%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n031.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 12:02:28 EDT 2023

% Result   : Theorem 0.35s 1.37s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n031.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 13:40:55 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.35/1.37  
% 0.35/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.35/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/1.37  %-----------------------------------------------------
% 0.35/1.37  ncf(matrix, plain, [(1109 ^ _149532) ^ [] : [1118 ^ _149532 : [(1119 ^ _149532) ^ [] : [-(in(1104 ^ [], 1106 ^ []))], (1121 ^ _149532) ^ [] : [-(in(1105 ^ [], 1107 ^ []))], (1123 ^ _149532) ^ [] : [in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ []))]], 1110 ^ _149532 : [(1111 ^ _149532) ^ [] : [-(in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ [])))], (1113 ^ _149532) ^ [] : [in(1104 ^ [], 1106 ^ []), in(1105 ^ [], 1107 ^ [])]]], (2 ^ _149532) ^ [_149676] : [-(_149676 = _149676)], (4 ^ _149532) ^ [_149783, _149785] : [_149785 = _149783, -(_149783 = _149785)], (10 ^ _149532) ^ [_149987, _149989, _149991] : [-(_149991 = _149987), _149991 = _149989, _149989 = _149987], (20 ^ _149532) ^ [_150328, _150330, _150332, _150334] : [-(proper_subset(_150332, _150328)), proper_subset(_150334, _150330), _150334 = _150332, _150330 = _150328], (34 ^ _149532) ^ [_150772, _150774, _150776, _150778] : [-(disjoint(_150776, _150772)), disjoint(_150778, _150774), _150778 = _150776, _150774 = _150772], (48 ^ _149532) ^ [_151188, _151190] : [-(empty(_151188)), _151190 = _151188, empty(_151190)], (58 ^ _149532) ^ [_151511, _151513, _151515, _151517] : [-(subset(_151515, _151511)), subset(_151517, _151513), _151517 = _151515, _151513 = _151511], (72 ^ _149532) ^ [_151935, _151937, _151939, _151941] : [-(in(_151939, _151935)), in(_151941, _151937), _151941 = _151939, _151937 = _151935], (86 ^ _149532) ^ [_152393, _152395, _152397, _152399] : [-(set_intersection2(_152399, _152395) = set_intersection2(_152397, _152393)), _152399 = _152397, _152395 = _152393], (96 ^ _149532) ^ [_152752, _152754, _152756, _152758] : [-(set_difference(_152758, _152754) = set_difference(_152756, _152752)), _152758 = _152756, _152754 = _152752], (106 ^ _149532) ^ [_153111, _153113, _153115, _153117] : [-(set_union2(_153117, _153113) = set_union2(_153115, _153111)), _153117 = _153115, _153113 = _153111], (116 ^ _149532) ^ [_153442, _153444] : [_153444 = _153442, -(union(_153444) = union(_153442))], (122 ^ _149532) ^ [_153660, _153662] : [_153662 = _153660, -(powerset(_153662) = powerset(_153660))], (128 ^ _149532) ^ [_153878, _153880] : [_153880 = _153878, -(singleton(_153880) = singleton(_153878))], (134 ^ _149532) ^ [_154124, _154126, _154128, _154130] : [-(unordered_pair(_154130, _154126) = unordered_pair(_154128, _154124)), _154130 = _154128, _154126 = _154124], (144 ^ _149532) ^ [_154483, _154485, _154487, _154489] : [-(ordered_pair(_154489, _154485) = ordered_pair(_154487, _154483)), _154489 = _154487, _154485 = _154483], (154 ^ _149532) ^ [_154822, _154824, _154826, _154828] : [-(cartesian_product2(_154828, _154824) = cartesian_product2(_154826, _154822)), _154828 = _154826, _154824 = _154822], (164 ^ _149532) ^ [_155185, _155187] : [in(_155187, _155185), in(_155185, _155187)], (170 ^ _149532) ^ [_155396, _155398] : [proper_subset(_155398, _155396), proper_subset(_155396, _155398)], (176 ^ _149532) ^ [_155592, _155594] : [-(unordered_pair(_155594, _155592) = unordered_pair(_155592, _155594))], (178 ^ _149532) ^ [_155692, _155694] : [-(set_union2(_155694, _155692) = set_union2(_155692, _155694))], (180 ^ _149532) ^ [_155792, _155794] : [-(set_intersection2(_155794, _155792) = set_intersection2(_155792, _155794))], (182 ^ _149532) ^ [_155936, _155938] : [_155938 = _155936, 185 ^ _149532 : [(186 ^ _149532) ^ [] : [-(subset(_155938, _155936))], (188 ^ _149532) ^ [] : [-(subset(_155936, _155938))]]], (190 ^ _149532) ^ [_156173, _156175] : [-(_156175 = _156173), subset(_156175, _156173), subset(_156173, _156175)], (216 ^ _149532) ^ [_157024, _157026] : [-(_157024 = singleton(_157026)), 220 ^ _149532 : [(221 ^ _149532) ^ [] : [-(in(217 ^ [_157024, _157026], _157024))], (223 ^ _149532) ^ [] : [217 ^ [_157024, _157026] = _157026]], 224 ^ _149532 : [(225 ^ _149532) ^ [] : [-(217 ^ [_157024, _157026] = _157026)], (227 ^ _149532) ^ [] : [in(217 ^ [_157024, _157026], _157024)]]], (200 ^ _149532) ^ [_156503, _156505] : [_156503 = singleton(_156505), 203 ^ _149532 : [(204 ^ _149532) ^ [_156673] : [in(_156673, _156503), -(_156673 = _156505)], (210 ^ _149532) ^ [_156845] : [_156845 = _156505, -(in(_156845, _156503))]]], (231 ^ _149532) ^ [_157575] : [_157575 = empty_set, 234 ^ _149532 : [(235 ^ _149532) ^ [_157688] : [in(_157688, _157575)]]], (237 ^ _149532) ^ [_157754] : [-(in(238 ^ [_157754], _157754)), -(_157754 = empty_set)], (260 ^ _149532) ^ [_158566, _158568] : [-(_158566 = powerset(_158568)), 264 ^ _149532 : [(265 ^ _149532) ^ [] : [-(in(261 ^ [_158566, _158568], _158566))], (267 ^ _149532) ^ [] : [subset(261 ^ [_158566, _158568], _158568)]], 268 ^ _149532 : [(269 ^ _149532) ^ [] : [-(subset(261 ^ [_158566, _158568], _158568))], (271 ^ _149532) ^ [] : [in(261 ^ [_158566, _158568], _158566)]]], (244 ^ _149532) ^ [_158045, _158047] : [_158045 = powerset(_158047), 247 ^ _149532 : [(248 ^ _149532) ^ [_158215] : [in(_158215, _158045), -(subset(_158215, _158047))], (254 ^ _149532) ^ [_158387] : [subset(_158387, _158047), -(in(_158387, _158045))]]], (297 ^ _149532) ^ [_159870, _159872, _159874] : [-(_159870 = unordered_pair(_159874, _159872)), 301 ^ _149532 : [(302 ^ _149532) ^ [] : [-(in(298 ^ [_159870, _159872, _159874], _159870))], (304 ^ _149532) ^ [] : [298 ^ [_159870, _159872, _159874] = _159874], (306 ^ _149532) ^ [] : [298 ^ [_159870, _159872, _159874] = _159872]], 307 ^ _149532 : [(314 ^ _149532) ^ [] : [in(298 ^ [_159870, _159872, _159874], _159870)], (308 ^ _149532) ^ [] : [-(298 ^ [_159870, _159872, _159874] = _159874), -(298 ^ [_159870, _159872, _159874] = _159872)]]], (275 ^ _149532) ^ [_159145, _159147, _159149] : [_159145 = unordered_pair(_159149, _159147), 278 ^ _149532 : [(289 ^ _149532) ^ [_159605] : [290 ^ _149532 : [(291 ^ _149532) ^ [] : [_159605 = _159149], (293 ^ _149532) ^ [] : [_159605 = _159147]], -(in(_159605, _159145))], (279 ^ _149532) ^ [_159327] : [in(_159327, _159145), -(_159327 = _159149), -(_159327 = _159147)]]], (340 ^ _149532) ^ [_161389, _161391, _161393] : [-(_161389 = set_union2(_161393, _161391)), 344 ^ _149532 : [(345 ^ _149532) ^ [] : [-(in(341 ^ [_161389, _161391, _161393], _161389))], (347 ^ _149532) ^ [] : [in(341 ^ [_161389, _161391, _161393], _161393)], (349 ^ _149532) ^ [] : [in(341 ^ [_161389, _161391, _161393], _161391)]], 350 ^ _149532 : [(357 ^ _149532) ^ [] : [in(341 ^ [_161389, _161391, _161393], _161389)], (351 ^ _149532) ^ [] : [-(in(341 ^ [_161389, _161391, _161393], _161393)), -(in(341 ^ [_161389, _161391, _161393], _161391))]]], (318 ^ _149532) ^ [_160664, _160666, _160668] : [_160664 = set_union2(_160668, _160666), 321 ^ _149532 : [(332 ^ _149532) ^ [_161124] : [333 ^ _149532 : [(334 ^ _149532) ^ [] : [in(_161124, _160668)], (336 ^ _149532) ^ [] : [in(_161124, _160666)]], -(in(_161124, _160664))], (322 ^ _149532) ^ [_160846] : [in(_160846, _160664), -(in(_160846, _160668)), -(in(_160846, _160666))]]], (391 ^ _149532) ^ [_163440, _163442, _163444] : [-(_163440 = cartesian_product2(_163444, _163442)), 409 ^ _149532 : [(410 ^ _149532) ^ [] : [-(in(407 ^ [_163440, _163442, _163444], _163444))], (412 ^ _149532) ^ [] : [-(in(408 ^ [_163440, _163442, _163444], _163442))], (414 ^ _149532) ^ [] : [-(392 ^ [_163440, _163442, _163444] = ordered_pair(407 ^ [_163440, _163442, _163444], 408 ^ [_163440, _163442, _163444]))], (416 ^ _149532) ^ [] : [in(392 ^ [_163440, _163442, _163444], _163440)]], 395 ^ _149532 : [(396 ^ _149532) ^ [] : [-(in(392 ^ [_163440, _163442, _163444], _163440))], (398 ^ _149532) ^ [_163778, _163780] : [in(_163780, _163444), in(_163778, _163442), 392 ^ [_163440, _163442, _163444] = ordered_pair(_163780, _163778)]]], (361 ^ _149532) ^ [_162183, _162185, _162187] : [_162183 = cartesian_product2(_162187, _162185), 364 ^ _149532 : [(365 ^ _149532) ^ [_162384] : [in(_162384, _162183), 370 ^ _149532 : [(371 ^ _149532) ^ [] : [-(in(368 ^ [_162183, _162185, _162187, _162384], _162187))], (373 ^ _149532) ^ [] : [-(in(369 ^ [_162183, _162185, _162187, _162384], _162185))], (375 ^ _149532) ^ [] : [-(_162384 = ordered_pair(368 ^ [_162183, _162185, _162187, _162384], 369 ^ [_162183, _162185, _162187, _162384]))]]], (377 ^ _149532) ^ [_162944] : [-(in(_162944, _162183)), 378 ^ _149532 : [(379 ^ _149532) ^ [_163074, _163076] : [in(_163076, _162187), in(_163074, _162185), _162944 = ordered_pair(_163076, _163074)]]]]], (430 ^ _149532) ^ [_165031, _165033] : [432 ^ _149532 : [(433 ^ _149532) ^ [] : [-(in(431 ^ [_165031, _165033], _165033))], (435 ^ _149532) ^ [] : [in(431 ^ [_165031, _165033], _165031)]], -(subset(_165033, _165031))], (420 ^ _149532) ^ [_164717, _164719] : [subset(_164719, _164717), 423 ^ _149532 : [(424 ^ _149532) ^ [_164854] : [in(_164854, _164719), -(in(_164854, _164717))]]], (461 ^ _149532) ^ [_166156, _166158, _166160] : [-(_166156 = set_intersection2(_166160, _166158)), 473 ^ _149532 : [(474 ^ _149532) ^ [] : [-(in(462 ^ [_166156, _166158, _166160], _166160))], (476 ^ _149532) ^ [] : [-(in(462 ^ [_166156, _166158, _166160], _166158))], (478 ^ _149532) ^ [] : [in(462 ^ [_166156, _166158, _166160], _166156)]], 465 ^ _149532 : [(466 ^ _149532) ^ [] : [-(in(462 ^ [_166156, _166158, _166160], _166156))], (468 ^ _149532) ^ [] : [in(462 ^ [_166156, _166158, _166160], _166160), in(462 ^ [_166156, _166158, _166160], _166158)]]], (439 ^ _149532) ^ [_165431, _165433, _165435] : [_165431 = set_intersection2(_165435, _165433), 442 ^ _149532 : [(443 ^ _149532) ^ [_165613] : [in(_165613, _165431), 446 ^ _149532 : [(447 ^ _149532) ^ [] : [-(in(_165613, _165435))], (449 ^ _149532) ^ [] : [-(in(_165613, _165433))]]], (451 ^ _149532) ^ [_165872] : [-(in(_165872, _165431)), in(_165872, _165435), in(_165872, _165433)]]], (505 ^ _149532) ^ [_167783, _167785] : [-(_167783 = union(_167785)), 518 ^ _149532 : [(519 ^ _149532) ^ [] : [-(in(506 ^ [_167783, _167785], 517 ^ [_167783, _167785]))], (521 ^ _149532) ^ [] : [-(in(517 ^ [_167783, _167785], _167785))], (523 ^ _149532) ^ [] : [in(506 ^ [_167783, _167785], _167783)]], 509 ^ _149532 : [(510 ^ _149532) ^ [] : [-(in(506 ^ [_167783, _167785], _167783))], (512 ^ _149532) ^ [_168066] : [in(506 ^ [_167783, _167785], _168066), in(_168066, _167785)]]], (482 ^ _149532) ^ [_166938, _166940] : [_166938 = union(_166940), 485 ^ _149532 : [(486 ^ _149532) ^ [_167119] : [in(_167119, _166938), 490 ^ _149532 : [(491 ^ _149532) ^ [] : [-(in(_167119, 489 ^ [_166938, _166940, _167119]))], (493 ^ _149532) ^ [] : [-(in(489 ^ [_166938, _166940, _167119], _166940))]]], (495 ^ _149532) ^ [_167446] : [-(in(_167446, _166938)), 496 ^ _149532 : [(497 ^ _149532) ^ [_167544] : [in(_167446, _167544), in(_167544, _166940)]]]]], (549 ^ _149532) ^ [_169404, _169406, _169408] : [-(_169404 = set_difference(_169408, _169406)), 561 ^ _149532 : [(562 ^ _149532) ^ [] : [-(in(550 ^ [_169404, _169406, _169408], _169408))], (564 ^ _149532) ^ [] : [in(550 ^ [_169404, _169406, _169408], _169406)], (566 ^ _149532) ^ [] : [in(550 ^ [_169404, _169406, _169408], _169404)]], 553 ^ _149532 : [(554 ^ _149532) ^ [] : [-(in(550 ^ [_169404, _169406, _169408], _169404))], (556 ^ _149532) ^ [] : [in(550 ^ [_169404, _169406, _169408], _169408), -(in(550 ^ [_169404, _169406, _169408], _169406))]]], (527 ^ _149532) ^ [_168673, _168675, _168677] : [_168673 = set_difference(_168677, _168675), 530 ^ _149532 : [(531 ^ _149532) ^ [_168857] : [in(_168857, _168673), 534 ^ _149532 : [(535 ^ _149532) ^ [] : [-(in(_168857, _168677))], (537 ^ _149532) ^ [] : [in(_168857, _168675)]]], (539 ^ _149532) ^ [_169117] : [-(in(_169117, _168673)), in(_169117, _168677), -(in(_169117, _168675))]]], (570 ^ _149532) ^ [_170146, _170148] : [-(ordered_pair(_170148, _170146) = unordered_pair(unordered_pair(_170148, _170146), singleton(_170148)))], (572 ^ _149532) ^ [_170295, _170297] : [disjoint(_170297, _170295), -(set_intersection2(_170297, _170295) = empty_set)], (578 ^ _149532) ^ [_170463, _170465] : [set_intersection2(_170465, _170463) = empty_set, -(disjoint(_170465, _170463))], (584 ^ _149532) ^ [_170710, _170712] : [proper_subset(_170712, _170710), 587 ^ _149532 : [(588 ^ _149532) ^ [] : [-(subset(_170712, _170710))], (590 ^ _149532) ^ [] : [_170712 = _170710]]], (592 ^ _149532) ^ [_170948, _170950] : [-(proper_subset(_170950, _170948)), subset(_170950, _170948), -(_170950 = _170948)], (602 ^ _149532) ^ [] : [true___, -(true___)], (608 ^ _149532) ^ [] : [true___, -(true___)], (614 ^ _149532) ^ [] : [true___, -(true___)], (620 ^ _149532) ^ [] : [true___, -(true___)], (626 ^ _149532) ^ [] : [true___, -(true___)], (632 ^ _149532) ^ [] : [true___, -(true___)], (638 ^ _149532) ^ [] : [true___, -(true___)], (644 ^ _149532) ^ [] : [true___, -(true___)], (650 ^ _149532) ^ [] : [true___, -(true___)], (656 ^ _149532) ^ [] : [true___, -(true___)], (662 ^ _149532) ^ [] : [-(empty(empty_set))], (664 ^ _149532) ^ [_172479, _172481] : [empty(ordered_pair(_172481, _172479))], (666 ^ _149532) ^ [_172590, _172592] : [-(empty(_172592)), empty(set_union2(_172592, _172590))], (672 ^ _149532) ^ [_172806, _172808] : [-(empty(_172808)), empty(set_union2(_172806, _172808))], (678 ^ _149532) ^ [_173007, _173009] : [-(set_union2(_173009, _173009) = _173009)], (680 ^ _149532) ^ [_173104, _173106] : [-(set_intersection2(_173106, _173106) = _173106)], (682 ^ _149532) ^ [_173200, _173202] : [proper_subset(_173202, _173202)], (684 ^ _149532) ^ [_173279] : [singleton(_173279) = empty_set], (686 ^ _149532) ^ [_173388, _173390] : [in(_173390, _173388), -(set_union2(singleton(_173390), _173388) = _173388)], (692 ^ _149532) ^ [_173608, _173610] : [disjoint(singleton(_173610), _173608), in(_173610, _173608)], (698 ^ _149532) ^ [_173821, _173823] : [-(in(_173823, _173821)), -(disjoint(singleton(_173823), _173821))], (704 ^ _149532) ^ [_174067, _174069] : [subset(singleton(_174069), _174067), -(in(_174069, _174067))], (710 ^ _149532) ^ [_174233, _174235] : [in(_174235, _174233), -(subset(singleton(_174235), _174233))], (716 ^ _149532) ^ [_174478, _174480] : [set_difference(_174480, _174478) = empty_set, -(subset(_174480, _174478))], (722 ^ _149532) ^ [_174646, _174648] : [subset(_174648, _174646), -(set_difference(_174648, _174646) = empty_set)], (728 ^ _149532) ^ [_174878, _174880, _174882] : [subset(_174882, _174880), -(in(_174878, _174882)), -(subset(_174882, set_difference(_174880, singleton(_174878))))], (748 ^ _149532) ^ [_175487, _175489] : [749 ^ _149532 : [(750 ^ _149532) ^ [] : [_175489 = empty_set], (752 ^ _149532) ^ [] : [_175489 = singleton(_175487)]], -(subset(_175489, singleton(_175487)))], (738 ^ _149532) ^ [_175227, _175229] : [subset(_175229, singleton(_175227)), -(_175229 = empty_set), -(_175229 = singleton(_175227))], (756 ^ _149532) ^ [_175781, _175783] : [in(_175783, _175781), -(subset(_175783, union(_175781)))], (762 ^ _149532) ^ [_176052, _176054, _176056, _176058] : [in(ordered_pair(_176058, _176056), cartesian_product2(_176054, _176052)), 765 ^ _149532 : [(766 ^ _149532) ^ [] : [-(in(_176058, _176054))], (768 ^ _149532) ^ [] : [-(in(_176056, _176052))]]], (770 ^ _149532) ^ [_176317, _176319, _176321, _176323] : [-(in(ordered_pair(_176323, _176321), cartesian_product2(_176319, _176317))), in(_176323, _176319), in(_176321, _176317)], (781 ^ _149532) ^ [] : [-(empty(779 ^ []))], (784 ^ _149532) ^ [] : [empty(782 ^ [])], (786 ^ _149532) ^ [_176814, _176816] : [-(subset(_176816, _176816))], (788 ^ _149532) ^ [_176923, _176925] : [disjoint(_176925, _176923), -(disjoint(_176923, _176925))], (794 ^ _149532) ^ [_177161, _177163, _177165, _177167] : [unordered_pair(_177167, _177165) = unordered_pair(_177163, _177161), -(_177167 = _177163), -(_177167 = _177161)], (804 ^ _149532) ^ [_177497, _177499] : [subset(_177499, _177497), -(set_union2(_177499, _177497) = _177497)], (810 ^ _149532) ^ [_177698, _177700] : [-(subset(set_intersection2(_177700, _177698), _177700))], (812 ^ _149532) ^ [_177824, _177826, _177828] : [-(subset(_177828, set_intersection2(_177826, _177824))), subset(_177828, _177826), subset(_177828, _177824)], (822 ^ _149532) ^ [_178110] : [-(set_union2(_178110, empty_set) = _178110)], (824 ^ _149532) ^ [_178234, _178236, _178238] : [-(subset(_178238, _178234)), subset(_178238, _178236), subset(_178236, _178234)], (834 ^ _149532) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (836 ^ _149532) ^ [_178610, _178612, _178614] : [subset(_178614, _178612), -(subset(set_intersection2(_178614, _178610), set_intersection2(_178612, _178610)))], (842 ^ _149532) ^ [_178838, _178840] : [subset(_178840, _178838), -(set_intersection2(_178840, _178838) = _178840)], (848 ^ _149532) ^ [_179025] : [-(set_intersection2(_179025, empty_set) = empty_set)], (850 ^ _149532) ^ [_179135, _179137] : [-(_179137 = _179135), 854 ^ _149532 : [(855 ^ _149532) ^ [] : [-(in(851 ^ [_179135, _179137], _179137))], (857 ^ _149532) ^ [] : [in(851 ^ [_179135, _179137], _179135)]], 858 ^ _149532 : [(859 ^ _149532) ^ [] : [-(in(851 ^ [_179135, _179137], _179135))], (861 ^ _149532) ^ [] : [in(851 ^ [_179135, _179137], _179137)]]], (865 ^ _149532) ^ [_179636] : [-(subset(empty_set, _179636))], (867 ^ _149532) ^ [_179757, _179759, _179761] : [subset(_179761, _179759), -(subset(set_difference(_179761, _179757), set_difference(_179759, _179757)))], (873 ^ _149532) ^ [_180013, _180015, _180017, _180019] : [ordered_pair(_180019, _180017) = ordered_pair(_180015, _180013), 876 ^ _149532 : [(877 ^ _149532) ^ [] : [-(_180019 = _180015)], (879 ^ _149532) ^ [] : [-(_180017 = _180013)]]], (881 ^ _149532) ^ [_180311, _180313] : [-(subset(set_difference(_180313, _180311), _180313))], (883 ^ _149532) ^ [_180452, _180454] : [set_difference(_180454, _180452) = empty_set, -(subset(_180454, _180452))], (889 ^ _149532) ^ [_180620, _180622] : [subset(_180622, _180620), -(set_difference(_180622, _180620) = empty_set)], (895 ^ _149532) ^ [_180867, _180869] : [subset(singleton(_180869), _180867), -(in(_180869, _180867))], (901 ^ _149532) ^ [_181033, _181035] : [in(_181035, _181033), -(subset(singleton(_181035), _181033))], (907 ^ _149532) ^ [_181292, _181294, _181296] : [subset(unordered_pair(_181296, _181294), _181292), 910 ^ _149532 : [(911 ^ _149532) ^ [] : [-(in(_181296, _181292))], (913 ^ _149532) ^ [] : [-(in(_181294, _181292))]]], (915 ^ _149532) ^ [_181543, _181545, _181547] : [-(subset(unordered_pair(_181547, _181545), _181543)), in(_181547, _181543), in(_181545, _181543)], (925 ^ _149532) ^ [_181845, _181847] : [-(set_union2(_181847, set_difference(_181845, _181847)) = set_union2(_181847, _181845))], (937 ^ _149532) ^ [_182252, _182254] : [938 ^ _149532 : [(939 ^ _149532) ^ [] : [_182254 = empty_set], (941 ^ _149532) ^ [] : [_182254 = singleton(_182252)]], -(subset(_182254, singleton(_182252)))], (927 ^ _149532) ^ [_181992, _181994] : [subset(_181994, singleton(_181992)), -(_181994 = empty_set), -(_181994 = singleton(_181992))], (945 ^ _149532) ^ [_182517] : [-(set_difference(_182517, empty_set) = _182517)], (947 ^ _149532) ^ [_182647, _182649] : [-(disjoint(_182649, _182647)), 951 ^ _149532 : [(952 ^ _149532) ^ [] : [-(in(950 ^ [_182647, _182649], _182649))], (954 ^ _149532) ^ [] : [-(in(950 ^ [_182647, _182649], _182647))]]], (956 ^ _149532) ^ [_182961, _182963] : [disjoint(_182963, _182961), 957 ^ _149532 : [(958 ^ _149532) ^ [_183053] : [in(_183053, _182963), in(_183053, _182961)]]], (966 ^ _149532) ^ [_183310] : [subset(_183310, empty_set), -(_183310 = empty_set)], (972 ^ _149532) ^ [_183499, _183501] : [-(set_difference(set_union2(_183501, _183499), _183499) = set_difference(_183501, _183499))], (974 ^ _149532) ^ [_183617, _183619] : [subset(_183619, _183617), -(_183617 = set_union2(_183619, set_difference(_183617, _183619)))], (980 ^ _149532) ^ [_183839, _183841] : [in(_183841, _183839), -(set_union2(singleton(_183841), _183839) = _183839)], (986 ^ _149532) ^ [_184044, _184046] : [-(set_difference(_184046, set_difference(_184046, _184044)) = set_intersection2(_184046, _184044))], (988 ^ _149532) ^ [_184133] : [-(set_difference(empty_set, _184133) = empty_set)], (990 ^ _149532) ^ [_184263, _184265] : [-(disjoint(_184265, _184263)), -(in(993 ^ [_184263, _184265], set_intersection2(_184265, _184263)))], (997 ^ _149532) ^ [_184498, _184500] : [998 ^ _149532 : [(999 ^ _149532) ^ [_184571] : [in(_184571, set_intersection2(_184500, _184498))]], disjoint(_184500, _184498)], (1003 ^ _149532) ^ [_184737, _184739] : [subset(_184739, _184737), proper_subset(_184737, _184739)], (1009 ^ _149532) ^ [_184960, _184962, _184964] : [-(disjoint(_184964, _184960)), subset(_184964, _184962), disjoint(_184962, _184960)], (1019 ^ _149532) ^ [_185298, _185300] : [set_difference(_185300, singleton(_185298)) = _185300, in(_185298, _185300)], (1025 ^ _149532) ^ [_185471, _185473] : [-(in(_185471, _185473)), -(set_difference(_185473, singleton(_185471)) = _185473)], (1031 ^ _149532) ^ [_185667] : [-(unordered_pair(_185667, _185667) = singleton(_185667))], (1033 ^ _149532) ^ [_185765] : [empty(_185765), -(_185765 = empty_set)], (1039 ^ _149532) ^ [_185967, _185969] : [subset(singleton(_185969), singleton(_185967)), -(_185969 = _185967)], (1045 ^ _149532) ^ [_186185, _186187] : [in(_186187, _186185), empty(_186185)], (1051 ^ _149532) ^ [_186377, _186379] : [-(subset(_186379, set_union2(_186379, _186377)))], (1053 ^ _149532) ^ [_186518, _186520] : [disjoint(_186520, _186518), -(set_difference(_186520, _186518) = _186520)], (1059 ^ _149532) ^ [_186686, _186688] : [set_difference(_186688, _186686) = _186688, -(disjoint(_186688, _186686))], (1065 ^ _149532) ^ [_186904, _186906] : [empty(_186906), -(_186906 = _186904), empty(_186904)], (1075 ^ _149532) ^ [_187215, _187217, _187219] : [-(subset(set_union2(_187219, _187215), _187217)), subset(_187219, _187217), subset(_187215, _187217)], (1085 ^ _149532) ^ [_187544, _187546, _187548] : [singleton(_187548) = unordered_pair(_187546, _187544), -(_187548 = _187546)], (1091 ^ _149532) ^ [_187770, _187772] : [in(_187772, _187770), -(subset(_187772, union(_187770)))], (1097 ^ _149532) ^ [_187955] : [-(union(powerset(_187955)) = _187955)], (1099 ^ _149532) ^ [_188060, _188062, _188064] : [singleton(_188064) = unordered_pair(_188062, _188060), -(_188062 = _188060)]], input).
% 0.35/1.37  ncf('1',plain,[1123 : in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ [])), 1113 : in(1104 ^ [], 1106 ^ []), 1113 : in(1105 ^ [], 1107 ^ [])],start(1109 ^ 0)).
% 0.35/1.37  ncf('1.1',plain,[-(in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ []))), in(1104 ^ [], 1106 ^ []), in(1105 ^ [], 1107 ^ [])],extension(770 ^ 3,bind([[_176317, _176319, _176321, _176323], [1107 ^ [], 1106 ^ [], 1105 ^ [], 1104 ^ []]]))).
% 0.35/1.37  ncf('1.1.1',plain,[-(in(1104 ^ [], 1106 ^ []))],extension(1119 ^ 4)).
% 0.35/1.37  ncf('1.1.2',plain,[-(in(1105 ^ [], 1107 ^ []))],extension(1121 ^ 4)).
% 0.35/1.37  ncf('1.2',plain,[-(in(1104 ^ [], 1106 ^ [])), in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ []))],extension(762 ^ 3,bind([[_176052, _176054, _176056, _176058], [1107 ^ [], 1106 ^ [], 1105 ^ [], 1104 ^ []]]))).
% 0.35/1.37  ncf('1.2.1',plain,[-(in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ [])))],extension(1111 ^ 4)).
% 0.35/1.37  ncf('1.3',plain,[-(in(1105 ^ [], 1107 ^ [])), in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ []))],extension(762 ^ 3,bind([[_176052, _176054, _176056, _176058], [1107 ^ [], 1106 ^ [], 1105 ^ [], 1104 ^ []]]))).
% 0.35/1.37  ncf('1.3.1',plain,[-(in(ordered_pair(1104 ^ [], 1105 ^ []), cartesian_product2(1106 ^ [], 1107 ^ [])))],extension(1111 ^ 4)).
% 0.35/1.37  %-----------------------------------------------------
% 0.35/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------