442) ^ [_186818] : [393 ^ _173442 : [(394 ^ _173442) ^ [] : [in(_186818, _186362)], (396 ^ _173442) ^ [] : [in(_186818, _186360)]], -(in(_186818, _186358))], (382 ^ _173442) ^ [_186540] : [in(_186540, _186358), -(in(_186540, _186362)), -(in(_186540, _186360))]]], (451 ^ _173442) ^ [_189134, _189136, _189138] : [-(_189134 = cartesian_product2(_189138, _189136)), 469 ^ _173442 : [(470 ^ _173442) ^ [] : [-(in(467 ^ [_189134, _189136, _189138], _189138))], (472 ^ _173442) ^ [] : [-(in(468 ^ [_189134, _189136, _189138], _189136))], (474 ^ _173442) ^ [] : [-(452 ^ [_189134, _189136, _189138] = ordered_pair(467 ^ [_189134, _189136, _189138], 468 ^ [_189134, _189136, _189138]))], (476 ^ _173442) ^ [] : [in(452 ^ [_189134, _189136, _189138], _189134)]], 455 ^ _173442 : [(456 ^ _173442) ^ [] : [-(in(452 ^ [_189134, _189136, _189138], _189134))], (458 ^ _173442) ^ [_189472, _189474] : [in(_189474, _189138), in(_189472, _189136), 452 ^ [_189134, _189136, _189138] = ordered_pair(_189474, _189472)]]], (421 ^ _173442) ^ [_187877, _187879, _187881] : [_187877 = cartesian_product2(_187881, _187879), 424 ^ _173442 : [(425 ^ _173442) ^ [_188078] : [in(_188078, _187877), 430 ^ _173442 : [(431 ^ _173442) ^ [] : [-(in(428 ^ [_187877, _187879, _187881, _188078], _187881))], (433 ^ _173442) ^ [] : [-(in(429 ^ [_187877, _187879, _187881, _188078], _187879))], (435 ^ _173442) ^ [] : [-(_188078 = ordered_pair(428 ^ [_187877, _187879, _187881, _188078], 429 ^ [_187877, _187879, _187881, _188078]))]]], (437 ^ _173442) ^ [_188638] : [-(in(_188638, _187877)), 438 ^ _173442 : [(439 ^ _173442) ^ [_188768, _188770] : [in(_188770, _187881), in(_188768, _187879), _188638 = ordered_pair(_188770, _188768)]]]]], (490 ^ _173442) ^ [_190725, _190727] : [492 ^ _173442 : [(493 ^ _173442) ^ [] : [-(in(491 ^ [_190725, _190727], _190727))], (495 ^ _173442) ^ [] : [in(491 ^ [_190725, _190727], _190725)]], -(subset(_190727, _190725))], (480 ^ _173442) ^ [_190411, _190413] : [subset(_190413, _190411), 483 ^ _173442 : [(484 ^ _173442) ^ [_190548] : [in(_190548, _190413), -(in(_190548, _190411))]]], (521 ^ _173442) ^ [_191850, _191852, _191854] : [-(_191850 = set_intersection2(_191854, _191852)), 533 ^ _173442 : [(534 ^ _173442) ^ [] : [-(in(522 ^ [_191850, _191852, _191854], _191854))], (536 ^ _173442) ^ [] : [-(in(522 ^ [_191850, _191852, _191854], _191852))], (538 ^ _173442) ^ [] : [in(522 ^ [_191850, _191852, _191854], _191850)]], 525 ^ _173442 : [(526 ^ _173442) ^ [] : [-(in(522 ^ [_191850, _191852, _191854], _191850))], (528 ^ _173442) ^ [] : [in(522 ^ [_191850, _191852, _191854], _191854), in(522 ^ [_191850, _191852, _191854], _191852)]]], (499 ^ _173442) ^ [_191125, _191127, _191129] : [_191125 = set_intersection2(_191129, _191127), 502 ^ _173442 : [(503 ^ _173442) ^ [_191307] : [in(_191307, _191125), 506 ^ _173442 : [(507 ^ _173442) ^ [] : [-(in(_191307, _191129))], (509 ^ _173442) ^ [] : [-(in(_191307, _191127))]]], (511 ^ _173442) ^ [_191566] : [-(in(_191566, _191125)), in(_191566, _191129), in(_191566, _191127)]]], (565 ^ _173442) ^ [_193477, _193479] : [-(_193477 = union(_193479)), 578 ^ _173442 : [(579 ^ _173442) ^ [] : [-(in(566 ^ [_193477, _193479], 577 ^ [_193477, _193479]))], (581 ^ _173442) ^ [] : [-(in(577 ^ [_193477, _193479], _193479))], (583 ^ _173442) ^ [] : [in(566 ^ [_193477, _193479], _193477)]], 569 ^ _173442 : [(570 ^ _173442) ^ [] : [-(in(566 ^ [_193477, _193479], _193477))], (572 ^ _173442) ^ [_193760] : [in(566 ^ [_193477, _193479], _193760), in(_193760, _193479)]]], (542 ^ _173442) ^ [_192632, _192634] : [_192632 = union(_192634), 545 ^ _173442 : [(546 ^ _173442) ^ [_192813] : [in(_192813, _192632), 550 ^ _173442 : [(551 ^ _173442) ^ [] : [-(in(_192813, 549 ^ [_192632, _192634, _192813]))], (553 ^ _173442) ^ [] : [-(in(549 ^ [_192632, _192634, _192813], _192634))]]], (555 ^ _173442) ^ [_193140] : [-(in(_193140, _192632)), 556 ^ _173442 : [(557 ^ _173442) ^ [_193238] : [in(_193140, _193238), in(_193238, _192634)]]]]], (609 ^ _173442) ^ [_195098, _195100, _195102] : [-(_195098 = set_difference(_195102, _195100)), 621 ^ _173442 : [(622 ^ _173442) ^ [] : [-(in(610 ^ [_195098, _195100, _195102], _195102))], (624 ^ _173442) ^ [] : [in(610 ^ [_195098, _195100, _195102], _195100)], (626 ^ _173442) ^ [] : [in(610 ^ [_195098, _195100, _195102], _195098)]], 613 ^ _173442 : [(614 ^ _173442) ^ [] : [-(in(610 ^ [_195098, _195100, _195102], _195098))], (616 ^ _173442) ^ [] : [in(610 ^ [_195098, _195100, _195102], _195102), -(in(610 ^ [_195098, _195100, _195102], _195100))]]], (587 ^ _173442) ^ [_194367, _194369, _194371] : [_194367 = set_difference(_194371, _194369), 590 ^ _173442 : [(591 ^ _173442) ^ [_194551] : [in(_194551, _194367), 594 ^ _173442 : [(595 ^ _173442) ^ [] : [-(in(_194551, _194371))], (597 ^ _173442) ^ [] : [in(_194551, _194369)]]], (599 ^ _173442) ^ [_194811] : [-(in(_194811, _194367)), in(_194811, _194371), -(in(_194811, _194369))]]], (630 ^ _173442) ^ [_195840, _195842] : [-(ordered_pair(_195842, _195840) = unordered_pair(unordered_pair(_195842, _195840), singleton(_195842)))], (632 ^ _173442) ^ [_195989, _195991] : [disjoint(_195991, _195989), -(set_intersection2(_195991, _195989) = empty_set)], (638 ^ _173442) ^ [_196157, _196159] : [set_intersection2(_196159, _196157) = empty_set, -(disjoint(_196159, _196157))], (644 ^ _173442) ^ [_196404, _196406] : [proper_subset(_196406, _196404), 647 ^ _173442 : [(648 ^ _173442) ^ [] : [-(subset(_196406, _196404))], (650 ^ _173442) ^ [] : [_196406 = _196404]]], (652 ^ _173442) ^ [_196642, _196644] : [-(proper_subset(_196644, _196642)), subset(_196644, _196642), -(_196644 = _196642)], (662 ^ _173442) ^ [] : [true___, -(true___)], (668 ^ _173442) ^ [] : [true___, -(true___)], (674 ^ _173442) ^ [] : [true___, -(true___)], (680 ^ _173442) ^ [] : [true___, -(true___)], (686 ^ _173442) ^ [] : [true___, -(true___)], (692 ^ _173442) ^ [] : [true___, -(true___)], (698 ^ _173442) ^ [] : [true___, -(true___)], (704 ^ _173442) ^ [] : [true___, -(true___)], (710 ^ _173442) ^ [] : [true___, -(true___)], (716 ^ _173442) ^ [] : [true___, -(true___)], (722 ^ _173442) ^ [] : [true___, -(true___)], (729 ^ _173442) ^ [_198265] : [-(element(727 ^ [_198265], _198265))], (731 ^ _173442) ^ [_198347] : [empty(powerset(_198347))], (733 ^ _173442) ^ [] : [-(empty(empty_set))], (735 ^ _173442) ^ [_198492, _198494] : [empty(ordered_pair(_198494, _198492))], (737 ^ _173442) ^ [_198603, _198605] : [-(empty(_198605)), empty(set_union2(_198605, _198603))], (743 ^ _173442) ^ [_198819, _198821] : [-(empty(_198821)), empty(set_union2(_198819, _198821))], (749 ^ _173442) ^ [_199020, _199022] : [-(set_union2(_199022, _199022) = _199022)], (751 ^ _173442) ^ [_199117, _199119] : [-(set_intersection2(_199119, _199119) = _199119)], (753 ^ _173442) ^ [_199213, _199215] : [proper_subset(_199215, _199215)], (755 ^ _173442) ^ [_199292] : [singleton(_199292) = empty_set], (757 ^ _173442) ^ [_199401, _199403] : [in(_199403, _199401), -(set_union2(singleton(_199403), _199401) = _199401)], (763 ^ _173442) ^ [_199621, _199623] : [disjoint(singleton(_199623), _199621), in(_199623, _199621)], (769 ^ _173442) ^ [_199834, _199836] : [-(in(_199836, _199834)), -(disjoint(singleton(_199836), _199834))], (775 ^ _173442) ^ [_200080, _200082] : [subset(singleton(_200082), _200080), -(in(_200082, _200080))], (781 ^ _173442) ^ [_200246, _200248] : [in(_200248, _200246), -(subset(singleton(_200248), _200246))], (787 ^ _173442) ^ [_200491, _200493] : [set_difference(_200493, _200491) = empty_set, -(subset(_200493, _200491))], (793 ^ _173442) ^ [_200659, _200661] : [subset(_200661, _200659), -(set_difference(_200661, _200659) = empty_set)], (799 ^ _173442) ^ [_200891, _200893, _200895] : [subset(_200895, _200893), -(in(_200891, _200895)), -(subset(_200895, set_difference(_200893, singleton(_200891))))], (819 ^ _173442) ^ [_201500, _201502] : [820 ^ _173442 : [(821 ^ _173442) ^ [] : [_201502 = empty_set], (823 ^ _173442) ^ [] : [_201502 = singleton(_201500)]], -(subset(_201502, singleton(_201500)))], (809 ^ _173442) ^ [_201240, _201242] : [subset(_201242, singleton(_201240)), -(_201242 = empty_set), -(_201242 = singleton(_201240))], (827 ^ _173442) ^ [_201794, _201796] : [in(_201796, _201794), -(subset(_201796, union(_201794)))], (833 ^ _173442) ^ [_202065, _202067, _202069, _202071] : [in(ordered_pair(_202071, _202069), cartesian_product2(_202067, _202065)), 836 ^ _173442 : [(837 ^ _173442) ^ [] : [-(in(_202071, _202067))], (839 ^ _173442) ^ [] : [-(in(_202069, _202065))]]], (841 ^ _173442) ^ [_202330, _202332, _202334, _202336] : [-(in(ordered_pair(_202336, _202334), cartesian_product2(_202332, _202330))), in(_202336, _202332), in(_202334, _202330)], (851 ^ _173442) ^ [_202649] : [-(empty(_202649)), 855 ^ _173442 : [(856 ^ _173442) ^ [] : [-(element(854 ^ [_202649], powerset(_202649)))], (858 ^ _173442) ^ [] : [empty(854 ^ [_202649])]]], (861 ^ _173442) ^ [] : [-(empty(859 ^ []))], (864 ^ _173442) ^ [] : [empty(862 ^ [])], (866 ^ _173442) ^ [_203159, _203161] : [-(subset(_203161, _203161))], (868 ^ _173442) ^ [_203268, _203270] : [disjoint(_203270, _203268), -(disjoint(_203268, _203270))], (874 ^ _173442) ^ [_203535, _203537, _203539, _203541] : [in(ordered_pair(_203541, _203539), cartesian_product2(_203537, _203535)), 877 ^ _173442 : [(878 ^ _173442) ^ [] : [-(in(_203541, _203537))], (880 ^ _173442) ^ [] : [-(in(_203539, _203535))]]], (882 ^ _173442) ^ [_203800, _203802, _203804, _203806] : [-(in(ordered_pair(_203806, _203804), cartesian_product2(_203802, _203800))), in(_203806, _203802), in(_203804, _203800)], (892 ^ _173442) ^ [_204161, _204163, _204165, _204167] : [unordered_pair(_204167, _204165) = unordered_pair(_204163, _204161), -(_204167 = _204163), -(_204167 = _204161)], (902 ^ _173442) ^ [_204511, _204513, _204515] : [subset(_204515, _204513), 905 ^ _173442 : [(906 ^ _173442) ^ [] : [-(subset(cartesian_product2(_204515, _204511), cartesian_product2(_204513, _204511)))], (908 ^ _173442) ^ [] : [-(subset(cartesian_product2(_204511, _204515), cartesian_product2(_204511, _204513)))]]], (910 ^ _173442) ^ [_204856, _204858, _204860, _204862] : [-(subset(cartesian_product2(_204862, _204858), cartesian_product2(_204860, _204856))), subset(_204862, _204860), subset(_204858, _204856)], (920 ^ _173442) ^ [_205187, _205189] : [subset(_205189, _205187), -(set_union2(_205189, _205187) = _205187)], (927 ^ _173442) ^ [_205509] : [-(in(_205509, 925 ^ [_205509]))], (929 ^ _173442) ^ [_205621, _205623, _205625] : [-(in(_205621, 925 ^ [_205625])), in(_205623, 925 ^ [_205625]), subset(_205621, _205623)], (939 ^ _173442) ^ [_205936, _205938] : [in(_205936, 925 ^ [_205938]), -(in(powerset(_205936), 925 ^ [_205938]))], (945 ^ _173442) ^ [_206136, _206138] : [subset(_206136, 925 ^ [_206138]), -(are_equipotent(_206136, 925 ^ [_206138])), -(in(_206136, 925 ^ [_206138]))], (955 ^ _173442) ^ [_206461, _206463] : [-(subset(set_intersection2(_206463, _206461), _206463))], (957 ^ _173442) ^ [_206587, _206589, _206591] : [-(subset(_206591, set_intersection2(_206589, _206587))), subset(_206591, _206589), subset(_206591, _206587)], (967 ^ _173442) ^ [_206873] : [-(set_union2(_206873, empty_set) = _206873)], (969 ^ _173442) ^ [_206997, _206999, _207001] : [-(subset(_207001, _206997)), subset(_207001, _206999), subset(_206999, _206997)], (979 ^ _173442) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (981 ^ _173442) ^ [_207373, _207375, _207377] : [subset(_207377, _207375), -(subset(set_intersection2(_207377, _207373), set_intersection2(_207375, _207373)))], (987 ^ _173442) ^ [_207601, _207603] : [subset(_207603, _207601), -(set_intersection2(_207603, _207601) = _207603)], (993 ^ _173442) ^ [_207788] : [-(set_intersection2(_207788, empty_set) = empty_set)], (995 ^ _173442) ^ [_207898, _207900] : [-(_207900 = _207898), 999 ^ _173442 : [(1000 ^ _173442) ^ [] : [-(in(996 ^ [_207898, _207900], _207900))], (1002 ^ _173442) ^ [] : [in(996 ^ [_207898, _207900], _207898)]], 1003 ^ _173442 : [(1004 ^ _173442) ^ [] : [-(in(996 ^ [_207898, _207900], _207898))], (1006 ^ _173442) ^ [] : [in(996 ^ [_207898, _207900], _207900)]]], (1010 ^ _173442) ^ [_208399] : [-(subset(empty_set, _208399))], (1012 ^ _173442) ^ [_208520, _208522, _208524] : [subset(_208524, _208522), -(subset(set_difference(_208524, _208520), set_difference(_208522, _208520)))], (1018 ^ _173442) ^ [_208776, _208778, _208780, _208782] : [ordered_pair(_208782, _208780) = ordered_pair(_208778, _208776), 1021 ^ _173442 : [(1022 ^ _173442) ^ [] : [-(_208782 = _208778)], (1024 ^ _173442) ^ [] : [-(_208780 = _208776)]]], (1026 ^ _173442) ^ [_209074, _209076] : [-(subset(set_difference(_209076, _209074), _209076))], (1028 ^ _173442) ^ [_209215, _209217] : [set_difference(_209217, _209215) = empty_set, -(subset(_209217, _209215))], (1034 ^ _173442) ^ [_209383, _209385] : [subset(_209385, _209383), -(set_difference(_209385, _209383) = empty_set)], (1040 ^ _173442) ^ [_209630, _209632] : [subset(singleton(_209632), _209630), -(in(_209632, _209630))], (1046 ^ _173442) ^ [_209796, _209798] : [in(_209798, _209796), -(subset(singleton(_209798), _209796))], (1052 ^ _173442) ^ [_210055, _210057, _210059] : [subset(unordered_pair(_210059, _210057), _210055), 1055 ^ _173442 : [(1056 ^ _173442) ^ [] : [-(in(_210059, _210055))], (1058 ^ _173442) ^ [] : [-(in(_210057, _210055))]]], (1060 ^ _173442) ^ [_210306, _210308, _210310] : [-(subset(unordered_pair(_210310, _210308), _210306)), in(_210310, _210306), in(_210308, _210306)], (1070 ^ _173442) ^ [_210608, _210610] : [-(set_union2(_210610, set_difference(_210608, _210610)) = set_union2(_210610, _210608))], (1082 ^ _173442) ^ [_211015, _211017] : [1083 ^ _173442 : [(1084 ^ _173442) ^ [] : [_211017 = empty_set], (1086 ^ _173442) ^ [] : [_211017 = singleton(_211015)]], -(subset(_211017, singleton(_211015)))], (1072 ^ _173442) ^ [_210755, _210757] : [subset(_210757, singleton(_210755)), -(_210757 = empty_set), -(_210757 = singleton(_210755))], (1090 ^ _173442) ^ [_211280] : [-(set_difference(_211280, empty_set) = _211280)], (1092 ^ _173442) ^ [_211410, _211412] : [-(disjoint(_211412, _211410)), 1096 ^ _173442 : [(1097 ^ _173442) ^ [] : [-(in(1095 ^ [_211410, _211412], _211412))], (1099 ^ _173442) ^ [] : [-(in(1095 ^ [_211410, _211412], _211410))]]], (1101 ^ _173442) ^ [_211724, _211726] : [disjoint(_211726, _211724), 1102 ^ _173442 : [(1103 ^ _173442) ^ [_211816] : [in(_211816, _211726), in(_211816, _211724)]]], (1111 ^ _173442) ^ [_212073] : [subset(_212073, empty_set), -(_212073 = empty_set)], (1117 ^ _173442) ^ [_212262, _212264] : [-(set_difference(set_union2(_212264, _212262), _212262) = set_difference(_212264, _212262))], (1119 ^ _173442) ^ [_212380, _212382] : [subset(_212382, _212380), -(_212380 = set_union2(_212382, set_difference(_212380, _212382)))], (1125 ^ _173442) ^ [_212602, _212604] : [in(_212604, _212602), -(set_union2(singleton(_212604), _212602) = _212602)], (1131 ^ _173442) ^ [_212807, _212809] : [-(set_difference(_212809, set_difference(_212809, _212807)) = set_intersection2(_212809, _212807))], (1133 ^ _173442) ^ [_212896] : [-(set_difference(empty_set, _212896) = empty_set)], (1135 ^ _173442) ^ [_213026, _213028] : [-(disjoint(_213028, _213026)), -(in(1138 ^ [_213026, _213028], set_intersection2(_213028, _213026)))], (1142 ^ _173442) ^ [_213261, _213263] : [1143 ^ _173442 : [(1144 ^ _173442) ^ [_213334] : [in(_213334, set_intersection2(_213263, _213261))]], disjoint(_213263, _213261)], (1148 ^ _173442) ^ [_213500, _213502] : [subset(_213502, _213500), proper_subset(_213500, _213502)], (1154 ^ _173442) ^ [_213723, _213725, _213727] : [-(disjoint(_213727, _213723)), subset(_213727, _213725), disjoint(_213725, _213723)], (1164 ^ _173442) ^ [_214061, _214063] : [set_difference(_214063, singleton(_214061)) = _214063, in(_214061, _214063)], (1170 ^ _173442) ^ [_214234, _214236] : [-(in(_214234, _214236)), -(set_difference(_214236, singleton(_214234)) = _214236)], (1176 ^ _173442) ^ [_214430] : [-(unordered_pair(_214430, _214430) = singleton(_214430))], (1178 ^ _173442) ^ [_214528] : [empty(_214528), -(_214528 = empty_set)], (1184 ^ _173442) ^ [_214730, _214732] : [subset(singleton(_214732), singleton(_214730)), -(_214732 = _214730)], (1190 ^ _173442) ^ [_214948, _214950] : [in(_214950, _214948), empty(_214948)], (1196 ^ _173442) ^ [_215140, _215142] : [-(subset(_215142, set_union2(_215142, _215140)))], (1198 ^ _173442) ^ [_215281, _215283] : [disjoint(_215283, _215281), -(set_difference(_215283, _215281) = _215283)], (1204 ^ _173442) ^ [_215449, _215451] : [set_difference(_215451, _215449) = _215451, -(disjoint(_215451, _215449))], (1210 ^ _173442) ^ [_215667, _215669] : [empty(_215669), -(_215669 = _215667), empty(_215667)], (1220 ^ _173442) ^ [_215978, _215980, _215982] : [-(subset(set_union2(_215982, _215978), _215980)), subset(_215982, _215980), subset(_215978, _215980)], (1230 ^ _173442) ^ [_216307, _216309, _216311] : [singleton(_216311) = unordered_pair(_216309, _216307), -(_216311 = _216309)], (1236 ^ _173442) ^ [_216533, _216535] : [in(_216535, _216533), -(subset(_216535, union(_216533)))], (1242 ^ _173442) ^ [_216718] : [-(union(powerset(_216718)) = _216718)], (1280 ^ _173442) ^ [_218239, _218241, _218243] : [singleton(_218243) = unordered_pair(_218241, _218239), -(_218241 = _218239)], (1245 ^ _173442) ^ [_216959] : [-(in(_216959, 1243 ^ [_216959]))], (1247 ^ _173442) ^ [_217071, _217073, _217075] : [-(in(_217071, 1243 ^ [_217075])), in(_217073, 1243 ^ [_217075]), subset(_217071, _217073)], (1257 ^ _173442) ^ [_217386, _217388] : [in(_217386, 1243 ^ [_217388]), 1261 ^ _173442 : [(1262 ^ _173442) ^ [] : [-(in(1260 ^ [_217386, _217388], 1243 ^ [_217388]))], (1264 ^ _173442) ^ [_217698] : [subset(_217698, _217386), -(in(_217698, 1260 ^ [_217386, _217388]))]]], (1270 ^ _173442) ^ [_217905, _217907] : [subset(_217905, 1243 ^ [_217907]), -(are_equipotent(_217905, 1243 ^ [_217907])), -(in(_217905, 1243 ^ [_217907]))]], input).
% 12.31/12.78  ncf('1',plain,[empty(powerset(1285 ^ []))],start(731 ^ 0,bind([[_198347], [1285 ^ []]]))).
% 12.31/12.78  ncf('1.1',plain,[-(empty(powerset(1285 ^ []))), 307 : element(1286 ^ [], powerset(1285 ^ [])), 307 : -(in(1286 ^ [], powerset(1285 ^ [])))],extension(303 ^ 1,bind([[_183926, _183928], [1286 ^ [], powerset(1285 ^ [])]]))).
% 12.31/12.78  ncf('1.1.1',plain,[-(element(1286 ^ [], powerset(1285 ^ [])))],extension(1288 ^ 4)).
% 12.31/12.78  ncf('1.1.2',plain,[in(1286 ^ [], powerset(1285 ^ [])), 276 : -(subset(1286 ^ [], 1285 ^ [])), 276 : powerset(1285 ^ []) = powerset(1285 ^ [])],extension(272 ^ 4,bind([[_182849, _182851, _183019], [powerset(1285 ^ []), 1285 ^ [], 1286 ^ []]]))).
% 12.31/12.78  ncf('1.1.2.1',plain,[subset(1286 ^ [], 1285 ^ []), 484 : in(1289 ^ [], 1286 ^ []), 484 : -(in(1289 ^ [], 1285 ^ []))],extension(480 ^ 7,bind([[_190411, _190413, _190548], [1285 ^ [], 1286 ^ [], 1289 ^ []]]))).
% 12.31/12.78  ncf('1.1.2.1.1',plain,[-(in(1289 ^ [], 1286 ^ []))],extension(1291 ^ 10)).
% 12.31/12.78  ncf('1.1.2.1.2',plain,[in(1289 ^ [], 1285 ^ [])],extension(1293 ^ 10)).
% 12.31/12.78  ncf('1.1.2.2',plain,[-(powerset(1285 ^ []) = powerset(1285 ^ []))],extension(2 ^ 5,bind([[_173586], [powerset(1285 ^ [])]]))).
% 12.31/12.78  %-----------------------------------------------------
% 12.31/12.78  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------