TSTP Solution File: NUM139-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM139-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n024.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 Sep 1 20:07:01 EDT 2023
% Result : Unsatisfiable 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 443
% Syntax : Number of formulae : 917 ( 210 unt; 0 def)
% Number of atoms : 2354 ( 272 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2519 (1082 ~;1153 |; 0 &)
% ( 284 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 302 ( 300 usr; 285 prp; 0-3 aty)
% Number of functors : 64 ( 64 usr; 20 con; 0-3 aty)
% Number of variables : 1009 (;1009 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2413,plain,
$false,
inference(avatar_sat_refutation,[],[f167,f172,f177,f182,f186,f191,f195,f199,f203,f208,f213,f217,f221,f225,f230,f235,f240,f244,f248,f252,f257,f261,f265,f269,f273,f277,f281,f285,f290,f294,f298,f302,f308,f315,f319,f323,f327,f331,f335,f339,f343,f347,f352,f357,f361,f365,f369,f373,f377,f381,f399,f403,f407,f411,f415,f419,f423,f427,f431,f435,f439,f443,f447,f451,f455,f459,f463,f467,f471,f475,f479,f484,f488,f512,f526,f533,f537,f541,f545,f549,f553,f559,f563,f568,f572,f576,f616,f631,f635,f639,f643,f647,f651,f655,f659,f663,f667,f671,f675,f679,f683,f691,f695,f699,f703,f707,f711,f748,f752,f756,f760,f764,f768,f777,f781,f785,f789,f793,f797,f801,f805,f809,f813,f876,f880,f884,f888,f892,f896,f900,f904,f908,f933,f937,f941,f945,f949,f953,f957,f965,f979,f983,f987,f991,f995,f1010,f1014,f1018,f1022,f1027,f1032,f1044,f1048,f1052,f1056,f1063,f1075,f1079,f1083,f1091,f1095,f1100,f1104,f1119,f1123,f1133,f1142,f1146,f1156,f1160,f1166,f1176,f1180,f1195,f1199,f1203,f1207,f1211,f1223,f1251,f1259,f1264,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1337,f1341,f1345,f1349,f1359,f1363,f1367,f1371,f1375,f1379,f1421,f1465,f1474,f1495,f1499,f1503,f1508,f1514,f1518,f1522,f1535,f1569,f1637,f1641,f1645,f1649,f1653,f1657,f1661,f1665,f1669,f1678,f1683,f1706,f1715,f1720,f1729,f1738,f1742,f1748,f1752,f1758,f1764,f1768,f1772,f1896,f1931,f1982,f1986,f1990,f1994,f1998,f2002,f2006,f2010,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2052,f2056,f2064,f2068,f2072,f2252,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2318,f2323,f2412]) ).
fof(f2412,plain,
( spl0_1
| spl0_2
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2363,f2279,f169,f164]) ).
fof(f164,plain,
( spl0_1
<=> subclass(intersection(power_class(x),z),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f169,plain,
( spl0_2
<=> member(not_subclass_element(intersection(power_class(x),z),x),z) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2279,plain,
( spl0_274
<=> ! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X5)
| subclass(intersection(X4,X5),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2363,plain,
( subclass(intersection(power_class(x),z),x)
| spl0_2
| ~ spl0_274 ),
inference(resolution,[],[f2280,f171]) ).
fof(f171,plain,
( ~ member(not_subclass_element(intersection(power_class(x),z),x),z)
| spl0_2 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f2280,plain,
( ! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X5)
| subclass(intersection(X4,X5),X6) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2279]) ).
fof(f2323,plain,
( spl0_284
| ~ spl0_21
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f921,f906,f254,f2320]) ).
fof(f2320,plain,
( spl0_284
<=> symmetric_difference(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f254,plain,
( spl0_21
<=> identity_relation = intersection(inverse(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f906,plain,
( spl0_135
<=> ! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f921,plain,
( symmetric_difference(inverse(subset_relation),subset_relation) = intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation))
| ~ spl0_21
| ~ spl0_135 ),
inference(superposition,[],[f907,f256]) ).
fof(f256,plain,
( identity_relation = intersection(inverse(subset_relation),subset_relation)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f907,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1))
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f2318,plain,
( spl0_283
| ~ spl0_29
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f917,f906,f287,f2315]) ).
fof(f2315,plain,
( spl0_283
<=> symmetric_difference(complement(kind_1_ordinals),ordinal_numbers) = intersection(complement(limit_ordinals),union(complement(kind_1_ordinals),ordinal_numbers)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f287,plain,
( spl0_29
<=> intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f917,plain,
( symmetric_difference(complement(kind_1_ordinals),ordinal_numbers) = intersection(complement(limit_ordinals),union(complement(kind_1_ordinals),ordinal_numbers))
| ~ spl0_29
| ~ spl0_135 ),
inference(superposition,[],[f907,f289]) ).
fof(f289,plain,
( intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f2313,plain,
( spl0_282
| ~ spl0_123
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f872,f811,f799,f2311]) ).
fof(f2311,plain,
( spl0_282
<=> ! [X2,X1,X3] :
( subclass(segment(X1,X2,X3),singleton(X3))
| ~ section(X1,singleton(X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f799,plain,
( spl0_123
<=> ! [X4,X5,X1] : segment(X5,X1,X4) = domain_of(restrict(X5,X1,singleton(X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f811,plain,
( spl0_126
<=> ! [X4,X5,X1] :
( ~ section(X5,X1,X4)
| subclass(domain_of(restrict(X5,X4,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f872,plain,
( ! [X2,X3,X1] :
( subclass(segment(X1,X2,X3),singleton(X3))
| ~ section(X1,singleton(X3),X2) )
| ~ spl0_123
| ~ spl0_126 ),
inference(superposition,[],[f812,f800]) ).
fof(f800,plain,
( ! [X1,X4,X5] : segment(X5,X1,X4) = domain_of(restrict(X5,X1,singleton(X4)))
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f812,plain,
( ! [X1,X4,X5] :
( subclass(domain_of(restrict(X5,X4,X1)),X1)
| ~ section(X5,X1,X4) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f2309,plain,
( spl0_281
| ~ spl0_34
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f725,f641,f313,f2307]) ).
fof(f2307,plain,
( spl0_281
<=> ! [X6,X5,X7] :
( ~ member(X7,union(X5,X6))
| ~ member(X7,intersection(complement(X5),complement(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f313,plain,
( spl0_34
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f641,plain,
( spl0_92
<=> ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f725,plain,
( ! [X6,X7,X5] :
( ~ member(X7,union(X5,X6))
| ~ member(X7,intersection(complement(X5),complement(X6))) )
| ~ spl0_34
| ~ spl0_92 ),
inference(superposition,[],[f314,f642]) ).
fof(f642,plain,
( ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f314,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f2305,plain,
( spl0_280
| ~ spl0_77
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f627,f574,f531,f2303]) ).
fof(f2303,plain,
( spl0_280
<=> ! [X2,X1] :
( ~ member(X1,universal_class)
| ~ subclass(rest_relation,X2)
| member(ordered_pair(X1,rest_of(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f531,plain,
( spl0_77
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f574,plain,
( spl0_87
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,rest_of(X0)),rest_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f627,plain,
( ! [X2,X1] :
( ~ member(X1,universal_class)
| ~ subclass(rest_relation,X2)
| member(ordered_pair(X1,rest_of(X1)),X2) )
| ~ spl0_77
| ~ spl0_87 ),
inference(resolution,[],[f575,f532]) ).
fof(f532,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f575,plain,
( ! [X0] :
( member(ordered_pair(X0,rest_of(X0)),rest_relation)
| ~ member(X0,universal_class) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f2301,plain,
( spl0_279
| ~ spl0_77
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f620,f561,f531,f2299]) ).
fof(f2299,plain,
( spl0_279
<=> ! [X2,X1] :
( ~ member(X1,universal_class)
| ~ subclass(domain_relation,X2)
| member(ordered_pair(X1,domain_of(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f561,plain,
( spl0_84
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f620,plain,
( ! [X2,X1] :
( ~ member(X1,universal_class)
| ~ subclass(domain_relation,X2)
| member(ordered_pair(X1,domain_of(X1)),X2) )
| ~ spl0_77
| ~ spl0_84 ),
inference(resolution,[],[f562,f532]) ).
fof(f562,plain,
( ! [X0] :
( member(ordered_pair(X0,domain_of(X0)),domain_relation)
| ~ member(X0,universal_class) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f2297,plain,
( spl0_278
| ~ spl0_30
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f606,f535,f292,f2295]) ).
fof(f2295,plain,
( spl0_278
<=> ! [X14] :
( ~ subclass(cross_product(universal_class,universal_class),rest_of(X14))
| cross_product(universal_class,universal_class) = rest_of(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f292,plain,
( spl0_30
<=> ! [X0] : subclass(rest_of(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f535,plain,
( spl0_78
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f606,plain,
( ! [X14] :
( ~ subclass(cross_product(universal_class,universal_class),rest_of(X14))
| cross_product(universal_class,universal_class) = rest_of(X14) )
| ~ spl0_30
| ~ spl0_78 ),
inference(resolution,[],[f536,f293]) ).
fof(f293,plain,
( ! [X0] : subclass(rest_of(X0),cross_product(universal_class,universal_class))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f536,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f2293,plain,
( spl0_277
| ~ spl0_25
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f602,f535,f271,f2291]) ).
fof(f2291,plain,
( spl0_277
<=> ! [X13] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X13))
| cross_product(universal_class,universal_class) = compose_class(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f271,plain,
( spl0_25
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f602,plain,
( ! [X13] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X13))
| cross_product(universal_class,universal_class) = compose_class(X13) )
| ~ spl0_25
| ~ spl0_78 ),
inference(resolution,[],[f536,f272]) ).
fof(f272,plain,
( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f2289,plain,
( spl0_276
| ~ spl0_36
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f595,f535,f321,f2287]) ).
fof(f2287,plain,
( spl0_276
<=> ! [X6] :
( ~ subclass(X6,image(successor_relation,X6))
| image(successor_relation,X6) = X6
| ~ inductive(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f321,plain,
( spl0_36
<=> ! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f595,plain,
( ! [X6] :
( ~ subclass(X6,image(successor_relation,X6))
| image(successor_relation,X6) = X6
| ~ inductive(X6) )
| ~ spl0_36
| ~ spl0_78 ),
inference(resolution,[],[f536,f322]) ).
fof(f322,plain,
( ! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f2285,plain,
( spl0_275
| ~ spl0_40
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f590,f535,f337,f2283]) ).
fof(f2283,plain,
( spl0_275
<=> ! [X2] :
( ~ subclass(cross_product(universal_class,universal_class),X2)
| cross_product(universal_class,universal_class) = X2
| ~ function(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f337,plain,
( spl0_40
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f590,plain,
( ! [X2] :
( ~ subclass(cross_product(universal_class,universal_class),X2)
| cross_product(universal_class,universal_class) = X2
| ~ function(X2) )
| ~ spl0_40
| ~ spl0_78 ),
inference(resolution,[],[f536,f338]) ).
fof(f338,plain,
( ! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f2281,plain,
( spl0_274
| ~ spl0_53
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f506,f425,f401,f2279]) ).
fof(f401,plain,
( spl0_53
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f425,plain,
( spl0_59
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f506,plain,
( ! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X5)
| subclass(intersection(X4,X5),X6) )
| ~ spl0_53
| ~ spl0_59 ),
inference(resolution,[],[f426,f402]) ).
fof(f402,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f426,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f2277,plain,
( spl0_273
| ~ spl0_53
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f501,f421,f401,f2275]) ).
fof(f2275,plain,
( spl0_273
<=> ! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X4)
| subclass(intersection(X4,X5),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f421,plain,
( spl0_58
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f501,plain,
( ! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X4)
| subclass(intersection(X4,X5),X6) )
| ~ spl0_53
| ~ spl0_58 ),
inference(resolution,[],[f422,f402]) ).
fof(f422,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f2252,plain,
( spl0_1
| ~ spl0_272
| spl0_2
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2172,f2004,f169,f2249,f164]) ).
fof(f2249,plain,
( spl0_272
<=> subclass(intersection(power_class(x),z),z) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2004,plain,
( spl0_255
<=> ! [X6,X4,X5] :
( ~ subclass(X4,X5)
| member(not_subclass_element(X4,X6),X5)
| subclass(X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2172,plain,
( ~ subclass(intersection(power_class(x),z),z)
| subclass(intersection(power_class(x),z),x)
| spl0_2
| ~ spl0_255 ),
inference(resolution,[],[f2005,f171]) ).
fof(f2005,plain,
( ! [X6,X4,X5] :
( member(not_subclass_element(X4,X6),X5)
| ~ subclass(X4,X5)
| subclass(X4,X6) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2004]) ).
fof(f2072,plain,
( spl0_271
| ~ spl0_63
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1005,f993,f441,f2070]) ).
fof(f2070,plain,
( spl0_271
<=> ! [X0] :
( ~ subclass(sum_class(X0),X0)
| section(element_relation,X0,universal_class)
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f441,plain,
( spl0_63
<=> ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f993,plain,
( spl0_148
<=> ! [X4,X5,X1] :
( ~ subclass(X1,X4)
| section(X5,X1,X4)
| ~ subclass(domain_of(restrict(X5,X4,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1005,plain,
( ! [X0] :
( ~ subclass(sum_class(X0),X0)
| section(element_relation,X0,universal_class)
| ~ subclass(X0,universal_class) )
| ~ spl0_63
| ~ spl0_148 ),
inference(superposition,[],[f994,f442]) ).
fof(f442,plain,
( ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f994,plain,
( ! [X1,X4,X5] :
( ~ subclass(domain_of(restrict(X5,X4,X1)),X1)
| section(X5,X1,X4)
| ~ subclass(X1,X4) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f2068,plain,
( spl0_270
| ~ spl0_58
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f928,f906,f421,f2066]) ).
fof(f2066,plain,
( spl0_270
<=> ! [X6,X7,X8] :
( ~ member(X8,symmetric_difference(X6,X7))
| member(X8,complement(intersection(X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f928,plain,
( ! [X8,X6,X7] :
( ~ member(X8,symmetric_difference(X6,X7))
| member(X8,complement(intersection(X6,X7))) )
| ~ spl0_58
| ~ spl0_135 ),
inference(superposition,[],[f422,f907]) ).
fof(f2064,plain,
( spl0_268
| spl0_269
| ~ spl0_12
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f910,f874,f215,f2061,f2058]) ).
fof(f2058,plain,
( spl0_268
<=> ! [X4,X3] : ~ inductive(cross_product(X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2061,plain,
( spl0_269
<=> null_class = ordered_pair(first(null_class),second(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f215,plain,
( spl0_12
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f874,plain,
( spl0_127
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f910,plain,
( ! [X3,X4] :
( null_class = ordered_pair(first(null_class),second(null_class))
| ~ inductive(cross_product(X3,X4)) )
| ~ spl0_12
| ~ spl0_127 ),
inference(resolution,[],[f875,f216]) ).
fof(f216,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f875,plain,
( ! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f2056,plain,
( spl0_267
| ~ spl0_59
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f852,f766,f425,f2054]) ).
fof(f2054,plain,
( spl0_267
<=> ! [X2,X3] :
( ~ member(X3,cantor(X2))
| member(X3,diagonalise(compose(inverse(element_relation),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f766,plain,
( spl0_115
<=> ! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f852,plain,
( ! [X2,X3] :
( ~ member(X3,cantor(X2))
| member(X3,diagonalise(compose(inverse(element_relation),X2))) )
| ~ spl0_59
| ~ spl0_115 ),
inference(superposition,[],[f426,f767]) ).
fof(f767,plain,
( ! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f2052,plain,
( spl0_265
| ~ spl0_266
| spl0_184
| ~ spl0_28
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f843,f762,f283,f1248,f2049,f2045]) ).
fof(f2045,plain,
( spl0_265
<=> well_ordering(element_relation,apply(choice,ordinal_numbers)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2049,plain,
( spl0_266
<=> member(ordinal_numbers,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1248,plain,
( spl0_184
<=> null_class = ordinal_numbers ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f283,plain,
( spl0_28
<=> ! [X0] :
( ~ member(X0,ordinal_numbers)
| well_ordering(element_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f762,plain,
( spl0_114
<=> ! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f843,plain,
( null_class = ordinal_numbers
| ~ member(ordinal_numbers,universal_class)
| well_ordering(element_relation,apply(choice,ordinal_numbers))
| ~ spl0_28
| ~ spl0_114 ),
inference(resolution,[],[f763,f284]) ).
fof(f284,plain,
( ! [X0] :
( ~ member(X0,ordinal_numbers)
| well_ordering(element_relation,X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f763,plain,
( ! [X1] :
( member(apply(choice,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f2043,plain,
( spl0_264
| ~ spl0_68
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f733,f649,f461,f2041]) ).
fof(f2041,plain,
( spl0_264
<=> ! [X13,X12] : diagonalise(cross_product(X12,X13)) = complement(domain_of(restrict(identity_relation,X12,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f461,plain,
( spl0_68
<=> ! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f649,plain,
( spl0_94
<=> ! [X5,X1,X0] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f733,plain,
( ! [X12,X13] : diagonalise(cross_product(X12,X13)) = complement(domain_of(restrict(identity_relation,X12,X13)))
| ~ spl0_68
| ~ spl0_94 ),
inference(superposition,[],[f462,f650]) ).
fof(f650,plain,
( ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f462,plain,
( ! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5)
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f2039,plain,
( spl0_263
| ~ spl0_59
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f726,f645,f425,f2037]) ).
fof(f2037,plain,
( spl0_263
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f645,plain,
( spl0_93
<=> ! [X5,X0,X1] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f726,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,restrict(X0,X1,X2))
| member(X3,cross_product(X1,X2)) )
| ~ spl0_59
| ~ spl0_93 ),
inference(superposition,[],[f426,f646]) ).
fof(f646,plain,
( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f2035,plain,
( spl0_262
| ~ spl0_20
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f621,f561,f250,f2033]) ).
fof(f2033,plain,
( spl0_262
<=> ! [X0] :
( member(ordered_pair(inverse(X0),range_of(X0)),domain_relation)
| ~ member(inverse(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f250,plain,
( spl0_20
<=> ! [X4] : domain_of(inverse(X4)) = range_of(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f621,plain,
( ! [X0] :
( member(ordered_pair(inverse(X0),range_of(X0)),domain_relation)
| ~ member(inverse(X0),universal_class) )
| ~ spl0_20
| ~ spl0_84 ),
inference(superposition,[],[f562,f251]) ).
fof(f251,plain,
( ! [X4] : domain_of(inverse(X4)) = range_of(X4)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f2031,plain,
( spl0_261
| ~ spl0_37
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f618,f551,f325,f2029]) ).
fof(f2029,plain,
( spl0_261
<=> ! [X2,X3] :
( member(apply(X2,X3),universal_class)
| ~ member(image(X2,singleton(X3)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f325,plain,
( spl0_37
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f551,plain,
( spl0_82
<=> ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f618,plain,
( ! [X2,X3] :
( member(apply(X2,X3),universal_class)
| ~ member(image(X2,singleton(X3)),universal_class) )
| ~ spl0_37
| ~ spl0_82 ),
inference(superposition,[],[f326,f552]) ).
fof(f552,plain,
( ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f326,plain,
( ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f2027,plain,
( spl0_260
| ~ spl0_48
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f598,f535,f371,f2025]) ).
fof(f2025,plain,
( spl0_260
<=> ! [X8] :
( ~ subclass(X8,sum_class(X8))
| sum_class(X8) = X8
| ~ member(X8,ordinal_numbers) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f371,plain,
( spl0_48
<=> ! [X0] :
( ~ member(X0,ordinal_numbers)
| subclass(sum_class(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f598,plain,
( ! [X8] :
( ~ subclass(X8,sum_class(X8))
| sum_class(X8) = X8
| ~ member(X8,ordinal_numbers) )
| ~ spl0_48
| ~ spl0_78 ),
inference(resolution,[],[f536,f372]) ).
fof(f372,plain,
( ! [X0] :
( subclass(sum_class(X0),X0)
| ~ member(X0,ordinal_numbers) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f2023,plain,
( spl0_259
| ~ spl0_56
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f586,f531,f413,f2021]) ).
fof(f2021,plain,
( spl0_259
<=> ! [X22,X20,X21] :
( ~ subclass(unordered_pair(X20,X21),X22)
| member(X21,X22)
| ~ member(X21,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f413,plain,
( spl0_56
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f586,plain,
( ! [X21,X22,X20] :
( ~ subclass(unordered_pair(X20,X21),X22)
| member(X21,X22)
| ~ member(X21,universal_class) )
| ~ spl0_56
| ~ spl0_77 ),
inference(resolution,[],[f532,f414]) ).
fof(f414,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f2019,plain,
( ~ spl0_257
| spl0_258
| ~ spl0_10
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1620,f1520,f205,f2016,f2012]) ).
fof(f2012,plain,
( spl0_257
<=> single_valued_class(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2016,plain,
( spl0_258
<=> function(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f205,plain,
( spl0_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1520,plain,
( spl0_214
<=> ! [X1] :
( ~ subclass(X1,cross_product(universal_class,universal_class))
| function(X1)
| ~ single_valued_class(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1620,plain,
( function(element_relation)
| ~ single_valued_class(element_relation)
| ~ spl0_10
| ~ spl0_214 ),
inference(resolution,[],[f1521,f207]) ).
fof(f207,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f1521,plain,
( ! [X1] :
( ~ subclass(X1,cross_product(universal_class,universal_class))
| function(X1)
| ~ single_valued_class(X1) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f2010,plain,
( spl0_256
| ~ spl0_55
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f585,f531,f409,f2008]) ).
fof(f2008,plain,
( spl0_256
<=> ! [X18,X17,X19] :
( ~ subclass(unordered_pair(X17,X18),X19)
| member(X17,X19)
| ~ member(X17,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f409,plain,
( spl0_55
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f585,plain,
( ! [X18,X19,X17] :
( ~ subclass(unordered_pair(X17,X18),X19)
| member(X17,X19)
| ~ member(X17,universal_class) )
| ~ spl0_55
| ~ spl0_77 ),
inference(resolution,[],[f532,f410]) ).
fof(f410,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f2006,plain,
( spl0_255
| ~ spl0_53
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f579,f531,f401,f2004]) ).
fof(f579,plain,
( ! [X6,X4,X5] :
( ~ subclass(X4,X5)
| member(not_subclass_element(X4,X6),X5)
| subclass(X4,X6) )
| ~ spl0_53
| ~ spl0_77 ),
inference(resolution,[],[f532,f402]) ).
fof(f2002,plain,
( spl0_254
| ~ spl0_53
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f529,f486,f401,f2000]) ).
fof(f2000,plain,
( spl0_254
<=> ! [X2,X3] :
( member(domain_of(not_subclass_element(recursion_equation_functions(X2),X3)),ordinal_numbers)
| subclass(recursion_equation_functions(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f486,plain,
( spl0_74
<=> ! [X4,X0] :
( ~ member(X0,recursion_equation_functions(X4))
| member(domain_of(X0),ordinal_numbers) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f529,plain,
( ! [X2,X3] :
( member(domain_of(not_subclass_element(recursion_equation_functions(X2),X3)),ordinal_numbers)
| subclass(recursion_equation_functions(X2),X3) )
| ~ spl0_53
| ~ spl0_74 ),
inference(resolution,[],[f487,f402]) ).
fof(f487,plain,
( ! [X0,X4] :
( ~ member(X0,recursion_equation_functions(X4))
| member(domain_of(X0),ordinal_numbers) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f1998,plain,
( spl0_253
| ~ spl0_64
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f517,f461,f445,f1996]) ).
fof(f1996,plain,
( spl0_253
<=> ! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f445,plain,
( spl0_64
<=> ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f517,plain,
( ! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0)))
| ~ spl0_64
| ~ spl0_68 ),
inference(superposition,[],[f446,f462]) ).
fof(f446,plain,
( ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1994,plain,
( spl0_252
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f513,f445,f1992]) ).
fof(f1992,plain,
( spl0_252
<=> ! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f513,plain,
( ! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0)))
| ~ spl0_64 ),
inference(superposition,[],[f446,f446]) ).
fof(f1990,plain,
( spl0_251
| ~ spl0_41
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f505,f425,f341,f1988]) ).
fof(f1988,plain,
( spl0_251
<=> ! [X2,X3] :
( member(regular(intersection(X2,X3)),X3)
| null_class = intersection(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f341,plain,
( spl0_41
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f505,plain,
( ! [X2,X3] :
( member(regular(intersection(X2,X3)),X3)
| null_class = intersection(X2,X3) )
| ~ spl0_41
| ~ spl0_59 ),
inference(resolution,[],[f426,f342]) ).
fof(f342,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f1986,plain,
( spl0_250
| ~ spl0_41
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f500,f421,f341,f1984]) ).
fof(f1984,plain,
( spl0_250
<=> ! [X2,X3] :
( member(regular(intersection(X2,X3)),X2)
| null_class = intersection(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f500,plain,
( ! [X2,X3] :
( member(regular(intersection(X2,X3)),X2)
| null_class = intersection(X2,X3) )
| ~ spl0_41
| ~ spl0_58 ),
inference(resolution,[],[f422,f342]) ).
fof(f1982,plain,
( spl0_249
| ~ spl0_49
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f490,f401,f375,f1980]) ).
fof(f1980,plain,
( spl0_249
<=> ! [X2] :
( subclass(omega,X2)
| not_subclass_element(omega,X2) = integer_of(not_subclass_element(omega,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f375,plain,
( spl0_49
<=> ! [X0] :
( ~ member(X0,omega)
| integer_of(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f490,plain,
( ! [X2] :
( subclass(omega,X2)
| not_subclass_element(omega,X2) = integer_of(not_subclass_element(omega,X2)) )
| ~ spl0_49
| ~ spl0_53 ),
inference(resolution,[],[f402,f376]) ).
fof(f376,plain,
( ! [X0] :
( ~ member(X0,omega)
| integer_of(X0) = X0 )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1931,plain,
( spl0_248
| ~ spl0_184
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f1744,f1740,f1248,f1929]) ).
fof(f1929,plain,
( spl0_248
<=> ! [X0,X1] :
( ordinal_numbers = X0
| ~ member(X1,ordinal_numbers)
| member(X1,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1740,plain,
( spl0_240
<=> ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1744,plain,
( ! [X0,X1] :
( ordinal_numbers = X0
| ~ member(X1,ordinal_numbers)
| member(X1,regular(X0)) )
| ~ spl0_184
| ~ spl0_240 ),
inference(forward_demodulation,[],[f1743,f1250]) ).
fof(f1250,plain,
( null_class = ordinal_numbers
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f1743,plain,
( ! [X0,X1] :
( ~ member(X1,ordinal_numbers)
| member(X1,regular(X0))
| null_class = X0 )
| ~ spl0_184
| ~ spl0_240 ),
inference(forward_demodulation,[],[f1741,f1250]) ).
fof(f1741,plain,
( ! [X0,X1] :
( member(X1,regular(X0))
| ~ member(X1,null_class)
| null_class = X0 )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f1740]) ).
fof(f1896,plain,
( ~ spl0_247
| ~ spl0_184
| spl0_186 ),
inference(avatar_split_clause,[],[f1694,f1261,f1248,f1893]) ).
fof(f1893,plain,
( spl0_247
<=> single_valued_class(ordinal_numbers) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1261,plain,
( spl0_186
<=> single_valued_class(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1694,plain,
( ~ single_valued_class(ordinal_numbers)
| ~ spl0_184
| spl0_186 ),
inference(superposition,[],[f1262,f1250]) ).
fof(f1262,plain,
( ~ single_valued_class(null_class)
| spl0_186 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f1772,plain,
( spl0_246
| ~ spl0_59
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f927,f906,f425,f1770]) ).
fof(f1770,plain,
( spl0_246
<=> ! [X4,X5,X3] :
( ~ member(X5,symmetric_difference(X3,X4))
| member(X5,union(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f927,plain,
( ! [X3,X4,X5] :
( ~ member(X5,symmetric_difference(X3,X4))
| member(X5,union(X3,X4)) )
| ~ spl0_59
| ~ spl0_135 ),
inference(superposition,[],[f426,f907]) ).
fof(f1768,plain,
( spl0_245
| ~ spl0_21
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f836,f754,f254,f1766]) ).
fof(f1766,plain,
( spl0_245
<=> ! [X12] :
( member(X12,identity_relation)
| ~ member(X12,subset_relation)
| ~ member(X12,inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f754,plain,
( spl0_112
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f836,plain,
( ! [X12] :
( member(X12,identity_relation)
| ~ member(X12,subset_relation)
| ~ member(X12,inverse(subset_relation)) )
| ~ spl0_21
| ~ spl0_112 ),
inference(superposition,[],[f755,f256]) ).
fof(f755,plain,
( ! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f1764,plain,
( spl0_244
| ~ spl0_29
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f834,f754,f287,f1762]) ).
fof(f1762,plain,
( spl0_244
<=> ! [X10] :
( member(X10,limit_ordinals)
| ~ member(X10,ordinal_numbers)
| ~ member(X10,complement(kind_1_ordinals)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f834,plain,
( ! [X10] :
( member(X10,limit_ordinals)
| ~ member(X10,ordinal_numbers)
| ~ member(X10,complement(kind_1_ordinals)) )
| ~ spl0_29
| ~ spl0_112 ),
inference(superposition,[],[f755,f289]) ).
fof(f1758,plain,
( spl0_243
| ~ spl0_55
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f824,f750,f409,f1756]) ).
fof(f1756,plain,
( spl0_243
<=> ! [X6,X5] :
( member(singleton(X5),ordered_pair(X5,X6))
| ~ member(singleton(X5),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f750,plain,
( spl0_111
<=> ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f824,plain,
( ! [X6,X5] :
( member(singleton(X5),ordered_pair(X5,X6))
| ~ member(singleton(X5),universal_class) )
| ~ spl0_55
| ~ spl0_111 ),
inference(superposition,[],[f410,f751]) ).
fof(f751,plain,
( ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1)
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f1752,plain,
( spl0_242
| ~ spl0_12
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f816,f746,f215,f1750]) ).
fof(f1750,plain,
( spl0_242
<=> ! [X4,X5] :
( null_class = X4
| null_class = X5
| ~ inductive(unordered_pair(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f746,plain,
( spl0_110
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f816,plain,
( ! [X4,X5] :
( null_class = X4
| null_class = X5
| ~ inductive(unordered_pair(X4,X5)) )
| ~ spl0_12
| ~ spl0_110 ),
inference(resolution,[],[f747,f216]) ).
fof(f747,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f1748,plain,
( spl0_241
| ~ spl0_58
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f625,f565,f421,f1746]) ).
fof(f1746,plain,
( spl0_241
<=> ! [X1] :
( ~ member(X1,singleton_relation)
| member(X1,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f565,plain,
( spl0_85
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f625,plain,
( ! [X1] :
( ~ member(X1,singleton_relation)
| member(X1,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_58
| ~ spl0_85 ),
inference(superposition,[],[f422,f567]) ).
fof(f567,plain,
( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f1742,plain,
( spl0_240
| ~ spl0_59
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f610,f547,f425,f1740]) ).
fof(f547,plain,
( spl0_81
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f610,plain,
( ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 )
| ~ spl0_59
| ~ spl0_81 ),
inference(superposition,[],[f426,f548]) ).
fof(f548,plain,
( ! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f1738,plain,
( spl0_238
| ~ spl0_239
| ~ spl0_17
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f608,f535,f237,f1735,f1731]) ).
fof(f1731,plain,
( spl0_238
<=> cross_product(universal_class,universal_class) = union_of_range_map ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1735,plain,
( spl0_239
<=> subclass(cross_product(universal_class,universal_class),union_of_range_map) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f237,plain,
( spl0_17
<=> subclass(union_of_range_map,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f608,plain,
( ~ subclass(cross_product(universal_class,universal_class),union_of_range_map)
| cross_product(universal_class,universal_class) = union_of_range_map
| ~ spl0_17
| ~ spl0_78 ),
inference(resolution,[],[f536,f239]) ).
fof(f239,plain,
( subclass(union_of_range_map,cross_product(universal_class,universal_class))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f1729,plain,
( spl0_236
| ~ spl0_237
| ~ spl0_16
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f607,f535,f232,f1726,f1722]) ).
fof(f1722,plain,
( spl0_236
<=> cross_product(universal_class,universal_class) = rest_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1726,plain,
( spl0_237
<=> subclass(cross_product(universal_class,universal_class),rest_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f232,plain,
( spl0_16
<=> subclass(rest_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f607,plain,
( ~ subclass(cross_product(universal_class,universal_class),rest_relation)
| cross_product(universal_class,universal_class) = rest_relation
| ~ spl0_16
| ~ spl0_78 ),
inference(resolution,[],[f536,f234]) ).
fof(f234,plain,
( subclass(rest_relation,cross_product(universal_class,universal_class))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f1720,plain,
( ~ spl0_235
| spl0_104
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1687,f1248,f688,f1717]) ).
fof(f1717,plain,
( spl0_235
<=> function(ordinal_numbers) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f688,plain,
( spl0_104
<=> function(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1687,plain,
( ~ function(ordinal_numbers)
| spl0_104
| ~ spl0_184 ),
inference(superposition,[],[f689,f1250]) ).
fof(f689,plain,
( ~ function(null_class)
| spl0_104 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f1715,plain,
( spl0_233
| ~ spl0_234
| ~ spl0_15
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f604,f535,f227,f1712,f1708]) ).
fof(f1708,plain,
( spl0_233
<=> cross_product(universal_class,universal_class) = domain_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1712,plain,
( spl0_234
<=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f227,plain,
( spl0_15
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f604,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_15
| ~ spl0_78 ),
inference(resolution,[],[f536,f229]) ).
fof(f229,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f1706,plain,
( spl0_231
| ~ spl0_232
| ~ spl0_11
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f596,f535,f210,f1703,f1699]) ).
fof(f1699,plain,
( spl0_231
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1703,plain,
( spl0_232
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f210,plain,
( spl0_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f596,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_11
| ~ spl0_78 ),
inference(resolution,[],[f536,f212]) ).
fof(f212,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f1683,plain,
( spl0_230
| ~ spl0_27
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1255,f1244,f279,f1680]) ).
fof(f1680,plain,
( spl0_230
<=> connected(element_relation,regular(ordinal_numbers)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f279,plain,
( spl0_27
<=> ! [X0,X1] :
( ~ well_ordering(X0,X1)
| connected(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1244,plain,
( spl0_183
<=> well_ordering(element_relation,regular(ordinal_numbers)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1255,plain,
( connected(element_relation,regular(ordinal_numbers))
| ~ spl0_27
| ~ spl0_183 ),
inference(resolution,[],[f1246,f280]) ).
fof(f280,plain,
( ! [X0,X1] :
( ~ well_ordering(X0,X1)
| connected(X0,X1) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f1246,plain,
( well_ordering(element_relation,regular(ordinal_numbers))
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f1678,plain,
( spl0_228
| ~ spl0_229
| ~ spl0_10
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f591,f535,f205,f1675,f1671]) ).
fof(f1671,plain,
( spl0_228
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1675,plain,
( spl0_229
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f591,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class)
| ~ spl0_10
| ~ spl0_78 ),
inference(resolution,[],[f536,f207]) ).
fof(f1669,plain,
( spl0_227
| ~ spl0_50
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f587,f531,f379,f1667]) ).
fof(f1667,plain,
( spl0_227
<=> ! [X24,X23] :
( ~ subclass(omega,X23)
| member(X24,X23)
| null_class = integer_of(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f379,plain,
( spl0_50
<=> ! [X0] :
( member(X0,omega)
| null_class = integer_of(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f587,plain,
( ! [X24,X23] :
( ~ subclass(omega,X23)
| member(X24,X23)
| null_class = integer_of(X24) )
| ~ spl0_50
| ~ spl0_77 ),
inference(resolution,[],[f532,f380]) ).
fof(f380,plain,
( ! [X0] :
( member(X0,omega)
| null_class = integer_of(X0) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f1665,plain,
( spl0_226
| ~ spl0_38
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f584,f531,f329,f1663]) ).
fof(f1663,plain,
( spl0_226
<=> ! [X16,X15] :
( ~ subclass(universal_class,X15)
| member(power_class(X16),X15)
| ~ member(X16,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f329,plain,
( spl0_38
<=> ! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f584,plain,
( ! [X16,X15] :
( ~ subclass(universal_class,X15)
| member(power_class(X16),X15)
| ~ member(X16,universal_class) )
| ~ spl0_38
| ~ spl0_77 ),
inference(resolution,[],[f532,f330]) ).
fof(f330,plain,
( ! [X2] :
( member(power_class(X2),universal_class)
| ~ member(X2,universal_class) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f1661,plain,
( spl0_225
| ~ spl0_37
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f583,f531,f325,f1659]) ).
fof(f1659,plain,
( spl0_225
<=> ! [X13,X14] :
( ~ subclass(universal_class,X13)
| member(sum_class(X14),X13)
| ~ member(X14,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f583,plain,
( ! [X14,X13] :
( ~ subclass(universal_class,X13)
| member(sum_class(X14),X13)
| ~ member(X14,universal_class) )
| ~ spl0_37
| ~ spl0_77 ),
inference(resolution,[],[f532,f326]) ).
fof(f1657,plain,
( spl0_224
| ~ spl0_41
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f578,f531,f341,f1655]) ).
fof(f1655,plain,
( spl0_224
<=> ! [X2,X3] :
( ~ subclass(X2,X3)
| member(regular(X2),X3)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f578,plain,
( ! [X2,X3] :
( ~ subclass(X2,X3)
| member(regular(X2),X3)
| null_class = X2 )
| ~ spl0_41
| ~ spl0_77 ),
inference(resolution,[],[f532,f342]) ).
fof(f1653,plain,
( spl0_223
| ~ spl0_41
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f528,f486,f341,f1651]) ).
fof(f1651,plain,
( spl0_223
<=> ! [X1] :
( member(domain_of(regular(recursion_equation_functions(X1))),ordinal_numbers)
| null_class = recursion_equation_functions(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f528,plain,
( ! [X1] :
( member(domain_of(regular(recursion_equation_functions(X1))),ordinal_numbers)
| null_class = recursion_equation_functions(X1) )
| ~ spl0_41
| ~ spl0_74 ),
inference(resolution,[],[f487,f342]) ).
fof(f1649,plain,
( spl0_222
| ~ spl0_20
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f519,f465,f250,f1647]) ).
fof(f1647,plain,
( spl0_222
<=> ! [X0] :
( subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ operation(inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f465,plain,
( spl0_69
<=> ! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f519,plain,
( ! [X0] :
( subclass(range_of(inverse(X0)),domain_of(range_of(X0)))
| ~ operation(inverse(X0)) )
| ~ spl0_20
| ~ spl0_69 ),
inference(superposition,[],[f466,f251]) ).
fof(f466,plain,
( ! [X8] :
( subclass(range_of(X8),domain_of(domain_of(X8)))
| ~ operation(X8) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1645,plain,
( spl0_221
| ~ spl0_34
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f518,f461,f313,f1643]) ).
fof(f1643,plain,
( spl0_221
<=> ! [X2,X1] :
( ~ member(X2,diagonalise(X1))
| ~ member(X2,domain_of(intersection(X1,identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f518,plain,
( ! [X2,X1] :
( ~ member(X2,diagonalise(X1))
| ~ member(X2,domain_of(intersection(X1,identity_relation))) )
| ~ spl0_34
| ~ spl0_68 ),
inference(superposition,[],[f314,f462]) ).
fof(f1641,plain,
( spl0_220
| ~ spl0_34
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f514,f445,f313,f1639]) ).
fof(f1639,plain,
( spl0_220
<=> ! [X0,X1] :
( ~ member(X1,power_class(X0))
| ~ member(X1,image(element_relation,complement(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ member(X1,power_class(X0))
| ~ member(X1,image(element_relation,complement(X0))) )
| ~ spl0_34
| ~ spl0_64 ),
inference(superposition,[],[f314,f446]) ).
fof(f1637,plain,
( spl0_219
| ~ spl0_34
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f489,f401,f313,f1635]) ).
fof(f1635,plain,
( spl0_219
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f489,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) )
| ~ spl0_34
| ~ spl0_53 ),
inference(resolution,[],[f402,f314]) ).
fof(f1569,plain,
( spl0_218
| ~ spl0_206
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1504,f1501,f1467,f1567]) ).
fof(f1567,plain,
( spl0_218
<=> ! [X1] :
( omega = integer_of(not_subclass_element(X1,omega))
| subclass(X1,omega) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1467,plain,
( spl0_206
<=> null_class = omega ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1501,plain,
( spl0_210
<=> ! [X1] :
( subclass(X1,omega)
| null_class = integer_of(not_subclass_element(X1,omega)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1504,plain,
( ! [X1] :
( omega = integer_of(not_subclass_element(X1,omega))
| subclass(X1,omega) )
| ~ spl0_206
| ~ spl0_210 ),
inference(forward_demodulation,[],[f1502,f1469]) ).
fof(f1469,plain,
( null_class = omega
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f1467]) ).
fof(f1502,plain,
( ! [X1] :
( subclass(X1,omega)
| null_class = integer_of(not_subclass_element(X1,omega)) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f1535,plain,
( ~ spl0_215
| spl0_216
| ~ spl0_217
| ~ spl0_5
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f969,f951,f184,f1532,f1528,f1524]) ).
fof(f1524,plain,
( spl0_215
<=> well_ordering(element_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1528,plain,
( spl0_216
<=> member(universal_class,ordinal_numbers) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1532,plain,
( spl0_217
<=> member(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f184,plain,
( spl0_5
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f951,plain,
( spl0_141
<=> ! [X0] :
( ~ well_ordering(element_relation,X0)
| ~ member(X0,universal_class)
| member(X0,ordinal_numbers)
| ~ subclass(sum_class(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f969,plain,
( ~ member(universal_class,universal_class)
| member(universal_class,ordinal_numbers)
| ~ well_ordering(element_relation,universal_class)
| ~ spl0_5
| ~ spl0_141 ),
inference(resolution,[],[f952,f185]) ).
fof(f185,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f952,plain,
( ! [X0] :
( ~ subclass(sum_class(X0),X0)
| ~ member(X0,universal_class)
| member(X0,ordinal_numbers)
| ~ well_ordering(element_relation,X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f1522,plain,
( spl0_214
| ~ spl0_65
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f967,f943,f449,f1520]) ).
fof(f449,plain,
( spl0_65
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f943,plain,
( spl0_139
<=> ! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f967,plain,
( ! [X1] :
( ~ subclass(X1,cross_product(universal_class,universal_class))
| function(X1)
| ~ single_valued_class(X1) )
| ~ spl0_65
| ~ spl0_139 ),
inference(resolution,[],[f944,f450]) ).
fof(f450,plain,
( ! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ single_valued_class(X0) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f944,plain,
( ! [X8] :
( ~ subclass(compose(X8,inverse(X8)),identity_relation)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| function(X8) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f1518,plain,
( spl0_213
| ~ spl0_19
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f826,f750,f246,f1516]) ).
fof(f1516,plain,
( spl0_213
<=> ! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f246,plain,
( spl0_19
<=> ! [X0] : unordered_pair(X0,X0) = singleton(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f826,plain,
( ! [X0] : ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0)))
| ~ spl0_19
| ~ spl0_111 ),
inference(forward_demodulation,[],[f821,f247]) ).
fof(f247,plain,
( ! [X0] : unordered_pair(X0,X0) = singleton(X0)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f821,plain,
( ! [X0] : ordered_pair(singleton(X0),X0) = unordered_pair(singleton(singleton(X0)),singleton(singleton(X0)))
| ~ spl0_19
| ~ spl0_111 ),
inference(superposition,[],[f751,f247]) ).
fof(f1514,plain,
( spl0_212
| ~ spl0_58
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f727,f645,f421,f1512]) ).
fof(f1512,plain,
( spl0_212
<=> ! [X5,X4,X7,X6] :
( ~ member(X7,restrict(X4,X5,X6))
| member(X7,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f727,plain,
( ! [X6,X7,X4,X5] :
( ~ member(X7,restrict(X4,X5,X6))
| member(X7,X4) )
| ~ spl0_58
| ~ spl0_93 ),
inference(superposition,[],[f422,f646]) ).
fof(f1508,plain,
( spl0_211
| ~ spl0_58
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f611,f547,f421,f1506]) ).
fof(f1506,plain,
( spl0_211
<=> ! [X2,X3] :
( ~ member(X3,null_class)
| member(X3,X2)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f611,plain,
( ! [X2,X3] :
( ~ member(X3,null_class)
| member(X3,X2)
| null_class = X2 )
| ~ spl0_58
| ~ spl0_81 ),
inference(superposition,[],[f422,f548]) ).
fof(f1503,plain,
( spl0_210
| ~ spl0_50
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f495,f405,f379,f1501]) ).
fof(f405,plain,
( spl0_54
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f495,plain,
( ! [X1] :
( subclass(X1,omega)
| null_class = integer_of(not_subclass_element(X1,omega)) )
| ~ spl0_50
| ~ spl0_54 ),
inference(resolution,[],[f406,f380]) ).
fof(f406,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f1499,plain,
( spl0_209
| ~ spl0_32
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f492,f401,f300,f1497]) ).
fof(f1497,plain,
( spl0_209
<=> ! [X4,X5] :
( subclass(recursion_equation_functions(X4),X5)
| function(not_subclass_element(recursion_equation_functions(X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f300,plain,
( spl0_32
<=> ! [X4,X0] :
( function(X0)
| ~ member(X0,recursion_equation_functions(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f492,plain,
( ! [X4,X5] :
( subclass(recursion_equation_functions(X4),X5)
| function(not_subclass_element(recursion_equation_functions(X4),X5)) )
| ~ spl0_32
| ~ spl0_53 ),
inference(resolution,[],[f402,f301]) ).
fof(f301,plain,
( ! [X0,X4] :
( ~ member(X0,recursion_equation_functions(X4))
| function(X0) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f1495,plain,
( ~ spl0_208
| spl0_104
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1478,f1467,f688,f1492]) ).
fof(f1492,plain,
( spl0_208
<=> function(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1478,plain,
( ~ function(omega)
| spl0_104
| ~ spl0_206 ),
inference(superposition,[],[f689,f1469]) ).
fof(f1474,plain,
( spl0_206
| spl0_207
| ~ spl0_41
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f389,f375,f341,f1471,f1467]) ).
fof(f1471,plain,
( spl0_207
<=> regular(omega) = integer_of(regular(omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f389,plain,
( regular(omega) = integer_of(regular(omega))
| null_class = omega
| ~ spl0_41
| ~ spl0_49 ),
inference(resolution,[],[f376,f342]) ).
fof(f1465,plain,
( spl0_205
| ~ spl0_34
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f386,f341,f313,f1463]) ).
fof(f1463,plain,
( spl0_205
<=> ! [X2] :
( null_class = complement(X2)
| ~ member(regular(complement(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f386,plain,
( ! [X2] :
( null_class = complement(X2)
| ~ member(regular(complement(X2)),X2) )
| ~ spl0_34
| ~ spl0_41 ),
inference(resolution,[],[f342,f314]) ).
fof(f1421,plain,
( ~ spl0_204
| ~ spl0_103
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1352,f1220,f685,f1418]) ).
fof(f1418,plain,
( spl0_204
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f685,plain,
( spl0_103
<=> ! [X0] : ~ inductive(recursion_equation_functions(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1220,plain,
( spl0_182
<=> null_class = recursion_equation_functions(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1352,plain,
( ~ inductive(null_class)
| ~ spl0_103
| ~ spl0_182 ),
inference(superposition,[],[f686,f1222]) ).
fof(f1222,plain,
( null_class = recursion_equation_functions(null_class)
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1220]) ).
fof(f686,plain,
( ! [X0] : ~ inductive(recursion_equation_functions(X0))
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f1379,plain,
( spl0_203
| ~ spl0_58
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1040,f1024,f421,f1377]) ).
fof(f1377,plain,
( spl0_203
<=> ! [X2] :
( ~ member(X2,subset_relation)
| member(X2,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1024,plain,
( spl0_153
<=> subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1040,plain,
( ! [X2] :
( ~ member(X2,subset_relation)
| member(X2,cross_product(universal_class,universal_class)) )
| ~ spl0_58
| ~ spl0_153 ),
inference(superposition,[],[f422,f1026]) ).
fof(f1026,plain,
( subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1375,plain,
( spl0_202
| ~ spl0_63
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f871,f811,f441,f1373]) ).
fof(f1373,plain,
( spl0_202
<=> ! [X0] :
( subclass(sum_class(X0),X0)
| ~ section(element_relation,X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f871,plain,
( ! [X0] :
( subclass(sum_class(X0),X0)
| ~ section(element_relation,X0,universal_class) )
| ~ spl0_63
| ~ spl0_126 ),
inference(superposition,[],[f812,f442]) ).
fof(f1371,plain,
( spl0_201
| ~ spl0_63
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f863,f799,f441,f1369]) ).
fof(f1369,plain,
( spl0_201
<=> ! [X0] : sum_class(singleton(X0)) = segment(element_relation,universal_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f863,plain,
( ! [X0] : sum_class(singleton(X0)) = segment(element_relation,universal_class,X0)
| ~ spl0_63
| ~ spl0_123 ),
inference(superposition,[],[f800,f442]) ).
fof(f1367,plain,
( spl0_200
| ~ spl0_58
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f853,f766,f421,f1365]) ).
fof(f1365,plain,
( spl0_200
<=> ! [X4,X5] :
( ~ member(X5,cantor(X4))
| member(X5,domain_of(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f853,plain,
( ! [X4,X5] :
( ~ member(X5,cantor(X4))
| member(X5,domain_of(X4)) )
| ~ spl0_58
| ~ spl0_115 ),
inference(superposition,[],[f422,f767]) ).
fof(f1363,plain,
( spl0_199
| ~ spl0_13
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f597,f535,f219,f1361]) ).
fof(f1361,plain,
( spl0_199
<=> ! [X7] :
( ~ subclass(X7,omega)
| omega = X7
| ~ inductive(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f219,plain,
( spl0_13
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f597,plain,
( ! [X7] :
( ~ subclass(X7,omega)
| omega = X7
| ~ inductive(X7) )
| ~ spl0_13
| ~ spl0_78 ),
inference(resolution,[],[f536,f220]) ).
fof(f220,plain,
( ! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f1359,plain,
( spl0_198
| ~ spl0_9
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f580,f531,f201,f1357]) ).
fof(f1357,plain,
( spl0_198
<=> ! [X9,X7,X8] :
( ~ subclass(universal_class,X7)
| member(unordered_pair(X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f201,plain,
( spl0_9
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f580,plain,
( ! [X8,X9,X7] :
( ~ subclass(universal_class,X7)
| member(unordered_pair(X8,X9),X7) )
| ~ spl0_9
| ~ spl0_77 ),
inference(resolution,[],[f532,f202]) ).
fof(f202,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f1349,plain,
( spl0_197
| ~ spl0_12
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f577,f531,f215,f1347]) ).
fof(f1347,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f577,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) )
| ~ spl0_12
| ~ spl0_77 ),
inference(resolution,[],[f532,f216]) ).
fof(f1345,plain,
( spl0_196
| ~ spl0_28
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f491,f401,f283,f1343]) ).
fof(f1343,plain,
( spl0_196
<=> ! [X3] :
( subclass(ordinal_numbers,X3)
| well_ordering(element_relation,not_subclass_element(ordinal_numbers,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f491,plain,
( ! [X3] :
( subclass(ordinal_numbers,X3)
| well_ordering(element_relation,not_subclass_element(ordinal_numbers,X3)) )
| ~ spl0_28
| ~ spl0_53 ),
inference(resolution,[],[f402,f284]) ).
fof(f1341,plain,
( spl0_195
| ~ spl0_49
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f390,f379,f375,f1339]) ).
fof(f1339,plain,
( spl0_195
<=> ! [X0] :
( null_class = integer_of(X0)
| integer_of(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f390,plain,
( ! [X0] :
( null_class = integer_of(X0)
| integer_of(X0) = X0 )
| ~ spl0_49
| ~ spl0_50 ),
inference(resolution,[],[f380,f376]) ).
fof(f1337,plain,
( spl0_194
| ~ spl0_32
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f384,f341,f300,f1335]) ).
fof(f1335,plain,
( spl0_194
<=> ! [X0] :
( null_class = recursion_equation_functions(X0)
| function(regular(recursion_equation_functions(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f384,plain,
( ! [X0] :
( null_class = recursion_equation_functions(X0)
| function(regular(recursion_equation_functions(X0))) )
| ~ spl0_32
| ~ spl0_41 ),
inference(resolution,[],[f342,f301]) ).
fof(f1293,plain,
( spl0_193
| ~ spl0_5
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1003,f993,f184,f1291]) ).
fof(f1291,plain,
( spl0_193
<=> ! [X4,X3] :
( section(X3,universal_class,X4)
| ~ subclass(universal_class,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1003,plain,
( ! [X3,X4] :
( section(X3,universal_class,X4)
| ~ subclass(universal_class,X4) )
| ~ spl0_5
| ~ spl0_148 ),
inference(resolution,[],[f994,f185]) ).
fof(f1289,plain,
( spl0_192
| ~ spl0_19
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f820,f746,f246,f1287]) ).
fof(f1287,plain,
( spl0_192
<=> ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f820,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 )
| ~ spl0_19
| ~ spl0_110 ),
inference(duplicate_literal_removal,[],[f819]) ).
fof(f819,plain,
( ! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 )
| ~ spl0_19
| ~ spl0_110 ),
inference(superposition,[],[f747,f247]) ).
fof(f1285,plain,
( spl0_191
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f744,f709,f1283]) ).
fof(f1283,plain,
( spl0_191
<=> ! [X2,X0,X1] : ordinal_multiply(X0,X1) = ordinal_multiply(X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f709,plain,
( spl0_109
<=> ! [X0,X1] : recursion(null_class,apply(add_relation,X0),union_of_range_map) = ordinal_multiply(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f744,plain,
( ! [X2,X0,X1] : ordinal_multiply(X0,X1) = ordinal_multiply(X0,X2)
| ~ spl0_109 ),
inference(superposition,[],[f710,f710]) ).
fof(f710,plain,
( ! [X0,X1] : recursion(null_class,apply(add_relation,X0),union_of_range_map) = ordinal_multiply(X0,X1)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f1281,plain,
( spl0_190
| ~ spl0_12
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f504,f425,f215,f1279]) ).
fof(f1279,plain,
( spl0_190
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f504,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl0_12
| ~ spl0_59 ),
inference(resolution,[],[f426,f216]) ).
fof(f1277,plain,
( spl0_189
| ~ spl0_29
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f503,f421,f287,f1275]) ).
fof(f1275,plain,
( spl0_189
<=> ! [X1] :
( ~ member(X1,limit_ordinals)
| member(X1,complement(kind_1_ordinals)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f503,plain,
( ! [X1] :
( ~ member(X1,limit_ordinals)
| member(X1,complement(kind_1_ordinals)) )
| ~ spl0_29
| ~ spl0_58 ),
inference(superposition,[],[f422,f289]) ).
fof(f1273,plain,
( spl0_188
| ~ spl0_21
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f502,f421,f254,f1271]) ).
fof(f1271,plain,
( spl0_188
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,inverse(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f502,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,inverse(subset_relation)) )
| ~ spl0_21
| ~ spl0_58 ),
inference(superposition,[],[f422,f256]) ).
fof(f1269,plain,
( spl0_187
| ~ spl0_12
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f499,f421,f215,f1267]) ).
fof(f1267,plain,
( spl0_187
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f499,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_12
| ~ spl0_58 ),
inference(resolution,[],[f422,f216]) ).
fof(f1264,plain,
( spl0_186
| ~ spl0_76
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1224,f688,f524,f1261]) ).
fof(f524,plain,
( spl0_76
<=> ! [X0] :
( ~ function(X0)
| single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1224,plain,
( single_valued_class(null_class)
| ~ spl0_76
| ~ spl0_104 ),
inference(resolution,[],[f690,f525]) ).
fof(f525,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f690,plain,
( function(null_class)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f1259,plain,
( spl0_185
| ~ spl0_19
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f497,f409,f246,f1257]) ).
fof(f1257,plain,
( spl0_185
<=> ! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f497,plain,
( ! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) )
| ~ spl0_19
| ~ spl0_55 ),
inference(superposition,[],[f410,f247]) ).
fof(f1251,plain,
( spl0_183
| spl0_184
| ~ spl0_28
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f383,f341,f283,f1248,f1244]) ).
fof(f383,plain,
( null_class = ordinal_numbers
| well_ordering(element_relation,regular(ordinal_numbers))
| ~ spl0_28
| ~ spl0_41 ),
inference(resolution,[],[f342,f284]) ).
fof(f1223,plain,
( spl0_182
| spl0_104
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1217,f1061,f688,f1220]) ).
fof(f1061,plain,
( spl0_159
<=> ! [X1] :
( null_class = recursion_equation_functions(X1)
| function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1217,plain,
( null_class = recursion_equation_functions(null_class)
| spl0_104
| ~ spl0_159 ),
inference(resolution,[],[f1062,f689]) ).
fof(f1062,plain,
( ! [X1] :
( function(X1)
| null_class = recursion_equation_functions(X1) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1061]) ).
fof(f1211,plain,
( spl0_181
| ~ spl0_59
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f624,f565,f425,f1209]) ).
fof(f1209,plain,
( spl0_181
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f624,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_59
| ~ spl0_85 ),
inference(superposition,[],[f426,f567]) ).
fof(f1207,plain,
( spl0_180
| ~ spl0_5
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f588,f535,f184,f1205]) ).
fof(f1205,plain,
( spl0_180
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f588,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_5
| ~ spl0_78 ),
inference(resolution,[],[f536,f185]) ).
fof(f1203,plain,
( spl0_179
| ~ spl0_6
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f582,f531,f188,f1201]) ).
fof(f1201,plain,
( spl0_179
<=> ! [X12] :
( ~ subclass(universal_class,X12)
| member(omega,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f188,plain,
( spl0_6
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f582,plain,
( ! [X12] :
( ~ subclass(universal_class,X12)
| member(omega,X12) )
| ~ spl0_6
| ~ spl0_77 ),
inference(resolution,[],[f532,f190]) ).
fof(f190,plain,
( member(omega,universal_class)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f1199,plain,
( spl0_178
| ~ spl0_29
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f508,f425,f287,f1197]) ).
fof(f1197,plain,
( spl0_178
<=> ! [X1] :
( ~ member(X1,limit_ordinals)
| member(X1,ordinal_numbers) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f508,plain,
( ! [X1] :
( ~ member(X1,limit_ordinals)
| member(X1,ordinal_numbers) )
| ~ spl0_29
| ~ spl0_59 ),
inference(superposition,[],[f426,f289]) ).
fof(f1195,plain,
( spl0_177
| ~ spl0_21
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f507,f425,f254,f1193]) ).
fof(f1193,plain,
( spl0_177
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f507,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_21
| ~ spl0_59 ),
inference(superposition,[],[f426,f256]) ).
fof(f1180,plain,
spl0_176,
inference(avatar_split_clause,[],[f91,f1178]) ).
fof(f1178,plain,
( spl0_176
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',homomorphism6) ).
fof(f1176,plain,
( spl0_175
| ~ spl0_31
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f493,f401,f296,f1174]) ).
fof(f1174,plain,
( spl0_175
<=> ! [X6,X7] :
( subclass(recursion_equation_functions(X6),X7)
| function(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f296,plain,
( spl0_31
<=> ! [X4,X0] :
( function(X4)
| ~ member(X0,recursion_equation_functions(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f493,plain,
( ! [X6,X7] :
( subclass(recursion_equation_functions(X6),X7)
| function(X6) )
| ~ spl0_31
| ~ spl0_53 ),
inference(resolution,[],[f402,f297]) ).
fof(f297,plain,
( ! [X0,X4] :
( ~ member(X0,recursion_equation_functions(X4))
| function(X4) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f1166,plain,
spl0_174,
inference(avatar_split_clause,[],[f89,f1164]) ).
fof(f1164,plain,
( spl0_174
<=> ! [X10,X11,X0,X9,X1] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',homomorphism4) ).
fof(f1160,plain,
spl0_173,
inference(avatar_split_clause,[],[f37,f1158]) ).
fof(f1158,plain,
( spl0_173
<=> ! [X3,X0,X6,X2] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',flip3) ).
fof(f1156,plain,
spl0_172,
inference(avatar_split_clause,[],[f34,f1154]) ).
fof(f1154,plain,
( spl0_172
<=> ! [X3,X0,X6,X2] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rotate3) ).
fof(f1146,plain,
spl0_171,
inference(avatar_split_clause,[],[f108,f1144]) ).
fof(f1144,plain,
( spl0_171
<=> ! [X4,X0,X1] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f108,axiom,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',application_function_defn4) ).
fof(f1142,plain,
spl0_170,
inference(avatar_split_clause,[],[f90,f1140]) ).
fof(f1140,plain,
( spl0_170
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',homomorphism5) ).
fof(f1133,plain,
spl0_169,
inference(avatar_split_clause,[],[f59,f1131]) ).
fof(f1131,plain,
( spl0_169
<=> ! [X4,X7,X5,X1] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose3) ).
fof(f1123,plain,
spl0_168,
inference(avatar_split_clause,[],[f81,f1121]) ).
fof(f1121,plain,
( spl0_168
<=> ! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',operation4) ).
fof(f1119,plain,
spl0_167,
inference(avatar_split_clause,[],[f130,f1117]) ).
fof(f1117,plain,
( spl0_167
<=> ! [X5,X1,X3] :
( ~ connected(X5,X1)
| well_ordering(X5,X1)
| ~ member(X3,not_well_ordering(X5,X1))
| null_class != segment(X5,not_well_ordering(X5,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f130,axiom,
! [X3,X1,X5] :
( ~ connected(X5,X1)
| well_ordering(X5,X1)
| ~ member(X3,not_well_ordering(X5,X1))
| null_class != segment(X5,not_well_ordering(X5,X1),X3) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering8) ).
fof(f1104,plain,
spl0_166,
inference(avatar_split_clause,[],[f151,f1102]) ).
fof(f1102,plain,
( spl0_166
<=> ! [X4,X0] :
( ~ function(X4)
| ~ function(X0)
| ~ member(domain_of(X0),ordinal_numbers)
| member(X0,recursion_equation_functions(X4))
| compose(X4,rest_of(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f151,axiom,
! [X0,X4] :
( ~ function(X4)
| ~ function(X0)
| ~ member(domain_of(X0),ordinal_numbers)
| member(X0,recursion_equation_functions(X4))
| compose(X4,rest_of(X0)) != X0 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',recursion_equation_functions5) ).
fof(f1100,plain,
( ~ spl0_3
| spl0_165
| ~ spl0_12
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f388,f375,f215,f1097,f174]) ).
fof(f174,plain,
( spl0_3
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1097,plain,
( spl0_165
<=> null_class = integer_of(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f388,plain,
( null_class = integer_of(null_class)
| ~ inductive(omega)
| ~ spl0_12
| ~ spl0_49 ),
inference(resolution,[],[f376,f216]) ).
fof(f1095,plain,
spl0_164,
inference(avatar_split_clause,[],[f94,f1093]) ).
fof(f1093,plain,
( spl0_164
<=> ! [X4,X0,X1] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f94,axiom,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose_class_definition3) ).
fof(f1091,plain,
spl0_163,
inference(avatar_split_clause,[],[f85,f1089]) ).
fof(f1089,plain,
( spl0_163
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compatible4) ).
fof(f1083,plain,
spl0_162,
inference(avatar_split_clause,[],[f154,f1081]) ).
fof(f1081,plain,
( spl0_162
<=> ! [X0,X1] :
( sum_class(range_of(X0)) != X1
| member(ordered_pair(X0,X1),union_of_range_map)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f154,axiom,
! [X0,X1] :
( sum_class(range_of(X0)) != X1
| member(ordered_pair(X0,X1),union_of_range_map)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',union_of_range_map3) ).
fof(f1079,plain,
spl0_161,
inference(avatar_split_clause,[],[f119,f1077]) ).
fof(f1077,plain,
( spl0_161
<=> ! [X5,X1] :
( transitive(X5,X1)
| ~ subclass(compose(restrict(X5,X1,X1),restrict(X5,X1,X1)),restrict(X5,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f119,axiom,
! [X1,X5] :
( transitive(X5,X1)
| ~ subclass(compose(restrict(X5,X1,X1),restrict(X5,X1,X1)),restrict(X5,X1,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',transitive2) ).
fof(f1075,plain,
spl0_160,
inference(avatar_split_clause,[],[f118,f1073]) ).
fof(f1073,plain,
( spl0_160
<=> ! [X5,X1] :
( ~ transitive(X5,X1)
| subclass(compose(restrict(X5,X1,X1),restrict(X5,X1,X1)),restrict(X5,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f118,axiom,
! [X1,X5] :
( ~ transitive(X5,X1)
| subclass(compose(restrict(X5,X1,X1),restrict(X5,X1,X1)),restrict(X5,X1,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',transitive1) ).
fof(f1063,plain,
( spl0_159
| ~ spl0_31
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f385,f341,f296,f1061]) ).
fof(f385,plain,
( ! [X1] :
( null_class = recursion_equation_functions(X1)
| function(X1) )
| ~ spl0_31
| ~ spl0_41 ),
inference(resolution,[],[f342,f297]) ).
fof(f1056,plain,
spl0_158,
inference(avatar_split_clause,[],[f143,f1054]) ).
fof(f1054,plain,
( spl0_158
<=> ! [X2,X0,X3] :
( ~ member(X2,domain_of(X0))
| restrict(X0,X2,universal_class) != X3
| member(ordered_pair(X2,X3),rest_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f143,axiom,
! [X2,X3,X0] :
( ~ member(X2,domain_of(X0))
| restrict(X0,X2,universal_class) != X3
| member(ordered_pair(X2,X3),rest_of(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_of4) ).
fof(f1052,plain,
spl0_157,
inference(avatar_split_clause,[],[f127,f1050]) ).
fof(f1050,plain,
( spl0_157
<=> ! [X3,X5,X2,X1] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| ~ member(ordered_pair(X3,least(X5,X2)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f127,axiom,
! [X2,X3,X1,X5] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| ~ member(ordered_pair(X3,least(X5,X2)),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering5) ).
fof(f1048,plain,
spl0_156,
inference(avatar_split_clause,[],[f97,f1046]) ).
fof(f1046,plain,
( spl0_156
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',definition_of_composition_function3) ).
fof(f1044,plain,
spl0_155,
inference(avatar_split_clause,[],[f46,f1042]) ).
fof(f1042,plain,
( spl0_155
<=> ! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',successor_relation3) ).
fof(f1032,plain,
( spl0_154
| ~ spl0_12
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f382,f313,f215,f1030]) ).
fof(f1030,plain,
( spl0_154
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f382,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_12
| ~ spl0_34 ),
inference(resolution,[],[f314,f216]) ).
fof(f1027,plain,
spl0_153,
inference(avatar_split_clause,[],[f162,f1024]) ).
fof(f162,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)),
inference(forward_demodulation,[],[f74,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',restriction2) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',subset_relation) ).
fof(f1022,plain,
spl0_152,
inference(avatar_split_clause,[],[f58,f1020]) ).
fof(f1020,plain,
( spl0_152
<=> ! [X4,X7,X5,X1] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose2) ).
fof(f1018,plain,
spl0_151,
inference(avatar_split_clause,[],[f36,f1016]) ).
fof(f1016,plain,
( spl0_151
<=> ! [X3,X0,X6,X2] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',flip2) ).
fof(f1014,plain,
spl0_150,
inference(avatar_split_clause,[],[f33,f1012]) ).
fof(f1012,plain,
( spl0_150
<=> ! [X3,X0,X6,X2] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rotate2) ).
fof(f1010,plain,
spl0_149,
inference(avatar_split_clause,[],[f20,f1008]) ).
fof(f1008,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',element_relation3) ).
fof(f995,plain,
spl0_148,
inference(avatar_split_clause,[],[f133,f993]) ).
fof(f133,axiom,
! [X1,X4,X5] :
( ~ subclass(X1,X4)
| section(X5,X1,X4)
| ~ subclass(domain_of(restrict(X5,X4,X1)),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',section3) ).
fof(f991,plain,
spl0_147,
inference(avatar_split_clause,[],[f126,f989]) ).
fof(f989,plain,
( spl0_147
<=> ! [X2,X5,X1] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| null_class = segment(X5,X2,least(X5,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f126,axiom,
! [X2,X1,X5] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| null_class = segment(X5,X2,least(X5,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering4) ).
fof(f987,plain,
spl0_146,
inference(avatar_split_clause,[],[f125,f985]) ).
fof(f985,plain,
( spl0_146
<=> ! [X3,X5,X2,X1] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| member(least(X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f125,axiom,
! [X2,X3,X1,X5] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| member(least(X5,X2),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering3) ).
fof(f983,plain,
spl0_145,
inference(avatar_split_clause,[],[f124,f981]) ).
fof(f981,plain,
( spl0_145
<=> ! [X2,X5,X1] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| null_class = X2
| member(least(X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f124,axiom,
! [X2,X1,X5] :
( ~ well_ordering(X5,X1)
| ~ subclass(X2,X1)
| null_class = X2
| member(least(X5,X2),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering2) ).
fof(f979,plain,
spl0_144,
inference(avatar_split_clause,[],[f31,f977]) ).
fof(f977,plain,
( spl0_144
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',domain2) ).
fof(f965,plain,
( spl0_143
| ~ spl0_14
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f555,f524,f223,f963]) ).
fof(f963,plain,
( spl0_143
<=> ! [X0] :
( single_valued_class(inverse(X0))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f223,plain,
( spl0_14
<=> ! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f555,plain,
( ! [X0] :
( single_valued_class(inverse(X0))
| ~ one_to_one(X0) )
| ~ spl0_14
| ~ spl0_76 ),
inference(resolution,[],[f525,f224]) ).
fof(f224,plain,
( ! [X8] :
( function(inverse(X8))
| ~ one_to_one(X8) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f957,plain,
spl0_142,
inference(avatar_split_clause,[],[f137,f955]) ).
fof(f955,plain,
( spl0_142
<=> ! [X0] :
( ~ well_ordering(element_relation,X0)
| ordinal_numbers = X0
| member(X0,ordinal_numbers)
| ~ subclass(sum_class(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f137,axiom,
! [X0] :
( ~ well_ordering(element_relation,X0)
| ordinal_numbers = X0
| member(X0,ordinal_numbers)
| ~ subclass(sum_class(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordinal_numbers4) ).
fof(f953,plain,
spl0_141,
inference(avatar_split_clause,[],[f136,f951]) ).
fof(f136,axiom,
! [X0] :
( ~ well_ordering(element_relation,X0)
| ~ member(X0,universal_class)
| member(X0,ordinal_numbers)
| ~ subclass(sum_class(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordinal_numbers3) ).
fof(f949,plain,
spl0_140,
inference(avatar_split_clause,[],[f103,f947]) ).
fof(f947,plain,
( spl0_140
<=> ! [X0] : domain(X0,image(inverse(X0),singleton(single_valued1(X0))),single_valued2(X0)) = single_valued3(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f103,axiom,
! [X0] : domain(X0,image(inverse(X0),singleton(single_valued1(X0))),single_valued2(X0)) = single_valued3(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',single_valued_term_defn3) ).
fof(f945,plain,
spl0_139,
inference(avatar_split_clause,[],[f64,f943]) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',function3) ).
fof(f941,plain,
spl0_138,
inference(avatar_split_clause,[],[f41,f939]) ).
fof(f939,plain,
( spl0_138
<=> ! [X4,X0,X1] : second(not_subclass_element(restrict(X4,singleton(X0),X1),null_class)) = range(X4,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f41,axiom,
! [X0,X1,X4] : second(not_subclass_element(restrict(X4,singleton(X0),X1),null_class)) = range(X4,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',range) ).
fof(f937,plain,
spl0_137,
inference(avatar_split_clause,[],[f40,f935]) ).
fof(f935,plain,
( spl0_137
<=> ! [X4,X0,X1] : first(not_subclass_element(restrict(X4,X0,singleton(X1)),null_class)) = domain(X4,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f40,axiom,
! [X0,X1,X4] : first(not_subclass_element(restrict(X4,X0,singleton(X1)),null_class)) = domain(X4,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',domain) ).
fof(f933,plain,
spl0_136,
inference(avatar_split_clause,[],[f16,f931]) ).
fof(f931,plain,
( spl0_136
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',cartesian_product3) ).
fof(f908,plain,
spl0_135,
inference(avatar_split_clause,[],[f161,f906]) ).
fof(f161,plain,
! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',union) ).
fof(f27,axiom,
! [X0,X1] : intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',symmetric_difference) ).
fof(f904,plain,
spl0_134,
inference(avatar_split_clause,[],[f142,f902]) ).
fof(f902,plain,
( spl0_134
<=> ! [X2,X0,X3] :
( ~ member(ordered_pair(X2,X3),rest_of(X0))
| restrict(X0,X2,universal_class) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f142,axiom,
! [X2,X3,X0] :
( ~ member(ordered_pair(X2,X3),rest_of(X0))
| restrict(X0,X2,universal_class) = X3 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_of3) ).
fof(f900,plain,
( spl0_133
| ~ spl0_9
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f825,f750,f201,f898]) ).
fof(f898,plain,
( spl0_133
<=> ! [X8,X7] : member(ordered_pair(X7,X8),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f825,plain,
( ! [X8,X7] : member(ordered_pair(X7,X8),universal_class)
| ~ spl0_9
| ~ spl0_111 ),
inference(superposition,[],[f202,f751]) ).
fof(f896,plain,
spl0_132,
inference(avatar_split_clause,[],[f121,f894]) ).
fof(f894,plain,
( spl0_132
<=> ! [X5,X1] :
( asymmetric(X5,X1)
| null_class != restrict(intersection(X5,inverse(X5)),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f121,axiom,
! [X1,X5] :
( asymmetric(X5,X1)
| null_class != restrict(intersection(X5,inverse(X5)),X1,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',asymmetric2) ).
fof(f892,plain,
spl0_131,
inference(avatar_split_clause,[],[f120,f890]) ).
fof(f890,plain,
( spl0_131
<=> ! [X5,X1] :
( ~ asymmetric(X5,X1)
| null_class = restrict(intersection(X5,inverse(X5)),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f120,axiom,
! [X1,X5] :
( ~ asymmetric(X5,X1)
| null_class = restrict(intersection(X5,inverse(X5)),X1,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',asymmetric1) ).
fof(f888,plain,
spl0_130,
inference(avatar_split_clause,[],[f107,f886]) ).
fof(f886,plain,
( spl0_130
<=> ! [X4,X0,X1] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f107,axiom,
! [X0,X1,X4] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',application_function_defn3) ).
fof(f884,plain,
spl0_129,
inference(avatar_split_clause,[],[f96,f882]) ).
fof(f882,plain,
( spl0_129
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f96,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',definition_of_composition_function2) ).
fof(f880,plain,
spl0_128,
inference(avatar_split_clause,[],[f79,f878]) ).
fof(f878,plain,
( spl0_128
<=> ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',operation2) ).
fof(f876,plain,
spl0_127,
inference(avatar_split_clause,[],[f17,f874]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',cartesian_product4) ).
fof(f813,plain,
spl0_126,
inference(avatar_split_clause,[],[f132,f811]) ).
fof(f132,axiom,
! [X1,X4,X5] :
( ~ section(X5,X1,X4)
| subclass(domain_of(restrict(X5,X4,X1)),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',section2) ).
fof(f809,plain,
spl0_125,
inference(avatar_split_clause,[],[f129,f807]) ).
fof(f807,plain,
( spl0_125
<=> ! [X5,X1] :
( ~ connected(X5,X1)
| well_ordering(X5,X1)
| subclass(not_well_ordering(X5,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f129,axiom,
! [X1,X5] :
( ~ connected(X5,X1)
| well_ordering(X5,X1)
| subclass(not_well_ordering(X5,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering7) ).
fof(f805,plain,
spl0_124,
inference(avatar_split_clause,[],[f128,f803]) ).
fof(f803,plain,
( spl0_124
<=> ! [X5,X1] :
( ~ connected(X5,X1)
| well_ordering(X5,X1)
| null_class != not_well_ordering(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f128,axiom,
! [X1,X5] :
( ~ connected(X5,X1)
| well_ordering(X5,X1)
| null_class != not_well_ordering(X5,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering6) ).
fof(f801,plain,
spl0_123,
inference(avatar_split_clause,[],[f122,f799]) ).
fof(f122,axiom,
! [X1,X4,X5] : segment(X5,X1,X4) = domain_of(restrict(X5,X1,singleton(X4))),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',segment) ).
fof(f797,plain,
spl0_122,
inference(avatar_split_clause,[],[f117,f795]) ).
fof(f795,plain,
( spl0_122
<=> ! [X0,X1] :
( connected(X0,X1)
| ~ subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f117,axiom,
! [X0,X1] :
( connected(X0,X1)
| ~ subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',connected2) ).
fof(f793,plain,
spl0_121,
inference(avatar_split_clause,[],[f116,f791]) ).
fof(f791,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ connected(X0,X1)
| subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ connected(X0,X1)
| subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',connected1) ).
fof(f789,plain,
spl0_120,
inference(avatar_split_clause,[],[f112,f787]) ).
fof(f787,plain,
( spl0_120
<=> ! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f112,axiom,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',maps4) ).
fof(f785,plain,
spl0_119,
inference(avatar_split_clause,[],[f106,f783]) ).
fof(f783,plain,
( spl0_119
<=> ! [X4,X0,X1] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f106,axiom,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',application_function_defn2) ).
fof(f781,plain,
spl0_118,
inference(avatar_split_clause,[],[f93,f779]) ).
fof(f779,plain,
( spl0_118
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f93,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose_class_definition2) ).
fof(f777,plain,
( spl0_116
| ~ spl0_117
| ~ spl0_5
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f736,f653,f184,f774,f770]) ).
fof(f770,plain,
( spl0_116
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f774,plain,
( spl0_117
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f653,plain,
( spl0_95
<=> ! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f736,plain,
( ~ member(null_class,universal_class)
| inductive(universal_class)
| ~ spl0_5
| ~ spl0_95 ),
inference(resolution,[],[f654,f185]) ).
fof(f654,plain,
( ! [X0] :
( ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0)
| inductive(X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f768,plain,
spl0_115,
inference(avatar_split_clause,[],[f77,f766]) ).
fof(f77,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',cantor_class) ).
fof(f764,plain,
spl0_114,
inference(avatar_split_clause,[],[f70,f762]) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',choice2) ).
fof(f760,plain,
spl0_113,
inference(avatar_split_clause,[],[f30,f758]) ).
fof(f758,plain,
( spl0_113
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',domain1) ).
fof(f756,plain,
spl0_112,
inference(avatar_split_clause,[],[f23,f754]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',intersection3) ).
fof(f752,plain,
spl0_111,
inference(avatar_split_clause,[],[f13,f750]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordered_pair) ).
fof(f748,plain,
spl0_110,
inference(avatar_split_clause,[],[f8,f746]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',unordered_pair_member) ).
fof(f711,plain,
spl0_109,
inference(avatar_split_clause,[],[f156,f709]) ).
fof(f156,axiom,
! [X0,X1] : recursion(null_class,apply(add_relation,X0),union_of_range_map) = ordinal_multiply(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordinal_multiplication) ).
fof(f707,plain,
spl0_108,
inference(avatar_split_clause,[],[f155,f705]) ).
fof(f705,plain,
( spl0_108
<=> ! [X0,X1] : apply(recursion(X0,successor_relation,union_of_range_map),X1) = ordinal_add(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f155,axiom,
! [X0,X1] : apply(recursion(X0,successor_relation,union_of_range_map),X1) = ordinal_add(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordinal_addition) ).
fof(f703,plain,
spl0_107,
inference(avatar_split_clause,[],[f153,f701]) ).
fof(f701,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),union_of_range_map)
| sum_class(range_of(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f153,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),union_of_range_map)
| sum_class(range_of(X0)) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',union_of_range_map2) ).
fof(f699,plain,
spl0_106,
inference(avatar_split_clause,[],[f150,f697]) ).
fof(f697,plain,
( spl0_106
<=> ! [X4,X0] :
( ~ member(X0,recursion_equation_functions(X4))
| compose(X4,rest_of(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f150,axiom,
! [X0,X4] :
( ~ member(X0,recursion_equation_functions(X4))
| compose(X4,rest_of(X0)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',recursion_equation_functions4) ).
fof(f695,plain,
spl0_105,
inference(avatar_split_clause,[],[f141,f693]) ).
fof(f693,plain,
( spl0_105
<=> ! [X2,X0,X3] :
( member(X2,domain_of(X0))
| ~ member(ordered_pair(X2,X3),rest_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f141,axiom,
! [X2,X3,X0] :
( member(X2,domain_of(X0))
| ~ member(ordered_pair(X2,X3),rest_of(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_of2) ).
fof(f691,plain,
( spl0_103
| spl0_104
| ~ spl0_12
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f311,f300,f215,f688,f685]) ).
fof(f311,plain,
( ! [X0] :
( function(null_class)
| ~ inductive(recursion_equation_functions(X0)) )
| ~ spl0_12
| ~ spl0_32 ),
inference(resolution,[],[f301,f216]) ).
fof(f683,plain,
spl0_102,
inference(avatar_split_clause,[],[f115,f681]) ).
fof(f681,plain,
( spl0_102
<=> ! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(restrict(X0,X1,X1),complement(identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f115,axiom,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(restrict(X0,X1,X1),complement(identity_relation)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',irreflexive2) ).
fof(f679,plain,
spl0_101,
inference(avatar_split_clause,[],[f114,f677]) ).
fof(f677,plain,
( spl0_101
<=> ! [X0,X1] :
( ~ irreflexive(X0,X1)
| subclass(restrict(X0,X1,X1),complement(identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f114,axiom,
! [X0,X1] :
( ~ irreflexive(X0,X1)
| subclass(restrict(X0,X1,X1),complement(identity_relation)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',irreflexive1) ).
fof(f675,plain,
spl0_100,
inference(avatar_split_clause,[],[f102,f673]) ).
fof(f673,plain,
( spl0_100
<=> ! [X0] : second(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued2(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f102,axiom,
! [X0] : second(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued2(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',single_valued_term_defn2) ).
fof(f671,plain,
spl0_99,
inference(avatar_split_clause,[],[f101,f669]) ).
fof(f669,plain,
( spl0_99
<=> ! [X0] : first(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f101,axiom,
! [X0] : first(not_subclass_element(compose(X0,inverse(X0)),identity_relation)) = single_valued1(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',single_valued_term_defn1) ).
fof(f667,plain,
spl0_98,
inference(avatar_split_clause,[],[f84,f665]) ).
fof(f665,plain,
( spl0_98
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compatible3) ).
fof(f663,plain,
spl0_97,
inference(avatar_split_clause,[],[f83,f661]) ).
fof(f661,plain,
( spl0_97
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compatible2) ).
fof(f659,plain,
spl0_96,
inference(avatar_split_clause,[],[f65,f657]) ).
fof(f657,plain,
( spl0_96
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',replacement) ).
fof(f655,plain,
spl0_95,
inference(avatar_split_clause,[],[f49,f653]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',inductive3) ).
fof(f651,plain,
spl0_94,
inference(avatar_split_clause,[],[f29,f649]) ).
fof(f647,plain,
spl0_93,
inference(avatar_split_clause,[],[f28,f645]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',restriction1) ).
fof(f643,plain,
spl0_92,
inference(avatar_split_clause,[],[f26,f641]) ).
fof(f639,plain,
spl0_91,
inference(avatar_split_clause,[],[f25,f637]) ).
fof(f637,plain,
( spl0_91
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',complement2) ).
fof(f635,plain,
spl0_90,
inference(avatar_split_clause,[],[f15,f633]) ).
fof(f633,plain,
( spl0_90
<=> ! [X2,X0,X1,X3] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',cartesian_product2) ).
fof(f631,plain,
spl0_89,
inference(avatar_split_clause,[],[f14,f629]) ).
fof(f629,plain,
( spl0_89
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',cartesian_product1) ).
fof(f616,plain,
( spl0_88
| ~ spl0_4
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f554,f524,f179,f613]) ).
fof(f613,plain,
( spl0_88
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f179,plain,
( spl0_4
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f554,plain,
( single_valued_class(choice)
| ~ spl0_4
| ~ spl0_76 ),
inference(resolution,[],[f525,f181]) ).
fof(f181,plain,
( function(choice)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f576,plain,
spl0_87,
inference(avatar_split_clause,[],[f146,f574]) ).
fof(f146,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,rest_of(X0)),rest_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_relation3) ).
fof(f572,plain,
spl0_86,
inference(avatar_split_clause,[],[f145,f570]) ).
fof(f570,plain,
( spl0_86
<=> ! [X0,X1] :
( rest_of(X0) = X1
| ~ member(ordered_pair(X0,X1),rest_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f145,axiom,
! [X0,X1] :
( rest_of(X0) = X1
| ~ member(ordered_pair(X0,X1),rest_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_relation2) ).
fof(f568,plain,
spl0_85,
inference(avatar_split_clause,[],[f104,f565]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose_can_define_singleton) ).
fof(f563,plain,
spl0_84,
inference(avatar_split_clause,[],[f100,f561]) ).
fof(f100,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',definition_of_domain_relation3) ).
fof(f559,plain,
spl0_83,
inference(avatar_split_clause,[],[f99,f557]) ).
fof(f557,plain,
( spl0_83
<=> ! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f99,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',definition_of_domain_relation2) ).
fof(f553,plain,
spl0_82,
inference(avatar_split_clause,[],[f68,f551]) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',apply) ).
fof(f549,plain,
spl0_81,
inference(avatar_split_clause,[],[f67,f547]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',regularity2) ).
fof(f545,plain,
spl0_80,
inference(avatar_split_clause,[],[f45,f543]) ).
fof(f543,plain,
( spl0_80
<=> ! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',successor_relation2) ).
fof(f541,plain,
spl0_79,
inference(avatar_split_clause,[],[f42,f539]) ).
fof(f539,plain,
( spl0_79
<=> ! [X5,X0] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',image) ).
fof(f537,plain,
spl0_78,
inference(avatar_split_clause,[],[f7,f535]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',subclass_implies_equal) ).
fof(f533,plain,
spl0_77,
inference(avatar_split_clause,[],[f1,f531]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',subclass_members) ).
fof(f526,plain,
( spl0_76
| ~ spl0_66
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f516,f457,f453,f524]) ).
fof(f453,plain,
( spl0_66
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f457,plain,
( spl0_67
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f516,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_66
| ~ spl0_67 ),
inference(resolution,[],[f458,f454]) ).
fof(f454,plain,
( ! [X0] :
( ~ subclass(compose(X0,inverse(X0)),identity_relation)
| single_valued_class(X0) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f458,plain,
( ! [X8] :
( subclass(compose(X8,inverse(X8)),identity_relation)
| ~ function(X8) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f512,plain,
( spl0_75
| ~ spl0_12
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f310,f296,f215,f510]) ).
fof(f510,plain,
( spl0_75
<=> ! [X0] :
( function(X0)
| ~ inductive(recursion_equation_functions(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f310,plain,
( ! [X0] :
( function(X0)
| ~ inductive(recursion_equation_functions(X0)) )
| ~ spl0_12
| ~ spl0_31 ),
inference(resolution,[],[f297,f216]) ).
fof(f488,plain,
spl0_74,
inference(avatar_split_clause,[],[f149,f486]) ).
fof(f149,axiom,
! [X0,X4] :
( ~ member(X0,recursion_equation_functions(X4))
| member(domain_of(X0),ordinal_numbers) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',recursion_equation_functions3) ).
fof(f484,plain,
spl0_73,
inference(avatar_split_clause,[],[f138,f481]) ).
fof(f481,plain,
( spl0_73
<=> union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f138,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',kind_1_ordinals) ).
fof(f479,plain,
spl0_72,
inference(avatar_split_clause,[],[f111,f477]) ).
fof(f477,plain,
( spl0_72
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',maps3) ).
fof(f475,plain,
spl0_71,
inference(avatar_split_clause,[],[f110,f473]) ).
fof(f473,plain,
( spl0_71
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',maps2) ).
fof(f471,plain,
spl0_70,
inference(avatar_split_clause,[],[f88,f469]) ).
fof(f469,plain,
( spl0_70
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',homomorphism3) ).
fof(f467,plain,
spl0_69,
inference(avatar_split_clause,[],[f80,f465]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',operation3) ).
fof(f463,plain,
spl0_68,
inference(avatar_split_clause,[],[f76,f461]) ).
fof(f76,axiom,
! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',diagonalisation) ).
fof(f459,plain,
spl0_67,
inference(avatar_split_clause,[],[f63,f457]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',function2) ).
fof(f455,plain,
spl0_66,
inference(avatar_split_clause,[],[f61,f453]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',single_valued_class2) ).
fof(f451,plain,
spl0_65,
inference(avatar_split_clause,[],[f60,f449]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',single_valued_class1) ).
fof(f447,plain,
spl0_64,
inference(avatar_split_clause,[],[f55,f445]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',power_class_definition) ).
fof(f443,plain,
spl0_63,
inference(avatar_split_clause,[],[f53,f441]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',sum_class_definition) ).
fof(f439,plain,
spl0_62,
inference(avatar_split_clause,[],[f38,f437]) ).
fof(f437,plain,
( spl0_62
<=> ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',inverse) ).
fof(f435,plain,
spl0_61,
inference(avatar_split_clause,[],[f35,f433]) ).
fof(f433,plain,
( spl0_61
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',flip1) ).
fof(f431,plain,
spl0_60,
inference(avatar_split_clause,[],[f32,f429]) ).
fof(f429,plain,
( spl0_60
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rotate1) ).
fof(f427,plain,
spl0_59,
inference(avatar_split_clause,[],[f22,f425]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',intersection2) ).
fof(f423,plain,
spl0_58,
inference(avatar_split_clause,[],[f21,f421]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',intersection1) ).
fof(f419,plain,
spl0_57,
inference(avatar_split_clause,[],[f19,f417]) ).
fof(f417,plain,
( spl0_57
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',element_relation2) ).
fof(f415,plain,
spl0_56,
inference(avatar_split_clause,[],[f10,f413]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',unordered_pair3) ).
fof(f411,plain,
spl0_55,
inference(avatar_split_clause,[],[f9,f409]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',unordered_pair2) ).
fof(f407,plain,
spl0_54,
inference(avatar_split_clause,[],[f3,f405]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',not_subclass_members2) ).
fof(f403,plain,
spl0_53,
inference(avatar_split_clause,[],[f2,f401]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',not_subclass_members1) ).
fof(f399,plain,
( ~ spl0_51
| spl0_52
| ~ spl0_12
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f309,f283,f215,f396,f392]) ).
fof(f392,plain,
( spl0_51
<=> inductive(ordinal_numbers) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f396,plain,
( spl0_52
<=> well_ordering(element_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f309,plain,
( well_ordering(element_relation,null_class)
| ~ inductive(ordinal_numbers)
| ~ spl0_12
| ~ spl0_28 ),
inference(resolution,[],[f284,f216]) ).
fof(f381,plain,
spl0_50,
inference(avatar_split_clause,[],[f158,f379]) ).
fof(f158,axiom,
! [X0] :
( member(X0,omega)
| null_class = integer_of(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',integer_function2) ).
fof(f377,plain,
spl0_49,
inference(avatar_split_clause,[],[f157,f375]) ).
fof(f157,axiom,
! [X0] :
( ~ member(X0,omega)
| integer_of(X0) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',integer_function1) ).
fof(f373,plain,
spl0_48,
inference(avatar_split_clause,[],[f135,f371]) ).
fof(f135,axiom,
! [X0] :
( ~ member(X0,ordinal_numbers)
| subclass(sum_class(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordinal_numbers2) ).
fof(f369,plain,
spl0_47,
inference(avatar_split_clause,[],[f131,f367]) ).
fof(f367,plain,
( spl0_47
<=> ! [X4,X5,X1] :
( subclass(X1,X4)
| ~ section(X5,X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f131,axiom,
! [X1,X4,X5] :
( subclass(X1,X4)
| ~ section(X5,X1,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',section1) ).
fof(f365,plain,
( spl0_46
| ~ spl0_9
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f304,f246,f201,f363]) ).
fof(f363,plain,
( spl0_46
<=> ! [X0] : member(singleton(X0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f304,plain,
( ! [X0] : member(singleton(X0),universal_class)
| ~ spl0_9
| ~ spl0_19 ),
inference(superposition,[],[f202,f247]) ).
fof(f361,plain,
spl0_45,
inference(avatar_split_clause,[],[f113,f359]) ).
fof(f359,plain,
( spl0_45
<=> ! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f113,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',symmetrization) ).
fof(f357,plain,
spl0_44,
inference(avatar_split_clause,[],[f105,f354]) ).
fof(f354,plain,
( spl0_44
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',application_function_defn1) ).
fof(f352,plain,
spl0_43,
inference(avatar_split_clause,[],[f95,f349]) ).
fof(f349,plain,
( spl0_43
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',definition_of_composition_function1) ).
fof(f347,plain,
spl0_42,
inference(avatar_split_clause,[],[f73,f345]) ).
fof(f345,plain,
( spl0_42
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',one_to_one3) ).
fof(f343,plain,
spl0_41,
inference(avatar_split_clause,[],[f66,f341]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',regularity1) ).
fof(f339,plain,
spl0_40,
inference(avatar_split_clause,[],[f62,f337]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',function1) ).
fof(f335,plain,
spl0_39,
inference(avatar_split_clause,[],[f57,f333]) ).
fof(f333,plain,
( spl0_39
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose1) ).
fof(f331,plain,
spl0_38,
inference(avatar_split_clause,[],[f56,f329]) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',power_class2) ).
fof(f327,plain,
spl0_37,
inference(avatar_split_clause,[],[f54,f325]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',sum_class2) ).
fof(f323,plain,
spl0_36,
inference(avatar_split_clause,[],[f48,f321]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',inductive2) ).
fof(f319,plain,
spl0_35,
inference(avatar_split_clause,[],[f43,f317]) ).
fof(f317,plain,
( spl0_35
<=> ! [X0] : union(X0,singleton(X0)) = successor(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',successor) ).
fof(f315,plain,
spl0_34,
inference(avatar_split_clause,[],[f24,f313]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',complement1) ).
fof(f308,plain,
( spl0_33
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f303,f242,f306]) ).
fof(f306,plain,
( spl0_33
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f242,plain,
( spl0_18
<=> ! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f303,plain,
( ! [X0] : subclass(X0,X0)
| ~ spl0_18 ),
inference(equality_resolution,[],[f243]) ).
fof(f243,plain,
( ! [X0,X1] :
( X0 != X1
| subclass(X1,X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f302,plain,
spl0_32,
inference(avatar_split_clause,[],[f148,f300]) ).
fof(f148,axiom,
! [X0,X4] :
( function(X0)
| ~ member(X0,recursion_equation_functions(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',recursion_equation_functions2) ).
fof(f298,plain,
spl0_31,
inference(avatar_split_clause,[],[f147,f296]) ).
fof(f147,axiom,
! [X0,X4] :
( function(X4)
| ~ member(X0,recursion_equation_functions(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',recursion_equation_functions1) ).
fof(f294,plain,
spl0_30,
inference(avatar_split_clause,[],[f140,f292]) ).
fof(f140,axiom,
! [X0] : subclass(rest_of(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_of1) ).
fof(f290,plain,
spl0_29,
inference(avatar_split_clause,[],[f139,f287]) ).
fof(f139,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',limit_ordinals) ).
fof(f285,plain,
spl0_28,
inference(avatar_split_clause,[],[f134,f283]) ).
fof(f134,axiom,
! [X0] :
( ~ member(X0,ordinal_numbers)
| well_ordering(element_relation,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',ordinal_numbers1) ).
fof(f281,plain,
spl0_27,
inference(avatar_split_clause,[],[f123,f279]) ).
fof(f123,axiom,
! [X0,X1] :
( ~ well_ordering(X0,X1)
| connected(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',well_ordering1) ).
fof(f277,plain,
spl0_26,
inference(avatar_split_clause,[],[f109,f275]) ).
fof(f275,plain,
( spl0_26
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',maps1) ).
fof(f273,plain,
spl0_25,
inference(avatar_split_clause,[],[f92,f271]) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compose_class_definition1) ).
fof(f269,plain,
spl0_24,
inference(avatar_split_clause,[],[f87,f267]) ).
fof(f267,plain,
( spl0_24
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',homomorphism2) ).
fof(f265,plain,
spl0_23,
inference(avatar_split_clause,[],[f86,f263]) ).
fof(f263,plain,
( spl0_23
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',homomorphism1) ).
fof(f261,plain,
spl0_22,
inference(avatar_split_clause,[],[f82,f259]) ).
fof(f259,plain,
( spl0_22
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',compatible1) ).
fof(f257,plain,
spl0_21,
inference(avatar_split_clause,[],[f75,f254]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',identity_relation) ).
fof(f252,plain,
spl0_20,
inference(avatar_split_clause,[],[f39,f250]) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',range_of) ).
fof(f248,plain,
spl0_19,
inference(avatar_split_clause,[],[f12,f246]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',singleton_set) ).
fof(f244,plain,
spl0_18,
inference(avatar_split_clause,[],[f6,f242]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',equal_implies_subclass2) ).
fof(f240,plain,
spl0_17,
inference(avatar_split_clause,[],[f152,f237]) ).
fof(f152,axiom,
subclass(union_of_range_map,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',union_of_range_map1) ).
fof(f235,plain,
spl0_16,
inference(avatar_split_clause,[],[f144,f232]) ).
fof(f144,axiom,
subclass(rest_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',rest_relation1) ).
fof(f230,plain,
spl0_15,
inference(avatar_split_clause,[],[f98,f227]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',definition_of_domain_relation1) ).
fof(f225,plain,
spl0_14,
inference(avatar_split_clause,[],[f72,f223]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',one_to_one2) ).
fof(f221,plain,
spl0_13,
inference(avatar_split_clause,[],[f51,f219]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',omega_is_inductive2) ).
fof(f217,plain,
spl0_12,
inference(avatar_split_clause,[],[f47,f215]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',inductive1) ).
fof(f213,plain,
spl0_11,
inference(avatar_split_clause,[],[f44,f210]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',successor_relation1) ).
fof(f208,plain,
spl0_10,
inference(avatar_split_clause,[],[f18,f205]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',element_relation1) ).
fof(f203,plain,
spl0_9,
inference(avatar_split_clause,[],[f11,f201]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',unordered_pairs_in_universal) ).
fof(f199,plain,
spl0_8,
inference(avatar_split_clause,[],[f78,f197]) ).
fof(f197,plain,
( spl0_8
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',operation1) ).
fof(f195,plain,
spl0_7,
inference(avatar_split_clause,[],[f71,f193]) ).
fof(f193,plain,
( spl0_7
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',one_to_one1) ).
fof(f191,plain,
spl0_6,
inference(avatar_split_clause,[],[f52,f188]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',omega_in_universal) ).
fof(f186,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f184]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',class_elements_are_sets) ).
fof(f182,plain,
spl0_4,
inference(avatar_split_clause,[],[f69,f179]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',choice1) ).
fof(f177,plain,
spl0_3,
inference(avatar_split_clause,[],[f50,f174]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',omega_is_inductive1) ).
fof(f172,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f159,f169]) ).
fof(f159,axiom,
~ member(not_subclass_element(intersection(power_class(x),z),x),z),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',prove_complete_induction3_1) ).
fof(f167,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f160,f164]) ).
fof(f160,axiom,
~ subclass(intersection(power_class(x),z),x),
file('/export/starexec/sandbox2/tmp/tmp.oLF8o1u8nX/Vampire---4.8_26953',prove_complete_induction3_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : NUM139-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n024.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 30 15:10:53 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.21/0.43 % (27073)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.44 % (27074)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.44 % (27077)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.44 % (27075)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.44 % (27078)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.21/0.44 % (27076)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.21/0.44 % (27079)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.21/0.44 % (27080)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.21/0.45 TRYING [1]
% 0.21/0.45 TRYING [2]
% 0.21/0.47 TRYING [1]
% 0.21/0.47 TRYING [2]
% 0.21/0.48 TRYING [3]
% 0.21/0.51 % (27078)First to succeed.
% 0.21/0.52 TRYING [1]
% 0.21/0.52 TRYING [2]
% 0.21/0.52 % (27078)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Unsatisfiable for Vampire---4
% 0.21/0.52 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.53 % (27078)------------------------------
% 0.21/0.53 % (27078)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.53 % (27078)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.53 % (27078)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (27078)Memory used [KB]: 7803
% 0.21/0.53 % (27078)Time elapsed: 0.083 s
% 0.21/0.53 % (27078)------------------------------
% 0.21/0.53 % (27078)------------------------------
% 0.21/0.53 % (27073)Success in time 0.151 s
% 0.21/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------