%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET231-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.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 : Sun May  5 09:12:51 EDT 2024

% Result   : Unsatisfiable 0.16s 0.48s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  382
% Syntax   : Number of formulae    :  982 ( 138 unt;   0 def)
%            Number of atoms       : 2938 ( 276 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives : 3528 (1572   ~;1679   |;   0   &)
%                                         ( 277 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :   27 (   4 avg)
%            Number of predicates  :  289 ( 287 usr; 278 prp; 0-3 aty)
%            Number of functors    :   41 (  41 usr;  15 con; 0-3 aty)
%            Number of variables   : 1263 (1263   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2691,plain,
    $false,
    inference(avatar_sat_refutation,[],[f209,f214,f219,f223,f228,f232,f236,f240,f244,f249,f254,f258,f262,f267,f271,f275,f279,f283,f287,f291,f295,f299,f303,f308,f313,f318,f323,f327,f331,f335,f339,f343,f347,f351,f355,f359,f363,f376,f380,f384,f389,f393,f398,f429,f433,f437,f441,f445,f453,f457,f461,f465,f469,f473,f477,f481,f508,f512,f516,f520,f525,f533,f537,f541,f548,f552,f561,f565,f569,f573,f578,f582,f593,f597,f601,f605,f618,f622,f633,f637,f646,f654,f659,f663,f673,f678,f682,f686,f691,f695,f701,f705,f711,f727,f732,f736,f740,f744,f748,f754,f759,f766,f770,f788,f798,f813,f820,f824,f828,f832,f893,f897,f901,f924,f928,f937,f947,f956,f960,f964,f968,f972,f977,f1013,f1017,f1021,f1025,f1029,f1033,f1092,f1096,f1105,f1109,f1113,f1117,f1164,f1168,f1172,f1176,f1180,f1230,f1239,f1248,f1252,f1256,f1287,f1291,f1295,f1299,f1303,f1307,f1325,f1329,f1360,f1370,f1374,f1378,f1382,f1386,f1453,f1457,f1461,f1465,f1474,f1482,f1486,f1524,f1532,f1539,f1552,f1558,f1565,f1587,f1593,f1606,f1611,f1623,f1629,f1648,f1665,f1669,f1714,f1720,f1754,f1782,f1803,f1808,f1818,f1822,f1878,f1916,f1923,f1933,f1945,f1955,f2004,f2008,f2036,f2066,f2077,f2090,f2103,f2107,f2120,f2130,f2134,f2147,f2149,f2233,f2237,f2267,f2271,f2275,f2287,f2297,f2315,f2321,f2344,f2352,f2357,f2362,f2366,f2370,f2374,f2382,f2387,f2391,f2396,f2404,f2412,f2420,f2424,f2434,f2443,f2454,f2458,f2462,f2466,f2471,f2489,f2498,f2505,f2509,f2513,f2529,f2535,f2539,f2548,f2566,f2690]) ).

fof(f2690,plain,
    ( spl0_44
    | spl0_1
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1794,f1780,f206,f426]) ).

fof(f426,plain,
    ( spl0_44
  <=> not_subclass_element(cross_product(x,y),z) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f206,plain,
    ( spl0_1
  <=> subclass(cross_product(x,y),z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f1780,plain,
    ( spl0_201
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1794,plain,
    ( not_subclass_element(cross_product(x,y),z) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z)))))
    | spl0_1
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f208]) ).

fof(f208,plain,
    ( ~ subclass(cross_product(x,y),z)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f1781,plain,
    ( ! [X2,X0,X1] :
        ( subclass(cross_product(X0,X1),X2)
        | not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))))) )
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f1780]) ).

fof(f2566,plain,
    ( spl0_277
    | ~ spl0_4
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1257,f1250,f221,f2564]) ).

fof(f2564,plain,
    ( spl0_277
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f221,plain,
    ( spl0_4
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1250,plain,
    ( spl0_152
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1257,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_152 ),
    inference(resolution,[],[f1251,f222]) ).

fof(f222,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f221]) ).

fof(f1251,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1250]) ).

fof(f2548,plain,
    ( spl0_275
    | spl0_276
    | ~ spl0_77
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1047,f1011,f615,f2545,f2541]) ).

fof(f2541,plain,
    ( spl0_275
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f2545,plain,
    ( spl0_276
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f615,plain,
    ( spl0_77
  <=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1011,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f1047,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_77
    | ~ spl0_129 ),
    inference(superposition,[],[f1012,f617]) ).

fof(f617,plain,
    ( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f615]) ).

fof(f1012,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1011]) ).

fof(f2539,plain,
    ( spl0_274
    | ~ spl0_20
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f999,f962,f289,f2537]) ).

fof(f2537,plain,
    ( spl0_274
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f289,plain,
    ( spl0_20
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f962,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f999,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_20
    | ~ spl0_125 ),
    inference(resolution,[],[f963,f290]) ).

fof(f290,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f963,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f962]) ).

fof(f2535,plain,
    ( ~ spl0_273
    | spl0_272
    | ~ spl0_25
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f877,f822,f310,f2526,f2532]) ).

fof(f2532,plain,
    ( spl0_273
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f2526,plain,
    ( spl0_272
  <=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f310,plain,
    ( spl0_25
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f822,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f877,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_25
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f312]) ).

fof(f312,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f310]) ).

fof(f823,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f822]) ).

fof(f2529,plain,
    ( ~ spl0_271
    | spl0_272
    | ~ spl0_24
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f875,f822,f305,f2526,f2522]) ).

fof(f2522,plain,
    ( spl0_271
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f305,plain,
    ( spl0_24
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f875,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_24
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f307]) ).

fof(f307,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f2513,plain,
    ( spl0_270
    | spl0_183
    | ~ spl0_22
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f863,f822,f297,f1545,f2511]) ).

fof(f2511,plain,
    ( spl0_270
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f1545,plain,
    ( spl0_183
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f297,plain,
    ( spl0_22
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f863,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f298]) ).

fof(f298,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f297]) ).

fof(f2509,plain,
    ( spl0_269
    | ~ spl0_20
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f857,f818,f289,f2507]) ).

fof(f2507,plain,
    ( spl0_269
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f818,plain,
    ( spl0_109
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f857,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_20
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f290]) ).

fof(f819,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f818]) ).

fof(f2505,plain,
    ( spl0_268
    | ~ spl0_73
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f840,f818,f591,f2503]) ).

fof(f2503,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f591,plain,
    ( spl0_73
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f840,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_73
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f592]) ).

fof(f592,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
        | compose(X0,X1) = X4 )
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f591]) ).

fof(f2498,plain,
    ( ~ spl0_267
    | ~ spl0_112
    | spl0_231 ),
    inference(avatar_split_clause,[],[f2288,f2284,f830,f2495]) ).

fof(f2495,plain,
    ( spl0_267
  <=> member(omega,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f830,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2284,plain,
    ( spl0_231
  <=> member(omega,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2288,plain,
    ( ~ member(omega,subset_relation)
    | ~ spl0_112
    | spl0_231 ),
    inference(resolution,[],[f2285,f831]) ).

fof(f831,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f830]) ).

fof(f2285,plain,
    ( ~ member(omega,cross_product(universal_class,universal_class))
    | spl0_231 ),
    inference(avatar_component_clause,[],[f2284]) ).

fof(f2489,plain,
    ( spl0_266
    | ~ spl0_38
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2437,f1545,f374,f2487]) ).

fof(f2487,plain,
    ( spl0_266
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f374,plain,
    ( spl0_38
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f2437,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_183 ),
    inference(resolution,[],[f1546,f375]) ).

fof(f375,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f374]) ).

fof(f1546,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1545]) ).

fof(f2471,plain,
    ( spl0_265
    | ~ spl0_43
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2259,f2235,f395,f2468]) ).

fof(f2468,plain,
    ( spl0_265
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f395,plain,
    ( spl0_43
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f2235,plain,
    ( spl0_225
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2259,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_43
    | ~ spl0_225 ),
    inference(superposition,[],[f2236,f397]) ).

fof(f397,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f395]) ).

fof(f2236,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f2235]) ).

fof(f2466,plain,
    ( spl0_264
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1078,f1019,f922,f2464]) ).

fof(f2464,plain,
    ( spl0_264
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f922,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1019,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f1078,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(duplicate_literal_removal,[],[f1067]) ).

fof(f1067,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f923]) ).

fof(f923,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f922]) ).

fof(f1020,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1019]) ).

fof(f2462,plain,
    ( spl0_263
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f994,f926,f891,f2460]) ).

fof(f2460,plain,
    ( spl0_263
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f891,plain,
    ( spl0_113
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f926,plain,
    ( spl0_117
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f994,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(duplicate_literal_removal,[],[f983]) ).

fof(f983,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f892]) ).

fof(f892,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f891]) ).

fof(f927,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f926]) ).

fof(f2458,plain,
    ( spl0_262
    | ~ spl0_21
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f918,f899,f293,f2456]) ).

fof(f2456,plain,
    ( spl0_262
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f293,plain,
    ( spl0_21
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f899,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f918,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f294]) ).

fof(f294,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f293]) ).

fof(f900,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f899]) ).

fof(f2454,plain,
    ( ~ spl0_260
    | spl0_261
    | ~ spl0_6
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f913,f899,f230,f2451,f2447]) ).

fof(f2447,plain,
    ( spl0_260
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f2451,plain,
    ( spl0_261
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f230,plain,
    ( spl0_6
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f913,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f231]) ).

fof(f231,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f2443,plain,
    ( ~ spl0_259
    | ~ spl0_112
    | spl0_258 ),
    inference(avatar_split_clause,[],[f2438,f2431,f830,f2440]) ).

fof(f2440,plain,
    ( spl0_259
  <=> member(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f2431,plain,
    ( spl0_258
  <=> member(identity_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f2438,plain,
    ( ~ member(identity_relation,subset_relation)
    | ~ spl0_112
    | spl0_258 ),
    inference(resolution,[],[f2432,f831]) ).

fof(f2432,plain,
    ( ~ member(identity_relation,cross_product(universal_class,universal_class))
    | spl0_258 ),
    inference(avatar_component_clause,[],[f2431]) ).

fof(f2434,plain,
    ( spl0_258
    | ~ spl0_183
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2429,f2308,f1545,f2431]) ).

fof(f2308,plain,
    ( spl0_234
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f2429,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_183
    | ~ spl0_234 ),
    inference(forward_demodulation,[],[f1546,f2310]) ).

fof(f2310,plain,
    ( null_class = identity_relation
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2308]) ).

fof(f2424,plain,
    ( spl0_257
    | spl0_183
    | ~ spl0_18
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f874,f822,f281,f1545,f2422]) ).

fof(f2422,plain,
    ( spl0_257
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f281,plain,
    ( spl0_18
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f874,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f282]) ).

fof(f282,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f281]) ).

fof(f2420,plain,
    ( spl0_255
    | ~ spl0_256
    | ~ spl0_98
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f860,f818,f738,f2417,f2414]) ).

fof(f2414,plain,
    ( spl0_255
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f2417,plain,
    ( spl0_256
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f738,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f860,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_98
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f739]) ).

fof(f739,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f738]) ).

fof(f2412,plain,
    ( spl0_253
    | ~ spl0_254
    | ~ spl0_103
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f859,f818,f764,f2409,f2406]) ).

fof(f2406,plain,
    ( spl0_253
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f2409,plain,
    ( spl0_254
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f764,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f859,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f765]) ).

fof(f765,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f764]) ).

fof(f2404,plain,
    ( spl0_251
    | ~ spl0_252
    | ~ spl0_88
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f844,f818,f680,f2401,f2398]) ).

fof(f2398,plain,
    ( spl0_251
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f2401,plain,
    ( spl0_252
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f680,plain,
    ( spl0_88
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f844,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_88
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f681]) ).

fof(f681,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
        | compose(X0,X1) = X4 )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f680]) ).

fof(f2396,plain,
    ( spl0_250
    | ~ spl0_41
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2258,f2235,f386,f2393]) ).

fof(f2393,plain,
    ( spl0_250
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f386,plain,
    ( spl0_41
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f2258,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_41
    | ~ spl0_225 ),
    inference(superposition,[],[f2236,f388]) ).

fof(f388,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f386]) ).

fof(f2391,plain,
    ( spl0_249
    | ~ spl0_68
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f834,f818,f563,f2389]) ).

fof(f2389,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f563,plain,
    ( spl0_68
  <=> ! [X0,X3,X2,X1] :
        ( member(X3,X1)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f834,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_68
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f564]) ).

fof(f564,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X3,X1) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f563]) ).

fof(f2387,plain,
    ( spl0_248
    | ~ spl0_69
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f833,f818,f567,f2385]) ).

fof(f2385,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f567,plain,
    ( spl0_69
  <=> ! [X0,X3,X2,X1] :
        ( member(X2,X0)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f833,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_69
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f568]) ).

fof(f568,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f567]) ).

fof(f2382,plain,
    ( spl0_246
    | ~ spl0_247
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f789,f391,f382,f2379,f2376]) ).

fof(f2376,plain,
    ( spl0_246
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2379,plain,
    ( spl0_247
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f382,plain,
    ( spl0_40
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f391,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f789,plain,
    ( ! [X0] :
        ( ~ inductive(null_class)
        | member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(superposition,[],[f392,f383]) ).

fof(f383,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f382]) ).

fof(f392,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(null_class,X0) )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f391]) ).

fof(f2374,plain,
    ( spl0_245
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f781,f764,f321,f2372]) ).

fof(f2372,plain,
    ( spl0_245
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f321,plain,
    ( spl0_27
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f781,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f322]) ).

fof(f322,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f321]) ).

fof(f2370,plain,
    ( spl0_244
    | ~ spl0_27
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f777,f738,f321,f2368]) ).

fof(f2368,plain,
    ( spl0_244
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f777,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_27
    | ~ spl0_98 ),
    inference(resolution,[],[f739,f322]) ).

fof(f2366,plain,
    ( spl0_243
    | ~ spl0_37
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f543,f514,f361,f2364]) ).

fof(f2364,plain,
    ( spl0_243
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f361,plain,
    ( spl0_37
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f514,plain,
    ( spl0_59
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f543,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_37
    | ~ spl0_59 ),
    inference(resolution,[],[f515,f362]) ).

fof(f362,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f361]) ).

fof(f515,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f514]) ).

fof(f2362,plain,
    ( ~ spl0_242
    | spl0_183
    | ~ spl0_14
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f876,f822,f264,f1545,f2359]) ).

fof(f2359,plain,
    ( spl0_242
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f264,plain,
    ( spl0_14
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f876,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_14
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f266]) ).

fof(f266,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f2357,plain,
    ( ~ spl0_241
    | spl0_183
    | ~ spl0_11
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f869,f822,f251,f1545,f2354]) ).

fof(f2354,plain,
    ( spl0_241
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f251,plain,
    ( spl0_11
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f869,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_11
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f253]) ).

fof(f253,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f251]) ).

fof(f2352,plain,
    ( spl0_239
    | ~ spl0_240
    | ~ spl0_87
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f843,f818,f676,f2349,f2346]) ).

fof(f2346,plain,
    ( spl0_239
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f2349,plain,
    ( spl0_240
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f676,plain,
    ( spl0_87
  <=> ! [X4,X0,X1] :
        ( member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f843,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_87
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f677]) ).

fof(f677,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
        | member(X1,domain_of(X0)) )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f676]) ).

fof(f2344,plain,
    ( spl0_237
    | ~ spl0_238
    | ~ spl0_65
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f841,f818,f546,f2341,f2338]) ).

fof(f2338,plain,
    ( spl0_237
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f2341,plain,
    ( spl0_238
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f546,plain,
    ( spl0_65
  <=> ! [X0,X1] :
        ( domain_of(X0) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f841,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_65
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f547]) ).

fof(f547,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f546]) ).

fof(f2321,plain,
    ( spl0_236
    | ~ spl0_232
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2316,f2308,f2290,f2318]) ).

fof(f2318,plain,
    ( spl0_236
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f2290,plain,
    ( spl0_232
  <=> null_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f2316,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_232
    | ~ spl0_234 ),
    inference(forward_demodulation,[],[f2310,f2292]) ).

fof(f2292,plain,
    ( null_class = singleton_relation
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2290]) ).

fof(f2315,plain,
    ( spl0_234
    | spl0_235
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f784,f764,f301,f2312,f2308]) ).

fof(f2312,plain,
    ( spl0_235
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f301,plain,
    ( spl0_23
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f784,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f302]) ).

fof(f302,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f2297,plain,
    ( spl0_232
    | spl0_233
    | ~ spl0_23
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f780,f738,f301,f2294,f2290]) ).

fof(f2294,plain,
    ( spl0_233
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f780,plain,
    ( member(regular(singleton_relation),element_relation)
    | null_class = singleton_relation
    | ~ spl0_23
    | ~ spl0_98 ),
    inference(resolution,[],[f739,f302]) ).

fof(f2287,plain,
    ( ~ spl0_230
    | spl0_231
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f773,f439,f297,f2284,f2280]) ).

fof(f2280,plain,
    ( spl0_230
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f439,plain,
    ( spl0_47
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f773,plain,
    ( member(omega,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(resolution,[],[f440,f298]) ).

fof(f440,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f439]) ).

fof(f2275,plain,
    ( spl0_229
    | ~ spl0_38
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f2179,f639,f374,f2273]) ).

fof(f2273,plain,
    ( spl0_229
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f639,plain,
    ( spl0_81
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f2179,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_81 ),
    inference(resolution,[],[f640,f375]) ).

fof(f640,plain,
    ( member(null_class,universal_class)
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f639]) ).

fof(f2271,plain,
    ( spl0_228
    | ~ spl0_18
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f919,f899,f281,f2269]) ).

fof(f2269,plain,
    ( spl0_228
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f919,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f282]) ).

fof(f2267,plain,
    ( spl0_226
    | ~ spl0_227
    | ~ spl0_62
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f836,f818,f531,f2264,f2261]) ).

fof(f2261,plain,
    ( spl0_226
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f2264,plain,
    ( spl0_227
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f531,plain,
    ( spl0_62
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f836,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_62
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f532]) ).

fof(f532,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f531]) ).

fof(f2237,plain,
    ( spl0_225
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1153,f1094,f325,f2235]) ).

fof(f325,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1094,plain,
    ( spl0_136
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1153,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1136]) ).

fof(f1136,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f326]) ).

fof(f326,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f325]) ).

fof(f1095,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1094]) ).

fof(f2233,plain,
    ( spl0_224
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1135,f1090,f325,f2231]) ).

fof(f2231,plain,
    ( spl0_224
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f1090,plain,
    ( spl0_135
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1135,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(duplicate_literal_removal,[],[f1118]) ).

fof(f1118,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f326]) ).

fof(f1091,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1090]) ).

fof(f2149,plain,
    ( ~ spl0_2
    | ~ spl0_223 ),
    inference(avatar_contradiction_clause,[],[f2148]) ).

fof(f2148,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_223 ),
    inference(resolution,[],[f2146,f213]) ).

fof(f213,plain,
    ( inductive(omega)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f211,plain,
    ( spl0_2
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f2146,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2145]) ).

fof(f2145,plain,
    ( spl0_223
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f2147,plain,
    ( spl0_223
    | spl0_81
    | ~ spl0_4
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f861,f822,f221,f639,f2145]) ).

fof(f861,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_4
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f222]) ).

fof(f2134,plain,
    ( spl0_222
    | ~ spl0_91
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f713,f709,f693,f2132]) ).

fof(f2132,plain,
    ( spl0_222
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f693,plain,
    ( spl0_91
  <=> ! [X9,X11,X10] :
        ( ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f709,plain,
    ( spl0_94
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f713,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_91
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f694]) ).

fof(f694,plain,
    ( ! [X10,X11,X9] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | ~ operation(X10) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f693]) ).

fof(f710,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f709]) ).

fof(f2130,plain,
    ( spl0_221
    | ~ spl0_51
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f762,f757,f693,f459,f2128]) ).

fof(f2128,plain,
    ( spl0_221
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f459,plain,
    ( spl0_51
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f757,plain,
    ( spl0_102
  <=> ! [X10,X11,X0,X9,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
        | ~ homomorphism(X9,X10,X11)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f762,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_51
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(forward_demodulation,[],[f760,f460]) ).

fof(f460,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f459]) ).

fof(f760,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(resolution,[],[f758,f694]) ).

fof(f758,plain,
    ( ! [X10,X0,X11,X1,X9] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
        | ~ homomorphism(X9,X10,X11)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f757]) ).

fof(f2120,plain,
    ( spl0_220
    | ~ spl0_72
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f761,f757,f580,f2118]) ).

fof(f2118,plain,
    ( spl0_220
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f580,plain,
    ( spl0_72
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,domain_of(X0))
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f761,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_72
    | ~ spl0_102 ),
    inference(resolution,[],[f758,f581]) ).

fof(f581,plain,
    ( ! [X0,X4] :
        ( member(X4,domain_of(X0))
        | ~ member(X4,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f580]) ).

fof(f2107,plain,
    ( spl0_219
    | ~ spl0_85
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f716,f709,f661,f2105]) ).

fof(f2105,plain,
    ( spl0_219
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f661,plain,
    ( spl0_85
  <=> ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f716,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_85
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f662]) ).

fof(f662,plain,
    ( ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f661]) ).

fof(f2103,plain,
    ( spl0_218
    | ~ spl0_80
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f666,f661,f635,f2101]) ).

fof(f2101,plain,
    ( spl0_218
  <=> ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f635,plain,
    ( spl0_80
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f666,plain,
    ( ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
    | ~ spl0_80
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f636]) ).

fof(f636,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f635]) ).

fof(f2090,plain,
    ( spl0_217
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f714,f709,f321,f2088]) ).

fof(f2088,plain,
    ( spl0_217
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f714,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f322]) ).

fof(f2077,plain,
    ( spl0_216
    | ~ spl0_23
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f717,f709,f301,f2075]) ).

fof(f2075,plain,
    ( spl0_216
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f717,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f302]) ).

fof(f2066,plain,
    ( spl0_215
    | ~ spl0_78
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f755,f752,f620,f2064]) ).

fof(f2064,plain,
    ( spl0_215
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f620,plain,
    ( spl0_78
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,X0)
        | ~ member(X3,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f752,plain,
    ( spl0_101
  <=> ! [X4,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f755,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) )
    | ~ spl0_78
    | ~ spl0_101 ),
    inference(resolution,[],[f753,f621]) ).

fof(f621,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | ~ member(X3,X1)
        | ~ member(X2,X0) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f620]) ).

fof(f753,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f752]) ).

fof(f2036,plain,
    ( ~ spl0_214
    | spl0_192
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f782,f764,f256,f1608,f2033]) ).

fof(f2033,plain,
    ( spl0_214
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f1608,plain,
    ( spl0_192
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f256,plain,
    ( spl0_12
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f782,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f257]) ).

fof(f257,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f2008,plain,
    ( spl0_213
    | ~ spl0_78
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f750,f746,f620,f2006]) ).

fof(f2006,plain,
    ( spl0_213
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f746,plain,
    ( spl0_100
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f750,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f621]) ).

fof(f747,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f746]) ).

fof(f2004,plain,
    ( spl0_212
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f749,f742,f620,f2002]) ).

fof(f2002,plain,
    ( spl0_212
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f742,plain,
    ( spl0_99
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f749,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(resolution,[],[f743,f621]) ).

fof(f743,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f742]) ).

fof(f1955,plain,
    ( spl0_211
    | ~ spl0_78
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f647,f635,f620,f1953]) ).

fof(f1953,plain,
    ( spl0_211
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f647,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) )
    | ~ spl0_78
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f621]) ).

fof(f1945,plain,
    ( spl0_210
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f722,f709,f382,f1943]) ).

fof(f1943,plain,
    ( spl0_210
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f722,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f383]) ).

fof(f1933,plain,
    ( spl0_209
    | ~ spl0_72
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f712,f709,f580,f1931]) ).

fof(f1931,plain,
    ( spl0_209
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f712,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_72
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f581]) ).

fof(f1923,plain,
    ( spl0_208
    | ~ spl0_49
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f665,f661,f451,f1921]) ).

fof(f1921,plain,
    ( spl0_208
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f451,plain,
    ( spl0_49
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f665,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_49
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f452]) ).

fof(f452,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f451]) ).

fof(f1916,plain,
    ( spl0_207
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f719,f709,f382,f1914]) ).

fof(f1914,plain,
    ( spl0_207
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f719,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f383]) ).

fof(f1878,plain,
    ( spl0_206
    | ~ spl0_38
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f707,f703,f374,f1876]) ).

fof(f1876,plain,
    ( spl0_206
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f703,plain,
    ( spl0_93
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f707,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
    | ~ spl0_38
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f375]) ).

fof(f704,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f703]) ).

fof(f1822,plain,
    ( spl0_205
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f721,f709,f459,f1820]) ).

fof(f1820,plain,
    ( spl0_205
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f721,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f460]) ).

fof(f1818,plain,
    ( spl0_204
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f718,f709,f459,f1816]) ).

fof(f1816,plain,
    ( spl0_204
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f718,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f460]) ).

fof(f1808,plain,
    ( ~ spl0_203
    | ~ spl0_12
    | spl0_192 ),
    inference(avatar_split_clause,[],[f1690,f1608,f256,f1805]) ).

fof(f1805,plain,
    ( spl0_203
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1690,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_12
    | spl0_192 ),
    inference(resolution,[],[f1610,f257]) ).

fof(f1610,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_192 ),
    inference(avatar_component_clause,[],[f1608]) ).

fof(f1803,plain,
    ( spl0_202
    | ~ spl0_12
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f715,f709,f256,f1801]) ).

fof(f1801,plain,
    ( spl0_202
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f715,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_12
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f257]) ).

fof(f1782,plain,
    ( spl0_201
    | ~ spl0_27
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f650,f635,f321,f1780]) ).

fof(f650,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f322]) ).

fof(f1754,plain,
    ( spl0_200
    | ~ spl0_38
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f696,f693,f374,f1752]) ).

fof(f1752,plain,
    ( spl0_200
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f696,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
    | ~ spl0_38
    | ~ spl0_91 ),
    inference(resolution,[],[f694,f375]) ).

fof(f1720,plain,
    ( spl0_199
    | ~ spl0_23
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f649,f635,f301,f1718]) ).

fof(f1718,plain,
    ( spl0_199
  <=> ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f649,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f302]) ).

fof(f1714,plain,
    ( spl0_198
    | ~ spl0_78
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f728,f725,f620,f1712]) ).

fof(f1712,plain,
    ( spl0_198
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f725,plain,
    ( spl0_95
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f728,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_95 ),
    inference(resolution,[],[f726,f621]) ).

fof(f726,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f725]) ).

fof(f1669,plain,
    ( spl0_197
    | ~ spl0_31
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f668,f661,f337,f1667]) ).

fof(f1667,plain,
    ( spl0_197
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f337,plain,
    ( spl0_31
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f668,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_31
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f338]) ).

fof(f338,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f337]) ).

fof(f1665,plain,
    ( spl0_196
    | ~ spl0_32
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f667,f661,f341,f1663]) ).

fof(f1663,plain,
    ( spl0_196
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f341,plain,
    ( spl0_32
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f667,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_32
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f342]) ).

fof(f342,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f1648,plain,
    ( spl0_195
    | ~ spl0_20
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f669,f661,f289,f1646]) ).

fof(f1646,plain,
    ( spl0_195
  <=> ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f669,plain,
    ( ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f290]) ).

fof(f1629,plain,
    ( spl0_194
    | ~ spl0_38
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f664,f661,f374,f1627]) ).

fof(f1627,plain,
    ( spl0_194
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f664,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_38
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f375]) ).

fof(f1623,plain,
    ( spl0_193
    | ~ spl0_39
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f544,f539,f378,f1621]) ).

fof(f1621,plain,
    ( spl0_193
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f378,plain,
    ( spl0_39
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f539,plain,
    ( spl0_64
  <=> ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f544,plain,
    ( ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_39
    | ~ spl0_64 ),
    inference(resolution,[],[f540,f379]) ).

fof(f379,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f378]) ).

fof(f540,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f539]) ).

fof(f1611,plain,
    ( ~ spl0_192
    | ~ spl0_112
    | spl0_183 ),
    inference(avatar_split_clause,[],[f1553,f1545,f830,f1608]) ).

fof(f1553,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_112
    | spl0_183 ),
    inference(resolution,[],[f1547,f831]) ).

fof(f1547,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_183 ),
    inference(avatar_component_clause,[],[f1545]) ).

fof(f1606,plain,
    ( ~ spl0_189
    | ~ spl0_190
    | spl0_191
    | ~ spl0_74
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f623,f615,f595,f1603,f1599,f1595]) ).

fof(f1595,plain,
    ( spl0_189
  <=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1599,plain,
    ( spl0_190
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1603,plain,
    ( spl0_191
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f595,plain,
    ( spl0_74
  <=> ! [X0,X8] :
        ( ~ function(X8)
        | ~ member(X0,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f623,plain,
    ( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(universal_class,universal_class)
    | ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_74
    | ~ spl0_77 ),
    inference(superposition,[],[f596,f617]) ).

fof(f596,plain,
    ( ! [X0,X8] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X8) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f1593,plain,
    ( spl0_188
    | ~ spl0_28
    | ~ spl0_51
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f589,f580,f459,f325,f1591]) ).

fof(f1591,plain,
    ( spl0_188
  <=> ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f589,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_51
    | ~ spl0_72 ),
    inference(forward_demodulation,[],[f588,f460]) ).

fof(f588,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_72 ),
    inference(resolution,[],[f581,f326]) ).

fof(f1587,plain,
    ( spl0_187
    | ~ spl0_78
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f687,f684,f620,f1585]) ).

fof(f1585,plain,
    ( spl0_187
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f684,plain,
    ( spl0_89
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f687,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_89 ),
    inference(resolution,[],[f685,f621]) ).

fof(f685,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f684]) ).

fof(f1565,plain,
    ( spl0_186
    | ~ spl0_50
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f624,f615,f455,f1563]) ).

fof(f1563,plain,
    ( spl0_186
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f455,plain,
    ( spl0_50
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f624,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_77 ),
    inference(superposition,[],[f456,f617]) ).

fof(f456,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f455]) ).

fof(f1558,plain,
    ( spl0_185
    | ~ spl0_38
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f629,f620,f374,f1556]) ).

fof(f1556,plain,
    ( spl0_185
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f629,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_38
    | ~ spl0_78 ),
    inference(resolution,[],[f621,f375]) ).

fof(f1552,plain,
    ( ~ spl0_182
    | ~ spl0_183
    | spl0_184
    | ~ spl0_22
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f613,f603,f297,f1549,f1545,f1541]) ).

fof(f1541,plain,
    ( spl0_182
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1549,plain,
    ( spl0_184
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f603,plain,
    ( spl0_76
  <=> ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f613,plain,
    ( inductive(cross_product(universal_class,universal_class))
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | ~ spl0_22
    | ~ spl0_76 ),
    inference(resolution,[],[f604,f298]) ).

fof(f604,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f1539,plain,
    ( spl0_181
    | ~ spl0_39
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f521,f510,f378,f1537]) ).

fof(f1537,plain,
    ( spl0_181
  <=> ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f510,plain,
    ( spl0_58
  <=> ! [X8] :
        ( ~ operation(X8)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f521,plain,
    ( ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
    | ~ spl0_39
    | ~ spl0_58 ),
    inference(resolution,[],[f511,f379]) ).

fof(f511,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f510]) ).

fof(f1532,plain,
    ( spl0_179
    | spl0_180
    | ~ spl0_40
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f608,f595,f382,f1529,f1526]) ).

fof(f1526,plain,
    ( spl0_179
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | null_class = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1529,plain,
    ( spl0_180
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f608,plain,
    ( ! [X0] :
        ( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | null_class = cross_product(X0,universal_class) )
    | ~ spl0_40
    | ~ spl0_74 ),
    inference(superposition,[],[f596,f383]) ).

fof(f1524,plain,
    ( spl0_178
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f554,f550,f539,f1522]) ).

fof(f1522,plain,
    ( spl0_178
  <=> ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f550,plain,
    ( spl0_66
  <=> ! [X1,X8] :
        ( ~ function(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | maps(X8,domain_of(X8),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f554,plain,
    ( ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) )
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f540]) ).

fof(f551,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f550]) ).

fof(f1486,plain,
    ( spl0_177
    | ~ spl0_78
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f674,f671,f620,f1484]) ).

fof(f1484,plain,
    ( spl0_177
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f671,plain,
    ( spl0_86
  <=> ! [X0,X1] :
        ( ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f674,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_86 ),
    inference(resolution,[],[f672,f621]) ).

fof(f672,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f671]) ).

fof(f1482,plain,
    ( spl0_175
    | spl0_176
    | ~ spl0_12
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f648,f635,f256,f1479,f1476]) ).

fof(f1476,plain,
    ( spl0_175
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1479,plain,
    ( spl0_176
  <=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f648,plain,
    ( ! [X0,X1] :
        ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f257]) ).

fof(f1474,plain,
    ( ~ spl0_173
    | spl0_174
    | ~ spl0_14
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f920,f899,f264,f1471,f1467]) ).

fof(f1467,plain,
    ( spl0_173
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1471,plain,
    ( spl0_174
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f920,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_14
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f266]) ).

fof(f1465,plain,
    ( spl0_172
    | ~ spl0_38
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f610,f599,f374,f1463]) ).

fof(f1463,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f599,plain,
    ( spl0_75
  <=> ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f610,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
    | ~ spl0_38
    | ~ spl0_75 ),
    inference(resolution,[],[f600,f375]) ).

fof(f600,plain,
    ( ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f599]) ).

fof(f1461,plain,
    ( spl0_171
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f606,f595,f374,f1459]) ).

fof(f1459,plain,
    ( spl0_171
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f606,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(resolution,[],[f596,f375]) ).

fof(f1457,plain,
    ( spl0_170
    | ~ spl0_39
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f501,f467,f378,f1455]) ).

fof(f1455,plain,
    ( spl0_170
  <=> ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f467,plain,
    ( spl0_53
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f501,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_53 ),
    inference(resolution,[],[f468,f379]) ).

fof(f468,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f467]) ).

fof(f1453,plain,
    ( spl0_169
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f500,f463,f378,f1451]) ).

fof(f1451,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f463,plain,
    ( spl0_52
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f500,plain,
    ( ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(resolution,[],[f464,f379]) ).

fof(f464,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f463]) ).

fof(f1386,plain,
    ( spl0_168
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f655,f652,f1384]) ).

fof(f1384,plain,
    ( spl0_168
  <=> ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f652,plain,
    ( spl0_83
  <=> ! [X9,X11,X10] :
        ( ~ function(X9)
        | compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) != domain_of(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f655,plain,
    ( ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
    | ~ spl0_83 ),
    inference(equality_resolution,[],[f653]) ).

fof(f653,plain,
    ( ! [X10,X11,X9] :
        ( domain_of(domain_of(X10)) != domain_of(X9)
        | compatible(X9,X10,X11)
        | ~ function(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f652]) ).

fof(f1382,plain,
    ( spl0_167
    | ~ spl0_38
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f587,f580,f374,f1380]) ).

fof(f1380,plain,
    ( spl0_167
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f587,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_72 ),
    inference(resolution,[],[f581,f375]) ).

fof(f1378,plain,
    ( spl0_166
    | ~ spl0_38
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f584,f559,f374,f1376]) ).

fof(f1376,plain,
    ( spl0_166
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f559,plain,
    ( spl0_67
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f584,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
    | ~ spl0_38
    | ~ spl0_67 ),
    inference(resolution,[],[f560,f375]) ).

fof(f560,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f559]) ).

fof(f1374,plain,
    ( spl0_165
    | ~ spl0_28
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f490,f455,f325,f1372]) ).

fof(f1372,plain,
    ( spl0_165
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f490,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_28
    | ~ spl0_50 ),
    inference(resolution,[],[f456,f326]) ).

fof(f1370,plain,
    ( spl0_164
    | ~ spl0_27
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f486,f451,f321,f1368]) ).

fof(f1368,plain,
    ( spl0_164
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f486,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_49 ),
    inference(resolution,[],[f452,f322]) ).

fof(f1360,plain,
    ( spl0_163
    | ~ spl0_32
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f625,f615,f341,f1358]) ).

fof(f1358,plain,
    ( spl0_163
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f625,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_32
    | ~ spl0_77 ),
    inference(superposition,[],[f342,f617]) ).

fof(f1329,plain,
    ( spl0_162
    | ~ spl0_51
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f607,f595,f459,f1327]) ).

fof(f1327,plain,
    ( spl0_162
  <=> ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f607,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_51
    | ~ spl0_74 ),
    inference(superposition,[],[f596,f460]) ).

fof(f1325,plain,
    ( spl0_161
    | ~ spl0_23
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f485,f451,f301,f1323]) ).

fof(f1323,plain,
    ( spl0_161
  <=> ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f485,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_49 ),
    inference(resolution,[],[f452,f302]) ).

fof(f1307,plain,
    ( spl0_160
    | ~ spl0_22
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f557,f550,f297,f1305]) ).

fof(f1305,plain,
    ( spl0_160
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f557,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_22
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f298]) ).

fof(f1303,plain,
    ( spl0_159
    | ~ spl0_40
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f529,f523,f382,f1301]) ).

fof(f1301,plain,
    ( spl0_159
  <=> ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f523,plain,
    ( spl0_61
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f529,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_61 ),
    inference(trivial_inequality_removal,[],[f527]) ).

fof(f527,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_61 ),
    inference(superposition,[],[f524,f383]) ).

fof(f524,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f523]) ).

fof(f1299,plain,
    ( spl0_158
    | ~ spl0_28
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f448,f431,f325,f1297]) ).

fof(f1297,plain,
    ( spl0_158
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f431,plain,
    ( spl0_45
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f448,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_28
    | ~ spl0_45 ),
    inference(resolution,[],[f432,f326]) ).

fof(f432,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f431]) ).

fof(f1295,plain,
    ( spl0_157
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f411,f378,f349,f1293]) ).

fof(f1293,plain,
    ( spl0_157
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f349,plain,
    ( spl0_34
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f411,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f350]) ).

fof(f350,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f349]) ).

fof(f1291,plain,
    ( spl0_156
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f410,f378,f345,f1289]) ).

fof(f1289,plain,
    ( spl0_156
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f345,plain,
    ( spl0_33
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f410,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f346]) ).

fof(f346,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f1287,plain,
    ( ~ spl0_154
    | spl0_155
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f916,f899,f251,f1284,f1280]) ).

fof(f1280,plain,
    ( spl0_154
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1284,plain,
    ( spl0_155
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f916,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f253]) ).

fof(f1256,plain,
    ( spl0_153
    | ~ spl0_38
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f504,f479,f374,f1254]) ).

fof(f1254,plain,
    ( spl0_153
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f479,plain,
    ( spl0_56
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f504,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_38
    | ~ spl0_56 ),
    inference(resolution,[],[f480,f375]) ).

fof(f480,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f479]) ).

fof(f1252,plain,
    ( spl0_152
    | ~ spl0_38
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f489,f455,f374,f1250]) ).

fof(f489,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_38
    | ~ spl0_50 ),
    inference(resolution,[],[f456,f375]) ).

fof(f1248,plain,
    ( spl0_150
    | ~ spl0_151
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f418,f378,f310,f1245,f1241]) ).

fof(f1241,plain,
    ( spl0_150
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1245,plain,
    ( spl0_151
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f418,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f312]) ).

fof(f1239,plain,
    ( spl0_148
    | ~ spl0_149
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f416,f378,f305,f1236,f1232]) ).

fof(f1232,plain,
    ( spl0_148
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1236,plain,
    ( spl0_149
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f416,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f307]) ).

fof(f1230,plain,
    ( spl0_147
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f414,f378,f293,f1228]) ).

fof(f1228,plain,
    ( spl0_147
  <=> ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f414,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f294]) ).

fof(f1180,plain,
    ( spl0_146
    | ~ spl0_51
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f526,f523,f459,f1178]) ).

fof(f1178,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f526,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_51
    | ~ spl0_61 ),
    inference(superposition,[],[f524,f460]) ).

fof(f1176,plain,
    ( spl0_145
    | ~ spl0_43
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f493,f455,f395,f1174]) ).

fof(f1174,plain,
    ( spl0_145
  <=> ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f493,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_50 ),
    inference(superposition,[],[f456,f397]) ).

fof(f1172,plain,
    ( spl0_144
    | ~ spl0_41
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f492,f455,f386,f1170]) ).

fof(f1170,plain,
    ( spl0_144
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f492,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_41
    | ~ spl0_50 ),
    inference(superposition,[],[f456,f388]) ).

fof(f1168,plain,
    ( spl0_143
    | ~ spl0_40
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f491,f455,f382,f1166]) ).

fof(f1166,plain,
    ( spl0_143
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f491,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_50 ),
    inference(superposition,[],[f456,f383]) ).

fof(f1164,plain,
    ( spl0_142
    | ~ spl0_38
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f447,f431,f374,f1162]) ).

fof(f1162,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f447,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_45 ),
    inference(resolution,[],[f432,f375]) ).

fof(f1117,plain,
    ( spl0_141
    | ~ spl0_6
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f556,f550,f230,f1115]) ).

fof(f1115,plain,
    ( spl0_141
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f556,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_6
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f231]) ).

fof(f1113,plain,
    ( spl0_140
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f415,f378,f281,f1111]) ).

fof(f1111,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f415,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f282]) ).

fof(f1109,plain,
    ( spl0_139
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f408,f378,f297,f1107]) ).

fof(f1107,plain,
    ( spl0_139
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f408,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f298]) ).

fof(f1105,plain,
    ( ~ spl0_137
    | spl0_138
    | ~ spl0_10
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f914,f899,f246,f1102,f1098]) ).

fof(f1098,plain,
    ( spl0_137
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1102,plain,
    ( spl0_138
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f246,plain,
    ( spl0_10
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f914,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_10
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f248]) ).

fof(f248,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f1096,plain,
    ( spl0_136
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f372,f341,f321,f1094]) ).

fof(f372,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(resolution,[],[f342,f322]) ).

fof(f1092,plain,
    ( spl0_135
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f369,f337,f321,f1090]) ).

fof(f369,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(resolution,[],[f338,f322]) ).

fof(f1033,plain,
    ( spl0_134
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f553,f550,f510,f1031]) ).

fof(f1031,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f553,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f511]) ).

fof(f1029,plain,
    ( spl0_133
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f405,f374,f333,f1027]) ).

fof(f1027,plain,
    ( spl0_133
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f333,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f405,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f334]) ).

fof(f334,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f333]) ).

fof(f1025,plain,
    ( spl0_132
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f404,f374,f329,f1023]) ).

fof(f1023,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f329,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f404,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f330]) ).

fof(f330,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f329]) ).

fof(f1021,plain,
    ( spl0_131
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f403,f374,f321,f1019]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f322]) ).

fof(f1017,plain,
    ( spl0_130
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f371,f341,f301,f1015]) ).

fof(f1015,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f371,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(resolution,[],[f342,f302]) ).

fof(f1013,plain,
    ( spl0_129
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f368,f337,f301,f1011]) ).

fof(f368,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(resolution,[],[f338,f302]) ).

fof(f977,plain,
    ( ~ spl0_128
    | ~ spl0_12
    | spl0_108 ),
    inference(avatar_split_clause,[],[f938,f810,f256,f974]) ).

fof(f974,plain,
    ( spl0_128
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f810,plain,
    ( spl0_108
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f938,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_12
    | spl0_108 ),
    inference(resolution,[],[f811,f257]) ).

fof(f811,plain,
    ( ~ member(null_class,element_relation)
    | spl0_108 ),
    inference(avatar_component_clause,[],[f810]) ).

fof(f972,plain,
    ( spl0_127
    | ~ spl0_12
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f484,f451,f256,f970]) ).

fof(f970,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f484,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_49 ),
    inference(resolution,[],[f452,f257]) ).

fof(f968,plain,
    ( spl0_126
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f424,f395,f337,f966]) ).

fof(f966,plain,
    ( spl0_126
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f424,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(superposition,[],[f338,f397]) ).

fof(f964,plain,
    ( spl0_125
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f422,f386,f337,f962]) ).

fof(f422,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(superposition,[],[f338,f388]) ).

fof(f960,plain,
    ( spl0_124
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f419,f382,f341,f958]) ).

fof(f958,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f419,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(superposition,[],[f342,f383]) ).

fof(f956,plain,
    ( spl0_122
    | ~ spl0_123
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f417,f378,f264,f953,f949]) ).

fof(f949,plain,
    ( spl0_122
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f953,plain,
    ( spl0_123
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f417,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f266]) ).

fof(f947,plain,
    ( spl0_120
    | ~ spl0_121
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f412,f378,f251,f944,f940]) ).

fof(f940,plain,
    ( spl0_120
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f944,plain,
    ( spl0_121
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f412,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f253]) ).

fof(f937,plain,
    ( spl0_118
    | ~ spl0_119
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f409,f378,f246,f934,f930]) ).

fof(f930,plain,
    ( spl0_118
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f934,plain,
    ( spl0_119
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f409,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f248]) ).

fof(f928,plain,
    ( spl0_117
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f402,f374,f301,f926]) ).

fof(f402,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f302]) ).

fof(f924,plain,
    ( spl0_116
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f364,f321,f289,f922]) ).

fof(f364,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(resolution,[],[f322,f290]) ).

fof(f901,plain,
    ( spl0_115
    | ~ spl0_52
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f586,f571,f463,f899]) ).

fof(f571,plain,
    ( spl0_70
  <=> ! [X8] :
        ( function(X8)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f586,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_52
    | ~ spl0_70 ),
    inference(resolution,[],[f572,f464]) ).

fof(f572,plain,
    ( ! [X8] :
        ( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | function(X8) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f571]) ).

fof(f897,plain,
    ( spl0_114
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f420,f382,f337,f895]) ).

fof(f895,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f420,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(superposition,[],[f338,f383]) ).

fof(f893,plain,
    ( spl0_113
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f319,f301,f289,f891]) ).

fof(f319,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(resolution,[],[f302,f290]) ).

fof(f832,plain,
    ( spl0_112
    | ~ spl0_31
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f626,f615,f337,f830]) ).

fof(f626,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_31
    | ~ spl0_77 ),
    inference(superposition,[],[f338,f617]) ).

fof(f828,plain,
    ( spl0_111
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f413,f378,f260,f826]) ).

fof(f826,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f260,plain,
    ( spl0_13
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f413,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f261]) ).

fof(f261,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f260]) ).

fof(f824,plain,
    ( spl0_110
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f401,f374,f256,f822]) ).

fof(f401,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f257]) ).

fof(f820,plain,
    ( spl0_109
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f400,f374,f242,f818]) ).

fof(f242,plain,
    ( spl0_9
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f400,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f243]) ).

fof(f243,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f242]) ).

fof(f813,plain,
    ( ~ spl0_107
    | spl0_108
    | ~ spl0_12
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f778,f738,f256,f810,f806]) ).

fof(f806,plain,
    ( spl0_107
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f778,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_12
    | ~ spl0_98 ),
    inference(resolution,[],[f739,f257]) ).

fof(f798,plain,
    ( spl0_106
    | ~ spl0_4
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f555,f550,f221,f796]) ).

fof(f796,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f555,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_4
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f222]) ).

fof(f788,plain,
    ( spl0_105
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f370,f341,f256,f786]) ).

fof(f786,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f370,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(resolution,[],[f342,f257]) ).

fof(f770,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f204,f768]) ).

fof(f768,plain,
    ( spl0_104
  <=> ! [X9,X11,X10] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
        | ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f204,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f203,f130]) ).

fof(f130,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).

fof(f203,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f202,f130]) ).

fof(f202,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f201,f130]) ).

fof(f201,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f200,f130]) ).

fof(f200,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f199,f130]) ).

fof(f199,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f198,f130]) ).

fof(f198,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f197,f130]) ).

fof(f197,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f196,f130]) ).

fof(f196,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f195,f130]) ).

fof(f195,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f177,f130]) ).

fof(f177,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f91,f118,f119,f118,f118,f118,f118,f119]) ).

fof(f119,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).

fof(f118,plain,
    ! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
    inference(definition_unfolding,[],[f68,f115,f117,f12]) ).

fof(f117,plain,
    ! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
    inference(definition_unfolding,[],[f42,f116,f29]) ).

fof(f116,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).

fof(f42,axiom,
    ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).

fof(f115,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f68,axiom,
    ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).

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/sandbox/benchmark/theBenchmark.p',homomorphism6) ).

fof(f766,plain,
    ( spl0_103
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f423,f395,f341,f764]) ).

fof(f423,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f342,f397]) ).

fof(f759,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f194,f757]) ).

fof(f194,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f193,f130]) ).

fof(f193,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f192,f130]) ).

fof(f192,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f191,f130]) ).

fof(f191,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f190,f130]) ).

fof(f190,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f169,f130]) ).

fof(f169,plain,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f89,f119,f118,f119,f118,f118,f118,f118,f119]) ).

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/sandbox/benchmark/theBenchmark.p',homomorphism4) ).

fof(f754,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f189,f752]) ).

fof(f189,plain,
    ! [X0,X1,X4] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
      | ~ member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(forward_demodulation,[],[f168,f130]) ).

fof(f168,plain,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(definition_unfolding,[],[f108,f119,f119,f118,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',application_function_defn4) ).

fof(f748,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f173,f746]) ).

fof(f173,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f37,f119,f119,f119,f119,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',flip3) ).

fof(f744,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f172,f742]) ).

fof(f172,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f34,f119,f119,f119,f119,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',rotate3) ).

fof(f740,plain,
    ( spl0_98
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f421,f386,f341,f738]) ).

fof(f421,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(superposition,[],[f342,f388]) ).

fof(f736,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f157,f734]) ).

fof(f734,plain,
    ( spl0_97
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f157,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
    inference(definition_unfolding,[],[f36,f119,f119,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',flip2) ).

fof(f732,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f156,f730]) ).

fof(f730,plain,
    ( spl0_96
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f156,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
    inference(definition_unfolding,[],[f33,f119,f119,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',rotate2) ).

fof(f727,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f180,f725]) ).

fof(f180,plain,
    ! [X0] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f46,f125,f119,f119]) ).

fof(f125,plain,
    ! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
    inference(definition_unfolding,[],[f43,f26,f12]) ).

fof(f26,axiom,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

fof(f43,axiom,
    ! [X0] : union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).

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/sandbox/benchmark/theBenchmark.p',successor_relation3) ).

fof(f711,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f171,f709]) ).

fof(f171,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f59,f119,f119,f117,f117,f12]) ).

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/sandbox/benchmark/theBenchmark.p',compose3) ).

fof(f705,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f154,f703]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
    inference(definition_unfolding,[],[f97,f119,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',definition_of_composition_function3) ).

fof(f701,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f185,f699]) ).

fof(f699,plain,
    ( spl0_92
  <=> ! [X4,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f185,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(forward_demodulation,[],[f151,f130]) ).

fof(f151,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f107,f118,f119,f119]) ).

fof(f107,axiom,
    ! [X0,X1,X4] :
      ( apply(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn3) ).

fof(f695,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f176,f693]) ).

fof(f176,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
    inference(definition_unfolding,[],[f90,f119]) ).

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/sandbox/benchmark/theBenchmark.p',homomorphism5) ).

fof(f691,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f155,f689]) ).

fof(f689,plain,
    ( spl0_90
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f155,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f58,f119,f117,f117,f12]) ).

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/sandbox/benchmark/theBenchmark.p',compose2) ).

fof(f686,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f181,f684]) ).

fof(f181,plain,
    ! [X0,X1] :
      ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f170]) ).

fof(f170,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f94,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',compose_class_definition3) ).

fof(f682,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f153,f680]) ).

fof(f153,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
    inference(definition_unfolding,[],[f96,f119,f119]) ).

fof(f96,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function2) ).

fof(f678,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f149,f676]) ).

fof(f149,plain,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f106,f119,f119]) ).

fof(f106,axiom,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn2) ).

fof(f673,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f164,f671]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f20,f119,f119]) ).

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/sandbox/benchmark/theBenchmark.p',element_relation3) ).

fof(f663,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f188,f661]) ).

fof(f188,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f187,f130]) ).

fof(f187,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f165,f130]) ).

fof(f165,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
    inference(definition_unfolding,[],[f70,f118]) ).

fof(f70,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(apply(choice,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).

fof(f659,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f174,f657]) ).

fof(f657,plain,
    ( spl0_84
  <=> ! [X8] :
        ( ~ function(X8)
        | operation(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),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_84])]) ).

fof(f174,plain,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f81,f116]) ).

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/sandbox/benchmark/theBenchmark.p',operation4) ).

fof(f654,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f175,f652]) ).

fof(f175,plain,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f85,f116]) ).

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/sandbox/benchmark/theBenchmark.p',compatible4) ).

fof(f646,plain,
    ( ~ spl0_81
    | spl0_82
    | ~ spl0_4
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f612,f603,f221,f643,f639]) ).

fof(f643,plain,
    ( spl0_82
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f612,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_4
    | ~ spl0_76 ),
    inference(resolution,[],[f604,f222]) ).

fof(f637,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f150,f635]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
    inference(definition_unfolding,[],[f17,f119]) ).

fof(f17,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).

fof(f633,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f147,f631]) ).

fof(f631,plain,
    ( spl0_79
  <=> ! [X0,X1] :
        ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
    inference(definition_unfolding,[],[f45,f125,f119]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( successor(X0) = X1
      | ~ member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).

fof(f622,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f163,f620]) ).

fof(f163,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f16,f119]) ).

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/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f618,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f131,f615]) ).

fof(f131,plain,
    subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
    inference(definition_unfolding,[],[f74,f38]) ).

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/sandbox/benchmark/theBenchmark.p',subset_relation) ).

fof(f605,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f186,f603]) ).

fof(f186,plain,
    ! [X0] :
      ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | inductive(X0)
      | ~ member(null_class,X0) ),
    inference(forward_demodulation,[],[f161,f130]) ).

fof(f161,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f117]) ).

fof(f49,axiom,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).

fof(f601,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f183,f599]) ).

fof(f183,plain,
    ! [X2] :
      ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
      | ~ member(X2,universal_class) ),
    inference(forward_demodulation,[],[f138,f130]) ).

fof(f138,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
    inference(definition_unfolding,[],[f56,f126]) ).

fof(f126,plain,
    ! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
    inference(definition_unfolding,[],[f55,f117]) ).

fof(f55,axiom,
    ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).

fof(f56,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).

fof(f597,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f159,f595]) ).

fof(f159,plain,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
    inference(definition_unfolding,[],[f65,f117]) ).

fof(f65,axiom,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(image(X8,X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).

fof(f593,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f152,f591]) ).

fof(f152,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
    inference(definition_unfolding,[],[f93,f119]) ).

fof(f93,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition2) ).

fof(f582,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f166,f580]) ).

fof(f166,plain,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12]) ).

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/sandbox/benchmark/theBenchmark.p',domain2) ).

fof(f578,plain,
    ( spl0_71
    | ~ spl0_3
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f542,f514,f216,f575]) ).

fof(f575,plain,
    ( spl0_71
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f216,plain,
    ( spl0_3
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f542,plain,
    ( single_valued_class(choice)
    | ~ spl0_3
    | ~ spl0_59 ),
    inference(resolution,[],[f515,f218]) ).

fof(f218,plain,
    ( function(choice)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f573,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f162,f571]) ).

fof(f162,plain,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f64,f38]) ).

fof(f64,axiom,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).

fof(f569,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f143,f567]) ).

fof(f143,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f14,f119]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f565,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f142,f563]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f15,f119]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f561,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f140,f559]) ).

fof(f140,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
    inference(definition_unfolding,[],[f100,f119]) ).

fof(f100,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation3) ).

fof(f552,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f160,f550]) ).

fof(f160,plain,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
      | maps(X8,domain_of(X8),X1) ),
    inference(definition_unfolding,[],[f112,f116]) ).

fof(f112,axiom,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(range_of(X8),X1)
      | maps(X8,domain_of(X8),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).

fof(f548,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f148,f546]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
    inference(definition_unfolding,[],[f99,f119]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(ordered_pair(X0,X1),domain_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation2) ).

fof(f541,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f182,f539]) ).

fof(f182,plain,
    ! [X0] :
      ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | ~ inductive(X0) ),
    inference(forward_demodulation,[],[f134,f130]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f48,f117]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).

fof(f537,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f146,f535]) ).

fof(f535,plain,
    ( spl0_63
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f146,plain,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f84,f116]) ).

fof(f84,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).

fof(f533,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f141,f531]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
    inference(definition_unfolding,[],[f19,f119]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).

fof(f525,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f144,f523]) ).

fof(f144,plain,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f30,f29,f12]) ).

fof(f30,axiom,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) != null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).

fof(f520,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f145,f518]) ).

fof(f518,plain,
    ( spl0_60
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f145,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f116]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).

fof(f516,plain,
    ( spl0_59
    | ~ spl0_53
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f502,f471,f467,f514]) ).

fof(f471,plain,
    ( spl0_54
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f502,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_53
    | ~ spl0_54 ),
    inference(resolution,[],[f472,f468]) ).

fof(f472,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f471]) ).

fof(f512,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f135,f510]) ).

fof(f135,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f116]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).

fof(f508,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f79,f506]) ).

fof(f506,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).

fof(f481,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f184,f479]) ).

fof(f184,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f139,f130]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f115]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).

fof(f477,plain,
    ( spl0_55
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f406,f378,f221,f475]) ).

fof(f475,plain,
    ( spl0_55
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f406,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f222]) ).

fof(f473,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f137,f471]) ).

fof(f137,plain,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f61,f38]) ).

fof(f61,axiom,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f469,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f136,f467]) ).

fof(f136,plain,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f63,f38]) ).

fof(f63,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).

fof(f465,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f132,f463]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f461,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f130,f459]) ).

fof(f457,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f23,f455]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).

fof(f453,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f8,f451]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f445,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f158,f443]) ).

fof(f443,plain,
    ( spl0_48
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f158,plain,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f73,f38]) ).

fof(f73,axiom,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(inverse(X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).

fof(f441,plain,
    ( spl0_47
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f399,f374,f225,f439]) ).

fof(f225,plain,
    ( spl0_5
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f399,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(resolution,[],[f375,f227]) ).

fof(f227,plain,
    ( member(omega,universal_class)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f437,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f83,f435]) ).

fof(f435,plain,
    ( spl0_46
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).

fof(f433,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f25,f431]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).

fof(f429,plain,
    ~ spl0_44,
    inference(avatar_split_clause,[],[f128,f426]) ).

fof(f128,plain,
    not_subclass_element(cross_product(x,y),z) != unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))))),
    inference(definition_unfolding,[],[f114,f119]) ).

fof(f114,axiom,
    not_subclass_element(cross_product(x,y),z) != ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property6_2) ).

fof(f398,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f129,f395]) ).

fof(f129,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).

fof(f393,plain,
    ( spl0_42
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f367,f337,f256,f391]) ).

fof(f367,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(resolution,[],[f338,f257]) ).

fof(f389,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f104,f386]) ).

fof(f104,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_can_define_singleton) ).

fof(f384,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f67,f382]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).

fof(f380,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f7,f378]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f376,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1,f374]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).

fof(f363,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f133,f361]) ).

fof(f133,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).

fof(f359,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f110,f357]) ).

fof(f357,plain,
    ( spl0_36
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).

fof(f355,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f88,f353]) ).

fof(f353,plain,
    ( spl0_35
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).

fof(f351,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f35,f349]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).

fof(f347,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f32,f345]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).

fof(f343,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f22,f341]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).

fof(f339,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f21,f337]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).

fof(f335,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f10,f333]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f331,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f9,f329]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f327,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f3,f325]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f323,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f2,f321]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f318,plain,
    ( spl0_26
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f314,f289,f256,f316]) ).

fof(f316,plain,
    ( spl0_26
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f314,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(resolution,[],[f290,f257]) ).

fof(f313,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f105,f310]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f308,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f95,f305]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f303,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f66,f301]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).

fof(f299,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f62,f297]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).

fof(f295,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f57,f293]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).

fof(f291,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f24,f289]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).

fof(f287,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f109,f285]) ).

fof(f285,plain,
    ( spl0_19
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).

fof(f283,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f92,f281]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f279,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f87,f277]) ).

fof(f277,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).

fof(f275,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f86,f273]) ).

fof(f273,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).

fof(f271,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f82,f269]) ).

fof(f269,plain,
    ( spl0_15
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).

fof(f267,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f98,f264]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f262,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f51,f260]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f258,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f47,f256]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).

fof(f254,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f44,f251]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).

fof(f249,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f18,f246]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).

fof(f244,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f11,f242]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f240,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f78,f238]) ).

fof(f238,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/sandbox/benchmark/theBenchmark.p',operation1) ).

fof(f236,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f71,f234]) ).

fof(f234,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/sandbox/benchmark/theBenchmark.p',one_to_one1) ).

fof(f232,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f178,f230]) ).

fof(f178,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).

fof(f228,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f52,f225]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f223,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f4,f221]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f219,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f69,f216]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).

fof(f214,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f50,f211]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f209,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f113,f206]) ).

fof(f113,axiom,
    ~ subclass(cross_product(x,y),z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property6_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET231-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n015.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 16:32:53 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  % (16826)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (16832)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 theBenchmark for (522ds/0Mi)
% 0.16/0.33  % (16833)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 theBenchmark for (497ds/0Mi)
% 0.16/0.33  % (16830)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33  % (16829)WARNING: value z3 for option sas not known
% 0.16/0.33  % (16827)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33  % (16831)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 theBenchmark for (531ds/0Mi)
% 0.16/0.33  % (16828)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33  % (16829)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 theBenchmark for (569ds/0Mi)
% 0.16/0.36  TRYING [1]
% 0.16/0.37  TRYING [2]
% 0.16/0.42  TRYING [3]
% 0.16/0.46  % (16831)First to succeed.
% 0.16/0.47  TRYING [1]
% 0.16/0.47  TRYING [2]
% 0.16/0.48  % (16831)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16826"
% 0.16/0.48  % (16831)Refutation found. Thanks to Tanya!
% 0.16/0.48  % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49  % (16831)------------------------------
% 0.16/0.49  % (16831)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.49  % (16831)Termination reason: Refutation
% 0.16/0.49  
% 0.16/0.49  % (16831)Memory used [KB]: 3060
% 0.16/0.49  % (16831)Time elapsed: 0.150 s
% 0.16/0.49  % (16831)Instructions burned: 301 (million)
% 0.16/0.49  % (16826)Success in time 0.168 s
%------------------------------------------------------------------------------