%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.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 12:02:34 EDT 2023

% Result   : Theorem 3.81s 4.47s
% Output   : Proof 3.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.32  % Computer : n008.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May 18 13:29:24 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 3.81/4.47  
% 3.81/4.47  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 3.81/4.47  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.81/4.47  %-----------------------------------------------------
% 3.81/4.47  ncf(matrix, plain, [(2126 ^ _291769) ^ [] : [-(relation(2124 ^ []))], (2128 ^ _291769) ^ [_367805, _367807] : [in(ordered_pair(_367807, _367805), 2124 ^ [])], (2130 ^ _291769) ^ [] : [2124 ^ [] = empty_set], (2 ^ _291769) ^ [_291913] : [-(_291913 = _291913)], (4 ^ _291769) ^ [_292020, _292022] : [_292022 = _292020, -(_292020 = _292022)], (10 ^ _291769) ^ [_292224, _292226, _292228] : [-(_292228 = _292224), _292228 = _292226, _292226 = _292224], (20 ^ _291769) ^ [_292565, _292567, _292569, _292571] : [-(element(_292569, _292565)), element(_292571, _292567), _292571 = _292569, _292567 = _292565], (34 ^ _291769) ^ [_293009, _293011, _293013, _293015] : [-(proper_subset(_293013, _293009)), proper_subset(_293015, _293011), _293015 = _293013, _293011 = _293009], (48 ^ _291769) ^ [_293453, _293455, _293457, _293459] : [-(disjoint(_293457, _293453)), disjoint(_293459, _293455), _293459 = _293457, _293455 = _293453], (62 ^ _291769) ^ [_293869, _293871] : [-(empty(_293869)), _293871 = _293869, empty(_293871)], (72 ^ _291769) ^ [_294192, _294194, _294196, _294198] : [-(subset(_294196, _294192)), subset(_294198, _294194), _294198 = _294196, _294194 = _294192], (86 ^ _291769) ^ [_294636, _294638, _294640, _294642] : [-(are_equipotent(_294640, _294636)), are_equipotent(_294642, _294638), _294642 = _294640, _294638 = _294636], (100 ^ _291769) ^ [_295052, _295054] : [-(relation(_295052)), _295054 = _295052, relation(_295054)], (110 ^ _291769) ^ [_295355, _295357, _295359, _295361] : [-(in(_295359, _295355)), in(_295361, _295357), _295361 = _295359, _295357 = _295355], (124 ^ _291769) ^ [_295791, _295793] : [_295793 = _295791, -(set_meet(_295793) = set_meet(_295791))], (130 ^ _291769) ^ [_296037, _296039, _296041, _296043] : [-(cartesian_product2(_296043, _296039) = cartesian_product2(_296041, _296037)), _296043 = _296041, _296039 = _296037], (140 ^ _291769) ^ [_296368, _296370] : [_296370 = _296368, -(relation_field(_296370) = relation_field(_296368))], (146 ^ _291769) ^ [_296586, _296588] : [_296588 = _296586, -(relation_inverse(_296588) = relation_inverse(_296586))], (152 ^ _291769) ^ [_296804, _296806] : [_296806 = _296804, -(relation_dom(_296806) = relation_dom(_296804))], (158 ^ _291769) ^ [_297050, _297052, _297054, _297056] : [-(relation_composition(_297056, _297052) = relation_composition(_297054, _297050)), _297056 = _297054, _297052 = _297050], (168 ^ _291769) ^ [_297381, _297383] : [_297383 = _297381, -(relation_rng(_297383) = relation_rng(_297381))], (174 ^ _291769) ^ [_297627, _297629, _297631, _297633] : [-(union_of_subsets(_297633, _297629) = union_of_subsets(_297631, _297627)), _297633 = _297631, _297629 = _297627], (184 ^ _291769) ^ [_297986, _297988, _297990, _297992] : [-(complements_of_subsets(_297992, _297988) = complements_of_subsets(_297990, _297986)), _297992 = _297990, _297988 = _297986], (194 ^ _291769) ^ [_298373, _298375, _298377, _298379, _298381, _298383] : [-(subset_difference(_298383, _298379, _298375) = subset_difference(_298381, _298377, _298373)), _298383 = _298381, _298379 = _298377, _298375 = _298373], (208 ^ _291769) ^ [_298833, _298835] : [_298835 = _298833, -(cast_to_subset(_298835) = cast_to_subset(_298833))], (214 ^ _291769) ^ [_299079, _299081, _299083, _299085] : [-(meet_of_subsets(_299085, _299081) = meet_of_subsets(_299083, _299079)), _299085 = _299083, _299081 = _299079], (224 ^ _291769) ^ [_299438, _299440, _299442, _299444] : [-(set_intersection2(_299444, _299440) = set_intersection2(_299442, _299438)), _299444 = _299442, _299440 = _299438], (234 ^ _291769) ^ [_299797, _299799, _299801, _299803] : [-(subset_complement(_299803, _299799) = subset_complement(_299801, _299797)), _299803 = _299801, _299799 = _299797], (244 ^ _291769) ^ [_300156, _300158, _300160, _300162] : [-(set_difference(_300162, _300158) = set_difference(_300160, _300156)), _300162 = _300160, _300158 = _300156], (254 ^ _291769) ^ [_300515, _300517, _300519, _300521] : [-(set_union2(_300521, _300517) = set_union2(_300519, _300515)), _300521 = _300519, _300517 = _300515], (264 ^ _291769) ^ [_300846, _300848] : [_300848 = _300846, -(union(_300848) = union(_300846))], (270 ^ _291769) ^ [_301064, _301066] : [_301066 = _301064, -(powerset(_301066) = powerset(_301064))], (276 ^ _291769) ^ [_301282, _301284] : [_301284 = _301282, -(singleton(_301284) = singleton(_301282))], (282 ^ _291769) ^ [_301528, _301530, _301532, _301534] : [-(unordered_pair(_301534, _301530) = unordered_pair(_301532, _301528)), _301534 = _301532, _301530 = _301528], (292 ^ _291769) ^ [_301867, _301869, _301871, _301873] : [-(ordered_pair(_301873, _301869) = ordered_pair(_301871, _301867)), _301873 = _301871, _301869 = _301867], (302 ^ _291769) ^ [_302292, _302294] : [in(_302294, _302292), in(_302292, _302294)], (308 ^ _291769) ^ [_302503, _302505] : [proper_subset(_302505, _302503), proper_subset(_302503, _302505)], (314 ^ _291769) ^ [_302700] : [empty(_302700), -(relation(_302700))], (320 ^ _291769) ^ [_302885, _302887] : [-(unordered_pair(_302887, _302885) = unordered_pair(_302885, _302887))], (322 ^ _291769) ^ [_302985, _302987] : [-(set_union2(_302987, _302985) = set_union2(_302985, _302987))], (324 ^ _291769) ^ [_303085, _303087] : [-(set_intersection2(_303087, _303085) = set_intersection2(_303085, _303087))], (326 ^ _291769) ^ [_303229, _303231] : [_303231 = _303229, 329 ^ _291769 : [(330 ^ _291769) ^ [] : [-(subset(_303231, _303229))], (332 ^ _291769) ^ [] : [-(subset(_303229, _303231))]]], (334 ^ _291769) ^ [_303466, _303468] : [-(_303468 = _303466), subset(_303468, _303466), subset(_303466, _303468)], (356 ^ _291769) ^ [_304243] : [358 ^ _291769 : [(359 ^ _291769) ^ [] : [-(in(357 ^ [_304243], _304243))], (361 ^ _291769) ^ [_304480, _304482] : [357 ^ [_304243] = ordered_pair(_304482, _304480)]], -(relation(_304243))], (344 ^ _291769) ^ [_303782] : [relation(_303782), 347 ^ _291769 : [(348 ^ _291769) ^ [_303930] : [in(_303930, _303782), -(_303930 = ordered_pair(351 ^ [_303782, _303930], 352 ^ [_303782, _303930]))]]], (414 ^ _291769) ^ [_306378, _306380] : [_306380 = empty_set, 417 ^ _291769 : [(418 ^ _291769) ^ [] : [_306378 = set_meet(_306380), -(_306378 = empty_set)], (424 ^ _291769) ^ [] : [_306378 = empty_set, -(_306378 = set_meet(_306380))]]], (365 ^ _291769) ^ [_304671, _304673] : [-(_304673 = empty_set), 368 ^ _291769 : [(392 ^ _291769) ^ [] : [-(_304671 = set_meet(_304673)), 396 ^ _291769 : [(397 ^ _291769) ^ [] : [-(in(393 ^ [_304671, _304673], _304671))], (400 ^ _291769) ^ [] : [-(in(398 ^ [_304671, _304673], _304673))], (402 ^ _291769) ^ [] : [in(393 ^ [_304671, _304673], 398 ^ [_304671, _304673])]], 403 ^ _291769 : [(410 ^ _291769) ^ [] : [in(393 ^ [_304671, _304673], _304671)], (404 ^ _291769) ^ [_306073] : [in(_306073, _304673), -(in(393 ^ [_304671, _304673], _306073))]]], (369 ^ _291769) ^ [] : [_304671 = set_meet(_304673), 372 ^ _291769 : [(383 ^ _291769) ^ [_305299] : [385 ^ _291769 : [(386 ^ _291769) ^ [] : [-(in(384 ^ [_304671, _304673, _305299], _304673))], (388 ^ _291769) ^ [] : [in(_305299, 384 ^ [_304671, _304673, _305299])]], -(in(_305299, _304671))], (373 ^ _291769) ^ [_304969] : [in(_304969, _304671), 376 ^ _291769 : [(377 ^ _291769) ^ [_305114] : [in(_305114, _304673), -(in(_304969, _305114))]]]]]]], (446 ^ _291769) ^ [_307396, _307398] : [-(_307396 = singleton(_307398)), 450 ^ _291769 : [(451 ^ _291769) ^ [] : [-(in(447 ^ [_307396, _307398], _307396))], (453 ^ _291769) ^ [] : [447 ^ [_307396, _307398] = _307398]], 454 ^ _291769 : [(455 ^ _291769) ^ [] : [-(447 ^ [_307396, _307398] = _307398)], (457 ^ _291769) ^ [] : [in(447 ^ [_307396, _307398], _307396)]]], (430 ^ _291769) ^ [_306875, _306877] : [_306875 = singleton(_306877), 433 ^ _291769 : [(434 ^ _291769) ^ [_307045] : [in(_307045, _306875), -(_307045 = _306877)], (440 ^ _291769) ^ [_307217] : [_307217 = _306877, -(in(_307217, _306875))]]], (461 ^ _291769) ^ [_307947] : [_307947 = empty_set, 464 ^ _291769 : [(465 ^ _291769) ^ [_308060] : [in(_308060, _307947)]]], (467 ^ _291769) ^ [_308126] : [-(in(468 ^ [_308126], _308126)), -(_308126 = empty_set)], (490 ^ _291769) ^ [_308938, _308940] : [-(_308938 = powerset(_308940)), 494 ^ _291769 : [(495 ^ _291769) ^ [] : [-(in(491 ^ [_308938, _308940], _308938))], (497 ^ _291769) ^ [] : [subset(491 ^ [_308938, _308940], _308940)]], 498 ^ _291769 : [(499 ^ _291769) ^ [] : [-(subset(491 ^ [_308938, _308940], _308940))], (501 ^ _291769) ^ [] : [in(491 ^ [_308938, _308940], _308938)]]], (474 ^ _291769) ^ [_308417, _308419] : [_308417 = powerset(_308419), 477 ^ _291769 : [(478 ^ _291769) ^ [_308587] : [in(_308587, _308417), -(subset(_308587, _308419))], (484 ^ _291769) ^ [_308759] : [subset(_308759, _308419), -(in(_308759, _308417))]]], (505 ^ _291769) ^ [_309494, _309496] : [-(empty(_309496)), 508 ^ _291769 : [(509 ^ _291769) ^ [] : [element(_309494, _309496), -(in(_309494, _309496))], (515 ^ _291769) ^ [] : [in(_309494, _309496), -(element(_309494, _309496))]]], (521 ^ _291769) ^ [_309907, _309909] : [empty(_309909), 524 ^ _291769 : [(525 ^ _291769) ^ [] : [element(_309907, _309909), -(empty(_309907))], (531 ^ _291769) ^ [] : [empty(_309907), -(element(_309907, _309909))]]], (559 ^ _291769) ^ [_311132, _311134, _311136] : [-(_311132 = unordered_pair(_311136, _311134)), 563 ^ _291769 : [(564 ^ _291769) ^ [] : [-(in(560 ^ [_311132, _311134, _311136], _311132))], (566 ^ _291769) ^ [] : [560 ^ [_311132, _311134, _311136] = _311136], (568 ^ _291769) ^ [] : [560 ^ [_311132, _311134, _311136] = _311134]], 569 ^ _291769 : [(576 ^ _291769) ^ [] : [in(560 ^ [_311132, _311134, _311136], _311132)], (570 ^ _291769) ^ [] : [-(560 ^ [_311132, _311134, _311136] = _311136), -(560 ^ [_311132, _311134, _311136] = _311134)]]], (537 ^ _291769) ^ [_310407, _310409, _310411] : [_310407 = unordered_pair(_310411, _310409), 540 ^ _291769 : [(551 ^ _291769) ^ [_310867] : [552 ^ _291769 : [(553 ^ _291769) ^ [] : [_310867 = _310411], (555 ^ _291769) ^ [] : [_310867 = _310409]], -(in(_310867, _310407))], (541 ^ _291769) ^ [_310589] : [in(_310589, _310407), -(_310589 = _310411), -(_310589 = _310409)]]], (602 ^ _291769) ^ [_312651, _312653, _312655] : [-(_312651 = set_union2(_312655, _312653)), 606 ^ _291769 : [(607 ^ _291769) ^ [] : [-(in(603 ^ [_312651, _312653, _312655], _312651))], (609 ^ _291769) ^ [] : [in(603 ^ [_312651, _312653, _312655], _312655)], (611 ^ _291769) ^ [] : [in(603 ^ [_312651, _312653, _312655], _312653)]], 612 ^ _291769 : [(619 ^ _291769) ^ [] : [in(603 ^ [_312651, _312653, _312655], _312651)], (613 ^ _291769) ^ [] : [-(in(603 ^ [_312651, _312653, _312655], _312655)), -(in(603 ^ [_312651, _312653, _312655], _312653))]]], (580 ^ _291769) ^ [_311926, _311928, _311930] : [_311926 = set_union2(_311930, _311928), 583 ^ _291769 : [(594 ^ _291769) ^ [_312386] : [595 ^ _291769 : [(596 ^ _291769) ^ [] : [in(_312386, _311930)], (598 ^ _291769) ^ [] : [in(_312386, _311928)]], -(in(_312386, _311926))], (584 ^ _291769) ^ [_312108] : [in(_312108, _311926), -(in(_312108, _311930)), -(in(_312108, _311928))]]], (653 ^ _291769) ^ [_314702, _314704, _314706] : [-(_314702 = cartesian_product2(_314706, _314704)), 671 ^ _291769 : [(672 ^ _291769) ^ [] : [-(in(669 ^ [_314702, _314704, _314706], _314706))], (674 ^ _291769) ^ [] : [-(in(670 ^ [_314702, _314704, _314706], _314704))], (676 ^ _291769) ^ [] : [-(654 ^ [_314702, _314704, _314706] = ordered_pair(669 ^ [_314702, _314704, _314706], 670 ^ [_314702, _314704, _314706]))], (678 ^ _291769) ^ [] : [in(654 ^ [_314702, _314704, _314706], _314702)]], 657 ^ _291769 : [(658 ^ _291769) ^ [] : [-(in(654 ^ [_314702, _314704, _314706], _314702))], (660 ^ _291769) ^ [_315040, _315042] : [in(_315042, _314706), in(_315040, _314704), 654 ^ [_314702, _314704, _314706] = ordered_pair(_315042, _315040)]]], (623 ^ _291769) ^ [_313445, _313447, _313449] : [_313445 = cartesian_product2(_313449, _313447), 626 ^ _291769 : [(627 ^ _291769) ^ [_313646] : [in(_313646, _313445), 632 ^ _291769 : [(633 ^ _291769) ^ [] : [-(in(630 ^ [_313445, _313447, _313449, _313646], _313449))], (635 ^ _291769) ^ [] : [-(in(631 ^ [_313445, _313447, _313449, _313646], _313447))], (637 ^ _291769) ^ [] : [-(_313646 = ordered_pair(630 ^ [_313445, _313447, _313449, _313646], 631 ^ [_313445, _313447, _313449, _313646]))]]], (639 ^ _291769) ^ [_314206] : [-(in(_314206, _313445)), 640 ^ _291769 : [(641 ^ _291769) ^ [_314336, _314338] : [in(_314338, _313449), in(_314336, _313447), _314206 = ordered_pair(_314338, _314336)]]]]], (692 ^ _291769) ^ [_316293, _316295] : [694 ^ _291769 : [(695 ^ _291769) ^ [] : [-(in(693 ^ [_316293, _316295], _316295))], (697 ^ _291769) ^ [] : [in(693 ^ [_316293, _316295], _316293)]], -(subset(_316295, _316293))], (682 ^ _291769) ^ [_315979, _315981] : [subset(_315981, _315979), 685 ^ _291769 : [(686 ^ _291769) ^ [_316116] : [in(_316116, _315981), -(in(_316116, _315979))]]], (723 ^ _291769) ^ [_317418, _317420, _317422] : [-(_317418 = set_intersection2(_317422, _317420)), 735 ^ _291769 : [(736 ^ _291769) ^ [] : [-(in(724 ^ [_317418, _317420, _317422], _317422))], (738 ^ _291769) ^ [] : [-(in(724 ^ [_317418, _317420, _317422], _317420))], (740 ^ _291769) ^ [] : [in(724 ^ [_317418, _317420, _317422], _317418)]], 727 ^ _291769 : [(728 ^ _291769) ^ [] : [-(in(724 ^ [_317418, _317420, _317422], _317418))], (730 ^ _291769) ^ [] : [in(724 ^ [_317418, _317420, _317422], _317422), in(724 ^ [_317418, _317420, _317422], _317420)]]], (701 ^ _291769) ^ [_316693, _316695, _316697] : [_316693 = set_intersection2(_316697, _316695), 704 ^ _291769 : [(705 ^ _291769) ^ [_316875] : [in(_316875, _316693), 708 ^ _291769 : [(709 ^ _291769) ^ [] : [-(in(_316875, _316697))], (711 ^ _291769) ^ [] : [-(in(_316875, _316695))]]], (713 ^ _291769) ^ [_317134] : [-(in(_317134, _316693)), in(_317134, _316697), in(_317134, _316695)]]], (744 ^ _291769) ^ [_318157] : [relation(_318157), 747 ^ _291769 : [(765 ^ _291769) ^ [_318969] : [-(_318969 = relation_dom(_318157)), 769 ^ _291769 : [(770 ^ _291769) ^ [] : [-(in(766 ^ [_318157, _318969], _318969))], (772 ^ _291769) ^ [_319232] : [in(ordered_pair(766 ^ [_318157, _318969], _319232), _318157)]], 774 ^ _291769 : [(775 ^ _291769) ^ [] : [-(in(ordered_pair(766 ^ [_318157, _318969], 773 ^ [_318157, _318969]), _318157))], (777 ^ _291769) ^ [] : [in(766 ^ [_318157, _318969], _318969)]]], (748 ^ _291769) ^ [_318338] : [_318338 = relation_dom(_318157), 751 ^ _291769 : [(752 ^ _291769) ^ [_318518] : [in(_318518, _318338), -(in(ordered_pair(_318518, 755 ^ [_318157, _318338, _318518]), _318157))], (759 ^ _291769) ^ [_318762] : [760 ^ _291769 : [(761 ^ _291769) ^ [_318841] : [in(ordered_pair(_318762, _318841), _318157)]], -(in(_318762, _318338))]]]]], (781 ^ _291769) ^ [_319583] : [-(cast_to_subset(_319583) = _319583)], (806 ^ _291769) ^ [_320566, _320568] : [-(_320566 = union(_320568)), 819 ^ _291769 : [(820 ^ _291769) ^ [] : [-(in(807 ^ [_320566, _320568], 818 ^ [_320566, _320568]))], (822 ^ _291769) ^ [] : [-(in(818 ^ [_320566, _320568], _320568))], (824 ^ _291769) ^ [] : [in(807 ^ [_320566, _320568], _320566)]], 810 ^ _291769 : [(811 ^ _291769) ^ [] : [-(in(807 ^ [_320566, _320568], _320566))], (813 ^ _291769) ^ [_320849] : [in(807 ^ [_320566, _320568], _320849), in(_320849, _320568)]]], (783 ^ _291769) ^ [_319721, _319723] : [_319721 = union(_319723), 786 ^ _291769 : [(787 ^ _291769) ^ [_319902] : [in(_319902, _319721), 791 ^ _291769 : [(792 ^ _291769) ^ [] : [-(in(_319902, 790 ^ [_319721, _319723, _319902]))], (794 ^ _291769) ^ [] : [-(in(790 ^ [_319721, _319723, _319902], _319723))]]], (796 ^ _291769) ^ [_320229] : [-(in(_320229, _319721)), 797 ^ _291769 : [(798 ^ _291769) ^ [_320327] : [in(_320229, _320327), in(_320327, _319723)]]]]], (850 ^ _291769) ^ [_322187, _322189, _322191] : [-(_322187 = set_difference(_322191, _322189)), 862 ^ _291769 : [(863 ^ _291769) ^ [] : [-(in(851 ^ [_322187, _322189, _322191], _322191))], (865 ^ _291769) ^ [] : [in(851 ^ [_322187, _322189, _322191], _322189)], (867 ^ _291769) ^ [] : [in(851 ^ [_322187, _322189, _322191], _322187)]], 854 ^ _291769 : [(855 ^ _291769) ^ [] : [-(in(851 ^ [_322187, _322189, _322191], _322187))], (857 ^ _291769) ^ [] : [in(851 ^ [_322187, _322189, _322191], _322191), -(in(851 ^ [_322187, _322189, _322191], _322189))]]], (828 ^ _291769) ^ [_321456, _321458, _321460] : [_321456 = set_difference(_321460, _321458), 831 ^ _291769 : [(832 ^ _291769) ^ [_321640] : [in(_321640, _321456), 835 ^ _291769 : [(836 ^ _291769) ^ [] : [-(in(_321640, _321460))], (838 ^ _291769) ^ [] : [in(_321640, _321458)]]], (840 ^ _291769) ^ [_321900] : [-(in(_321900, _321456)), in(_321900, _321460), -(in(_321900, _321458))]]], (871 ^ _291769) ^ [_322930] : [relation(_322930), 874 ^ _291769 : [(892 ^ _291769) ^ [_323742] : [-(_323742 = relation_rng(_322930)), 896 ^ _291769 : [(897 ^ _291769) ^ [] : [-(in(893 ^ [_322930, _323742], _323742))], (899 ^ _291769) ^ [_324005] : [in(ordered_pair(_324005, 893 ^ [_322930, _323742]), _322930)]], 901 ^ _291769 : [(902 ^ _291769) ^ [] : [-(in(ordered_pair(900 ^ [_322930, _323742], 893 ^ [_322930, _323742]), _322930))], (904 ^ _291769) ^ [] : [in(893 ^ [_322930, _323742], _323742)]]], (875 ^ _291769) ^ [_323111] : [_323111 = relation_rng(_322930), 878 ^ _291769 : [(879 ^ _291769) ^ [_323291] : [in(_323291, _323111), -(in(ordered_pair(882 ^ [_322930, _323111, _323291], _323291), _322930))], (886 ^ _291769) ^ [_323535] : [887 ^ _291769 : [(888 ^ _291769) ^ [_323614] : [in(ordered_pair(_323614, _323535), _322930)]], -(in(_323535, _323111))]]]]], (908 ^ _291769) ^ [_324385, _324387] : [element(_324385, powerset(_324387)), -(subset_complement(_324387, _324385) = set_difference(_324387, _324385))], (914 ^ _291769) ^ [_324596, _324598] : [-(ordered_pair(_324598, _324596) = unordered_pair(unordered_pair(_324598, _324596), singleton(_324598)))], (916 ^ _291769) ^ [_324702] : [relation(_324702), -(relation_field(_324702) = set_union2(relation_dom(_324702), relation_rng(_324702)))], (922 ^ _291769) ^ [_324908] : [relation(_324908), 925 ^ _291769 : [(926 ^ _291769) ^ [_325068] : [relation(_325068), 929 ^ _291769 : [(946 ^ _291769) ^ [] : [-(_325068 = relation_inverse(_324908)), 951 ^ _291769 : [(952 ^ _291769) ^ [] : [-(in(ordered_pair(947 ^ [_324908, _325068], 948 ^ [_324908, _325068]), _325068))], (954 ^ _291769) ^ [] : [in(ordered_pair(948 ^ [_324908, _325068], 947 ^ [_324908, _325068]), _324908)]], 955 ^ _291769 : [(956 ^ _291769) ^ [] : [-(in(ordered_pair(948 ^ [_324908, _325068], 947 ^ [_324908, _325068]), _324908))], (958 ^ _291769) ^ [] : [in(ordered_pair(947 ^ [_324908, _325068], 948 ^ [_324908, _325068]), _325068)]]], (930 ^ _291769) ^ [] : [_325068 = relation_inverse(_324908), 933 ^ _291769 : [(934 ^ _291769) ^ [_325377, _325379] : [in(ordered_pair(_325379, _325377), _325068), -(in(ordered_pair(_325377, _325379), _324908))], (940 ^ _291769) ^ [_325567, _325569] : [in(ordered_pair(_325567, _325569), _324908), -(in(ordered_pair(_325569, _325567), _325068))]]]]]]], (962 ^ _291769) ^ [_326415, _326417] : [disjoint(_326417, _326415), -(set_intersection2(_326417, _326415) = empty_set)], (968 ^ _291769) ^ [_326583, _326585] : [set_intersection2(_326585, _326583) = empty_set, -(disjoint(_326585, _326583))], (974 ^ _291769) ^ [_326787] : [relation(_326787), 977 ^ _291769 : [(978 ^ _291769) ^ [_326972] : [relation(_326972), 981 ^ _291769 : [(982 ^ _291769) ^ [_327153] : [relation(_327153), 985 ^ _291769 : [(1009 ^ _291769) ^ [] : [-(_327153 = relation_composition(_326787, _326972)), 1023 ^ _291769 : [(1024 ^ _291769) ^ [] : [-(in(ordered_pair(1010 ^ [_326787, _326972, _327153], 1022 ^ [_326787, _326972, _327153]), _326787))], (1026 ^ _291769) ^ [] : [-(in(ordered_pair(1022 ^ [_326787, _326972, _327153], 1011 ^ [_326787, _326972, _327153]), _326972))], (1028 ^ _291769) ^ [] : [in(ordered_pair(1010 ^ [_326787, _326972, _327153], 1011 ^ [_326787, _326972, _327153]), _327153)]], 1014 ^ _291769 : [(1015 ^ _291769) ^ [] : [-(in(ordered_pair(1010 ^ [_326787, _326972, _327153], 1011 ^ [_326787, _326972, _327153]), _327153))], (1017 ^ _291769) ^ [_328617] : [in(ordered_pair(1010 ^ [_326787, _326972, _327153], _328617), _326787), in(ordered_pair(_328617, 1011 ^ [_326787, _326972, _327153]), _326972)]]], (986 ^ _291769) ^ [] : [_327153 = relation_composition(_326787, _326972), 989 ^ _291769 : [(990 ^ _291769) ^ [_327488, _327490] : [in(ordered_pair(_327490, _327488), _327153), 994 ^ _291769 : [(995 ^ _291769) ^ [] : [-(in(ordered_pair(_327490, 993 ^ [_326787, _326972, _327153, _327488, _327490]), _326787))], (997 ^ _291769) ^ [] : [-(in(ordered_pair(993 ^ [_326787, _326972, _327153, _327488, _327490], _327488), _326972))]]], (999 ^ _291769) ^ [_327873, _327875] : [-(in(ordered_pair(_327875, _327873), _327153)), 1000 ^ _291769 : [(1001 ^ _291769) ^ [_327986] : [in(ordered_pair(_327875, _327986), _326787), in(ordered_pair(_327986, _327873), _326972)]]]]]]]]]]], (1032 ^ _291769) ^ [_329303, _329305] : [element(_329303, powerset(powerset(_329305))), 1035 ^ _291769 : [(1036 ^ _291769) ^ [_329483] : [element(_329483, powerset(powerset(_329305))), 1039 ^ _291769 : [(1060 ^ _291769) ^ [] : [-(_329483 = complements_of_subsets(_329305, _329303)), 1062 ^ _291769 : [(1063 ^ _291769) ^ [] : [-(element(1061 ^ [_329303, _329305, _329483], powerset(_329305)))], (1065 ^ _291769) ^ [] : [1066 ^ _291769 : [(1067 ^ _291769) ^ [] : [-(in(1061 ^ [_329303, _329305, _329483], _329483))], (1069 ^ _291769) ^ [] : [in(subset_complement(_329305, 1061 ^ [_329303, _329305, _329483]), _329303)]], 1070 ^ _291769 : [(1071 ^ _291769) ^ [] : [-(in(subset_complement(_329305, 1061 ^ [_329303, _329305, _329483]), _329303))], (1073 ^ _291769) ^ [] : [in(1061 ^ [_329303, _329305, _329483], _329483)]]]]], (1040 ^ _291769) ^ [] : [_329483 = complements_of_subsets(_329305, _329303), 1043 ^ _291769 : [(1044 ^ _291769) ^ [_329771] : [element(_329771, powerset(_329305)), 1047 ^ _291769 : [(1048 ^ _291769) ^ [] : [in(_329771, _329483), -(in(subset_complement(_329305, _329771), _329303))], (1054 ^ _291769) ^ [] : [in(subset_complement(_329305, _329771), _329303), -(in(_329771, _329483))]]]]]]]]], (1077 ^ _291769) ^ [_330894, _330896] : [proper_subset(_330896, _330894), 1080 ^ _291769 : [(1081 ^ _291769) ^ [] : [-(subset(_330896, _330894))], (1083 ^ _291769) ^ [] : [_330896 = _330894]]], (1085 ^ _291769) ^ [_331132, _331134] : [-(proper_subset(_331134, _331132)), subset(_331134, _331132), -(_331134 = _331132)], (1095 ^ _291769) ^ [] : [true___, -(true___)], (1101 ^ _291769) ^ [] : [true___, -(true___)], (1107 ^ _291769) ^ [] : [true___, -(true___)], (1113 ^ _291769) ^ [] : [true___, -(true___)], (1119 ^ _291769) ^ [] : [true___, -(true___)], (1125 ^ _291769) ^ [] : [true___, -(true___)], (1131 ^ _291769) ^ [_332121] : [-(element(cast_to_subset(_332121), powerset(_332121)))], (1133 ^ _291769) ^ [] : [true___, -(true___)], (1139 ^ _291769) ^ [] : [true___, -(true___)], (1145 ^ _291769) ^ [] : [true___, -(true___)], (1151 ^ _291769) ^ [] : [true___, -(true___)], (1157 ^ _291769) ^ [_332708, _332710] : [element(_332708, powerset(_332710)), -(element(subset_complement(_332710, _332708), powerset(_332710)))], (1163 ^ _291769) ^ [] : [true___, -(true___)], (1169 ^ _291769) ^ [] : [true___, -(true___)], (1175 ^ _291769) ^ [_333156] : [relation(_333156), -(relation(relation_inverse(_333156)))], (1181 ^ _291769) ^ [] : [true___, -(true___)], (1187 ^ _291769) ^ [] : [true___, -(true___)], (1193 ^ _291769) ^ [_333598, _333600] : [-(relation(relation_composition(_333600, _333598))), relation(_333600), relation(_333598)], (1203 ^ _291769) ^ [_333897, _333899] : [element(_333897, powerset(powerset(_333899))), -(element(union_of_subsets(_333899, _333897), powerset(_333899)))], (1209 ^ _291769) ^ [_334125, _334127] : [element(_334125, powerset(powerset(_334127))), -(element(meet_of_subsets(_334127, _334125), powerset(_334127)))], (1215 ^ _291769) ^ [_334367, _334369, _334371] : [-(element(subset_difference(_334371, _334369, _334367), powerset(_334371))), element(_334369, powerset(_334371)), element(_334367, powerset(_334371))], (1225 ^ _291769) ^ [_334696, _334698] : [element(_334696, powerset(powerset(_334698))), -(element(complements_of_subsets(_334698, _334696), powerset(powerset(_334698))))], (1231 ^ _291769) ^ [] : [true___, -(true___)], (1238 ^ _291769) ^ [_335057] : [-(element(1236 ^ [_335057], _335057))], (1240 ^ _291769) ^ [_335139] : [empty(powerset(_335139))], (1242 ^ _291769) ^ [] : [-(empty(empty_set))], (1244 ^ _291769) ^ [_335284, _335286] : [empty(ordered_pair(_335286, _335284))], (1246 ^ _291769) ^ [_335395, _335397] : [-(relation(set_union2(_335397, _335395))), relation(_335397), relation(_335395)], (1256 ^ _291769) ^ [_335664] : [empty(singleton(_335664))], (1258 ^ _291769) ^ [_335772, _335774] : [-(empty(_335774)), empty(set_union2(_335774, _335772))], (1264 ^ _291769) ^ [_335972, _335974] : [empty(unordered_pair(_335974, _335972))], (1266 ^ _291769) ^ [_336083, _336085] : [-(empty(_336085)), empty(set_union2(_336083, _336085))], (1272 ^ _291769) ^ [] : [-(empty(empty_set))], (1274 ^ _291769) ^ [] : [-(relation(empty_set))], (1276 ^ _291769) ^ [_336407, _336409] : [empty(cartesian_product2(_336409, _336407)), -(empty(_336409)), -(empty(_336407))], (1286 ^ _291769) ^ [_336698, _336700] : [-(set_union2(_336700, _336700) = _336700)], (1288 ^ _291769) ^ [_336795, _336797] : [-(set_intersection2(_336797, _336797) = _336797)], (1290 ^ _291769) ^ [_336907, _336909] : [element(_336907, powerset(_336909)), -(subset_complement(_336909, subset_complement(_336909, _336907)) = _336907)], (1296 ^ _291769) ^ [_337119] : [relation(_337119), -(relation_inverse(relation_inverse(_337119)) = _337119)], (1302 ^ _291769) ^ [_337329, _337331] : [element(_337329, powerset(powerset(_337331))), -(complements_of_subsets(_337331, complements_of_subsets(_337331, _337329)) = _337329)], (1308 ^ _291769) ^ [_337543, _337545] : [proper_subset(_337545, _337545)], (1310 ^ _291769) ^ [_337622] : [singleton(_337622) = empty_set], (1312 ^ _291769) ^ [_337731, _337733] : [in(_337733, _337731), -(set_union2(singleton(_337733), _337731) = _337731)], (1318 ^ _291769) ^ [_337951, _337953] : [disjoint(singleton(_337953), _337951), in(_337953, _337951)], (1324 ^ _291769) ^ [_338164, _338166] : [-(in(_338166, _338164)), -(disjoint(singleton(_338166), _338164))], (1330 ^ _291769) ^ [_338410, _338412] : [subset(singleton(_338412), _338410), -(in(_338412, _338410))], (1336 ^ _291769) ^ [_338576, _338578] : [in(_338578, _338576), -(subset(singleton(_338578), _338576))], (1342 ^ _291769) ^ [_338821, _338823] : [set_difference(_338823, _338821) = empty_set, -(subset(_338823, _338821))], (1348 ^ _291769) ^ [_338989, _338991] : [subset(_338991, _338989), -(set_difference(_338991, _338989) = empty_set)], (1354 ^ _291769) ^ [_339207, _339209] : [element(_339207, powerset(_339209)), 1357 ^ _291769 : [(1358 ^ _291769) ^ [_339348] : [in(_339348, _339207), -(in(_339348, _339209))]]], (1364 ^ _291769) ^ [_339587, _339589, _339591] : [subset(_339591, _339589), -(in(_339587, _339591)), -(subset(_339591, set_difference(_339589, singleton(_339587))))], (1384 ^ _291769) ^ [_340196, _340198] : [1385 ^ _291769 : [(1386 ^ _291769) ^ [] : [_340198 = empty_set], (1388 ^ _291769) ^ [] : [_340198 = singleton(_340196)]], -(subset(_340198, singleton(_340196)))], (1374 ^ _291769) ^ [_339936, _339938] : [subset(_339938, singleton(_339936)), -(_339938 = empty_set), -(_339938 = singleton(_339936))], (1392 ^ _291769) ^ [_340490, _340492] : [in(_340492, _340490), -(subset(_340492, union(_340490)))], (1398 ^ _291769) ^ [_340761, _340763, _340765, _340767] : [in(ordered_pair(_340767, _340765), cartesian_product2(_340763, _340761)), 1401 ^ _291769 : [(1402 ^ _291769) ^ [] : [-(in(_340767, _340763))], (1404 ^ _291769) ^ [] : [-(in(_340765, _340761))]]], (1406 ^ _291769) ^ [_341026, _341028, _341030, _341032] : [-(in(ordered_pair(_341032, _341030), cartesian_product2(_341028, _341026))), in(_341032, _341028), in(_341030, _341026)], (1416 ^ _291769) ^ [_341359, _341361] : [1418 ^ _291769 : [(1419 ^ _291769) ^ [] : [-(in(1417 ^ [_341359, _341361], _341361))], (1421 ^ _291769) ^ [] : [in(1417 ^ [_341359, _341361], _341359)]], -(element(_341361, powerset(_341359)))], (1426 ^ _291769) ^ [] : [-(empty(1424 ^ []))], (1428 ^ _291769) ^ [] : [-(relation(1424 ^ []))], (1430 ^ _291769) ^ [_341853] : [-(empty(_341853)), 1434 ^ _291769 : [(1435 ^ _291769) ^ [] : [-(element(1433 ^ [_341853], powerset(_341853)))], (1437 ^ _291769) ^ [] : [empty(1433 ^ [_341853])]]], (1440 ^ _291769) ^ [] : [-(empty(1438 ^ []))], (1443 ^ _291769) ^ [] : [empty(1441 ^ [])], (1445 ^ _291769) ^ [] : [-(relation(1441 ^ []))], (1448 ^ _291769) ^ [_342475] : [-(element(1446 ^ [_342475], powerset(_342475)))], (1450 ^ _291769) ^ [_342526] : [-(empty(1446 ^ [_342526]))], (1453 ^ _291769) ^ [] : [empty(1451 ^ [])], (1455 ^ _291769) ^ [_342729, _342731] : [element(_342729, powerset(powerset(_342731))), -(union_of_subsets(_342731, _342729) = union(_342729))], (1461 ^ _291769) ^ [_342957, _342959] : [element(_342957, powerset(powerset(_342959))), -(meet_of_subsets(_342959, _342957) = set_meet(_342957))], (1467 ^ _291769) ^ [_343199, _343201, _343203] : [-(subset_difference(_343203, _343201, _343199) = set_difference(_343201, _343199)), element(_343201, powerset(_343203)), element(_343199, powerset(_343203))], (1477 ^ _291769) ^ [_343515, _343517] : [-(subset(_343517, _343517))], (1479 ^ _291769) ^ [_343624, _343626] : [disjoint(_343626, _343624), -(disjoint(_343624, _343626))], (1485 ^ _291769) ^ [_343891, _343893, _343895, _343897] : [in(ordered_pair(_343897, _343895), cartesian_product2(_343893, _343891)), 1488 ^ _291769 : [(1489 ^ _291769) ^ [] : [-(in(_343897, _343893))], (1491 ^ _291769) ^ [] : [-(in(_343895, _343891))]]], (1493 ^ _291769) ^ [_344156, _344158, _344160, _344162] : [-(in(ordered_pair(_344162, _344160), cartesian_product2(_344158, _344156))), in(_344162, _344158), in(_344160, _344156)], (1503 ^ _291769) ^ [_344517, _344519, _344521, _344523] : [unordered_pair(_344523, _344521) = unordered_pair(_344519, _344517), -(_344523 = _344519), -(_344523 = _344517)], (1513 ^ _291769) ^ [_344867, _344869, _344871] : [subset(_344871, _344869), 1516 ^ _291769 : [(1517 ^ _291769) ^ [] : [-(subset(cartesian_product2(_344871, _344867), cartesian_product2(_344869, _344867)))], (1519 ^ _291769) ^ [] : [-(subset(cartesian_product2(_344867, _344871), cartesian_product2(_344867, _344869)))]]], (1521 ^ _291769) ^ [_345212, _345214, _345216, _345218] : [-(subset(cartesian_product2(_345218, _345214), cartesian_product2(_345216, _345212))), subset(_345218, _345216), subset(_345214, _345212)], (1531 ^ _291769) ^ [_345543, _345545] : [subset(_345545, _345543), -(set_union2(_345545, _345543) = _345543)], (1538 ^ _291769) ^ [_345865] : [-(in(_345865, 1536 ^ [_345865]))], (1540 ^ _291769) ^ [_345977, _345979, _345981] : [-(in(_345977, 1536 ^ [_345981])), in(_345979, 1536 ^ [_345981]), subset(_345977, _345979)], (1550 ^ _291769) ^ [_346292, _346294] : [in(_346292, 1536 ^ [_346294]), -(in(powerset(_346292), 1536 ^ [_346294]))], (1556 ^ _291769) ^ [_346492, _346494] : [subset(_346492, 1536 ^ [_346494]), -(are_equipotent(_346492, 1536 ^ [_346494])), -(in(_346492, 1536 ^ [_346494]))], (1566 ^ _291769) ^ [_346817, _346819] : [-(subset(set_intersection2(_346819, _346817), _346819))], (1568 ^ _291769) ^ [_346943, _346945, _346947] : [-(subset(_346947, set_intersection2(_346945, _346943))), subset(_346947, _346945), subset(_346947, _346943)], (1578 ^ _291769) ^ [_347229] : [-(set_union2(_347229, empty_set) = _347229)], (1580 ^ _291769) ^ [_347339, _347341] : [in(_347341, _347339), -(element(_347341, _347339))], (1586 ^ _291769) ^ [_347563, _347565, _347567] : [-(subset(_347567, _347563)), subset(_347567, _347565), subset(_347565, _347563)], (1596 ^ _291769) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1598 ^ _291769) ^ [_347939, _347941, _347943] : [relation(_347939), in(ordered_pair(_347943, _347941), _347939), 1605 ^ _291769 : [(1606 ^ _291769) ^ [] : [-(in(_347943, relation_dom(_347939)))], (1608 ^ _291769) ^ [] : [-(in(_347941, relation_rng(_347939)))]]], (1610 ^ _291769) ^ [_348323] : [relation(_348323), -(subset(_348323, cartesian_product2(relation_dom(_348323), relation_rng(_348323))))], (1616 ^ _291769) ^ [_348525] : [relation(_348525), 1619 ^ _291769 : [(1620 ^ _291769) ^ [_348675] : [relation(_348675), subset(_348525, _348675), 1627 ^ _291769 : [(1628 ^ _291769) ^ [] : [-(subset(relation_dom(_348525), relation_dom(_348675)))], (1630 ^ _291769) ^ [] : [-(subset(relation_rng(_348525), relation_rng(_348675)))]]]]], (1632 ^ _291769) ^ [_349084, _349086, _349088] : [subset(_349088, _349086), -(subset(set_intersection2(_349088, _349084), set_intersection2(_349086, _349084)))], (1638 ^ _291769) ^ [_349312, _349314] : [subset(_349314, _349312), -(set_intersection2(_349314, _349312) = _349314)], (1644 ^ _291769) ^ [_349499] : [-(set_intersection2(_349499, empty_set) = empty_set)], (1646 ^ _291769) ^ [_349609, _349611] : [element(_349611, _349609), -(empty(_349609)), -(in(_349611, _349609))], (1656 ^ _291769) ^ [_349907, _349909] : [-(_349909 = _349907), 1660 ^ _291769 : [(1661 ^ _291769) ^ [] : [-(in(1657 ^ [_349907, _349909], _349909))], (1663 ^ _291769) ^ [] : [in(1657 ^ [_349907, _349909], _349907)]], 1664 ^ _291769 : [(1665 ^ _291769) ^ [] : [-(in(1657 ^ [_349907, _349909], _349907))], (1667 ^ _291769) ^ [] : [in(1657 ^ [_349907, _349909], _349909)]]], (1671 ^ _291769) ^ [_350408] : [-(subset(empty_set, _350408))], (1673 ^ _291769) ^ [_350529, _350531, _350533] : [relation(_350529), in(ordered_pair(_350533, _350531), _350529), 1680 ^ _291769 : [(1681 ^ _291769) ^ [] : [-(in(_350533, relation_field(_350529)))], (1683 ^ _291769) ^ [] : [-(in(_350531, relation_field(_350529)))]]], (1685 ^ _291769) ^ [_350941, _350943, _350945] : [subset(_350945, _350943), -(subset(set_difference(_350945, _350941), set_difference(_350943, _350941)))], (1691 ^ _291769) ^ [_351197, _351199, _351201, _351203] : [ordered_pair(_351203, _351201) = ordered_pair(_351199, _351197), 1694 ^ _291769 : [(1695 ^ _291769) ^ [] : [-(_351203 = _351199)], (1697 ^ _291769) ^ [] : [-(_351201 = _351197)]]], (1699 ^ _291769) ^ [_351495, _351497] : [-(subset(set_difference(_351497, _351495), _351497))], (1701 ^ _291769) ^ [_351593] : [relation(_351593), 1704 ^ _291769 : [(1705 ^ _291769) ^ [] : [-(relation_rng(_351593) = relation_dom(relation_inverse(_351593)))], (1707 ^ _291769) ^ [] : [-(relation_dom(_351593) = relation_rng(relation_inverse(_351593)))]]], (1709 ^ _291769) ^ [_351921, _351923] : [set_difference(_351923, _351921) = empty_set, -(subset(_351923, _351921))], (1715 ^ _291769) ^ [_352089, _352091] : [subset(_352091, _352089), -(set_difference(_352091, _352089) = empty_set)], (1721 ^ _291769) ^ [_352336, _352338] : [subset(singleton(_352338), _352336), -(in(_352338, _352336))], (1727 ^ _291769) ^ [_352502, _352504] : [in(_352504, _352502), -(subset(singleton(_352504), _352502))], (1733 ^ _291769) ^ [_352761, _352763, _352765] : [subset(unordered_pair(_352765, _352763), _352761), 1736 ^ _291769 : [(1737 ^ _291769) ^ [] : [-(in(_352765, _352761))], (1739 ^ _291769) ^ [] : [-(in(_352763, _352761))]]], (1741 ^ _291769) ^ [_353012, _353014, _353016] : [-(subset(unordered_pair(_353016, _353014), _353012)), in(_353016, _353012), in(_353014, _353012)], (1751 ^ _291769) ^ [_353314, _353316] : [-(set_union2(_353316, set_difference(_353314, _353316)) = set_union2(_353316, _353314))], (1763 ^ _291769) ^ [_353721, _353723] : [1764 ^ _291769 : [(1765 ^ _291769) ^ [] : [_353723 = empty_set], (1767 ^ _291769) ^ [] : [_353723 = singleton(_353721)]], -(subset(_353723, singleton(_353721)))], (1753 ^ _291769) ^ [_353461, _353463] : [subset(_353463, singleton(_353461)), -(_353463 = empty_set), -(_353463 = singleton(_353461))], (1771 ^ _291769) ^ [_353986] : [-(set_difference(_353986, empty_set) = _353986)], (1773 ^ _291769) ^ [_354125, _354127] : [element(_354127, powerset(_354125)), -(subset(_354127, _354125))], (1779 ^ _291769) ^ [_354291, _354293] : [subset(_354293, _354291), -(element(_354293, powerset(_354291)))], (1785 ^ _291769) ^ [_354527, _354529] : [-(disjoint(_354529, _354527)), 1789 ^ _291769 : [(1790 ^ _291769) ^ [] : [-(in(1788 ^ [_354527, _354529], _354529))], (1792 ^ _291769) ^ [] : [-(in(1788 ^ [_354527, _354529], _354527))]]], (1794 ^ _291769) ^ [_354841, _354843] : [disjoint(_354843, _354841), 1795 ^ _291769 : [(1796 ^ _291769) ^ [_354933] : [in(_354933, _354843), in(_354933, _354841)]]], (1804 ^ _291769) ^ [_355190] : [subset(_355190, empty_set), -(_355190 = empty_set)], (1810 ^ _291769) ^ [_355379, _355381] : [-(set_difference(set_union2(_355381, _355379), _355379) = set_difference(_355381, _355379))], (1812 ^ _291769) ^ [_355497, _355499] : [element(_355497, powerset(_355499)), 1815 ^ _291769 : [(1816 ^ _291769) ^ [_355649] : [element(_355649, powerset(_355499)), 1819 ^ _291769 : [(1820 ^ _291769) ^ [] : [disjoint(_355497, _355649), -(subset(_355497, subset_complement(_355499, _355649)))], (1826 ^ _291769) ^ [] : [subset(_355497, subset_complement(_355499, _355649)), -(disjoint(_355497, _355649))]]]]], (1832 ^ _291769) ^ [_356133] : [relation(_356133), 1835 ^ _291769 : [(1836 ^ _291769) ^ [_356270] : [relation(_356270), -(subset(relation_dom(relation_composition(_356133, _356270)), relation_dom(_356133)))]]], (1842 ^ _291769) ^ [_356485] : [relation(_356485), 1845 ^ _291769 : [(1846 ^ _291769) ^ [_356622] : [relation(_356622), -(subset(relation_rng(relation_composition(_356485, _356622)), relation_rng(_356622)))]]], (1852 ^ _291769) ^ [_356851, _356853] : [subset(_356853, _356851), -(_356851 = set_union2(_356853, set_difference(_356851, _356853)))], (1858 ^ _291769) ^ [_357059] : [relation(_357059), 1861 ^ _291769 : [(1862 ^ _291769) ^ [_357206] : [relation(_357206), subset(relation_rng(_357059), relation_dom(_357206)), -(relation_dom(relation_composition(_357059, _357206)) = relation_dom(_357059))]]], (1872 ^ _291769) ^ [_357532, _357534] : [element(_357532, powerset(powerset(_357534))), -(_357532 = empty_set), complements_of_subsets(_357534, _357532) = empty_set], (1882 ^ _291769) ^ [_357849, _357851] : [in(_357851, _357849), -(set_union2(singleton(_357851), _357849) = _357849)], (1888 ^ _291769) ^ [_358055] : [relation(_358055), 1891 ^ _291769 : [(1892 ^ _291769) ^ [_358202] : [relation(_358202), subset(relation_dom(_358055), relation_rng(_358202)), -(relation_rng(relation_composition(_358202, _358055)) = relation_rng(_358055))]]], (1902 ^ _291769) ^ [_358528, _358530] : [element(_358528, powerset(powerset(_358530))), -(_358528 = empty_set), -(subset_difference(_358530, cast_to_subset(_358530), union_of_subsets(_358530, _358528)) = meet_of_subsets(_358530, complements_of_subsets(_358530, _358528)))], (1912 ^ _291769) ^ [_358868, _358870] : [element(_358868, powerset(powerset(_358870))), -(_358868 = empty_set), -(union_of_subsets(_358870, complements_of_subsets(_358870, _358868)) = subset_difference(_358870, cast_to_subset(_358870), meet_of_subsets(_358870, _358868)))], (1922 ^ _291769) ^ [_359193, _359195] : [-(set_difference(_359195, set_difference(_359195, _359193)) = set_intersection2(_359195, _359193))], (1924 ^ _291769) ^ [_359282] : [-(set_difference(empty_set, _359282) = empty_set)], (1926 ^ _291769) ^ [_359406, _359408, _359410] : [-(element(_359410, _359406)), in(_359410, _359408), element(_359408, powerset(_359406))], (1936 ^ _291769) ^ [_359739, _359741] : [-(disjoint(_359741, _359739)), -(in(1939 ^ [_359739, _359741], set_intersection2(_359741, _359739)))], (1943 ^ _291769) ^ [_359974, _359976] : [1944 ^ _291769 : [(1945 ^ _291769) ^ [_360047] : [in(_360047, set_intersection2(_359976, _359974))]], disjoint(_359976, _359974)], (1949 ^ _291769) ^ [_360199] : [-(_360199 = empty_set), 1952 ^ _291769 : [(1953 ^ _291769) ^ [_360359] : [element(_360359, powerset(_360199)), 1956 ^ _291769 : [(1957 ^ _291769) ^ [_360513] : [element(_360513, _360199), -(in(_360513, _360359)), -(in(_360513, subset_complement(_360199, _360359)))]]]]], (1967 ^ _291769) ^ [_360859, _360861, _360863] : [element(_360859, powerset(_360863)), in(_360861, subset_complement(_360863, _360859)), in(_360861, _360859)], (1977 ^ _291769) ^ [_361193, _361195, _361197] : [in(_361197, _361195), element(_361195, powerset(_361193)), empty(_361193)], (1987 ^ _291769) ^ [_361503, _361505] : [subset(_361505, _361503), proper_subset(_361503, _361505)], (1993 ^ _291769) ^ [_361726, _361728, _361730] : [-(disjoint(_361730, _361726)), subset(_361730, _361728), disjoint(_361728, _361726)], (2003 ^ _291769) ^ [_362064, _362066] : [set_difference(_362066, singleton(_362064)) = _362066, in(_362064, _362066)], (2009 ^ _291769) ^ [_362237, _362239] : [-(in(_362237, _362239)), -(set_difference(_362239, singleton(_362237)) = _362239)], (2015 ^ _291769) ^ [_362433] : [-(unordered_pair(_362433, _362433) = singleton(_362433))], (2017 ^ _291769) ^ [_362531] : [empty(_362531), -(_362531 = empty_set)], (2023 ^ _291769) ^ [_362733, _362735] : [subset(singleton(_362735), singleton(_362733)), -(_362735 = _362733)], (2029 ^ _291769) ^ [_362951, _362953] : [in(_362953, _362951), empty(_362951)], (2035 ^ _291769) ^ [_363143, _363145] : [-(subset(_363145, set_union2(_363145, _363143)))], (2037 ^ _291769) ^ [_363284, _363286] : [disjoint(_363286, _363284), -(set_difference(_363286, _363284) = _363286)], (2043 ^ _291769) ^ [_363452, _363454] : [set_difference(_363454, _363452) = _363454, -(disjoint(_363454, _363452))], (2049 ^ _291769) ^ [_363670, _363672] : [empty(_363672), -(_363672 = _363670), empty(_363670)], (2059 ^ _291769) ^ [_363981, _363983, _363985] : [-(subset(set_union2(_363985, _363981), _363983)), subset(_363985, _363983), subset(_363981, _363983)], (2069 ^ _291769) ^ [_364310, _364312, _364314] : [singleton(_364314) = unordered_pair(_364312, _364310), -(_364314 = _364312)], (2075 ^ _291769) ^ [_364536, _364538] : [in(_364538, _364536), -(subset(_364538, union(_364536)))], (2081 ^ _291769) ^ [_364721] : [-(union(powerset(_364721)) = _364721)], (2119 ^ _291769) ^ [_366242, _366244, _366246] : [singleton(_366246) = unordered_pair(_366244, _366242), -(_366244 = _366242)], (2084 ^ _291769) ^ [_364962] : [-(in(_364962, 2082 ^ [_364962]))], (2086 ^ _291769) ^ [_365074, _365076, _365078] : [-(in(_365074, 2082 ^ [_365078])), in(_365076, 2082 ^ [_365078]), subset(_365074, _365076)], (2096 ^ _291769) ^ [_365389, _365391] : [in(_365389, 2082 ^ [_365391]), 2100 ^ _291769 : [(2101 ^ _291769) ^ [] : [-(in(2099 ^ [_365389, _365391], 2082 ^ [_365391]))], (2103 ^ _291769) ^ [_365701] : [subset(_365701, _365389), -(in(_365701, 2099 ^ [_365389, _365391]))]]], (2109 ^ _291769) ^ [_365908, _365910] : [subset(_365908, 2082 ^ [_365910]), -(are_equipotent(_365908, 2082 ^ [_365910])), -(in(_365908, 2082 ^ [_365910]))]], input).
% 3.81/4.47  ncf('1',plain,[in(ordered_pair(351 ^ [2124 ^ [], 468 ^ [2124 ^ []]], 352 ^ [2124 ^ [], 468 ^ [2124 ^ []]]), 2124 ^ [])],start(2128 ^ 0,bind([[_367805, _367807], [352 ^ [2124 ^ [], 468 ^ [2124 ^ []]], 351 ^ [2124 ^ [], 468 ^ [2124 ^ []]]]]))).
% 3.81/4.47  ncf('1.1',plain,[-(in(ordered_pair(351 ^ [2124 ^ [], 468 ^ [2124 ^ []]], 352 ^ [2124 ^ [], 468 ^ [2124 ^ []]]), 2124 ^ [])), in(468 ^ [2124 ^ []], 2124 ^ []), 468 ^ [2124 ^ []] = ordered_pair(351 ^ [2124 ^ [], 468 ^ [2124 ^ []]], 352 ^ [2124 ^ [], 468 ^ [2124 ^ []]]), 2124 ^ [] = 2124 ^ []],extension(110 ^ 1,bind([[_295355, _295357, _295359, _295361], [2124 ^ [], 2124 ^ [], ordered_pair(351 ^ [2124 ^ [], 468 ^ [2124 ^ []]], 352 ^ [2124 ^ [], 468 ^ [2124 ^ []]]), 468 ^ [2124 ^ []]]]))).
% 3.81/4.47  ncf('1.1.1',plain,[-(in(468 ^ [2124 ^ []], 2124 ^ [])), in(468 ^ [2124 ^ []], 2124 ^ []), 468 ^ [2124 ^ []] = 468 ^ [2124 ^ []], 2124 ^ [] = 2124 ^ []],extension(110 ^ 2,bind([[_295355, _295357, _295359, _295361], [2124 ^ [], 2124 ^ [], 468 ^ [2124 ^ []], 468 ^ [2124 ^ []]]]))).
% 3.81/4.47  ncf('1.1.1.1',plain,[-(in(468 ^ [2124 ^ []], 2124 ^ [])), -(2124 ^ [] = empty_set)],extension(467 ^ 3,bind([[_308126], [2124 ^ []]]))).
% 3.81/4.47  ncf('1.1.1.1.1',plain,[2124 ^ [] = empty_set],extension(2130 ^ 4)).
% 3.81/4.47  ncf('1.1.1.2',plain,[-(468 ^ [2124 ^ []] = 468 ^ [2124 ^ []])],extension(2 ^ 3,bind([[_291913], [468 ^ [2124 ^ []]]]))).
% 3.81/4.47  ncf('1.1.1.3',plain,[-(2124 ^ [] = 2124 ^ [])],extension(2 ^ 3,bind([[_291913], [2124 ^ []]]))).
% 3.81/4.47  ncf('1.1.2',plain,[-(468 ^ [2124 ^ []] = ordered_pair(351 ^ [2124 ^ [], 468 ^ [2124 ^ []]], 352 ^ [2124 ^ [], 468 ^ [2124 ^ []]])), 348 : in(468 ^ [2124 ^ []], 2124 ^ []), 348 : relation(2124 ^ [])],extension(344 ^ 2,bind([[_303782, _303930], [2124 ^ [], 468 ^ [2124 ^ []]]]))).
% 3.81/4.47  ncf('1.1.2.1',plain,[-(in(468 ^ [2124 ^ []], 2124 ^ [])), -(2124 ^ [] = empty_set)],extension(467 ^ 5,bind([[_308126], [2124 ^ []]]))).
% 3.81/4.47  ncf('1.1.2.1.1',plain,[2124 ^ [] = empty_set],extension(2130 ^ 6)).
% 3.81/4.47  ncf('1.1.2.2',plain,[-(relation(2124 ^ []))],extension(2126 ^ 3)).
% 3.81/4.47  ncf('1.1.3',plain,[-(2124 ^ [] = 2124 ^ [])],extension(2 ^ 2,bind([[_291913], [2124 ^ []]]))).
% 3.81/4.47  %-----------------------------------------------------
% 3.81/4.47  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------