%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU225+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.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 12:02:45 EDT 2023

% Result   : Theorem 15.22s 15.85s
% Output   : Proof 15.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU225+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n020.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 13:07:32 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 15.22/15.85  
% 15.22/15.85  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 15.22/15.85  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.22/15.85  %-----------------------------------------------------
% 15.22/15.85  ncf(matrix, plain, [(3512 ^ _20835) ^ [] : [-(relation(3510 ^ []))], (3514 ^ _20835) ^ [] : [-(function(3510 ^ []))], (3516 ^ _20835) ^ [] : [-(in(3509 ^ [], 3508 ^ []))], (3518 ^ _20835) ^ [] : [apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ [])], (2 ^ _20835) ^ [_20865] : [-(_20865 = _20865)], (4 ^ _20835) ^ [_20888, _20890] : [_20890 = _20888, -(_20888 = _20890)], (10 ^ _20835) ^ [_20961, _20963, _20965] : [-(_20965 = _20961), _20965 = _20963, _20963 = _20961], (20 ^ _20835) ^ [_21098, _21100] : [-(relation_empty_yielding(_21098)), _21100 = _21098, relation_empty_yielding(_21100)], (30 ^ _20835) ^ [_21223, _21225, _21227, _21229] : [-(element(_21227, _21223)), element(_21229, _21225), _21229 = _21227, _21225 = _21223], (44 ^ _20835) ^ [_21416, _21418, _21420, _21422] : [-(proper_subset(_21420, _21416)), proper_subset(_21422, _21418), _21422 = _21420, _21418 = _21416], (58 ^ _20835) ^ [_21609, _21611] : [-(one_to_one(_21609)), _21611 = _21609, one_to_one(_21611)], (68 ^ _20835) ^ [_21734, _21736, _21738, _21740] : [-(disjoint(_21738, _21734)), disjoint(_21740, _21736), _21740 = _21738, _21736 = _21734], (82 ^ _20835) ^ [_21927, _21929] : [-(empty(_21927)), _21929 = _21927, empty(_21929)], (92 ^ _20835) ^ [_22052, _22054, _22056, _22058] : [-(subset(_22056, _22052)), subset(_22058, _22054), _22058 = _22056, _22054 = _22052], (106 ^ _20835) ^ [_22245, _22247, _22249, _22251] : [-(are_equipotent(_22249, _22245)), are_equipotent(_22251, _22247), _22251 = _22249, _22247 = _22245], (120 ^ _20835) ^ [_22438, _22440] : [-(relation(_22438)), _22440 = _22438, relation(_22440)], (130 ^ _20835) ^ [_22563, _22565] : [-(function(_22563)), _22565 = _22563, function(_22565)], (140 ^ _20835) ^ [_22684, _22686, _22688, _22690] : [-(in(_22688, _22684)), in(_22690, _22686), _22690 = _22688, _22686 = _22684], (154 ^ _20835) ^ [_22903, _22905] : [_22905 = _22903, -(set_meet(_22905) = set_meet(_22903))], (160 ^ _20835) ^ [_22988, _22990, _22992, _22994] : [-(relation_rng_restriction(_22994, _22990) = relation_rng_restriction(_22992, _22988)), _22994 = _22992, _22990 = _22988], (170 ^ _20835) ^ [_23137, _23139, _23141, _23143] : [-(relation_image(_23143, _23139) = relation_image(_23141, _23137)), _23143 = _23141, _23139 = _23137], (180 ^ _20835) ^ [_23286, _23288, _23290, _23292] : [-(relation_inverse_image(_23292, _23288) = relation_inverse_image(_23290, _23286)), _23292 = _23290, _23288 = _23286], (190 ^ _20835) ^ [_23435, _23437, _23439, _23441] : [-(cartesian_product2(_23441, _23437) = cartesian_product2(_23439, _23435)), _23441 = _23439, _23437 = _23435], (200 ^ _20835) ^ [_23584, _23586] : [_23586 = _23584, -(relation_field(_23586) = relation_field(_23584))], (206 ^ _20835) ^ [_23669, _23671] : [_23671 = _23669, -(relation_inverse(_23671) = relation_inverse(_23669))], (212 ^ _20835) ^ [_23754, _23756, _23758, _23760] : [-(union_of_subsets(_23760, _23756) = union_of_subsets(_23758, _23754)), _23760 = _23758, _23756 = _23754], (222 ^ _20835) ^ [_23903, _23905, _23907, _23909] : [-(complements_of_subsets(_23909, _23905) = complements_of_subsets(_23907, _23903)), _23909 = _23907, _23905 = _23903], (232 ^ _20835) ^ [_24052, _24054, _24056, _24058, _24060, _24062] : [-(subset_difference(_24062, _24058, _24054) = subset_difference(_24060, _24056, _24052)), _24062 = _24060, _24058 = _24056, _24054 = _24052], (246 ^ _20835) ^ [_24273, _24275] : [_24275 = _24273, -(cast_to_subset(_24275) = cast_to_subset(_24273))], (252 ^ _20835) ^ [_24358, _24360, _24362, _24364] : [-(meet_of_subsets(_24364, _24360) = meet_of_subsets(_24362, _24358)), _24364 = _24362, _24360 = _24358], (262 ^ _20835) ^ [_24507, _24509, _24511, _24513] : [-(subset_complement(_24513, _24509) = subset_complement(_24511, _24507)), _24513 = _24511, _24509 = _24507], (272 ^ _20835) ^ [_24656, _24658] : [_24658 = _24656, -(function_inverse(_24658) = function_inverse(_24656))], (278 ^ _20835) ^ [_24741, _24743, _24745, _24747] : [-(set_difference(_24747, _24743) = set_difference(_24745, _24741)), _24747 = _24745, _24743 = _24741], (288 ^ _20835) ^ [_24890, _24892, _24894, _24896] : [-(ordered_pair(_24896, _24892) = ordered_pair(_24894, _24890)), _24896 = _24894, _24892 = _24890], (298 ^ _20835) ^ [_25039, _25041, _25043, _25045] : [-(set_union2(_25045, _25041) = set_union2(_25043, _25039)), _25045 = _25043, _25041 = _25039], (308 ^ _20835) ^ [_25188, _25190, _25192, _25194] : [-(set_intersection2(_25194, _25190) = set_intersection2(_25192, _25188)), _25194 = _25192, _25190 = _25188], (318 ^ _20835) ^ [_25337, _25339] : [_25339 = _25337, -(relation_dom(_25339) = relation_dom(_25337))], (324 ^ _20835) ^ [_25422, _25424, _25426, _25428] : [-(relation_composition(_25428, _25424) = relation_composition(_25426, _25422)), _25428 = _25426, _25424 = _25422], (334 ^ _20835) ^ [_25571, _25573] : [_25573 = _25571, -(identity_relation(_25573) = identity_relation(_25571))], (340 ^ _20835) ^ [_25656, _25658] : [_25658 = _25656, -(relation_rng(_25658) = relation_rng(_25656))], (346 ^ _20835) ^ [_25741, _25743] : [_25743 = _25741, -(union(_25743) = union(_25741))], (352 ^ _20835) ^ [_25826, _25828] : [_25828 = _25826, -(powerset(_25828) = powerset(_25826))], (358 ^ _20835) ^ [_25911, _25913] : [_25913 = _25911, -(singleton(_25913) = singleton(_25911))], (364 ^ _20835) ^ [_25996, _25998, _26000, _26002] : [-(unordered_pair(_26002, _25998) = unordered_pair(_26000, _25996)), _26002 = _26000, _25998 = _25996], (374 ^ _20835) ^ [_26145, _26147, _26149, _26151] : [-(relation_dom_restriction(_26151, _26147) = relation_dom_restriction(_26149, _26145)), _26151 = _26149, _26147 = _26145], (384 ^ _20835) ^ [_26290, _26292, _26294, _26296] : [-(apply(_26296, _26292) = apply(_26294, _26290)), _26296 = _26294, _26292 = _26290], (394 ^ _20835) ^ [_26537, _26539] : [in(_26539, _26537), in(_26537, _26539)], (400 ^ _20835) ^ [_26615, _26617] : [proper_subset(_26617, _26615), proper_subset(_26615, _26617)], (406 ^ _20835) ^ [_26693] : [empty(_26693), -(function(_26693))], (412 ^ _20835) ^ [_26764] : [empty(_26764), -(relation(_26764))], (418 ^ _20835) ^ [_26835] : [429 ^ _20835 : [(430 ^ _20835) ^ [] : [-(relation(_26835))], (432 ^ _20835) ^ [] : [-(function(_26835))], (434 ^ _20835) ^ [] : [-(one_to_one(_26835))]], relation(_26835), empty(_26835), function(_26835)], (436 ^ _20835) ^ [_27048, _27050] : [-(unordered_pair(_27050, _27048) = unordered_pair(_27048, _27050))], (438 ^ _20835) ^ [_27079, _27081] : [-(set_union2(_27081, _27079) = set_union2(_27079, _27081))], (440 ^ _20835) ^ [_27110, _27112] : [-(set_intersection2(_27112, _27110) = set_intersection2(_27110, _27112))], (442 ^ _20835) ^ [_27141, _27143] : [relation(_27141), 445 ^ _20835 : [(468 ^ _20835) ^ [] : [-(_27141 = identity_relation(_27143)), 481 ^ _20835 : [(482 ^ _20835) ^ [] : [-(in(469 ^ [_27141, _27143], _27143))], (484 ^ _20835) ^ [] : [-(469 ^ [_27141, _27143] = 470 ^ [_27141, _27143])], (486 ^ _20835) ^ [] : [in(ordered_pair(469 ^ [_27141, _27143], 470 ^ [_27141, _27143]), _27141)]], 473 ^ _20835 : [(474 ^ _20835) ^ [] : [-(in(ordered_pair(469 ^ [_27141, _27143], 470 ^ [_27141, _27143]), _27141))], (476 ^ _20835) ^ [] : [in(469 ^ [_27141, _27143], _27143), 469 ^ [_27141, _27143] = 470 ^ [_27141, _27143]]]], (446 ^ _20835) ^ [] : [_27141 = identity_relation(_27143), 449 ^ _20835 : [(450 ^ _20835) ^ [_27294, _27296] : [in(ordered_pair(_27296, _27294), _27141), 453 ^ _20835 : [(454 ^ _20835) ^ [] : [-(in(_27296, _27143))], (456 ^ _20835) ^ [] : [-(_27296 = _27294)]]], (458 ^ _20835) ^ [_27403, _27405] : [-(in(ordered_pair(_27405, _27403), _27141)), in(_27405, _27143), _27405 = _27403]]]]], (490 ^ _20835) ^ [_27930, _27932] : [_27932 = _27930, 493 ^ _20835 : [(494 ^ _20835) ^ [] : [-(subset(_27932, _27930))], (496 ^ _20835) ^ [] : [-(subset(_27930, _27932))]]], (498 ^ _20835) ^ [_28029, _28031] : [-(_28031 = _28029), subset(_28031, _28029), subset(_28029, _28031)], (508 ^ _20835) ^ [_28160] : [relation(_28160), 511 ^ _20835 : [(512 ^ _20835) ^ [_28260, _28262] : [relation(_28260), 515 ^ _20835 : [(538 ^ _20835) ^ [] : [-(_28260 = relation_dom_restriction(_28160, _28262)), 551 ^ _20835 : [(552 ^ _20835) ^ [] : [-(in(539 ^ [_28160, _28260, _28262], _28262))], (554 ^ _20835) ^ [] : [-(in(ordered_pair(539 ^ [_28160, _28260, _28262], 540 ^ [_28160, _28260, _28262]), _28160))], (556 ^ _20835) ^ [] : [in(ordered_pair(539 ^ [_28160, _28260, _28262], 540 ^ [_28160, _28260, _28262]), _28260)]], 543 ^ _20835 : [(544 ^ _20835) ^ [] : [-(in(ordered_pair(539 ^ [_28160, _28260, _28262], 540 ^ [_28160, _28260, _28262]), _28260))], (546 ^ _20835) ^ [] : [in(539 ^ [_28160, _28260, _28262], _28262), in(ordered_pair(539 ^ [_28160, _28260, _28262], 540 ^ [_28160, _28260, _28262]), _28160)]]], (516 ^ _20835) ^ [] : [_28260 = relation_dom_restriction(_28160, _28262), 519 ^ _20835 : [(520 ^ _20835) ^ [_28422, _28424] : [in(ordered_pair(_28424, _28422), _28260), 523 ^ _20835 : [(524 ^ _20835) ^ [] : [-(in(_28424, _28262))], (526 ^ _20835) ^ [] : [-(in(ordered_pair(_28424, _28422), _28160))]]], (528 ^ _20835) ^ [_28539, _28541] : [-(in(ordered_pair(_28541, _28539), _28260)), in(_28541, _28262), in(ordered_pair(_28541, _28539), _28160)]]]]]]], (560 ^ _20835) ^ [_29109, _29111] : [relation(_29109), 563 ^ _20835 : [(564 ^ _20835) ^ [_29206] : [relation(_29206), 567 ^ _20835 : [(590 ^ _20835) ^ [] : [-(_29206 = relation_rng_restriction(_29111, _29109)), 603 ^ _20835 : [(604 ^ _20835) ^ [] : [-(in(592 ^ [_29109, _29111, _29206], _29111))], (606 ^ _20835) ^ [] : [-(in(ordered_pair(591 ^ [_29109, _29111, _29206], 592 ^ [_29109, _29111, _29206]), _29109))], (608 ^ _20835) ^ [] : [in(ordered_pair(591 ^ [_29109, _29111, _29206], 592 ^ [_29109, _29111, _29206]), _29206)]], 595 ^ _20835 : [(596 ^ _20835) ^ [] : [-(in(ordered_pair(591 ^ [_29109, _29111, _29206], 592 ^ [_29109, _29111, _29206]), _29206))], (598 ^ _20835) ^ [] : [in(592 ^ [_29109, _29111, _29206], _29111), in(ordered_pair(591 ^ [_29109, _29111, _29206], 592 ^ [_29109, _29111, _29206]), _29109)]]], (568 ^ _20835) ^ [] : [_29206 = relation_rng_restriction(_29111, _29109), 571 ^ _20835 : [(572 ^ _20835) ^ [_29368, _29370] : [in(ordered_pair(_29370, _29368), _29206), 575 ^ _20835 : [(576 ^ _20835) ^ [] : [-(in(_29368, _29111))], (578 ^ _20835) ^ [] : [-(in(ordered_pair(_29370, _29368), _29109))]]], (580 ^ _20835) ^ [_29485, _29487] : [-(in(ordered_pair(_29487, _29485), _29206)), in(_29485, _29111), in(ordered_pair(_29487, _29485), _29109)]]]]]]], (612 ^ _20835) ^ [_30046] : [relation(_30046), 615 ^ _20835 : [(639 ^ _20835) ^ [_30551, _30553] : [-(_30551 = relation_image(_30046, _30553)), 652 ^ _20835 : [(653 ^ _20835) ^ [] : [-(in(ordered_pair(651 ^ [_30046, _30551, _30553], 640 ^ [_30046, _30551, _30553]), _30046))], (655 ^ _20835) ^ [] : [-(in(651 ^ [_30046, _30551, _30553], _30553))], (657 ^ _20835) ^ [] : [in(640 ^ [_30046, _30551, _30553], _30551)]], 643 ^ _20835 : [(644 ^ _20835) ^ [] : [-(in(640 ^ [_30046, _30551, _30553], _30551))], (646 ^ _20835) ^ [_30699] : [in(ordered_pair(_30699, 640 ^ [_30046, _30551, _30553]), _30046), in(_30699, _30553)]]], (616 ^ _20835) ^ [_30153, _30155] : [_30153 = relation_image(_30046, _30155), 619 ^ _20835 : [(620 ^ _20835) ^ [_30250] : [in(_30250, _30153), 624 ^ _20835 : [(625 ^ _20835) ^ [] : [-(in(ordered_pair(623 ^ [_30046, _30153, _30155, _30250], _30250), _30046))], (627 ^ _20835) ^ [] : [-(in(623 ^ [_30046, _30153, _30155, _30250], _30155))]]], (629 ^ _20835) ^ [_30386] : [-(in(_30386, _30153)), 630 ^ _20835 : [(631 ^ _20835) ^ [_30433] : [in(ordered_pair(_30433, _30386), _30046), in(_30433, _30155)]]]]]]], (661 ^ _20835) ^ [_30953] : [relation(_30953), 664 ^ _20835 : [(688 ^ _20835) ^ [_31458, _31460] : [-(_31458 = relation_inverse_image(_30953, _31460)), 701 ^ _20835 : [(702 ^ _20835) ^ [] : [-(in(ordered_pair(689 ^ [_30953, _31458, _31460], 700 ^ [_30953, _31458, _31460]), _30953))], (704 ^ _20835) ^ [] : [-(in(700 ^ [_30953, _31458, _31460], _31460))], (706 ^ _20835) ^ [] : [in(689 ^ [_30953, _31458, _31460], _31458)]], 692 ^ _20835 : [(693 ^ _20835) ^ [] : [-(in(689 ^ [_30953, _31458, _31460], _31458))], (695 ^ _20835) ^ [_31606] : [in(ordered_pair(689 ^ [_30953, _31458, _31460], _31606), _30953), in(_31606, _31460)]]], (665 ^ _20835) ^ [_31060, _31062] : [_31060 = relation_inverse_image(_30953, _31062), 668 ^ _20835 : [(669 ^ _20835) ^ [_31157] : [in(_31157, _31060), 673 ^ _20835 : [(674 ^ _20835) ^ [] : [-(in(ordered_pair(_31157, 672 ^ [_30953, _31060, _31062, _31157]), _30953))], (676 ^ _20835) ^ [] : [-(in(672 ^ [_30953, _31060, _31062, _31157], _31062))]]], (678 ^ _20835) ^ [_31293] : [-(in(_31293, _31060)), 679 ^ _20835 : [(680 ^ _20835) ^ [_31340] : [in(ordered_pair(_31293, _31340), _30953), in(_31340, _31062)]]]]]]], (722 ^ _20835) ^ [_32057] : [724 ^ _20835 : [(725 ^ _20835) ^ [] : [-(in(723 ^ [_32057], _32057))], (727 ^ _20835) ^ [_32170, _32172] : [723 ^ [_32057] = ordered_pair(_32172, _32170)]], -(relation(_32057))], (710 ^ _20835) ^ [_31872] : [relation(_31872), 713 ^ _20835 : [(714 ^ _20835) ^ [_31948] : [in(_31948, _31872), -(_31948 = ordered_pair(717 ^ [_31872, _31948], 718 ^ [_31872, _31948]))]]], (780 ^ _20835) ^ [_33035, _33037] : [_33037 = empty_set, 783 ^ _20835 : [(784 ^ _20835) ^ [] : [_33035 = set_meet(_33037), -(_33035 = empty_set)], (790 ^ _20835) ^ [] : [_33035 = empty_set, -(_33035 = set_meet(_33037))]]], (731 ^ _20835) ^ [_32242, _32244] : [-(_32244 = empty_set), 734 ^ _20835 : [(758 ^ _20835) ^ [] : [-(_32242 = set_meet(_32244)), 762 ^ _20835 : [(763 ^ _20835) ^ [] : [-(in(759 ^ [_32242, _32244], _32242))], (766 ^ _20835) ^ [] : [-(in(764 ^ [_32242, _32244], _32244))], (768 ^ _20835) ^ [] : [in(759 ^ [_32242, _32244], 764 ^ [_32242, _32244])]], 769 ^ _20835 : [(776 ^ _20835) ^ [] : [in(759 ^ [_32242, _32244], _32242)], (770 ^ _20835) ^ [_32879] : [in(_32879, _32244), -(in(759 ^ [_32242, _32244], _32879))]]], (735 ^ _20835) ^ [] : [_32242 = set_meet(_32244), 738 ^ _20835 : [(749 ^ _20835) ^ [_32535] : [751 ^ _20835 : [(752 ^ _20835) ^ [] : [-(in(750 ^ [_32242, _32244, _32535], _32244))], (754 ^ _20835) ^ [] : [in(_32535, 750 ^ [_32242, _32244, _32535])]], -(in(_32535, _32242))], (739 ^ _20835) ^ [_32389] : [in(_32389, _32242), 742 ^ _20835 : [(743 ^ _20835) ^ [_32454] : [in(_32454, _32244), -(in(_32389, _32454))]]]]]]], (812 ^ _20835) ^ [_33500, _33502] : [-(_33500 = singleton(_33502)), 816 ^ _20835 : [(817 ^ _20835) ^ [] : [-(in(813 ^ [_33500, _33502], _33500))], (819 ^ _20835) ^ [] : [813 ^ [_33500, _33502] = _33502]], 820 ^ _20835 : [(821 ^ _20835) ^ [] : [-(813 ^ [_33500, _33502] = _33502)], (823 ^ _20835) ^ [] : [in(813 ^ [_33500, _33502], _33500)]]], (796 ^ _20835) ^ [_33265, _33267] : [_33265 = singleton(_33267), 799 ^ _20835 : [(800 ^ _20835) ^ [_33344] : [in(_33344, _33265), -(_33344 = _33267)], (806 ^ _20835) ^ [_33419] : [_33419 = _33267, -(in(_33419, _33265))]]], (827 ^ _20835) ^ [_33754] : [_33754 = empty_set, 830 ^ _20835 : [(831 ^ _20835) ^ [_33815] : [in(_33815, _33754)]]], (833 ^ _20835) ^ [_33836] : [-(in(834 ^ [_33836], _33836)), -(_33836 = empty_set)], (856 ^ _20835) ^ [_34127, _34129] : [-(_34127 = powerset(_34129)), 860 ^ _20835 : [(861 ^ _20835) ^ [] : [-(in(857 ^ [_34127, _34129], _34127))], (863 ^ _20835) ^ [] : [subset(857 ^ [_34127, _34129], _34129)]], 864 ^ _20835 : [(865 ^ _20835) ^ [] : [-(subset(857 ^ [_34127, _34129], _34129))], (867 ^ _20835) ^ [] : [in(857 ^ [_34127, _34129], _34127)]]], (840 ^ _20835) ^ [_33892, _33894] : [_33892 = powerset(_33894), 843 ^ _20835 : [(844 ^ _20835) ^ [_33971] : [in(_33971, _33892), -(subset(_33971, _33894))], (850 ^ _20835) ^ [_34046] : [subset(_34046, _33894), -(in(_34046, _33892))]]], (871 ^ _20835) ^ [_34369] : [relation(_34369), 874 ^ _20835 : [(875 ^ _20835) ^ [_34455] : [relation(_34455), 878 ^ _20835 : [(895 ^ _20835) ^ [] : [-(_34369 = _34455), 900 ^ _20835 : [(901 ^ _20835) ^ [] : [-(in(ordered_pair(896 ^ [_34369, _34455], 897 ^ [_34369, _34455]), _34369))], (903 ^ _20835) ^ [] : [in(ordered_pair(896 ^ [_34369, _34455], 897 ^ [_34369, _34455]), _34455)]], 904 ^ _20835 : [(905 ^ _20835) ^ [] : [-(in(ordered_pair(896 ^ [_34369, _34455], 897 ^ [_34369, _34455]), _34455))], (907 ^ _20835) ^ [] : [in(ordered_pair(896 ^ [_34369, _34455], 897 ^ [_34369, _34455]), _34369)]]], (879 ^ _20835) ^ [] : [_34369 = _34455, 882 ^ _20835 : [(883 ^ _20835) ^ [_34601, _34603] : [in(ordered_pair(_34603, _34601), _34369), -(in(ordered_pair(_34603, _34601), _34455))], (889 ^ _20835) ^ [_34690, _34692] : [in(ordered_pair(_34692, _34690), _34455), -(in(ordered_pair(_34692, _34690), _34369))]]]]]]], (911 ^ _20835) ^ [_35080, _35082] : [-(empty(_35082)), 914 ^ _20835 : [(915 ^ _20835) ^ [] : [element(_35080, _35082), -(in(_35080, _35082))], (921 ^ _20835) ^ [] : [in(_35080, _35082), -(element(_35080, _35082))]]], (927 ^ _20835) ^ [_35280, _35282] : [empty(_35282), 930 ^ _20835 : [(931 ^ _20835) ^ [] : [element(_35280, _35282), -(empty(_35280))], (937 ^ _20835) ^ [] : [empty(_35280), -(element(_35280, _35282))]]], (965 ^ _20835) ^ [_35802, _35804, _35806] : [-(_35802 = unordered_pair(_35806, _35804)), 969 ^ _20835 : [(970 ^ _20835) ^ [] : [-(in(966 ^ [_35802, _35804, _35806], _35802))], (972 ^ _20835) ^ [] : [966 ^ [_35802, _35804, _35806] = _35806], (974 ^ _20835) ^ [] : [966 ^ [_35802, _35804, _35806] = _35804]], 975 ^ _20835 : [(982 ^ _20835) ^ [] : [in(966 ^ [_35802, _35804, _35806], _35802)], (976 ^ _20835) ^ [] : [-(966 ^ [_35802, _35804, _35806] = _35806), -(966 ^ [_35802, _35804, _35806] = _35804)]]], (943 ^ _20835) ^ [_35502, _35504, _35506] : [_35502 = unordered_pair(_35506, _35504), 946 ^ _20835 : [(957 ^ _20835) ^ [_35681] : [958 ^ _20835 : [(959 ^ _20835) ^ [] : [_35681 = _35506], (961 ^ _20835) ^ [] : [_35681 = _35504]], -(in(_35681, _35502))], (947 ^ _20835) ^ [_35591] : [in(_35591, _35502), -(_35591 = _35506), -(_35591 = _35504)]]], (1008 ^ _20835) ^ [_36442, _36444, _36446] : [-(_36442 = set_union2(_36446, _36444)), 1012 ^ _20835 : [(1013 ^ _20835) ^ [] : [-(in(1009 ^ [_36442, _36444, _36446], _36442))], (1015 ^ _20835) ^ [] : [in(1009 ^ [_36442, _36444, _36446], _36446)], (1017 ^ _20835) ^ [] : [in(1009 ^ [_36442, _36444, _36446], _36444)]], 1018 ^ _20835 : [(1025 ^ _20835) ^ [] : [in(1009 ^ [_36442, _36444, _36446], _36442)], (1019 ^ _20835) ^ [] : [-(in(1009 ^ [_36442, _36444, _36446], _36446)), -(in(1009 ^ [_36442, _36444, _36446], _36444))]]], (986 ^ _20835) ^ [_36142, _36144, _36146] : [_36142 = set_union2(_36146, _36144), 989 ^ _20835 : [(1000 ^ _20835) ^ [_36321] : [1001 ^ _20835 : [(1002 ^ _20835) ^ [] : [in(_36321, _36146)], (1004 ^ _20835) ^ [] : [in(_36321, _36144)]], -(in(_36321, _36142))], (990 ^ _20835) ^ [_36231] : [in(_36231, _36142), -(in(_36231, _36146)), -(in(_36231, _36144))]]], (1059 ^ _20835) ^ [_37315, _37317, _37319] : [-(_37315 = cartesian_product2(_37319, _37317)), 1077 ^ _20835 : [(1078 ^ _20835) ^ [] : [-(in(1075 ^ [_37315, _37317, _37319], _37319))], (1080 ^ _20835) ^ [] : [-(in(1076 ^ [_37315, _37317, _37319], _37317))], (1082 ^ _20835) ^ [] : [-(1060 ^ [_37315, _37317, _37319] = ordered_pair(1075 ^ [_37315, _37317, _37319], 1076 ^ [_37315, _37317, _37319]))], (1084 ^ _20835) ^ [] : [in(1060 ^ [_37315, _37317, _37319], _37315)]], 1063 ^ _20835 : [(1064 ^ _20835) ^ [] : [-(in(1060 ^ [_37315, _37317, _37319], _37315))], (1066 ^ _20835) ^ [_37485, _37487] : [in(_37487, _37319), in(_37485, _37317), 1060 ^ [_37315, _37317, _37319] = ordered_pair(_37487, _37485)]]], (1029 ^ _20835) ^ [_36782, _36784, _36786] : [_36782 = cartesian_product2(_36786, _36784), 1032 ^ _20835 : [(1033 ^ _20835) ^ [_36890] : [in(_36890, _36782), 1038 ^ _20835 : [(1039 ^ _20835) ^ [] : [-(in(1036 ^ [_36782, _36784, _36786, _36890], _36786))], (1041 ^ _20835) ^ [] : [-(in(1037 ^ [_36782, _36784, _36786, _36890], _36784))], (1043 ^ _20835) ^ [] : [-(_36890 = ordered_pair(1036 ^ [_36782, _36784, _36786, _36890], 1037 ^ [_36782, _36784, _36786, _36890]))]]], (1045 ^ _20835) ^ [_37077] : [-(in(_37077, _36782)), 1046 ^ _20835 : [(1047 ^ _20835) ^ [_37135, _37137] : [in(_37137, _36786), in(_37135, _36784), _37077 = ordered_pair(_37137, _37135)]]]]], (1088 ^ _20835) ^ [_37833] : [relation(_37833), 1091 ^ _20835 : [(1092 ^ _20835) ^ [_37919] : [relation(_37919), 1095 ^ _20835 : [(1106 ^ _20835) ^ [] : [1109 ^ _20835 : [(1110 ^ _20835) ^ [] : [-(in(ordered_pair(1107 ^ [_37833, _37919], 1108 ^ [_37833, _37919]), _37833))], (1112 ^ _20835) ^ [] : [in(ordered_pair(1107 ^ [_37833, _37919], 1108 ^ [_37833, _37919]), _37919)]], -(subset(_37833, _37919))], (1096 ^ _20835) ^ [] : [subset(_37833, _37919), 1099 ^ _20835 : [(1100 ^ _20835) ^ [_38050, _38052] : [in(ordered_pair(_38052, _38050), _37833), -(in(ordered_pair(_38052, _38050), _37919))]]]]]]], (1126 ^ _20835) ^ [_38463, _38465] : [1128 ^ _20835 : [(1129 ^ _20835) ^ [] : [-(in(1127 ^ [_38463, _38465], _38465))], (1131 ^ _20835) ^ [] : [in(1127 ^ [_38463, _38465], _38463)]], -(subset(_38465, _38463))], (1116 ^ _20835) ^ [_38321, _38323] : [subset(_38323, _38321), 1119 ^ _20835 : [(1120 ^ _20835) ^ [_38384] : [in(_38384, _38323), -(in(_38384, _38321))]]], (1157 ^ _20835) ^ [_38954, _38956, _38958] : [-(_38954 = set_intersection2(_38958, _38956)), 1169 ^ _20835 : [(1170 ^ _20835) ^ [] : [-(in(1158 ^ [_38954, _38956, _38958], _38958))], (1172 ^ _20835) ^ [] : [-(in(1158 ^ [_38954, _38956, _38958], _38956))], (1174 ^ _20835) ^ [] : [in(1158 ^ [_38954, _38956, _38958], _38954)]], 1161 ^ _20835 : [(1162 ^ _20835) ^ [] : [-(in(1158 ^ [_38954, _38956, _38958], _38954))], (1164 ^ _20835) ^ [] : [in(1158 ^ [_38954, _38956, _38958], _38958), in(1158 ^ [_38954, _38956, _38958], _38956)]]], (1135 ^ _20835) ^ [_38623, _38625, _38627] : [_38623 = set_intersection2(_38627, _38625), 1138 ^ _20835 : [(1139 ^ _20835) ^ [_38712] : [in(_38712, _38623), 1142 ^ _20835 : [(1143 ^ _20835) ^ [] : [-(in(_38712, _38627))], (1145 ^ _20835) ^ [] : [-(in(_38712, _38625))]]], (1147 ^ _20835) ^ [_38815] : [-(in(_38815, _38623)), in(_38815, _38627), in(_38815, _38625)]]], (1178 ^ _20835) ^ [_39308] : [relation(_39308), function(_39308), 1185 ^ _20835 : [(1186 ^ _20835) ^ [_39468, _39470] : [in(_39470, relation_dom(_39308)), 1189 ^ _20835 : [(1190 ^ _20835) ^ [] : [_39468 = apply(_39308, _39470), -(in(ordered_pair(_39470, _39468), _39308))], (1196 ^ _20835) ^ [] : [in(ordered_pair(_39470, _39468), _39308), -(_39468 = apply(_39308, _39470))]]], (1202 ^ _20835) ^ [_39698, _39700] : [-(in(_39700, relation_dom(_39308))), 1205 ^ _20835 : [(1206 ^ _20835) ^ [] : [_39698 = apply(_39308, _39700), -(_39698 = empty_set)], (1212 ^ _20835) ^ [] : [_39698 = empty_set, -(_39698 = apply(_39308, _39700))]]]]], (1218 ^ _20835) ^ [_39929] : [relation(_39929), 1221 ^ _20835 : [(1239 ^ _20835) ^ [_40303] : [-(_40303 = relation_dom(_39929)), 1243 ^ _20835 : [(1244 ^ _20835) ^ [] : [-(in(1240 ^ [_39929, _40303], _40303))], (1246 ^ _20835) ^ [_40437] : [in(ordered_pair(1240 ^ [_39929, _40303], _40437), _39929)]], 1248 ^ _20835 : [(1249 ^ _20835) ^ [] : [-(in(ordered_pair(1240 ^ [_39929, _40303], 1247 ^ [_39929, _40303]), _39929))], (1251 ^ _20835) ^ [] : [in(1240 ^ [_39929, _40303], _40303)]]], (1222 ^ _20835) ^ [_40021] : [_40021 = relation_dom(_39929), 1225 ^ _20835 : [(1226 ^ _20835) ^ [_40108] : [in(_40108, _40021), -(in(ordered_pair(_40108, 1229 ^ [_39929, _40021, _40108]), _39929))], (1233 ^ _20835) ^ [_40203] : [1234 ^ _20835 : [(1235 ^ _20835) ^ [_40247] : [in(ordered_pair(_40203, _40247), _39929)]], -(in(_40203, _40021))]]]]], (1255 ^ _20835) ^ [_40584] : [-(cast_to_subset(_40584) = _40584)], (1280 ^ _20835) ^ [_40990, _40992] : [-(_40990 = union(_40992)), 1293 ^ _20835 : [(1294 ^ _20835) ^ [] : [-(in(1281 ^ [_40990, _40992], 1292 ^ [_40990, _40992]))], (1296 ^ _20835) ^ [] : [-(in(1292 ^ [_40990, _40992], _40992))], (1298 ^ _20835) ^ [] : [in(1281 ^ [_40990, _40992], _40990)]], 1284 ^ _20835 : [(1285 ^ _20835) ^ [] : [-(in(1281 ^ [_40990, _40992], _40990))], (1287 ^ _20835) ^ [_41123] : [in(1281 ^ [_40990, _40992], _41123), in(_41123, _40992)]]], (1257 ^ _20835) ^ [_40624, _40626] : [_40624 = union(_40626), 1260 ^ _20835 : [(1261 ^ _20835) ^ [_40714] : [in(_40714, _40624), 1265 ^ _20835 : [(1266 ^ _20835) ^ [] : [-(in(_40714, 1264 ^ [_40624, _40626, _40714]))], (1268 ^ _20835) ^ [] : [-(in(1264 ^ [_40624, _40626, _40714], _40626))]]], (1270 ^ _20835) ^ [_40838] : [-(in(_40838, _40624)), 1271 ^ _20835 : [(1272 ^ _20835) ^ [_40880] : [in(_40838, _40880), in(_40880, _40626)]]]]], (1324 ^ _20835) ^ [_41711, _41713, _41715] : [-(_41711 = set_difference(_41715, _41713)), 1336 ^ _20835 : [(1337 ^ _20835) ^ [] : [-(in(1325 ^ [_41711, _41713, _41715], _41715))], (1339 ^ _20835) ^ [] : [in(1325 ^ [_41711, _41713, _41715], _41713)], (1341 ^ _20835) ^ [] : [in(1325 ^ [_41711, _41713, _41715], _41711)]], 1328 ^ _20835 : [(1329 ^ _20835) ^ [] : [-(in(1325 ^ [_41711, _41713, _41715], _41711))], (1331 ^ _20835) ^ [] : [in(1325 ^ [_41711, _41713, _41715], _41715), -(in(1325 ^ [_41711, _41713, _41715], _41713))]]], (1302 ^ _20835) ^ [_41367, _41369, _41371] : [_41367 = set_difference(_41371, _41369), 1305 ^ _20835 : [(1306 ^ _20835) ^ [_41458] : [in(_41458, _41367), 1309 ^ _20835 : [(1310 ^ _20835) ^ [] : [-(in(_41458, _41371))], (1312 ^ _20835) ^ [] : [in(_41458, _41369)]]], (1314 ^ _20835) ^ [_41569] : [-(in(_41569, _41367)), in(_41569, _41371), -(in(_41569, _41369))]]], (1345 ^ _20835) ^ [_42077] : [relation(_42077), 1348 ^ _20835 : [(1366 ^ _20835) ^ [_42451] : [-(_42451 = relation_rng(_42077)), 1370 ^ _20835 : [(1371 ^ _20835) ^ [] : [-(in(1367 ^ [_42077, _42451], _42451))], (1373 ^ _20835) ^ [_42585] : [in(ordered_pair(_42585, 1367 ^ [_42077, _42451]), _42077)]], 1375 ^ _20835 : [(1376 ^ _20835) ^ [] : [-(in(ordered_pair(1374 ^ [_42077, _42451], 1367 ^ [_42077, _42451]), _42077))], (1378 ^ _20835) ^ [] : [in(1367 ^ [_42077, _42451], _42451)]]], (1349 ^ _20835) ^ [_42169] : [_42169 = relation_rng(_42077), 1352 ^ _20835 : [(1353 ^ _20835) ^ [_42256] : [in(_42256, _42169), -(in(ordered_pair(1356 ^ [_42077, _42169, _42256], _42256), _42077))], (1360 ^ _20835) ^ [_42351] : [1361 ^ _20835 : [(1362 ^ _20835) ^ [_42395] : [in(ordered_pair(_42395, _42351), _42077)]], -(in(_42351, _42169))]]]]], (1382 ^ _20835) ^ [_42732, _42734] : [element(_42732, powerset(_42734)), -(subset_complement(_42734, _42732) = set_difference(_42734, _42732))], (1388 ^ _20835) ^ [_42825, _42827] : [-(ordered_pair(_42827, _42825) = unordered_pair(unordered_pair(_42827, _42825), singleton(_42827)))], (1390 ^ _20835) ^ [_42861] : [relation(_42861), -(relation_field(_42861) = set_union2(relation_dom(_42861), relation_rng(_42861)))], (1396 ^ _20835) ^ [_42952] : [relation(_42952), 1399 ^ _20835 : [(1400 ^ _20835) ^ [_43040] : [relation(_43040), 1403 ^ _20835 : [(1420 ^ _20835) ^ [] : [-(_43040 = relation_inverse(_42952)), 1425 ^ _20835 : [(1426 ^ _20835) ^ [] : [-(in(ordered_pair(1421 ^ [_42952, _43040], 1422 ^ [_42952, _43040]), _43040))], (1428 ^ _20835) ^ [] : [in(ordered_pair(1422 ^ [_42952, _43040], 1421 ^ [_42952, _43040]), _42952)]], 1429 ^ _20835 : [(1430 ^ _20835) ^ [] : [-(in(ordered_pair(1422 ^ [_42952, _43040], 1421 ^ [_42952, _43040]), _42952))], (1432 ^ _20835) ^ [] : [in(ordered_pair(1421 ^ [_42952, _43040], 1422 ^ [_42952, _43040]), _43040)]]], (1404 ^ _20835) ^ [] : [_43040 = relation_inverse(_42952), 1407 ^ _20835 : [(1408 ^ _20835) ^ [_43190, _43192] : [in(ordered_pair(_43192, _43190), _43040), -(in(ordered_pair(_43190, _43192), _42952))], (1414 ^ _20835) ^ [_43279, _43281] : [in(ordered_pair(_43279, _43281), _42952), -(in(ordered_pair(_43281, _43279), _43040))]]]]]]], (1436 ^ _20835) ^ [_43678, _43680] : [disjoint(_43680, _43678), -(set_intersection2(_43680, _43678) = empty_set)], (1442 ^ _20835) ^ [_43757, _43759] : [set_intersection2(_43759, _43757) = empty_set, -(disjoint(_43759, _43757))], (1448 ^ _20835) ^ [_43842] : [relation(_43842), function(_43842), 1455 ^ _20835 : [(1474 ^ _20835) ^ [] : [1477 ^ _20835 : [(1478 ^ _20835) ^ [] : [-(in(1475 ^ [_43842], relation_dom(_43842)))], (1480 ^ _20835) ^ [] : [-(in(1476 ^ [_43842], relation_dom(_43842)))], (1482 ^ _20835) ^ [] : [-(apply(_43842, 1475 ^ [_43842]) = apply(_43842, 1476 ^ [_43842]))], (1484 ^ _20835) ^ [] : [1475 ^ [_43842] = 1476 ^ [_43842]]], -(one_to_one(_43842))], (1456 ^ _20835) ^ [] : [one_to_one(_43842), 1459 ^ _20835 : [(1460 ^ _20835) ^ [_44031, _44033] : [-(_44033 = _44031), in(_44033, relation_dom(_43842)), in(_44031, relation_dom(_43842)), apply(_43842, _44033) = apply(_43842, _44031)]]]]], (1488 ^ _20835) ^ [_44434] : [relation(_44434), 1491 ^ _20835 : [(1492 ^ _20835) ^ [_44547] : [relation(_44547), 1495 ^ _20835 : [(1496 ^ _20835) ^ [_44652] : [relation(_44652), 1499 ^ _20835 : [(1523 ^ _20835) ^ [] : [-(_44652 = relation_composition(_44434, _44547)), 1537 ^ _20835 : [(1538 ^ _20835) ^ [] : [-(in(ordered_pair(1524 ^ [_44434, _44547, _44652], 1536 ^ [_44434, _44547, _44652]), _44434))], (1540 ^ _20835) ^ [] : [-(in(ordered_pair(1536 ^ [_44434, _44547, _44652], 1525 ^ [_44434, _44547, _44652]), _44547))], (1542 ^ _20835) ^ [] : [in(ordered_pair(1524 ^ [_44434, _44547, _44652], 1525 ^ [_44434, _44547, _44652]), _44652)]], 1528 ^ _20835 : [(1529 ^ _20835) ^ [] : [-(in(ordered_pair(1524 ^ [_44434, _44547, _44652], 1525 ^ [_44434, _44547, _44652]), _44652))], (1531 ^ _20835) ^ [_45308] : [in(ordered_pair(1524 ^ [_44434, _44547, _44652], _45308), _44434), in(ordered_pair(_45308, 1525 ^ [_44434, _44547, _44652]), _44547)]]], (1500 ^ _20835) ^ [] : [_44652 = relation_composition(_44434, _44547), 1503 ^ _20835 : [(1504 ^ _20835) ^ [_44822, _44824] : [in(ordered_pair(_44824, _44822), _44652), 1508 ^ _20835 : [(1509 ^ _20835) ^ [] : [-(in(ordered_pair(_44824, 1507 ^ [_44434, _44547, _44652, _44822, _44824]), _44434))], (1511 ^ _20835) ^ [] : [-(in(ordered_pair(1507 ^ [_44434, _44547, _44652, _44822, _44824], _44822), _44547))]]], (1513 ^ _20835) ^ [_44976, _44978] : [-(in(ordered_pair(_44978, _44976), _44652)), 1514 ^ _20835 : [(1515 ^ _20835) ^ [_45031] : [in(ordered_pair(_44978, _45031), _44434), in(ordered_pair(_45031, _44976), _44547)]]]]]]]]]]], (1546 ^ _20835) ^ [_45618, _45620] : [element(_45618, powerset(powerset(_45620))), 1549 ^ _20835 : [(1550 ^ _20835) ^ [_45724] : [element(_45724, powerset(powerset(_45620))), 1553 ^ _20835 : [(1574 ^ _20835) ^ [] : [-(_45724 = complements_of_subsets(_45620, _45618)), 1576 ^ _20835 : [(1577 ^ _20835) ^ [] : [-(element(1575 ^ [_45618, _45620, _45724], powerset(_45620)))], (1579 ^ _20835) ^ [] : [1580 ^ _20835 : [(1581 ^ _20835) ^ [] : [-(in(1575 ^ [_45618, _45620, _45724], _45724))], (1583 ^ _20835) ^ [] : [in(subset_complement(_45620, 1575 ^ [_45618, _45620, _45724]), _45618)]], 1584 ^ _20835 : [(1585 ^ _20835) ^ [] : [-(in(subset_complement(_45620, 1575 ^ [_45618, _45620, _45724]), _45618))], (1587 ^ _20835) ^ [] : [in(1575 ^ [_45618, _45620, _45724], _45724)]]]]], (1554 ^ _20835) ^ [] : [_45724 = complements_of_subsets(_45620, _45618), 1557 ^ _20835 : [(1558 ^ _20835) ^ [_45875] : [element(_45875, powerset(_45620)), 1561 ^ _20835 : [(1562 ^ _20835) ^ [] : [in(_45875, _45724), -(in(subset_complement(_45620, _45875), _45618))], (1568 ^ _20835) ^ [] : [in(subset_complement(_45620, _45875), _45618), -(in(_45875, _45724))]]]]]]]]], (1591 ^ _20835) ^ [_46415, _46417] : [proper_subset(_46417, _46415), 1594 ^ _20835 : [(1595 ^ _20835) ^ [] : [-(subset(_46417, _46415))], (1597 ^ _20835) ^ [] : [_46417 = _46415]]], (1599 ^ _20835) ^ [_46522, _46524] : [-(proper_subset(_46524, _46522)), subset(_46524, _46522), -(_46524 = _46522)], (1609 ^ _20835) ^ [_46656] : [relation(_46656), function(_46656), one_to_one(_46656), -(function_inverse(_46656) = relation_inverse(_46656))], (1623 ^ _20835) ^ [] : [true___, -(true___)], (1629 ^ _20835) ^ [] : [true___, -(true___)], (1635 ^ _20835) ^ [] : [true___, -(true___)], (1641 ^ _20835) ^ [] : [true___, -(true___)], (1647 ^ _20835) ^ [] : [true___, -(true___)], (1653 ^ _20835) ^ [] : [true___, -(true___)], (1659 ^ _20835) ^ [] : [true___, -(true___)], (1665 ^ _20835) ^ [_47248] : [1672 ^ _20835 : [(1673 ^ _20835) ^ [] : [-(relation(function_inverse(_47248)))], (1675 ^ _20835) ^ [] : [-(function(function_inverse(_47248)))]], relation(_47248), function(_47248)], (1677 ^ _20835) ^ [] : [true___, -(true___)], (1683 ^ _20835) ^ [_47458] : [-(element(cast_to_subset(_47458), powerset(_47458)))], (1685 ^ _20835) ^ [] : [true___, -(true___)], (1691 ^ _20835) ^ [] : [true___, -(true___)], (1697 ^ _20835) ^ [] : [true___, -(true___)], (1703 ^ _20835) ^ [] : [true___, -(true___)], (1709 ^ _20835) ^ [_47864, _47866] : [element(_47864, powerset(_47866)), -(element(subset_complement(_47866, _47864), powerset(_47866)))], (1715 ^ _20835) ^ [] : [true___, -(true___)], (1721 ^ _20835) ^ [] : [true___, -(true___)], (1727 ^ _20835) ^ [_48312] : [relation(_48312), -(relation(relation_inverse(_48312)))], (1733 ^ _20835) ^ [] : [true___, -(true___)], (1739 ^ _20835) ^ [] : [true___, -(true___)], (1745 ^ _20835) ^ [_48754, _48756] : [-(relation(relation_composition(_48756, _48754))), relation(_48756), relation(_48754)], (1755 ^ _20835) ^ [_49053, _49055] : [element(_49053, powerset(powerset(_49055))), -(element(union_of_subsets(_49055, _49053), powerset(_49055)))], (1761 ^ _20835) ^ [_49252] : [-(relation(identity_relation(_49252)))], (1763 ^ _20835) ^ [_49360, _49362] : [element(_49360, powerset(powerset(_49362))), -(element(meet_of_subsets(_49362, _49360), powerset(_49362)))], (1769 ^ _20835) ^ [_49602, _49604, _49606] : [-(element(subset_difference(_49606, _49604, _49602), powerset(_49606))), element(_49604, powerset(_49606)), element(_49602, powerset(_49606))], (1779 ^ _20835) ^ [_49931, _49933] : [relation(_49933), -(relation(relation_dom_restriction(_49933, _49931)))], (1785 ^ _20835) ^ [_50143, _50145] : [element(_50143, powerset(powerset(_50145))), -(element(complements_of_subsets(_50145, _50143), powerset(powerset(_50145))))], (1791 ^ _20835) ^ [_50375, _50377] : [relation(_50375), -(relation(relation_rng_restriction(_50377, _50375)))], (1797 ^ _20835) ^ [] : [true___, -(true___)], (1803 ^ _20835) ^ [] : [true___, -(true___)], (1810 ^ _20835) ^ [_50835] : [-(element(1808 ^ [_50835], _50835))], (1812 ^ _20835) ^ [_50947, _50949] : [1819 ^ _20835 : [(1820 ^ _20835) ^ [] : [-(empty(relation_composition(_50947, _50949)))], (1822 ^ _20835) ^ [] : [-(relation(relation_composition(_50947, _50949)))]], empty(_50949), relation(_50947)], (1824 ^ _20835) ^ [_51311] : [empty(_51311), 1827 ^ _20835 : [(1828 ^ _20835) ^ [] : [-(empty(relation_inverse(_51311)))], (1830 ^ _20835) ^ [] : [-(relation(relation_inverse(_51311)))]]], (1832 ^ _20835) ^ [] : [-(empty(empty_set))], (1834 ^ _20835) ^ [] : [-(relation(empty_set))], (1836 ^ _20835) ^ [] : [-(relation_empty_yielding(empty_set))], (1838 ^ _20835) ^ [_51753, _51755] : [1845 ^ _20835 : [(1846 ^ _20835) ^ [] : [-(relation(relation_dom_restriction(_51755, _51753)))], (1848 ^ _20835) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_51755, _51753)))]], relation(_51755), relation_empty_yielding(_51755)], (1850 ^ _20835) ^ [_52131, _52133] : [1865 ^ _20835 : [(1866 ^ _20835) ^ [] : [-(relation(relation_composition(_52133, _52131)))], (1868 ^ _20835) ^ [] : [-(function(relation_composition(_52133, _52131)))]], relation(_52133), function(_52133), relation(_52131), function(_52131)], (1870 ^ _20835) ^ [_52683, _52685] : [-(relation(set_intersection2(_52685, _52683))), relation(_52685), relation(_52683)], (1880 ^ _20835) ^ [_52952] : [empty(powerset(_52952))], (1882 ^ _20835) ^ [] : [-(empty(empty_set))], (1884 ^ _20835) ^ [_53097, _53099] : [empty(ordered_pair(_53099, _53097))], (1886 ^ _20835) ^ [_53199] : [-(relation(identity_relation(_53199)))], (1888 ^ _20835) ^ [_53244] : [-(function(identity_relation(_53244)))], (1890 ^ _20835) ^ [_53354, _53356] : [-(relation(set_union2(_53356, _53354))), relation(_53356), relation(_53354)], (1900 ^ _20835) ^ [_53623] : [empty(singleton(_53623))], (1902 ^ _20835) ^ [_53731, _53733] : [-(empty(_53733)), empty(set_union2(_53733, _53731))], (1908 ^ _20835) ^ [_53933] : [1919 ^ _20835 : [(1920 ^ _20835) ^ [] : [-(relation(relation_inverse(_53933)))], (1922 ^ _20835) ^ [] : [-(function(relation_inverse(_53933)))]], relation(_53933), function(_53933), one_to_one(_53933)], (1924 ^ _20835) ^ [_54362, _54364] : [empty(unordered_pair(_54364, _54362))], (1926 ^ _20835) ^ [_54473, _54475] : [-(empty(_54475)), empty(set_union2(_54473, _54475))], (1932 ^ _20835) ^ [_54689, _54691] : [1939 ^ _20835 : [(1940 ^ _20835) ^ [] : [-(relation(relation_dom_restriction(_54691, _54689)))], (1942 ^ _20835) ^ [] : [-(function(relation_dom_restriction(_54691, _54689)))]], relation(_54691), function(_54691)], (1944 ^ _20835) ^ [] : [-(empty(empty_set))], (1946 ^ _20835) ^ [] : [-(relation(empty_set))], (1948 ^ _20835) ^ [_55175, _55177] : [empty(cartesian_product2(_55177, _55175)), -(empty(_55177)), -(empty(_55175))], (1958 ^ _20835) ^ [_55467] : [empty(relation_dom(_55467)), -(empty(_55467)), relation(_55467)], (1968 ^ _20835) ^ [_55744] : [empty(relation_rng(_55744)), -(empty(_55744)), relation(_55744)], (1978 ^ _20835) ^ [_56021] : [empty(_56021), 1981 ^ _20835 : [(1982 ^ _20835) ^ [] : [-(empty(relation_dom(_56021)))], (1984 ^ _20835) ^ [] : [-(relation(relation_dom(_56021)))]]], (1986 ^ _20835) ^ [_56286] : [empty(_56286), 1989 ^ _20835 : [(1990 ^ _20835) ^ [] : [-(empty(relation_rng(_56286)))], (1992 ^ _20835) ^ [] : [-(relation(relation_rng(_56286)))]]], (1994 ^ _20835) ^ [_56565, _56567] : [2001 ^ _20835 : [(2002 ^ _20835) ^ [] : [-(empty(relation_composition(_56567, _56565)))], (2004 ^ _20835) ^ [] : [-(relation(relation_composition(_56567, _56565)))]], empty(_56567), relation(_56565)], (2006 ^ _20835) ^ [_56928, _56930] : [-(set_union2(_56930, _56930) = _56930)], (2008 ^ _20835) ^ [_57025, _57027] : [-(set_intersection2(_57027, _57027) = _57027)], (2010 ^ _20835) ^ [_57137, _57139] : [element(_57137, powerset(_57139)), -(subset_complement(_57139, subset_complement(_57139, _57137)) = _57137)], (2016 ^ _20835) ^ [_57349] : [relation(_57349), -(relation_inverse(relation_inverse(_57349)) = _57349)], (2022 ^ _20835) ^ [_57559, _57561] : [element(_57559, powerset(powerset(_57561))), -(complements_of_subsets(_57561, complements_of_subsets(_57561, _57559)) = _57559)], (2028 ^ _20835) ^ [_57773, _57775] : [proper_subset(_57775, _57775)], (2030 ^ _20835) ^ [_57852] : [singleton(_57852) = empty_set], (2032 ^ _20835) ^ [_57961, _57963] : [in(_57963, _57961), -(set_union2(singleton(_57963), _57961) = _57961)], (2038 ^ _20835) ^ [_58181, _58183] : [disjoint(singleton(_58183), _58181), in(_58183, _58181)], (2044 ^ _20835) ^ [_58394, _58396] : [-(in(_58396, _58394)), -(disjoint(singleton(_58396), _58394))], (2050 ^ _20835) ^ [_58640, _58642] : [subset(singleton(_58642), _58640), -(in(_58642, _58640))], (2056 ^ _20835) ^ [_58806, _58808] : [in(_58808, _58806), -(subset(singleton(_58808), _58806))], (2062 ^ _20835) ^ [_59051, _59053] : [set_difference(_59053, _59051) = empty_set, -(subset(_59053, _59051))], (2068 ^ _20835) ^ [_59219, _59221] : [subset(_59221, _59219), -(set_difference(_59221, _59219) = empty_set)], (2074 ^ _20835) ^ [_59437, _59439] : [element(_59437, powerset(_59439)), 2077 ^ _20835 : [(2078 ^ _20835) ^ [_59578] : [in(_59578, _59437), -(in(_59578, _59439))]]], (2084 ^ _20835) ^ [_59817, _59819, _59821] : [subset(_59821, _59819), -(in(_59817, _59821)), -(subset(_59821, set_difference(_59819, singleton(_59817))))], (2104 ^ _20835) ^ [_60426, _60428] : [2105 ^ _20835 : [(2106 ^ _20835) ^ [] : [_60428 = empty_set], (2108 ^ _20835) ^ [] : [_60428 = singleton(_60426)]], -(subset(_60428, singleton(_60426)))], (2094 ^ _20835) ^ [_60166, _60168] : [subset(_60168, singleton(_60166)), -(_60168 = empty_set), -(_60168 = singleton(_60166))], (2112 ^ _20835) ^ [_60720, _60722] : [in(_60722, _60720), -(subset(_60722, union(_60720)))], (2118 ^ _20835) ^ [_60991, _60993, _60995, _60997] : [in(ordered_pair(_60997, _60995), cartesian_product2(_60993, _60991)), 2121 ^ _20835 : [(2122 ^ _20835) ^ [] : [-(in(_60997, _60993))], (2124 ^ _20835) ^ [] : [-(in(_60995, _60991))]]], (2126 ^ _20835) ^ [_61256, _61258, _61260, _61262] : [-(in(ordered_pair(_61262, _61260), cartesian_product2(_61258, _61256))), in(_61262, _61258), in(_61260, _61256)], (2136 ^ _20835) ^ [_61589, _61591] : [2138 ^ _20835 : [(2139 ^ _20835) ^ [] : [-(in(2137 ^ [_61589, _61591], _61591))], (2141 ^ _20835) ^ [] : [in(2137 ^ [_61589, _61591], _61589)]], -(element(_61591, powerset(_61589)))], (2145 ^ _20835) ^ [_61962, _61964, _61966] : [relation(_61962), function(_61962), 2152 ^ _20835 : [(2153 ^ _20835) ^ [] : [in(_61964, relation_dom(relation_dom_restriction(_61962, _61966))), 2156 ^ _20835 : [(2157 ^ _20835) ^ [] : [-(in(_61964, relation_dom(_61962)))], (2159 ^ _20835) ^ [] : [-(in(_61964, _61966))]]], (2161 ^ _20835) ^ [] : [-(in(_61964, relation_dom(relation_dom_restriction(_61962, _61966)))), in(_61964, relation_dom(_61962)), in(_61964, _61966)]]], (2172 ^ _20835) ^ [] : [-(relation(2170 ^ []))], (2174 ^ _20835) ^ [] : [-(function(2170 ^ []))], (2177 ^ _20835) ^ [] : [-(empty(2175 ^ []))], (2179 ^ _20835) ^ [] : [-(relation(2175 ^ []))], (2181 ^ _20835) ^ [_62998] : [-(empty(_62998)), 2185 ^ _20835 : [(2186 ^ _20835) ^ [] : [-(element(2184 ^ [_62998], powerset(_62998)))], (2188 ^ _20835) ^ [] : [empty(2184 ^ [_62998])]]], (2191 ^ _20835) ^ [] : [-(empty(2189 ^ []))], (2194 ^ _20835) ^ [] : [-(relation(2192 ^ []))], (2196 ^ _20835) ^ [] : [-(empty(2192 ^ []))], (2198 ^ _20835) ^ [] : [-(function(2192 ^ []))], (2201 ^ _20835) ^ [] : [empty(2199 ^ [])], (2203 ^ _20835) ^ [] : [-(relation(2199 ^ []))], (2206 ^ _20835) ^ [_63829] : [-(element(2204 ^ [_63829], powerset(_63829)))], (2208 ^ _20835) ^ [_63880] : [-(empty(2204 ^ [_63880]))], (2211 ^ _20835) ^ [] : [empty(2209 ^ [])], (2214 ^ _20835) ^ [] : [-(relation(2212 ^ []))], (2216 ^ _20835) ^ [] : [-(function(2212 ^ []))], (2218 ^ _20835) ^ [] : [-(one_to_one(2212 ^ []))], (2221 ^ _20835) ^ [] : [-(relation(2219 ^ []))], (2223 ^ _20835) ^ [] : [-(relation_empty_yielding(2219 ^ []))], (2225 ^ _20835) ^ [_64441, _64443] : [element(_64441, powerset(powerset(_64443))), -(union_of_subsets(_64443, _64441) = union(_64441))], (2231 ^ _20835) ^ [_64669, _64671] : [element(_64669, powerset(powerset(_64671))), -(meet_of_subsets(_64671, _64669) = set_meet(_64669))], (2237 ^ _20835) ^ [_64911, _64913, _64915] : [-(subset_difference(_64915, _64913, _64911) = set_difference(_64913, _64911)), element(_64913, powerset(_64915)), element(_64911, powerset(_64915))], (2247 ^ _20835) ^ [_65227, _65229] : [-(subset(_65229, _65229))], (2249 ^ _20835) ^ [_65336, _65338] : [disjoint(_65338, _65336), -(disjoint(_65336, _65338))], (2255 ^ _20835) ^ [_65603, _65605, _65607, _65609] : [in(ordered_pair(_65609, _65607), cartesian_product2(_65605, _65603)), 2258 ^ _20835 : [(2259 ^ _20835) ^ [] : [-(in(_65609, _65605))], (2261 ^ _20835) ^ [] : [-(in(_65607, _65603))]]], (2263 ^ _20835) ^ [_65868, _65870, _65872, _65874] : [-(in(ordered_pair(_65874, _65872), cartesian_product2(_65870, _65868))), in(_65874, _65870), in(_65872, _65868)], (2273 ^ _20835) ^ [_66229, _66231, _66233, _66235] : [unordered_pair(_66235, _66233) = unordered_pair(_66231, _66229), -(_66235 = _66231), -(_66235 = _66229)], (2283 ^ _20835) ^ [_66579, _66581, _66583] : [relation(_66579), 2286 ^ _20835 : [(2287 ^ _20835) ^ [] : [in(_66583, relation_rng(relation_rng_restriction(_66581, _66579))), 2290 ^ _20835 : [(2291 ^ _20835) ^ [] : [-(in(_66583, _66581))], (2293 ^ _20835) ^ [] : [-(in(_66583, relation_rng(_66579)))]]], (2295 ^ _20835) ^ [] : [-(in(_66583, relation_rng(relation_rng_restriction(_66581, _66579)))), in(_66583, _66581), in(_66583, relation_rng(_66579))]]], (2305 ^ _20835) ^ [_67238, _67240] : [relation(_67238), -(subset(relation_rng(relation_rng_restriction(_67240, _67238)), _67240))], (2311 ^ _20835) ^ [_67456, _67458] : [relation(_67456), -(subset(relation_rng_restriction(_67458, _67456), _67456))], (2317 ^ _20835) ^ [_67670, _67672] : [relation(_67670), -(subset(relation_rng(relation_rng_restriction(_67672, _67670)), relation_rng(_67670)))], (2323 ^ _20835) ^ [_67906, _67908, _67910] : [subset(_67910, _67908), 2326 ^ _20835 : [(2327 ^ _20835) ^ [] : [-(subset(cartesian_product2(_67910, _67906), cartesian_product2(_67908, _67906)))], (2329 ^ _20835) ^ [] : [-(subset(cartesian_product2(_67906, _67910), cartesian_product2(_67906, _67908)))]]], (2331 ^ _20835) ^ [_68223, _68225] : [relation(_68223), -(relation_rng(relation_rng_restriction(_68225, _68223)) = set_intersection2(relation_rng(_68223), _68225))], (2337 ^ _20835) ^ [_68479, _68481, _68483, _68485] : [-(subset(cartesian_product2(_68485, _68481), cartesian_product2(_68483, _68479))), subset(_68485, _68483), subset(_68481, _68479)], (2347 ^ _20835) ^ [_68810, _68812] : [subset(_68812, _68810), -(set_union2(_68812, _68810) = _68810)], (2354 ^ _20835) ^ [_69132] : [-(in(_69132, 2352 ^ [_69132]))], (2356 ^ _20835) ^ [_69244, _69246, _69248] : [-(in(_69244, 2352 ^ [_69248])), in(_69246, 2352 ^ [_69248]), subset(_69244, _69246)], (2366 ^ _20835) ^ [_69559, _69561] : [in(_69559, 2352 ^ [_69561]), -(in(powerset(_69559), 2352 ^ [_69561]))], (2372 ^ _20835) ^ [_69759, _69761] : [subset(_69759, 2352 ^ [_69761]), -(are_equipotent(_69759, 2352 ^ [_69761])), -(in(_69759, 2352 ^ [_69761]))], (2382 ^ _20835) ^ [_70113, _70115, _70117] : [relation(_70113), -(relation_dom_restriction(relation_rng_restriction(_70117, _70113), _70115) = relation_rng_restriction(_70117, relation_dom_restriction(_70113, _70115)))], (2388 ^ _20835) ^ [_70365, _70367, _70369] : [relation(_70365), 2391 ^ _20835 : [(2392 ^ _20835) ^ [] : [in(_70369, relation_image(_70365, _70367)), 2396 ^ _20835 : [(2397 ^ _20835) ^ [] : [-(in(2395 ^ [_70365, _70367, _70369], relation_dom(_70365)))], (2399 ^ _20835) ^ [] : [-(in(ordered_pair(2395 ^ [_70365, _70367, _70369], _70369), _70365))], (2401 ^ _20835) ^ [] : [-(in(2395 ^ [_70365, _70367, _70369], _70367))]]], (2403 ^ _20835) ^ [] : [-(in(_70369, relation_image(_70365, _70367))), 2404 ^ _20835 : [(2405 ^ _20835) ^ [_70966] : [in(_70966, relation_dom(_70365)), in(ordered_pair(_70966, _70369), _70365), in(_70966, _70367)]]]]], (2417 ^ _20835) ^ [_71363, _71365] : [relation(_71363), -(subset(relation_image(_71363, _71365), relation_rng(_71363)))], (2423 ^ _20835) ^ [_71581, _71583] : [relation(_71581), -(relation_image(_71581, _71583) = relation_image(_71581, set_intersection2(relation_dom(_71581), _71583)))], (2429 ^ _20835) ^ [_71797] : [relation(_71797), -(relation_image(_71797, relation_dom(_71797)) = relation_rng(_71797))], (2435 ^ _20835) ^ [_71999] : [relation(_71999), 2438 ^ _20835 : [(2439 ^ _20835) ^ [_72139] : [relation(_72139), -(relation_rng(relation_composition(_71999, _72139)) = relation_image(_72139, relation_rng(_71999)))]]], (2445 ^ _20835) ^ [_72388, _72390, _72392] : [relation(_72388), 2448 ^ _20835 : [(2449 ^ _20835) ^ [] : [in(_72392, relation_inverse_image(_72388, _72390)), 2453 ^ _20835 : [(2454 ^ _20835) ^ [] : [-(in(2452 ^ [_72388, _72390, _72392], relation_rng(_72388)))], (2456 ^ _20835) ^ [] : [-(in(ordered_pair(_72392, 2452 ^ [_72388, _72390, _72392]), _72388))], (2458 ^ _20835) ^ [] : [-(in(2452 ^ [_72388, _72390, _72392], _72390))]]], (2460 ^ _20835) ^ [] : [-(in(_72392, relation_inverse_image(_72388, _72390))), 2461 ^ _20835 : [(2462 ^ _20835) ^ [_72989] : [in(_72989, relation_rng(_72388)), in(ordered_pair(_72392, _72989), _72388), in(_72989, _72390)]]]]], (2474 ^ _20835) ^ [_73386, _73388] : [relation(_73386), -(subset(relation_inverse_image(_73386, _73388), relation_dom(_73386)))], (2480 ^ _20835) ^ [_73604, _73606] : [relation(_73604), -(_73606 = empty_set), subset(_73606, relation_rng(_73604)), relation_inverse_image(_73604, _73606) = empty_set], (2494 ^ _20835) ^ [_74018, _74020, _74022] : [relation(_74018), subset(_74022, _74020), -(subset(relation_inverse_image(_74018, _74022), relation_inverse_image(_74018, _74020)))], (2504 ^ _20835) ^ [_74322, _74324] : [-(subset(set_intersection2(_74324, _74322), _74324))], (2506 ^ _20835) ^ [_74448, _74450, _74452] : [-(subset(_74452, set_intersection2(_74450, _74448))), subset(_74452, _74450), subset(_74452, _74448)], (2516 ^ _20835) ^ [_74734] : [-(set_union2(_74734, empty_set) = _74734)], (2518 ^ _20835) ^ [_74844, _74846] : [in(_74846, _74844), -(element(_74846, _74844))], (2524 ^ _20835) ^ [_75068, _75070, _75072] : [-(subset(_75072, _75068)), subset(_75072, _75070), subset(_75070, _75068)], (2534 ^ _20835) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2536 ^ _20835) ^ [_75444, _75446, _75448] : [relation(_75444), in(ordered_pair(_75448, _75446), _75444), 2543 ^ _20835 : [(2544 ^ _20835) ^ [] : [-(in(_75448, relation_dom(_75444)))], (2546 ^ _20835) ^ [] : [-(in(_75446, relation_rng(_75444)))]]], (2548 ^ _20835) ^ [_75842, _75844] : [relation(_75842), function(_75842), 2555 ^ _20835 : [(2556 ^ _20835) ^ [_76092] : [relation(_76092), function(_76092), 2563 ^ _20835 : [(2564 ^ _20835) ^ [] : [in(_75844, relation_dom(relation_composition(_76092, _75842))), 2567 ^ _20835 : [(2568 ^ _20835) ^ [] : [-(in(_75844, relation_dom(_76092)))], (2570 ^ _20835) ^ [] : [-(in(apply(_76092, _75844), relation_dom(_75842)))]]], (2572 ^ _20835) ^ [] : [-(in(_75844, relation_dom(relation_composition(_76092, _75842)))), in(_75844, relation_dom(_76092)), in(apply(_76092, _75844), relation_dom(_75842))]]]]], (2582 ^ _20835) ^ [_76856] : [relation(_76856), -(subset(_76856, cartesian_product2(relation_dom(_76856), relation_rng(_76856))))], (2588 ^ _20835) ^ [_77072, _77074] : [relation(_77072), function(_77072), 2595 ^ _20835 : [(2596 ^ _20835) ^ [_77321] : [relation(_77321), function(_77321), in(_77074, relation_dom(relation_composition(_77321, _77072))), -(apply(relation_composition(_77321, _77072), _77074) = apply(_77072, apply(_77321, _77074)))]]], (2610 ^ _20835) ^ [_77766, _77768] : [relation(_77766), function(_77766), 2617 ^ _20835 : [(2618 ^ _20835) ^ [_78012] : [relation(_78012), function(_78012), in(_77768, relation_dom(_77766)), -(apply(relation_composition(_77766, _78012), _77768) = apply(_78012, apply(_77766, _77768)))]]], (2632 ^ _20835) ^ [_78437] : [relation(_78437), 2635 ^ _20835 : [(2636 ^ _20835) ^ [_78587] : [relation(_78587), subset(_78437, _78587), 2643 ^ _20835 : [(2644 ^ _20835) ^ [] : [-(subset(relation_dom(_78437), relation_dom(_78587)))], (2646 ^ _20835) ^ [] : [-(subset(relation_rng(_78437), relation_rng(_78587)))]]]]], (2648 ^ _20835) ^ [_78996, _78998, _79000] : [subset(_79000, _78998), -(subset(set_intersection2(_79000, _78996), set_intersection2(_78998, _78996)))], (2654 ^ _20835) ^ [_79224, _79226] : [subset(_79226, _79224), -(set_intersection2(_79226, _79224) = _79226)], (2660 ^ _20835) ^ [_79411] : [-(set_intersection2(_79411, empty_set) = empty_set)], (2662 ^ _20835) ^ [_79521, _79523] : [element(_79523, _79521), -(empty(_79521)), -(in(_79523, _79521))], (2672 ^ _20835) ^ [_79819, _79821] : [-(_79821 = _79819), 2676 ^ _20835 : [(2677 ^ _20835) ^ [] : [-(in(2673 ^ [_79819, _79821], _79821))], (2679 ^ _20835) ^ [] : [in(2673 ^ [_79819, _79821], _79819)]], 2680 ^ _20835 : [(2681 ^ _20835) ^ [] : [-(in(2673 ^ [_79819, _79821], _79819))], (2683 ^ _20835) ^ [] : [in(2673 ^ [_79819, _79821], _79821)]]], (2687 ^ _20835) ^ [_80320] : [-(subset(empty_set, _80320))], (2689 ^ _20835) ^ [_80441, _80443, _80445] : [relation(_80441), in(ordered_pair(_80445, _80443), _80441), 2696 ^ _20835 : [(2697 ^ _20835) ^ [] : [-(in(_80445, relation_field(_80441)))], (2699 ^ _20835) ^ [] : [-(in(_80443, relation_field(_80441)))]]], (2701 ^ _20835) ^ [_80853, _80855, _80857] : [subset(_80857, _80855), -(subset(set_difference(_80857, _80853), set_difference(_80855, _80853)))], (2707 ^ _20835) ^ [_81109, _81111, _81113, _81115] : [ordered_pair(_81115, _81113) = ordered_pair(_81111, _81109), 2710 ^ _20835 : [(2711 ^ _20835) ^ [] : [-(_81115 = _81111)], (2713 ^ _20835) ^ [] : [-(_81113 = _81109)]]], (2715 ^ _20835) ^ [_81422, _81424] : [relation(_81422), function(_81422), 2722 ^ _20835 : [(2723 ^ _20835) ^ [] : [_81422 = identity_relation(_81424), 2726 ^ _20835 : [(2727 ^ _20835) ^ [] : [-(relation_dom(_81422) = _81424)], (2729 ^ _20835) ^ [_81841] : [in(_81841, _81424), -(apply(_81422, _81841) = _81841)]]], (2735 ^ _20835) ^ [] : [-(_81422 = identity_relation(_81424)), relation_dom(_81422) = _81424, 2741 ^ _20835 : [(2742 ^ _20835) ^ [] : [-(in(2740 ^ [_81422, _81424], _81424))], (2744 ^ _20835) ^ [] : [apply(_81422, 2740 ^ [_81422, _81424]) = 2740 ^ [_81422, _81424]]]]]], (2748 ^ _20835) ^ [_82446, _82448] : [in(_82446, _82448), -(apply(identity_relation(_82448), _82446) = _82446)], (2754 ^ _20835) ^ [_82651, _82653] : [-(subset(set_difference(_82653, _82651), _82653))], (2756 ^ _20835) ^ [_82749] : [relation(_82749), 2759 ^ _20835 : [(2760 ^ _20835) ^ [] : [-(relation_rng(_82749) = relation_dom(relation_inverse(_82749)))], (2762 ^ _20835) ^ [] : [-(relation_dom(_82749) = relation_rng(relation_inverse(_82749)))]]], (2764 ^ _20835) ^ [_83077, _83079] : [set_difference(_83079, _83077) = empty_set, -(subset(_83079, _83077))], (2770 ^ _20835) ^ [_83245, _83247] : [subset(_83247, _83245), -(set_difference(_83247, _83245) = empty_set)], (2776 ^ _20835) ^ [_83492, _83494] : [subset(singleton(_83494), _83492), -(in(_83494, _83492))], (2782 ^ _20835) ^ [_83658, _83660] : [in(_83660, _83658), -(subset(singleton(_83660), _83658))], (2788 ^ _20835) ^ [_83917, _83919, _83921] : [subset(unordered_pair(_83921, _83919), _83917), 2791 ^ _20835 : [(2792 ^ _20835) ^ [] : [-(in(_83921, _83917))], (2794 ^ _20835) ^ [] : [-(in(_83919, _83917))]]], (2796 ^ _20835) ^ [_84168, _84170, _84172] : [-(subset(unordered_pair(_84172, _84170), _84168)), in(_84172, _84168), in(_84170, _84168)], (2806 ^ _20835) ^ [_84470, _84472] : [-(set_union2(_84472, set_difference(_84470, _84472)) = set_union2(_84472, _84470))], (2818 ^ _20835) ^ [_84877, _84879] : [2819 ^ _20835 : [(2820 ^ _20835) ^ [] : [_84879 = empty_set], (2822 ^ _20835) ^ [] : [_84879 = singleton(_84877)]], -(subset(_84879, singleton(_84877)))], (2808 ^ _20835) ^ [_84617, _84619] : [subset(_84619, singleton(_84617)), -(_84619 = empty_set), -(_84619 = singleton(_84617))], (2826 ^ _20835) ^ [_85142] : [-(set_difference(_85142, empty_set) = _85142)], (2828 ^ _20835) ^ [_85281, _85283] : [element(_85283, powerset(_85281)), -(subset(_85283, _85281))], (2834 ^ _20835) ^ [_85447, _85449] : [subset(_85449, _85447), -(element(_85449, powerset(_85447)))], (2840 ^ _20835) ^ [_85683, _85685] : [-(disjoint(_85685, _85683)), 2844 ^ _20835 : [(2845 ^ _20835) ^ [] : [-(in(2843 ^ [_85683, _85685], _85685))], (2847 ^ _20835) ^ [] : [-(in(2843 ^ [_85683, _85685], _85683))]]], (2849 ^ _20835) ^ [_85997, _85999] : [disjoint(_85999, _85997), 2850 ^ _20835 : [(2851 ^ _20835) ^ [_86089] : [in(_86089, _85999), in(_86089, _85997)]]], (2859 ^ _20835) ^ [_86346] : [subset(_86346, empty_set), -(_86346 = empty_set)], (2865 ^ _20835) ^ [_86535, _86537] : [-(set_difference(set_union2(_86537, _86535), _86535) = set_difference(_86537, _86535))], (2867 ^ _20835) ^ [_86653, _86655] : [element(_86653, powerset(_86655)), 2870 ^ _20835 : [(2871 ^ _20835) ^ [_86805] : [element(_86805, powerset(_86655)), 2874 ^ _20835 : [(2875 ^ _20835) ^ [] : [disjoint(_86653, _86805), -(subset(_86653, subset_complement(_86655, _86805)))], (2881 ^ _20835) ^ [] : [subset(_86653, subset_complement(_86655, _86805)), -(disjoint(_86653, _86805))]]]]], (2887 ^ _20835) ^ [_87289] : [relation(_87289), 2890 ^ _20835 : [(2891 ^ _20835) ^ [_87426] : [relation(_87426), -(subset(relation_dom(relation_composition(_87289, _87426)), relation_dom(_87289)))]]], (2897 ^ _20835) ^ [_87641] : [relation(_87641), 2900 ^ _20835 : [(2901 ^ _20835) ^ [_87778] : [relation(_87778), -(subset(relation_rng(relation_composition(_87641, _87778)), relation_rng(_87778)))]]], (2907 ^ _20835) ^ [_88007, _88009] : [subset(_88009, _88007), -(_88007 = set_union2(_88009, set_difference(_88007, _88009)))], (2913 ^ _20835) ^ [_88215] : [relation(_88215), 2916 ^ _20835 : [(2917 ^ _20835) ^ [_88362] : [relation(_88362), subset(relation_rng(_88215), relation_dom(_88362)), -(relation_dom(relation_composition(_88215, _88362)) = relation_dom(_88215))]]], (2927 ^ _20835) ^ [_88688, _88690] : [element(_88688, powerset(powerset(_88690))), -(_88688 = empty_set), complements_of_subsets(_88690, _88688) = empty_set], (2937 ^ _20835) ^ [_89005, _89007] : [in(_89007, _89005), -(set_union2(singleton(_89007), _89005) = _89005)], (2943 ^ _20835) ^ [_89211] : [relation(_89211), 2946 ^ _20835 : [(2947 ^ _20835) ^ [_89358] : [relation(_89358), subset(relation_dom(_89211), relation_rng(_89358)), -(relation_rng(relation_composition(_89358, _89211)) = relation_rng(_89211))]]], (2957 ^ _20835) ^ [_89684, _89686] : [element(_89684, powerset(powerset(_89686))), -(_89684 = empty_set), -(subset_difference(_89686, cast_to_subset(_89686), union_of_subsets(_89686, _89684)) = meet_of_subsets(_89686, complements_of_subsets(_89686, _89684)))], (2967 ^ _20835) ^ [_90024, _90026] : [element(_90024, powerset(powerset(_90026))), -(_90024 = empty_set), -(union_of_subsets(_90026, complements_of_subsets(_90026, _90024)) = subset_difference(_90026, cast_to_subset(_90026), meet_of_subsets(_90026, _90024)))], (2977 ^ _20835) ^ [_90349, _90351] : [-(set_difference(_90351, set_difference(_90351, _90349)) = set_intersection2(_90351, _90349))], (2979 ^ _20835) ^ [_90438] : [-(set_difference(empty_set, _90438) = empty_set)], (2981 ^ _20835) ^ [_90562, _90564, _90566] : [-(element(_90566, _90562)), in(_90566, _90564), element(_90564, powerset(_90562))], (2991 ^ _20835) ^ [_90895, _90897] : [-(disjoint(_90897, _90895)), -(in(2994 ^ [_90895, _90897], set_intersection2(_90897, _90895)))], (2998 ^ _20835) ^ [_91130, _91132] : [2999 ^ _20835 : [(3000 ^ _20835) ^ [_91203] : [in(_91203, set_intersection2(_91132, _91130))]], disjoint(_91132, _91130)], (3004 ^ _20835) ^ [_91355] : [-(_91355 = empty_set), 3007 ^ _20835 : [(3008 ^ _20835) ^ [_91515] : [element(_91515, powerset(_91355)), 3011 ^ _20835 : [(3012 ^ _20835) ^ [_91669] : [element(_91669, _91355), -(in(_91669, _91515)), -(in(_91669, subset_complement(_91355, _91515)))]]]]], (3022 ^ _20835) ^ [_91987] : [relation(_91987), function(_91987), one_to_one(_91987), 3033 ^ _20835 : [(3034 ^ _20835) ^ [_92374] : [relation(_92374), function(_92374), 3041 ^ _20835 : [(3072 ^ _20835) ^ [] : [-(_92374 = function_inverse(_91987)), relation_dom(_92374) = relation_rng(_91987), 3081 ^ _20835 : [(3082 ^ _20835) ^ [] : [-(in(3077 ^ [_91987, _92374], relation_rng(_91987)))], (3084 ^ _20835) ^ [] : [-(3078 ^ [_91987, _92374] = apply(_92374, 3077 ^ [_91987, _92374]))], (3086 ^ _20835) ^ [] : [in(3078 ^ [_91987, _92374], relation_dom(_91987)), 3077 ^ [_91987, _92374] = apply(_91987, 3078 ^ [_91987, _92374])]], 3091 ^ _20835 : [(3092 ^ _20835) ^ [] : [-(in(3078 ^ [_91987, _92374], relation_dom(_91987)))], (3094 ^ _20835) ^ [] : [-(3077 ^ [_91987, _92374] = apply(_91987, 3078 ^ [_91987, _92374]))], (3096 ^ _20835) ^ [] : [in(3077 ^ [_91987, _92374], relation_rng(_91987)), 3078 ^ [_91987, _92374] = apply(_92374, 3077 ^ [_91987, _92374])]]], (3042 ^ _20835) ^ [] : [_92374 = function_inverse(_91987), 3045 ^ _20835 : [(3046 ^ _20835) ^ [] : [-(relation_dom(_92374) = relation_rng(_91987))], (3048 ^ _20835) ^ [_92891, _92893] : [3055 ^ _20835 : [(3056 ^ _20835) ^ [] : [-(in(_92891, relation_dom(_91987)))], (3058 ^ _20835) ^ [] : [-(_92893 = apply(_91987, _92891))]], in(_92893, relation_rng(_91987)), _92891 = apply(_92374, _92893)], (3060 ^ _20835) ^ [_93265, _93267] : [3067 ^ _20835 : [(3068 ^ _20835) ^ [] : [-(in(_93267, relation_rng(_91987)))], (3070 ^ _20835) ^ [] : [-(_93265 = apply(_92374, _93267))]], in(_93265, relation_dom(_91987)), _93267 = apply(_91987, _93265)]]]]]]], (3104 ^ _20835) ^ [_94840, _94842, _94844] : [element(_94840, powerset(_94844)), in(_94842, subset_complement(_94844, _94840)), in(_94842, _94840)], (3114 ^ _20835) ^ [_95146] : [relation(_95146), function(_95146), one_to_one(_95146), 3125 ^ _20835 : [(3126 ^ _20835) ^ [] : [-(relation_rng(_95146) = relation_dom(function_inverse(_95146)))], (3128 ^ _20835) ^ [] : [-(relation_dom(_95146) = relation_rng(function_inverse(_95146)))]]], (3130 ^ _20835) ^ [_95599] : [relation(_95599), -(in(ordered_pair(3135 ^ [_95599], 3136 ^ [_95599]), _95599)), -(_95599 = empty_set)], (3142 ^ _20835) ^ [_96017, _96019] : [relation(_96017), function(_96017), 3157 ^ _20835 : [(3158 ^ _20835) ^ [] : [-(_96019 = apply(_96017, apply(function_inverse(_96017), _96019)))], (3160 ^ _20835) ^ [] : [-(_96019 = apply(relation_composition(function_inverse(_96017), _96017), _96019))]], one_to_one(_96017), in(_96019, relation_rng(_96017))], (3162 ^ _20835) ^ [_96615, _96617, _96619] : [in(_96619, _96617), element(_96617, powerset(_96615)), empty(_96615)], (3172 ^ _20835) ^ [] : [-(relation_dom(empty_set) = empty_set)], (3174 ^ _20835) ^ [] : [-(relation_rng(empty_set) = empty_set)], (3176 ^ _20835) ^ [_97033, _97035] : [subset(_97035, _97033), proper_subset(_97033, _97035)], (3182 ^ _20835) ^ [_97228] : [relation(_97228), function(_97228), one_to_one(_97228), -(one_to_one(function_inverse(_97228)))], (3196 ^ _20835) ^ [_97614, _97616, _97618] : [-(disjoint(_97618, _97614)), subset(_97618, _97616), disjoint(_97616, _97614)], (3206 ^ _20835) ^ [_97909] : [relation(_97909), 3211 ^ _20835 : [(3212 ^ _20835) ^ [] : [relation_dom(_97909) = empty_set], (3214 ^ _20835) ^ [] : [relation_rng(_97909) = empty_set]], -(_97909 = empty_set)], (3218 ^ _20835) ^ [_98262] : [relation(_98262), 3221 ^ _20835 : [(3222 ^ _20835) ^ [] : [relation_dom(_98262) = empty_set, -(relation_rng(_98262) = empty_set)], (3228 ^ _20835) ^ [] : [relation_rng(_98262) = empty_set, -(relation_dom(_98262) = empty_set)]]], (3234 ^ _20835) ^ [_98745, _98747] : [set_difference(_98747, singleton(_98745)) = _98747, in(_98745, _98747)], (3240 ^ _20835) ^ [_98918, _98920] : [-(in(_98918, _98920)), -(set_difference(_98920, singleton(_98918)) = _98920)], (3246 ^ _20835) ^ [_99143, _99145] : [relation(_99143), function(_99143), 3253 ^ _20835 : [(3254 ^ _20835) ^ [_99410] : [relation(_99410), function(_99410), 3261 ^ _20835 : [(3262 ^ _20835) ^ [] : [_99143 = relation_dom_restriction(_99410, _99145), 3265 ^ _20835 : [(3266 ^ _20835) ^ [] : [-(relation_dom(_99143) = set_intersection2(relation_dom(_99410), _99145))], (3268 ^ _20835) ^ [_99864] : [in(_99864, relation_dom(_99143)), -(apply(_99143, _99864) = apply(_99410, _99864))]]], (3274 ^ _20835) ^ [] : [-(_99143 = relation_dom_restriction(_99410, _99145)), relation_dom(_99143) = set_intersection2(relation_dom(_99410), _99145), 3280 ^ _20835 : [(3281 ^ _20835) ^ [] : [-(in(3279 ^ [_99143, _99145, _99410], relation_dom(_99143)))], (3283 ^ _20835) ^ [] : [apply(_99143, 3279 ^ [_99143, _99145, _99410]) = apply(_99410, 3279 ^ [_99143, _99145, _99410])]]]]]]], (3287 ^ _20835) ^ [_100503] : [-(unordered_pair(_100503, _100503) = singleton(_100503))], (3289 ^ _20835) ^ [_100601] : [empty(_100601), -(_100601 = empty_set)], (3295 ^ _20835) ^ [_100803, _100805] : [subset(singleton(_100805), singleton(_100803)), -(_100805 = _100803)], (3301 ^ _20835) ^ [_101035, _101037, _101039] : [relation(_101035), function(_101035), in(_101037, relation_dom(relation_dom_restriction(_101035, _101039))), -(apply(relation_dom_restriction(_101035, _101039), _101037) = apply(_101035, _101037))], (3315 ^ _20835) ^ [_101454] : [-(relation_dom(identity_relation(_101454)) = _101454)], (3317 ^ _20835) ^ [_101502] : [-(relation_rng(identity_relation(_101502)) = _101502)], (3319 ^ _20835) ^ [_101643, _101645, _101647, _101649] : [relation(_101643), 3322 ^ _20835 : [(3323 ^ _20835) ^ [] : [in(ordered_pair(_101649, _101647), relation_composition(identity_relation(_101645), _101643)), 3326 ^ _20835 : [(3327 ^ _20835) ^ [] : [-(in(_101649, _101645))], (3329 ^ _20835) ^ [] : [-(in(ordered_pair(_101649, _101647), _101643))]]], (3331 ^ _20835) ^ [] : [-(in(ordered_pair(_101649, _101647), relation_composition(identity_relation(_101645), _101643))), in(_101649, _101645), in(ordered_pair(_101649, _101647), _101643)]]], (3341 ^ _20835) ^ [_102336, _102338] : [in(_102338, _102336), empty(_102336)], (3347 ^ _20835) ^ [_102528, _102530] : [-(subset(_102530, set_union2(_102530, _102528)))], (3349 ^ _20835) ^ [_102669, _102671] : [disjoint(_102671, _102669), -(set_difference(_102671, _102669) = _102671)], (3355 ^ _20835) ^ [_102837, _102839] : [set_difference(_102839, _102837) = _102839, -(disjoint(_102839, _102837))], (3361 ^ _20835) ^ [_103069, _103071, _103073] : [relation(_103069), 3364 ^ _20835 : [(3365 ^ _20835) ^ [] : [in(_103073, relation_dom(relation_dom_restriction(_103069, _103071))), 3368 ^ _20835 : [(3369 ^ _20835) ^ [] : [-(in(_103073, _103071))], (3371 ^ _20835) ^ [] : [-(in(_103073, relation_dom(_103069)))]]], (3373 ^ _20835) ^ [] : [-(in(_103073, relation_dom(relation_dom_restriction(_103069, _103071)))), in(_103073, _103071), in(_103073, relation_dom(_103069))]]], (3383 ^ _20835) ^ [_103728, _103730] : [relation(_103728), -(subset(relation_dom_restriction(_103728, _103730), _103728))], (3389 ^ _20835) ^ [_103942, _103944] : [empty(_103944), -(_103944 = _103942), empty(_103942)], (3399 ^ _20835) ^ [_104253, _104255, _104257] : [relation(_104253), function(_104253), 3406 ^ _20835 : [(3407 ^ _20835) ^ [] : [in(ordered_pair(_104257, _104255), _104253), 3410 ^ _20835 : [(3411 ^ _20835) ^ [] : [-(in(_104257, relation_dom(_104253)))], (3413 ^ _20835) ^ [] : [-(_104255 = apply(_104253, _104257))]]], (3415 ^ _20835) ^ [] : [-(in(ordered_pair(_104257, _104255), _104253)), in(_104257, relation_dom(_104253)), _104255 = apply(_104253, _104257)]]], (3425 ^ _20835) ^ [_105022, _105024, _105026] : [-(subset(set_union2(_105026, _105022), _105024)), subset(_105026, _105024), subset(_105022, _105024)], (3435 ^ _20835) ^ [_105351, _105353, _105355] : [singleton(_105355) = unordered_pair(_105353, _105351), -(_105355 = _105353)], (3441 ^ _20835) ^ [_105577, _105579] : [relation(_105577), -(relation_dom(relation_dom_restriction(_105577, _105579)) = set_intersection2(relation_dom(_105577), _105579))], (3447 ^ _20835) ^ [_105805, _105807] : [in(_105807, _105805), -(subset(_105807, union(_105805)))], (3453 ^ _20835) ^ [_106019, _106021] : [relation(_106019), -(relation_dom_restriction(_106019, _106021) = relation_composition(identity_relation(_106021), _106019))], (3459 ^ _20835) ^ [_106243, _106245] : [relation(_106243), -(subset(relation_rng(relation_dom_restriction(_106243, _106245)), relation_rng(_106243)))], (3465 ^ _20835) ^ [_106436] : [-(union(powerset(_106436)) = _106436)], (3503 ^ _20835) ^ [_107957, _107959, _107961] : [singleton(_107961) = unordered_pair(_107959, _107957), -(_107959 = _107957)], (3468 ^ _20835) ^ [_106677] : [-(in(_106677, 3466 ^ [_106677]))], (3470 ^ _20835) ^ [_106789, _106791, _106793] : [-(in(_106789, 3466 ^ [_106793])), in(_106791, 3466 ^ [_106793]), subset(_106789, _106791)], (3480 ^ _20835) ^ [_107104, _107106] : [in(_107104, 3466 ^ [_107106]), 3484 ^ _20835 : [(3485 ^ _20835) ^ [] : [-(in(3483 ^ [_107104, _107106], 3466 ^ [_107106]))], (3487 ^ _20835) ^ [_107416] : [subset(_107416, _107104), -(in(_107416, 3483 ^ [_107104, _107106]))]]], (3493 ^ _20835) ^ [_107623, _107625] : [subset(_107623, 3466 ^ [_107625]), -(are_equipotent(_107623, 3466 ^ [_107625])), -(in(_107623, 3466 ^ [_107625]))]], input).
% 15.22/15.85  ncf('1',plain,[apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ [])],start(3518 ^ 0)).
% 15.22/15.85  ncf('1.1',plain,[-(apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ [])), 1212 : apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = empty_set, 1212 : -(in(3509 ^ [], relation_dom(3510 ^ []))), 1202 : relation(3510 ^ []), 1202 : function(3510 ^ [])],extension(1178 ^ 1,bind([[_39308, _39698, _39700], [3510 ^ [], apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []), 3509 ^ []]]))).
% 15.22/15.85  ncf('1.1.1',plain,[-(apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = empty_set), 1206 : apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []), 1206 : -(in(3509 ^ [], relation_dom(relation_dom_restriction(3510 ^ [], 3508 ^ [])))), 1202 : relation(relation_dom_restriction(3510 ^ [], 3508 ^ [])), 1202 : function(relation_dom_restriction(3510 ^ [], 3508 ^ []))],extension(1178 ^ 6,bind([[_39308, _39698, _39700], [relation_dom_restriction(3510 ^ [], 3508 ^ []), apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []), 3509 ^ []]]))).
% 15.22/15.85  ncf('1.1.1.1',plain,[-(apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []))],extension(2 ^ 11,bind([[_20865], [apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ [])]]))).
% 15.22/15.85  ncf('1.1.1.2',plain,[in(3509 ^ [], relation_dom(relation_dom_restriction(3510 ^ [], 3508 ^ []))), relation(3510 ^ []), function(3510 ^ []), -(apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ []))],extension(3301 ^ 9,bind([[_101035, _101037, _101039], [3510 ^ [], 3509 ^ [], 3508 ^ []]]))).
% 15.22/15.85  ncf('1.1.1.2.1',plain,[-(relation(3510 ^ []))],extension(3512 ^ 10)).
% 15.22/15.85  ncf('1.1.1.2.2',plain,[-(function(3510 ^ []))],extension(3514 ^ 10)).
% 15.22/15.85  ncf('1.1.1.2.3',plain,[apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ [])],reduction('1')).
% 15.22/15.85  ncf('1.1.1.3',plain,[-(relation(relation_dom_restriction(3510 ^ [], 3508 ^ []))), relation(3510 ^ [])],extension(1779 ^ 7,bind([[_49931, _49933], [3508 ^ [], 3510 ^ []]]))).
% 15.22/15.85  ncf('1.1.1.3.1',plain,[-(relation(3510 ^ []))],extension(3512 ^ 8)).
% 15.22/15.85  ncf('1.1.1.4',plain,[-(function(relation_dom_restriction(3510 ^ [], 3508 ^ []))), relation(3510 ^ []), function(3510 ^ [])],extension(1932 ^ 7,bind([[_54689, _54691], [3508 ^ [], 3510 ^ []]]))).
% 15.22/15.85  ncf('1.1.1.4.1',plain,[-(relation(3510 ^ []))],extension(3512 ^ 8)).
% 15.22/15.85  ncf('1.1.1.4.2',plain,[-(function(3510 ^ []))],extension(3514 ^ 8)).
% 15.22/15.85  ncf('1.1.2',plain,[in(3509 ^ [], relation_dom(3510 ^ [])), 2161 : -(in(3509 ^ [], relation_dom(relation_dom_restriction(3510 ^ [], 3508 ^ [])))), 2161 : in(3509 ^ [], 3508 ^ []), 2161 : relation(3510 ^ []), 2161 : function(3510 ^ [])],extension(2145 ^ 4,bind([[_61962, _61964, _61966], [3510 ^ [], 3509 ^ [], 3508 ^ []]]))).
% 15.22/15.85  ncf('1.1.2.1',plain,[in(3509 ^ [], relation_dom(relation_dom_restriction(3510 ^ [], 3508 ^ []))), relation(3510 ^ []), function(3510 ^ []), -(apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ []))],extension(3301 ^ 7,bind([[_101035, _101037, _101039], [3510 ^ [], 3509 ^ [], 3508 ^ []]]))).
% 15.22/15.85  ncf('1.1.2.1.1',plain,[-(relation(3510 ^ []))],extension(3512 ^ 8)).
% 15.22/15.85  ncf('1.1.2.1.2',plain,[-(function(3510 ^ []))],extension(3514 ^ 8)).
% 15.22/15.85  ncf('1.1.2.1.3',plain,[apply(relation_dom_restriction(3510 ^ [], 3508 ^ []), 3509 ^ []) = apply(3510 ^ [], 3509 ^ [])],reduction('1')).
% 15.22/15.85  ncf('1.1.2.2',plain,[-(in(3509 ^ [], 3508 ^ []))],extension(3516 ^ 7)).
% 15.22/15.85  ncf('1.1.2.3',plain,[-(relation(3510 ^ []))],extension(3512 ^ 5)).
% 15.22/15.85  ncf('1.1.2.4',plain,[-(function(3510 ^ []))],extension(3514 ^ 5)).
% 15.22/15.85  ncf('1.1.3',plain,[-(relation(3510 ^ []))],extension(3512 ^ 2)).
% 15.22/15.85  ncf('1.1.4',plain,[-(function(3510 ^ []))],extension(3514 ^ 2)).
% 15.22/15.85  %-----------------------------------------------------
% 15.22/15.85  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------