%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n025.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 12:02:26 EDT 2023

% Result   : Theorem 0.51s 1.37s
% Output   : Proof 0.51s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n025.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 12:53:18 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.51/1.37  
% 0.51/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.51/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.51/1.37  %-----------------------------------------------------
% 0.51/1.37  ncf(matrix, plain, [(1063 ^ _142456) ^ [] : [1064 ^ _142456 : [(1065 ^ _142456) ^ [] : [-(subset(1060 ^ [], singleton(1061 ^ [])))], (1067 ^ _142456) ^ [] : [1060 ^ [] = empty_set], (1069 ^ _142456) ^ [] : [1060 ^ [] = singleton(1061 ^ [])]], 1070 ^ _142456 : [(1077 ^ _142456) ^ [] : [subset(1060 ^ [], singleton(1061 ^ []))], (1071 ^ _142456) ^ [] : [-(1060 ^ [] = empty_set), -(1060 ^ [] = singleton(1061 ^ []))]]], (2 ^ _142456) ^ [_142600] : [-(_142600 = _142600)], (4 ^ _142456) ^ [_142707, _142709] : [_142709 = _142707, -(_142707 = _142709)], (10 ^ _142456) ^ [_142911, _142913, _142915] : [-(_142915 = _142911), _142915 = _142913, _142913 = _142911], (20 ^ _142456) ^ [_143252, _143254, _143256, _143258] : [-(proper_subset(_143256, _143252)), proper_subset(_143258, _143254), _143258 = _143256, _143254 = _143252], (34 ^ _142456) ^ [_143696, _143698, _143700, _143702] : [-(in(_143700, _143696)), in(_143702, _143698), _143702 = _143700, _143698 = _143696], (48 ^ _142456) ^ [_144140, _144142, _144144, _144146] : [-(disjoint(_144144, _144140)), disjoint(_144146, _144142), _144146 = _144144, _144142 = _144140], (62 ^ _142456) ^ [_144556, _144558] : [-(empty(_144556)), _144558 = _144556, empty(_144558)], (72 ^ _142456) ^ [_144859, _144861, _144863, _144865] : [-(subset(_144863, _144859)), subset(_144865, _144861), _144865 = _144863, _144861 = _144859], (86 ^ _142456) ^ [_145289, _145291] : [_145291 = _145289, -(union(_145291) = union(_145289))], (92 ^ _142456) ^ [_145535, _145537, _145539, _145541] : [-(cartesian_product2(_145541, _145537) = cartesian_product2(_145539, _145535)), _145541 = _145539, _145537 = _145535], (102 ^ _142456) ^ [_145866, _145868] : [_145868 = _145866, -(powerset(_145868) = powerset(_145866))], (108 ^ _142456) ^ [_146112, _146114, _146116, _146118] : [-(ordered_pair(_146118, _146114) = ordered_pair(_146116, _146112)), _146118 = _146116, _146114 = _146112], (118 ^ _142456) ^ [_146471, _146473, _146475, _146477] : [-(set_intersection2(_146477, _146473) = set_intersection2(_146475, _146471)), _146477 = _146475, _146473 = _146471], (128 ^ _142456) ^ [_146830, _146832, _146834, _146836] : [-(set_difference(_146836, _146832) = set_difference(_146834, _146830)), _146836 = _146834, _146832 = _146830], (138 ^ _142456) ^ [_147189, _147191, _147193, _147195] : [-(set_union2(_147195, _147191) = set_union2(_147193, _147189)), _147195 = _147193, _147191 = _147189], (158 ^ _142456) ^ [_147859, _147861] : [_147861 = _147859, -(singleton(_147861) = singleton(_147859))], (148 ^ _142456) ^ [_147548, _147550, _147552, _147554] : [-(unordered_pair(_147554, _147550) = unordered_pair(_147552, _147548)), _147554 = _147552, _147550 = _147548], (164 ^ _142456) ^ [_148109, _148111] : [in(_148111, _148109), in(_148109, _148111)], (170 ^ _142456) ^ [_148320, _148322] : [proper_subset(_148322, _148320), proper_subset(_148320, _148322)], (176 ^ _142456) ^ [_148516, _148518] : [-(unordered_pair(_148518, _148516) = unordered_pair(_148516, _148518))], (178 ^ _142456) ^ [_148616, _148618] : [-(set_union2(_148618, _148616) = set_union2(_148616, _148618))], (180 ^ _142456) ^ [_148716, _148718] : [-(set_intersection2(_148718, _148716) = set_intersection2(_148716, _148718))], (182 ^ _142456) ^ [_148860, _148862] : [_148862 = _148860, 185 ^ _142456 : [(186 ^ _142456) ^ [] : [-(subset(_148862, _148860))], (188 ^ _142456) ^ [] : [-(subset(_148860, _148862))]]], (190 ^ _142456) ^ [_149097, _149099] : [-(_149099 = _149097), subset(_149099, _149097), subset(_149097, _149099)], (216 ^ _142456) ^ [_149948, _149950] : [-(_149948 = singleton(_149950)), 220 ^ _142456 : [(221 ^ _142456) ^ [] : [-(in(217 ^ [_149948, _149950], _149948))], (223 ^ _142456) ^ [] : [217 ^ [_149948, _149950] = _149950]], 224 ^ _142456 : [(225 ^ _142456) ^ [] : [-(217 ^ [_149948, _149950] = _149950)], (227 ^ _142456) ^ [] : [in(217 ^ [_149948, _149950], _149948)]]], (200 ^ _142456) ^ [_149427, _149429] : [_149427 = singleton(_149429), 203 ^ _142456 : [(204 ^ _142456) ^ [_149597] : [in(_149597, _149427), -(_149597 = _149429)], (210 ^ _142456) ^ [_149769] : [_149769 = _149429, -(in(_149769, _149427))]]], (231 ^ _142456) ^ [_150499] : [_150499 = empty_set, 234 ^ _142456 : [(235 ^ _142456) ^ [_150612] : [in(_150612, _150499)]]], (237 ^ _142456) ^ [_150678] : [-(in(238 ^ [_150678], _150678)), -(_150678 = empty_set)], (260 ^ _142456) ^ [_151490, _151492] : [-(_151490 = powerset(_151492)), 264 ^ _142456 : [(265 ^ _142456) ^ [] : [-(in(261 ^ [_151490, _151492], _151490))], (267 ^ _142456) ^ [] : [subset(261 ^ [_151490, _151492], _151492)]], 268 ^ _142456 : [(269 ^ _142456) ^ [] : [-(subset(261 ^ [_151490, _151492], _151492))], (271 ^ _142456) ^ [] : [in(261 ^ [_151490, _151492], _151490)]]], (244 ^ _142456) ^ [_150969, _150971] : [_150969 = powerset(_150971), 247 ^ _142456 : [(248 ^ _142456) ^ [_151139] : [in(_151139, _150969), -(subset(_151139, _150971))], (254 ^ _142456) ^ [_151311] : [subset(_151311, _150971), -(in(_151311, _150969))]]], (297 ^ _142456) ^ [_152794, _152796, _152798] : [-(_152794 = unordered_pair(_152798, _152796)), 301 ^ _142456 : [(302 ^ _142456) ^ [] : [-(in(298 ^ [_152794, _152796, _152798], _152794))], (304 ^ _142456) ^ [] : [298 ^ [_152794, _152796, _152798] = _152798], (306 ^ _142456) ^ [] : [298 ^ [_152794, _152796, _152798] = _152796]], 307 ^ _142456 : [(314 ^ _142456) ^ [] : [in(298 ^ [_152794, _152796, _152798], _152794)], (308 ^ _142456) ^ [] : [-(298 ^ [_152794, _152796, _152798] = _152798), -(298 ^ [_152794, _152796, _152798] = _152796)]]], (275 ^ _142456) ^ [_152069, _152071, _152073] : [_152069 = unordered_pair(_152073, _152071), 278 ^ _142456 : [(289 ^ _142456) ^ [_152529] : [290 ^ _142456 : [(291 ^ _142456) ^ [] : [_152529 = _152073], (293 ^ _142456) ^ [] : [_152529 = _152071]], -(in(_152529, _152069))], (279 ^ _142456) ^ [_152251] : [in(_152251, _152069), -(_152251 = _152073), -(_152251 = _152071)]]], (340 ^ _142456) ^ [_154313, _154315, _154317] : [-(_154313 = set_union2(_154317, _154315)), 344 ^ _142456 : [(345 ^ _142456) ^ [] : [-(in(341 ^ [_154313, _154315, _154317], _154313))], (347 ^ _142456) ^ [] : [in(341 ^ [_154313, _154315, _154317], _154317)], (349 ^ _142456) ^ [] : [in(341 ^ [_154313, _154315, _154317], _154315)]], 350 ^ _142456 : [(357 ^ _142456) ^ [] : [in(341 ^ [_154313, _154315, _154317], _154313)], (351 ^ _142456) ^ [] : [-(in(341 ^ [_154313, _154315, _154317], _154317)), -(in(341 ^ [_154313, _154315, _154317], _154315))]]], (318 ^ _142456) ^ [_153588, _153590, _153592] : [_153588 = set_union2(_153592, _153590), 321 ^ _142456 : [(332 ^ _142456) ^ [_154048] : [333 ^ _142456 : [(334 ^ _142456) ^ [] : [in(_154048, _153592)], (336 ^ _142456) ^ [] : [in(_154048, _153590)]], -(in(_154048, _153588))], (322 ^ _142456) ^ [_153770] : [in(_153770, _153588), -(in(_153770, _153592)), -(in(_153770, _153590))]]], (391 ^ _142456) ^ [_156364, _156366, _156368] : [-(_156364 = cartesian_product2(_156368, _156366)), 409 ^ _142456 : [(410 ^ _142456) ^ [] : [-(in(407 ^ [_156364, _156366, _156368], _156368))], (412 ^ _142456) ^ [] : [-(in(408 ^ [_156364, _156366, _156368], _156366))], (414 ^ _142456) ^ [] : [-(392 ^ [_156364, _156366, _156368] = ordered_pair(407 ^ [_156364, _156366, _156368], 408 ^ [_156364, _156366, _156368]))], (416 ^ _142456) ^ [] : [in(392 ^ [_156364, _156366, _156368], _156364)]], 395 ^ _142456 : [(396 ^ _142456) ^ [] : [-(in(392 ^ [_156364, _156366, _156368], _156364))], (398 ^ _142456) ^ [_156702, _156704] : [in(_156704, _156368), in(_156702, _156366), 392 ^ [_156364, _156366, _156368] = ordered_pair(_156704, _156702)]]], (361 ^ _142456) ^ [_155107, _155109, _155111] : [_155107 = cartesian_product2(_155111, _155109), 364 ^ _142456 : [(365 ^ _142456) ^ [_155308] : [in(_155308, _155107), 370 ^ _142456 : [(371 ^ _142456) ^ [] : [-(in(368 ^ [_155107, _155109, _155111, _155308], _155111))], (373 ^ _142456) ^ [] : [-(in(369 ^ [_155107, _155109, _155111, _155308], _155109))], (375 ^ _142456) ^ [] : [-(_155308 = ordered_pair(368 ^ [_155107, _155109, _155111, _155308], 369 ^ [_155107, _155109, _155111, _155308]))]]], (377 ^ _142456) ^ [_155868] : [-(in(_155868, _155107)), 378 ^ _142456 : [(379 ^ _142456) ^ [_155998, _156000] : [in(_156000, _155111), in(_155998, _155109), _155868 = ordered_pair(_156000, _155998)]]]]], (430 ^ _142456) ^ [_157955, _157957] : [432 ^ _142456 : [(433 ^ _142456) ^ [] : [-(in(431 ^ [_157955, _157957], _157957))], (435 ^ _142456) ^ [] : [in(431 ^ [_157955, _157957], _157955)]], -(subset(_157957, _157955))], (420 ^ _142456) ^ [_157641, _157643] : [subset(_157643, _157641), 423 ^ _142456 : [(424 ^ _142456) ^ [_157778] : [in(_157778, _157643), -(in(_157778, _157641))]]], (461 ^ _142456) ^ [_159080, _159082, _159084] : [-(_159080 = set_intersection2(_159084, _159082)), 473 ^ _142456 : [(474 ^ _142456) ^ [] : [-(in(462 ^ [_159080, _159082, _159084], _159084))], (476 ^ _142456) ^ [] : [-(in(462 ^ [_159080, _159082, _159084], _159082))], (478 ^ _142456) ^ [] : [in(462 ^ [_159080, _159082, _159084], _159080)]], 465 ^ _142456 : [(466 ^ _142456) ^ [] : [-(in(462 ^ [_159080, _159082, _159084], _159080))], (468 ^ _142456) ^ [] : [in(462 ^ [_159080, _159082, _159084], _159084), in(462 ^ [_159080, _159082, _159084], _159082)]]], (439 ^ _142456) ^ [_158355, _158357, _158359] : [_158355 = set_intersection2(_158359, _158357), 442 ^ _142456 : [(443 ^ _142456) ^ [_158537] : [in(_158537, _158355), 446 ^ _142456 : [(447 ^ _142456) ^ [] : [-(in(_158537, _158359))], (449 ^ _142456) ^ [] : [-(in(_158537, _158357))]]], (451 ^ _142456) ^ [_158796] : [-(in(_158796, _158355)), in(_158796, _158359), in(_158796, _158357)]]], (505 ^ _142456) ^ [_160707, _160709] : [-(_160707 = union(_160709)), 518 ^ _142456 : [(519 ^ _142456) ^ [] : [-(in(506 ^ [_160707, _160709], 517 ^ [_160707, _160709]))], (521 ^ _142456) ^ [] : [-(in(517 ^ [_160707, _160709], _160709))], (523 ^ _142456) ^ [] : [in(506 ^ [_160707, _160709], _160707)]], 509 ^ _142456 : [(510 ^ _142456) ^ [] : [-(in(506 ^ [_160707, _160709], _160707))], (512 ^ _142456) ^ [_160990] : [in(506 ^ [_160707, _160709], _160990), in(_160990, _160709)]]], (482 ^ _142456) ^ [_159862, _159864] : [_159862 = union(_159864), 485 ^ _142456 : [(486 ^ _142456) ^ [_160043] : [in(_160043, _159862), 490 ^ _142456 : [(491 ^ _142456) ^ [] : [-(in(_160043, 489 ^ [_159862, _159864, _160043]))], (493 ^ _142456) ^ [] : [-(in(489 ^ [_159862, _159864, _160043], _159864))]]], (495 ^ _142456) ^ [_160370] : [-(in(_160370, _159862)), 496 ^ _142456 : [(497 ^ _142456) ^ [_160468] : [in(_160370, _160468), in(_160468, _159864)]]]]], (549 ^ _142456) ^ [_162328, _162330, _162332] : [-(_162328 = set_difference(_162332, _162330)), 561 ^ _142456 : [(562 ^ _142456) ^ [] : [-(in(550 ^ [_162328, _162330, _162332], _162332))], (564 ^ _142456) ^ [] : [in(550 ^ [_162328, _162330, _162332], _162330)], (566 ^ _142456) ^ [] : [in(550 ^ [_162328, _162330, _162332], _162328)]], 553 ^ _142456 : [(554 ^ _142456) ^ [] : [-(in(550 ^ [_162328, _162330, _162332], _162328))], (556 ^ _142456) ^ [] : [in(550 ^ [_162328, _162330, _162332], _162332), -(in(550 ^ [_162328, _162330, _162332], _162330))]]], (527 ^ _142456) ^ [_161597, _161599, _161601] : [_161597 = set_difference(_161601, _161599), 530 ^ _142456 : [(531 ^ _142456) ^ [_161781] : [in(_161781, _161597), 534 ^ _142456 : [(535 ^ _142456) ^ [] : [-(in(_161781, _161601))], (537 ^ _142456) ^ [] : [in(_161781, _161599)]]], (539 ^ _142456) ^ [_162041] : [-(in(_162041, _161597)), in(_162041, _161601), -(in(_162041, _161599))]]], (570 ^ _142456) ^ [_163070, _163072] : [-(ordered_pair(_163072, _163070) = unordered_pair(unordered_pair(_163072, _163070), singleton(_163072)))], (572 ^ _142456) ^ [_163219, _163221] : [disjoint(_163221, _163219), -(set_intersection2(_163221, _163219) = empty_set)], (578 ^ _142456) ^ [_163387, _163389] : [set_intersection2(_163389, _163387) = empty_set, -(disjoint(_163389, _163387))], (584 ^ _142456) ^ [_163634, _163636] : [proper_subset(_163636, _163634), 587 ^ _142456 : [(588 ^ _142456) ^ [] : [-(subset(_163636, _163634))], (590 ^ _142456) ^ [] : [_163636 = _163634]]], (592 ^ _142456) ^ [_163872, _163874] : [-(proper_subset(_163874, _163872)), subset(_163874, _163872), -(_163874 = _163872)], (602 ^ _142456) ^ [] : [true___, -(true___)], (608 ^ _142456) ^ [] : [true___, -(true___)], (614 ^ _142456) ^ [] : [true___, -(true___)], (620 ^ _142456) ^ [] : [true___, -(true___)], (626 ^ _142456) ^ [] : [true___, -(true___)], (632 ^ _142456) ^ [] : [true___, -(true___)], (638 ^ _142456) ^ [] : [true___, -(true___)], (644 ^ _142456) ^ [] : [true___, -(true___)], (650 ^ _142456) ^ [] : [true___, -(true___)], (656 ^ _142456) ^ [] : [true___, -(true___)], (662 ^ _142456) ^ [] : [-(empty(empty_set))], (664 ^ _142456) ^ [_165403, _165405] : [empty(ordered_pair(_165405, _165403))], (666 ^ _142456) ^ [_165514, _165516] : [-(empty(_165516)), empty(set_union2(_165516, _165514))], (672 ^ _142456) ^ [_165730, _165732] : [-(empty(_165732)), empty(set_union2(_165730, _165732))], (678 ^ _142456) ^ [_165931, _165933] : [-(set_union2(_165933, _165933) = _165933)], (680 ^ _142456) ^ [_166028, _166030] : [-(set_intersection2(_166030, _166030) = _166030)], (682 ^ _142456) ^ [_166124, _166126] : [proper_subset(_166126, _166126)], (684 ^ _142456) ^ [_166203] : [singleton(_166203) = empty_set], (686 ^ _142456) ^ [_166312, _166314] : [in(_166314, _166312), -(set_union2(singleton(_166314), _166312) = _166312)], (692 ^ _142456) ^ [_166532, _166534] : [disjoint(singleton(_166534), _166532), in(_166534, _166532)], (698 ^ _142456) ^ [_166745, _166747] : [-(in(_166747, _166745)), -(disjoint(singleton(_166747), _166745))], (704 ^ _142456) ^ [_166991, _166993] : [subset(singleton(_166993), _166991), -(in(_166993, _166991))], (710 ^ _142456) ^ [_167157, _167159] : [in(_167159, _167157), -(subset(singleton(_167159), _167157))], (716 ^ _142456) ^ [_167402, _167404] : [set_difference(_167404, _167402) = empty_set, -(subset(_167404, _167402))], (722 ^ _142456) ^ [_167570, _167572] : [subset(_167572, _167570), -(set_difference(_167572, _167570) = empty_set)], (728 ^ _142456) ^ [_167802, _167804, _167806] : [subset(_167806, _167804), -(in(_167802, _167806)), -(subset(_167806, set_difference(_167804, singleton(_167802))))], (748 ^ _142456) ^ [_168411, _168413] : [749 ^ _142456 : [(750 ^ _142456) ^ [] : [_168413 = empty_set], (752 ^ _142456) ^ [] : [_168413 = singleton(_168411)]], -(subset(_168413, singleton(_168411)))], (738 ^ _142456) ^ [_168151, _168153] : [subset(_168153, singleton(_168151)), -(_168153 = empty_set), -(_168153 = singleton(_168151))], (756 ^ _142456) ^ [_168705, _168707] : [in(_168707, _168705), -(subset(_168707, union(_168705)))], (762 ^ _142456) ^ [_168976, _168978, _168980, _168982] : [in(ordered_pair(_168982, _168980), cartesian_product2(_168978, _168976)), 765 ^ _142456 : [(766 ^ _142456) ^ [] : [-(in(_168982, _168978))], (768 ^ _142456) ^ [] : [-(in(_168980, _168976))]]], (770 ^ _142456) ^ [_169241, _169243, _169245, _169247] : [-(in(ordered_pair(_169247, _169245), cartesian_product2(_169243, _169241))), in(_169247, _169243), in(_169245, _169241)], (781 ^ _142456) ^ [] : [-(empty(779 ^ []))], (784 ^ _142456) ^ [] : [empty(782 ^ [])], (786 ^ _142456) ^ [_169738, _169740] : [-(subset(_169740, _169740))], (788 ^ _142456) ^ [_169847, _169849] : [disjoint(_169849, _169847), -(disjoint(_169847, _169849))], (794 ^ _142456) ^ [_170085, _170087, _170089, _170091] : [unordered_pair(_170091, _170089) = unordered_pair(_170087, _170085), -(_170091 = _170087), -(_170091 = _170085)], (804 ^ _142456) ^ [_170421, _170423] : [subset(_170423, _170421), -(set_union2(_170423, _170421) = _170421)], (810 ^ _142456) ^ [_170622, _170624] : [-(subset(set_intersection2(_170624, _170622), _170624))], (812 ^ _142456) ^ [_170748, _170750, _170752] : [-(subset(_170752, set_intersection2(_170750, _170748))), subset(_170752, _170750), subset(_170752, _170748)], (822 ^ _142456) ^ [_171034] : [-(set_union2(_171034, empty_set) = _171034)], (824 ^ _142456) ^ [_171158, _171160, _171162] : [-(subset(_171162, _171158)), subset(_171162, _171160), subset(_171160, _171158)], (834 ^ _142456) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (836 ^ _142456) ^ [_171534, _171536, _171538] : [subset(_171538, _171536), -(subset(set_intersection2(_171538, _171534), set_intersection2(_171536, _171534)))], (842 ^ _142456) ^ [_171762, _171764] : [subset(_171764, _171762), -(set_intersection2(_171764, _171762) = _171764)], (848 ^ _142456) ^ [_171949] : [-(set_intersection2(_171949, empty_set) = empty_set)], (850 ^ _142456) ^ [_172059, _172061] : [-(_172061 = _172059), 854 ^ _142456 : [(855 ^ _142456) ^ [] : [-(in(851 ^ [_172059, _172061], _172061))], (857 ^ _142456) ^ [] : [in(851 ^ [_172059, _172061], _172059)]], 858 ^ _142456 : [(859 ^ _142456) ^ [] : [-(in(851 ^ [_172059, _172061], _172059))], (861 ^ _142456) ^ [] : [in(851 ^ [_172059, _172061], _172061)]]], (865 ^ _142456) ^ [_172560] : [-(subset(empty_set, _172560))], (867 ^ _142456) ^ [_172681, _172683, _172685] : [subset(_172685, _172683), -(subset(set_difference(_172685, _172681), set_difference(_172683, _172681)))], (873 ^ _142456) ^ [_172937, _172939, _172941, _172943] : [ordered_pair(_172943, _172941) = ordered_pair(_172939, _172937), 876 ^ _142456 : [(877 ^ _142456) ^ [] : [-(_172943 = _172939)], (879 ^ _142456) ^ [] : [-(_172941 = _172937)]]], (881 ^ _142456) ^ [_173235, _173237] : [-(subset(set_difference(_173237, _173235), _173237))], (883 ^ _142456) ^ [_173376, _173378] : [set_difference(_173378, _173376) = empty_set, -(subset(_173378, _173376))], (889 ^ _142456) ^ [_173544, _173546] : [subset(_173546, _173544), -(set_difference(_173546, _173544) = empty_set)], (895 ^ _142456) ^ [_173791, _173793] : [subset(singleton(_173793), _173791), -(in(_173793, _173791))], (901 ^ _142456) ^ [_173957, _173959] : [in(_173959, _173957), -(subset(singleton(_173959), _173957))], (907 ^ _142456) ^ [_174216, _174218, _174220] : [subset(unordered_pair(_174220, _174218), _174216), 910 ^ _142456 : [(911 ^ _142456) ^ [] : [-(in(_174220, _174216))], (913 ^ _142456) ^ [] : [-(in(_174218, _174216))]]], (915 ^ _142456) ^ [_174467, _174469, _174471] : [-(subset(unordered_pair(_174471, _174469), _174467)), in(_174471, _174467), in(_174469, _174467)], (925 ^ _142456) ^ [_174769, _174771] : [-(set_union2(_174771, set_difference(_174769, _174771)) = set_union2(_174771, _174769))], (927 ^ _142456) ^ [_174858] : [-(set_difference(_174858, empty_set) = _174858)], (929 ^ _142456) ^ [_174988, _174990] : [-(disjoint(_174990, _174988)), 933 ^ _142456 : [(934 ^ _142456) ^ [] : [-(in(932 ^ [_174988, _174990], _174990))], (936 ^ _142456) ^ [] : [-(in(932 ^ [_174988, _174990], _174988))]]], (938 ^ _142456) ^ [_175302, _175304] : [disjoint(_175304, _175302), 939 ^ _142456 : [(940 ^ _142456) ^ [_175394] : [in(_175394, _175304), in(_175394, _175302)]]], (948 ^ _142456) ^ [_175651] : [subset(_175651, empty_set), -(_175651 = empty_set)], (954 ^ _142456) ^ [_175840, _175842] : [-(set_difference(set_union2(_175842, _175840), _175840) = set_difference(_175842, _175840))], (956 ^ _142456) ^ [_175958, _175960] : [subset(_175960, _175958), -(_175958 = set_union2(_175960, set_difference(_175958, _175960)))], (962 ^ _142456) ^ [_176165, _176167] : [-(set_difference(_176167, set_difference(_176167, _176165)) = set_intersection2(_176167, _176165))], (964 ^ _142456) ^ [_176254] : [-(set_difference(empty_set, _176254) = empty_set)], (966 ^ _142456) ^ [_176384, _176386] : [-(disjoint(_176386, _176384)), -(in(969 ^ [_176384, _176386], set_intersection2(_176386, _176384)))], (973 ^ _142456) ^ [_176619, _176621] : [974 ^ _142456 : [(975 ^ _142456) ^ [_176692] : [in(_176692, set_intersection2(_176621, _176619))]], disjoint(_176621, _176619)], (979 ^ _142456) ^ [_176858, _176860] : [subset(_176860, _176858), proper_subset(_176858, _176860)], (985 ^ _142456) ^ [_177081, _177083, _177085] : [-(disjoint(_177085, _177081)), subset(_177085, _177083), disjoint(_177083, _177081)], (995 ^ _142456) ^ [_177361] : [-(unordered_pair(_177361, _177361) = singleton(_177361))], (997 ^ _142456) ^ [_177459] : [empty(_177459), -(_177459 = empty_set)], (1003 ^ _142456) ^ [_177661, _177663] : [subset(singleton(_177663), singleton(_177661)), -(_177663 = _177661)], (1009 ^ _142456) ^ [_177879, _177881] : [in(_177881, _177879), empty(_177879)], (1015 ^ _142456) ^ [_178071, _178073] : [-(subset(_178073, set_union2(_178073, _178071)))], (1017 ^ _142456) ^ [_178212, _178214] : [disjoint(_178214, _178212), -(set_difference(_178214, _178212) = _178214)], (1023 ^ _142456) ^ [_178380, _178382] : [set_difference(_178382, _178380) = _178382, -(disjoint(_178382, _178380))], (1029 ^ _142456) ^ [_178598, _178600] : [empty(_178600), -(_178600 = _178598), empty(_178598)], (1039 ^ _142456) ^ [_178909, _178911, _178913] : [-(subset(set_union2(_178913, _178909), _178911)), subset(_178913, _178911), subset(_178909, _178911)], (1049 ^ _142456) ^ [_179238, _179240, _179242] : [singleton(_179242) = unordered_pair(_179240, _179238), -(_179242 = _179240)], (1055 ^ _142456) ^ [_179458, _179460, _179462] : [singleton(_179462) = unordered_pair(_179460, _179458), -(_179460 = _179458)]], input).
% 0.51/1.37  ncf('1',plain,[1060 ^ [] = empty_set, 235 : in(431 ^ [singleton(1061 ^ []), 1060 ^ []], 1060 ^ [])],start(231 ^ 0,bind([[_150499, _150612], [1060 ^ [], 431 ^ [singleton(1061 ^ []), 1060 ^ []]]]))).
% 0.51/1.37  ncf('1.1',plain,[-(1060 ^ [] = empty_set), 1071 : -(1060 ^ [] = singleton(1061 ^ [])), 1065 : -(subset(1060 ^ [], singleton(1061 ^ [])))],extension(1063 ^ 1)).
% 0.51/1.37  ncf('1.1.1',plain,[1060 ^ [] = singleton(1061 ^ []), 186 : -(subset(1060 ^ [], singleton(1061 ^ [])))],extension(182 ^ 4,bind([[_148860, _148862], [singleton(1061 ^ []), 1060 ^ []]]))).
% 0.51/1.37  ncf('1.1.1.1',plain,[subset(1060 ^ [], singleton(1061 ^ []))],extension(1077 ^ 7)).
% 0.51/1.37  ncf('1.1.2',plain,[subset(1060 ^ [], singleton(1061 ^ [])), -(1060 ^ [] = empty_set), -(1060 ^ [] = singleton(1061 ^ []))],extension(738 ^ 4,bind([[_168151, _168153], [1061 ^ [], 1060 ^ []]]))).
% 0.51/1.37  ncf('1.1.2.1',plain,[1060 ^ [] = empty_set],reduction('1')).
% 0.51/1.37  ncf('1.1.2.2',plain,[1060 ^ [] = singleton(1061 ^ [])],extension(1069 ^ 5)).
% 0.51/1.37  ncf('1.2',plain,[-(in(431 ^ [singleton(1061 ^ []), 1060 ^ []], 1060 ^ [])), in(431 ^ [singleton(1061 ^ []), 1060 ^ []], 1060 ^ []), 431 ^ [singleton(1061 ^ []), 1060 ^ []] = 431 ^ [singleton(1061 ^ []), 1060 ^ []], 1060 ^ [] = 1060 ^ []],extension(34 ^ 3,bind([[_143696, _143698, _143700, _143702], [1060 ^ [], 1060 ^ [], 431 ^ [singleton(1061 ^ []), 1060 ^ []], 431 ^ [singleton(1061 ^ []), 1060 ^ []]]]))).
% 0.51/1.37  ncf('1.2.1',plain,[-(in(431 ^ [singleton(1061 ^ []), 1060 ^ []], 1060 ^ [])), -(subset(1060 ^ [], singleton(1061 ^ [])))],extension(430 ^ 4,bind([[_157955, _157957], [singleton(1061 ^ []), 1060 ^ []]]))).
% 0.51/1.37  ncf('1.2.1.1',plain,[subset(1060 ^ [], singleton(1061 ^ [])), 1067 : 1060 ^ [] = empty_set],extension(1063 ^ 5)).
% 0.51/1.37  ncf('1.2.1.1.1',plain,[-(1060 ^ [] = empty_set)],lemmata('x')).
% 0.51/1.37  ncf('1.2.2',plain,[-(431 ^ [singleton(1061 ^ []), 1060 ^ []] = 431 ^ [singleton(1061 ^ []), 1060 ^ []])],extension(2 ^ 4,bind([[_142600], [431 ^ [singleton(1061 ^ []), 1060 ^ []]]]))).
% 0.51/1.37  ncf('1.2.3',plain,[-(1060 ^ [] = 1060 ^ [])],extension(2 ^ 4,bind([[_142600], [1060 ^ []]]))).
% 0.51/1.37  %-----------------------------------------------------
% 0.51/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------