%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 : Tue Apr 30 15:21:54 EDT 2024

% Result   : Theorem 2.74s 1.02s
% Output   : Refutation 2.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  504
% Syntax   : Number of formulae    : 1692 ( 108 unt;   0 def)
%            Number of atoms       : 6230 ( 897 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 8393 (3855   ~;3907   |; 134   &)
%                                         ( 451 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :  457 ( 455 usr; 448 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  10 con; 0-2 aty)
%            Number of variables   : 1533 (1502   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7192,plain,
    $false,
    inference(avatar_sat_refutation,[],[f207,f212,f217,f222,f227,f232,f237,f242,f247,f252,f257,f262,f267,f272,f277,f282,f287,f292,f297,f302,f306,f310,f314,f318,f322,f331,f335,f339,f343,f357,f361,f365,f369,f373,f377,f381,f385,f390,f409,f413,f418,f422,f426,f430,f434,f438,f442,f446,f451,f468,f472,f476,f480,f485,f489,f493,f497,f541,f551,f561,f566,f570,f574,f578,f582,f594,f599,f607,f611,f615,f619,f627,f632,f644,f654,f666,f675,f680,f686,f695,f700,f705,f717,f722,f728,f732,f737,f744,f750,f751,f752,f753,f754,f777,f787,f857,f861,f875,f884,f889,f897,f937,f941,f949,f953,f957,f962,f966,f970,f974,f978,f1021,f1025,f1029,f1033,f1037,f1081,f1086,f1090,f1100,f1104,f1108,f1112,f1120,f1167,f1180,f1191,f1204,f1227,f1231,f1241,f1247,f1251,f1255,f1260,f1264,f1268,f1297,f1301,f1342,f1349,f1353,f1383,f1388,f1393,f1398,f1422,f1442,f1457,f1461,f1465,f1491,f1502,f1515,f1525,f1529,f1533,f1537,f1541,f1545,f1550,f1554,f1558,f1562,f1566,f1570,f1574,f1578,f1617,f1809,f1813,f1817,f1821,f1830,f1834,f1848,f1900,f1904,f1908,f1912,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f2106,f2213,f2217,f2221,f2225,f2229,f2233,f2237,f2241,f2245,f2249,f2253,f2257,f2261,f2284,f2288,f2292,f2505,f2561,f2567,f2578,f2584,f2600,f2606,f2617,f2642,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2689,f2693,f2697,f2701,f2705,f2847,f2919,f2923,f2927,f2931,f2935,f2939,f2943,f3079,f3083,f3087,f3141,f3145,f3149,f3153,f3157,f3161,f3316,f3331,f3336,f3363,f3367,f3371,f3375,f3689,f3709,f3732,f3767,f3772,f3776,f3780,f3821,f3825,f3829,f3833,f3837,f3842,f3847,f3851,f3855,f3859,f3860,f3882,f3896,f3901,f3902,f3921,f3930,f3934,f3938,f3943,f3947,f3951,f4130,f4161,f4166,f4171,f4186,f4188,f4212,f4228,f4233,f4242,f4247,f4252,f4292,f4334,f4338,f4342,f4346,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4391,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4513,f4748,f4896,f4900,f4904,f4908,f5002,f5006,f5010,f5014,f5018,f5022,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5081,f5085,f5464,f5468,f5472,f5476,f5480,f5484,f5488,f5492,f5496,f5500,f5504,f5518,f5522,f5824,f5846,f5868,f5900,f5922,f5926,f5930,f5934,f5938,f5942,f5946,f5950,f5964,f5968,f5972,f5976,f6239,f6243,f6247,f6269,f6291,f6313,f6336,f6645,f6667,f6674,f6689,f6697,f6702,f6707,f6712,f6717,f6721,f6725,f6729,f6733,f6738,f6743,f6748,f6753,f6758,f6763,f6767,f6772,f6777,f6782,f6787,f6791,f6795,f6800,f6806,f6896,f6939,f6943,f6947,f6951,f6955,f6959,f6963,f6967,f6971,f7031,f7035,f7039,f7043,f7047,f7123,f7127,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7156,f7185,f7189,f7190,f7191]) ).

fof(f7191,plain,
    ( ~ spl13_158
    | ~ spl13_159
    | spl13_26
    | ~ spl13_294
    | ~ spl13_73
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f661,f651,f625,f3923,f324,f1508,f1504]) ).

fof(f1504,plain,
    ( spl13_158
  <=> relation(relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_158])]) ).

fof(f1508,plain,
    ( spl13_159
  <=> function(relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_159])]) ).

fof(f324,plain,
    ( spl13_26
  <=> relation_composition(sK0,function_inverse(sK0)) = identity_relation(relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).

fof(f3923,plain,
    ( spl13_294
  <=> sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) = apply(relation_composition(sK0,function_inverse(sK0)),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_294])]) ).

fof(f625,plain,
    ( spl13_73
  <=> ! [X1] :
        ( identity_relation(relation_dom(X1)) = X1
        | sK4(relation_dom(X1),X1) != apply(X1,sK4(relation_dom(X1),X1))
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).

fof(f651,plain,
    ( spl13_76
  <=> relation_dom(sK0) = relation_dom(relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).

fof(f661,plain,
    ( sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) != apply(relation_composition(sK0,function_inverse(sK0)),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))))
    | relation_composition(sK0,function_inverse(sK0)) = identity_relation(relation_dom(sK0))
    | ~ function(relation_composition(sK0,function_inverse(sK0)))
    | ~ relation(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_73
    | ~ spl13_76 ),
    inference(superposition,[],[f626,f653]) ).

fof(f653,plain,
    ( relation_dom(sK0) = relation_dom(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_76 ),
    inference(avatar_component_clause,[],[f651]) ).

fof(f626,plain,
    ( ! [X1] :
        ( sK4(relation_dom(X1),X1) != apply(X1,sK4(relation_dom(X1),X1))
        | identity_relation(relation_dom(X1)) = X1
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_73 ),
    inference(avatar_component_clause,[],[f625]) ).

fof(f7190,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_3
    | spl13_294
    | ~ spl13_72
    | ~ spl13_160 ),
    inference(avatar_split_clause,[],[f3907,f1512,f617,f3923,f214,f209,f204]) ).

fof(f204,plain,
    ( spl13_1
  <=> relation(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f209,plain,
    ( spl13_2
  <=> function(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f214,plain,
    ( spl13_3
  <=> one_to_one(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f617,plain,
    ( spl13_72
  <=> ! [X0,X1] :
        ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
        | ~ in(X0,relation_dom(X1))
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).

fof(f1512,plain,
    ( spl13_160
  <=> in(sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))),relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_160])]) ).

fof(f3907,plain,
    ( sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) = apply(relation_composition(sK0,function_inverse(sK0)),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))))
    | ~ one_to_one(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_72
    | ~ spl13_160 ),
    inference(resolution,[],[f1514,f618]) ).

fof(f618,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,relation_dom(X1))
        | apply(relation_composition(X1,function_inverse(X1)),X0) = X0
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_72 ),
    inference(avatar_component_clause,[],[f617]) ).

fof(f1514,plain,
    ( in(sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))),relation_dom(sK0))
    | ~ spl13_160 ),
    inference(avatar_component_clause,[],[f1512]) ).

fof(f7189,plain,
    ( spl13_447
    | ~ spl13_35
    | ~ spl13_200 ),
    inference(avatar_split_clause,[],[f2541,f2104,f371,f7187]) ).

fof(f7187,plain,
    ( spl13_447
  <=> ! [X0] :
        ( sK6 = relation_composition(sK0,relation_dom(relation_dom(X0)))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_447])]) ).

fof(f371,plain,
    ( spl13_35
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).

fof(f2104,plain,
    ( spl13_200
  <=> ! [X0] :
        ( sK6 = relation_composition(sK0,relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_200])]) ).

fof(f2541,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK0,relation_dom(relation_dom(X0)))
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_200 ),
    inference(resolution,[],[f2105,f372]) ).

fof(f372,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_35 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f2105,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK0,relation_dom(X0)) )
    | ~ spl13_200 ),
    inference(avatar_component_clause,[],[f2104]) ).

fof(f7185,plain,
    ( ~ spl13_446
    | ~ spl13_27
    | spl13_291 ),
    inference(avatar_split_clause,[],[f4137,f3898,f328,f7182]) ).

fof(f7182,plain,
    ( spl13_446
  <=> sK4(relation_rng(sK0),identity_relation(relation_rng(sK0))) = apply(identity_relation(relation_rng(sK0)),sK4(relation_rng(sK0),identity_relation(relation_rng(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_446])]) ).

fof(f328,plain,
    ( spl13_27
  <=> relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).

fof(f3898,plain,
    ( spl13_291
  <=> sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)) = apply(relation_composition(function_inverse(sK0),sK0),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_291])]) ).

fof(f4137,plain,
    ( sK4(relation_rng(sK0),identity_relation(relation_rng(sK0))) != apply(identity_relation(relation_rng(sK0)),sK4(relation_rng(sK0),identity_relation(relation_rng(sK0))))
    | ~ spl13_27
    | spl13_291 ),
    inference(superposition,[],[f3900,f329]) ).

fof(f329,plain,
    ( relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
    | ~ spl13_27 ),
    inference(avatar_component_clause,[],[f328]) ).

fof(f3900,plain,
    ( sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)) != apply(relation_composition(function_inverse(sK0),sK0),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)))
    | spl13_291 ),
    inference(avatar_component_clause,[],[f3898]) ).

fof(f7156,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_3
    | spl13_291
    | ~ spl13_70
    | ~ spl13_156 ),
    inference(avatar_split_clause,[],[f3883,f1488,f609,f3898,f214,f209,f204]) ).

fof(f609,plain,
    ( spl13_70
  <=> ! [X0,X1] :
        ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        | ~ in(X0,relation_rng(X1))
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).

fof(f1488,plain,
    ( spl13_156
  <=> in(sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)),relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_156])]) ).

fof(f3883,plain,
    ( sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)) = apply(relation_composition(function_inverse(sK0),sK0),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)))
    | ~ one_to_one(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_70
    | ~ spl13_156 ),
    inference(resolution,[],[f1490,f610]) ).

fof(f610,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,relation_rng(X1))
        | apply(relation_composition(function_inverse(X1),X1),X0) = X0
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_70 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f1490,plain,
    ( in(sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)),relation_rng(sK0))
    | ~ spl13_156 ),
    inference(avatar_component_clause,[],[f1488]) ).

fof(f7155,plain,
    ( spl13_445
    | ~ spl13_143
    | ~ spl13_263 ),
    inference(avatar_split_clause,[],[f3603,f3373,f1351,f7153]) ).

fof(f7153,plain,
    ( spl13_445
  <=> ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_445])]) ).

fof(f1351,plain,
    ( spl13_143
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK0,X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_143])]) ).

fof(f3373,plain,
    ( spl13_263
  <=> ! [X0] :
        ( empty(relation_rng(X0))
        | sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_263])]) ).

fof(f3603,plain,
    ( ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) )
    | ~ spl13_143
    | ~ spl13_263 ),
    inference(resolution,[],[f3374,f1352]) ).

fof(f1352,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | relation_composition(sK0,X0) = X1
        | ~ empty(X0) )
    | ~ spl13_143 ),
    inference(avatar_component_clause,[],[f1351]) ).

fof(f3374,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_263 ),
    inference(avatar_component_clause,[],[f3373]) ).

fof(f7151,plain,
    ( spl13_444
    | ~ spl13_142
    | ~ spl13_263 ),
    inference(avatar_split_clause,[],[f3602,f3373,f1347,f7149]) ).

fof(f7149,plain,
    ( spl13_444
  <=> ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_444])]) ).

fof(f1347,plain,
    ( spl13_142
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_142])]) ).

fof(f3602,plain,
    ( ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) )
    | ~ spl13_142
    | ~ spl13_263 ),
    inference(resolution,[],[f3374,f1348]) ).

fof(f1348,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | relation_composition(X0,sK0) = X1
        | ~ empty(X0) )
    | ~ spl13_142 ),
    inference(avatar_component_clause,[],[f1347]) ).

fof(f7147,plain,
    ( spl13_443
    | ~ spl13_143
    | ~ spl13_262 ),
    inference(avatar_split_clause,[],[f3534,f3369,f1351,f7145]) ).

fof(f7145,plain,
    ( spl13_443
  <=> ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_443])]) ).

fof(f3369,plain,
    ( spl13_262
  <=> ! [X0] :
        ( empty(relation_rng(X0))
        | sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_262])]) ).

fof(f3534,plain,
    ( ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) )
    | ~ spl13_143
    | ~ spl13_262 ),
    inference(resolution,[],[f3370,f1352]) ).

fof(f3370,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_262 ),
    inference(avatar_component_clause,[],[f3369]) ).

fof(f7143,plain,
    ( spl13_442
    | ~ spl13_142
    | ~ spl13_262 ),
    inference(avatar_split_clause,[],[f3533,f3369,f1347,f7141]) ).

fof(f7141,plain,
    ( spl13_442
  <=> ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_442])]) ).

fof(f3533,plain,
    ( ! [X0,X1] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_rng(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) )
    | ~ spl13_142
    | ~ spl13_262 ),
    inference(resolution,[],[f3370,f1348]) ).

fof(f7139,plain,
    ( spl13_441
    | ~ spl13_143
    | ~ spl13_261 ),
    inference(avatar_split_clause,[],[f3463,f3365,f1351,f7137]) ).

fof(f7137,plain,
    ( spl13_441
  <=> ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_441])]) ).

fof(f3365,plain,
    ( spl13_261
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_261])]) ).

fof(f3463,plain,
    ( ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) )
    | ~ spl13_143
    | ~ spl13_261 ),
    inference(resolution,[],[f3366,f1352]) ).

fof(f3366,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_261 ),
    inference(avatar_component_clause,[],[f3365]) ).

fof(f7135,plain,
    ( spl13_440
    | ~ spl13_33
    | ~ spl13_196 ),
    inference(avatar_split_clause,[],[f2426,f1950,f363,f7133]) ).

fof(f7133,plain,
    ( spl13_440
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_rng(relation_rng(X0)),sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_440])]) ).

fof(f363,plain,
    ( spl13_33
  <=> ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).

fof(f1950,plain,
    ( spl13_196
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_rng(X0),sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_196])]) ).

fof(f2426,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_rng(relation_rng(X0)),sK0)
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_196 ),
    inference(resolution,[],[f1951,f364]) ).

fof(f364,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_33 ),
    inference(avatar_component_clause,[],[f363]) ).

fof(f1951,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_rng(X0),sK0) )
    | ~ spl13_196 ),
    inference(avatar_component_clause,[],[f1950]) ).

fof(f7131,plain,
    ( spl13_439
    | ~ spl13_142
    | ~ spl13_261 ),
    inference(avatar_split_clause,[],[f3462,f3365,f1347,f7129]) ).

fof(f7129,plain,
    ( spl13_439
  <=> ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_439])]) ).

fof(f3462,plain,
    ( ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) )
    | ~ spl13_142
    | ~ spl13_261 ),
    inference(resolution,[],[f3366,f1348]) ).

fof(f7127,plain,
    ( spl13_438
    | ~ spl13_143
    | ~ spl13_260 ),
    inference(avatar_split_clause,[],[f3391,f3361,f1351,f7125]) ).

fof(f7125,plain,
    ( spl13_438
  <=> ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_438])]) ).

fof(f3361,plain,
    ( spl13_260
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_260])]) ).

fof(f3391,plain,
    ( ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(sK0,X1)
        | ~ empty(X1) )
    | ~ spl13_143
    | ~ spl13_260 ),
    inference(resolution,[],[f3362,f1352]) ).

fof(f3362,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_260 ),
    inference(avatar_component_clause,[],[f3361]) ).

fof(f7123,plain,
    ( spl13_437
    | ~ spl13_142
    | ~ spl13_260 ),
    inference(avatar_split_clause,[],[f3390,f3361,f1347,f7121]) ).

fof(f7121,plain,
    ( spl13_437
  <=> ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_437])]) ).

fof(f3390,plain,
    ( ! [X0,X1] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | relation_dom(X0) = relation_composition(X1,sK0)
        | ~ empty(X1) )
    | ~ spl13_142
    | ~ spl13_260 ),
    inference(resolution,[],[f3362,f1348]) ).

fof(f7047,plain,
    ( spl13_436
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_176 ),
    inference(avatar_split_clause,[],[f1876,f1811,f683,f219,f7045]) ).

fof(f7045,plain,
    ( spl13_436
  <=> ! [X0] : sK6 = relation_composition(identity_relation(X0),sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_436])]) ).

fof(f219,plain,
    ( spl13_4
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f683,plain,
    ( spl13_80
  <=> empty_set = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).

fof(f1811,plain,
    ( spl13_176
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(identity_relation(X0),X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_176])]) ).

fof(f1876,plain,
    ( ! [X0] : sK6 = relation_composition(identity_relation(X0),sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_176 ),
    inference(forward_demodulation,[],[f1868,f685]) ).

fof(f685,plain,
    ( empty_set = sK6
    | ~ spl13_80 ),
    inference(avatar_component_clause,[],[f683]) ).

fof(f1868,plain,
    ( ! [X0] : sK6 = relation_composition(identity_relation(X0),empty_set)
    | ~ spl13_4
    | ~ spl13_176 ),
    inference(resolution,[],[f1812,f221]) ).

fof(f221,plain,
    ( empty(empty_set)
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f1812,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | sK6 = relation_composition(identity_relation(X0),X1) )
    | ~ spl13_176 ),
    inference(avatar_component_clause,[],[f1811]) ).

fof(f7043,plain,
    ( spl13_435
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_175 ),
    inference(avatar_split_clause,[],[f1862,f1807,f683,f219,f7041]) ).

fof(f7041,plain,
    ( spl13_435
  <=> ! [X0] : sK6 = relation_composition(sK6,identity_relation(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_435])]) ).

fof(f1807,plain,
    ( spl13_175
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(X0,identity_relation(X1))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_175])]) ).

fof(f1862,plain,
    ( ! [X0] : sK6 = relation_composition(sK6,identity_relation(X0))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_175 ),
    inference(forward_demodulation,[],[f1854,f685]) ).

fof(f1854,plain,
    ( ! [X0] : sK6 = relation_composition(empty_set,identity_relation(X0))
    | ~ spl13_4
    | ~ spl13_175 ),
    inference(resolution,[],[f1808,f221]) ).

fof(f1808,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,identity_relation(X1)) )
    | ~ spl13_175 ),
    inference(avatar_component_clause,[],[f1807]) ).

fof(f7039,plain,
    ( spl13_434
    | ~ spl13_29
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f1467,f1459,f337,f7037]) ).

fof(f7037,plain,
    ( spl13_434
  <=> ! [X0] :
        ( ~ empty(X0)
        | relation(sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_434])]) ).

fof(f337,plain,
    ( spl13_29
  <=> ! [X0] :
        ( relation(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).

fof(f1459,plain,
    ( spl13_152
  <=> ! [X0] :
        ( ~ empty(X0)
        | empty(sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_152])]) ).

fof(f1467,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation(sK2(powerset(X0))) )
    | ~ spl13_29
    | ~ spl13_152 ),
    inference(resolution,[],[f1460,f338]) ).

fof(f338,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation(X0) )
    | ~ spl13_29 ),
    inference(avatar_component_clause,[],[f337]) ).

fof(f1460,plain,
    ( ! [X0] :
        ( empty(sK2(powerset(X0)))
        | ~ empty(X0) )
    | ~ spl13_152 ),
    inference(avatar_component_clause,[],[f1459]) ).

fof(f7035,plain,
    ( spl13_433
    | ~ spl13_35
    | ~ spl13_196 ),
    inference(avatar_split_clause,[],[f2425,f1950,f371,f7033]) ).

fof(f7033,plain,
    ( spl13_433
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_rng(relation_dom(X0)),sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_433])]) ).

fof(f2425,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_rng(relation_dom(X0)),sK0)
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_196 ),
    inference(resolution,[],[f1951,f372]) ).

fof(f7031,plain,
    ( spl13_432
    | ~ spl13_28
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f1466,f1459,f333,f7029]) ).

fof(f7029,plain,
    ( spl13_432
  <=> ! [X0] :
        ( ~ empty(X0)
        | function(sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_432])]) ).

fof(f333,plain,
    ( spl13_28
  <=> ! [X0] :
        ( function(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).

fof(f1466,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(sK2(powerset(X0))) )
    | ~ spl13_28
    | ~ spl13_152 ),
    inference(resolution,[],[f1460,f334]) ).

fof(f334,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(X0) )
    | ~ spl13_28 ),
    inference(avatar_component_clause,[],[f333]) ).

fof(f6971,plain,
    ( spl13_431
    | ~ spl13_124
    | ~ spl13_263 ),
    inference(avatar_split_clause,[],[f3601,f3373,f1118,f6969]) ).

fof(f6969,plain,
    ( spl13_431
  <=> ! [X0] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_431])]) ).

fof(f1118,plain,
    ( spl13_124
  <=> ! [X0] :
        ( sK6 = relation_composition(sK0,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_124])]) ).

fof(f3601,plain,
    ( ! [X0] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_rng(X0)) )
    | ~ spl13_124
    | ~ spl13_263 ),
    inference(resolution,[],[f3374,f1119]) ).

fof(f1119,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK0,X0) )
    | ~ spl13_124 ),
    inference(avatar_component_clause,[],[f1118]) ).

fof(f6967,plain,
    ( spl13_430
    | ~ spl13_157
    | ~ spl13_205 ),
    inference(avatar_split_clause,[],[f2360,f2227,f1499,f6965]) ).

fof(f6965,plain,
    ( spl13_430
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,function_inverse(sK0)))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_430])]) ).

fof(f1499,plain,
    ( spl13_157
  <=> relation(function_inverse(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_157])]) ).

fof(f2227,plain,
    ( spl13_205
  <=> ! [X0,X1] :
        ( sK6 = relation_dom(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_205])]) ).

fof(f2360,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,function_inverse(sK0)))
        | ~ empty(X0) )
    | ~ spl13_157
    | ~ spl13_205 ),
    inference(resolution,[],[f2228,f1500]) ).

fof(f1500,plain,
    ( relation(function_inverse(sK0))
    | ~ spl13_157 ),
    inference(avatar_component_clause,[],[f1499]) ).

fof(f2228,plain,
    ( ! [X0,X1] :
        ( ~ relation(X1)
        | sK6 = relation_dom(relation_composition(X0,X1))
        | ~ empty(X0) )
    | ~ spl13_205 ),
    inference(avatar_component_clause,[],[f2227]) ).

fof(f6963,plain,
    ( spl13_429
    | ~ spl13_117
    | ~ spl13_263 ),
    inference(avatar_split_clause,[],[f3600,f3373,f1079,f6961]) ).

fof(f6961,plain,
    ( spl13_429
  <=> ! [X0] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_rng(X0),sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_429])]) ).

fof(f1079,plain,
    ( spl13_117
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_117])]) ).

fof(f3600,plain,
    ( ! [X0] :
        ( sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_rng(X0),sK0) )
    | ~ spl13_117
    | ~ spl13_263 ),
    inference(resolution,[],[f3374,f1080]) ).

fof(f1080,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,sK0) )
    | ~ spl13_117 ),
    inference(avatar_component_clause,[],[f1079]) ).

fof(f6959,plain,
    ( spl13_428
    | ~ spl13_124
    | ~ spl13_262 ),
    inference(avatar_split_clause,[],[f3532,f3369,f1118,f6957]) ).

fof(f6957,plain,
    ( spl13_428
  <=> ! [X0] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_428])]) ).

fof(f3532,plain,
    ( ! [X0] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_rng(X0)) )
    | ~ spl13_124
    | ~ spl13_262 ),
    inference(resolution,[],[f3370,f1119]) ).

fof(f6955,plain,
    ( spl13_427
    | ~ spl13_117
    | ~ spl13_262 ),
    inference(avatar_split_clause,[],[f3531,f3369,f1079,f6953]) ).

fof(f6953,plain,
    ( spl13_427
  <=> ! [X0] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_rng(X0),sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_427])]) ).

fof(f3531,plain,
    ( ! [X0] :
        ( sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_rng(X0),sK0) )
    | ~ spl13_117
    | ~ spl13_262 ),
    inference(resolution,[],[f3370,f1080]) ).

fof(f6951,plain,
    ( spl13_426
    | ~ spl13_124
    | ~ spl13_261 ),
    inference(avatar_split_clause,[],[f3461,f3365,f1118,f6949]) ).

fof(f6949,plain,
    ( spl13_426
  <=> ! [X0] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_426])]) ).

fof(f3461,plain,
    ( ! [X0] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_dom(X0)) )
    | ~ spl13_124
    | ~ spl13_261 ),
    inference(resolution,[],[f3366,f1119]) ).

fof(f6947,plain,
    ( spl13_425
    | ~ spl13_117
    | ~ spl13_261 ),
    inference(avatar_split_clause,[],[f3460,f3365,f1079,f6945]) ).

fof(f6945,plain,
    ( spl13_425
  <=> ! [X0] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_dom(X0),sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_425])]) ).

fof(f3460,plain,
    ( ! [X0] :
        ( sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_dom(X0),sK0) )
    | ~ spl13_117
    | ~ spl13_261 ),
    inference(resolution,[],[f3366,f1080]) ).

fof(f6943,plain,
    ( spl13_424
    | ~ spl13_124
    | ~ spl13_260 ),
    inference(avatar_split_clause,[],[f3389,f3361,f1118,f6941]) ).

fof(f6941,plain,
    ( spl13_424
  <=> ! [X0] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_424])]) ).

fof(f3389,plain,
    ( ! [X0] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(sK0,relation_dom(X0)) )
    | ~ spl13_124
    | ~ spl13_260 ),
    inference(resolution,[],[f3362,f1119]) ).

fof(f6939,plain,
    ( spl13_423
    | ~ spl13_117
    | ~ spl13_260 ),
    inference(avatar_split_clause,[],[f3388,f3361,f1079,f6937]) ).

fof(f6937,plain,
    ( spl13_423
  <=> ! [X0] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_dom(X0),sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_423])]) ).

fof(f3388,plain,
    ( ! [X0] :
        ( sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | sK6 = relation_composition(relation_dom(X0),sK0) )
    | ~ spl13_117
    | ~ spl13_260 ),
    inference(resolution,[],[f3362,f1080]) ).

fof(f6896,plain,
    ( spl13_422
    | ~ spl13_157
    | ~ spl13_204 ),
    inference(avatar_split_clause,[],[f2338,f2223,f1499,f6894]) ).

fof(f6894,plain,
    ( spl13_422
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(function_inverse(sK0),X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_422])]) ).

fof(f2223,plain,
    ( spl13_204
  <=> ! [X0,X1] :
        ( sK6 = relation_dom(relation_composition(X0,X1))
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_204])]) ).

fof(f2338,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(function_inverse(sK0),X0))
        | ~ empty(X0) )
    | ~ spl13_157
    | ~ spl13_204 ),
    inference(resolution,[],[f2224,f1500]) ).

fof(f2224,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | sK6 = relation_dom(relation_composition(X0,X1))
        | ~ empty(X1) )
    | ~ spl13_204 ),
    inference(avatar_component_clause,[],[f2223]) ).

fof(f6806,plain,
    ( spl13_421
    | ~ spl13_157
    | ~ spl13_202 ),
    inference(avatar_split_clause,[],[f2316,f2215,f1499,f6804]) ).

fof(f6804,plain,
    ( spl13_421
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,function_inverse(sK0)))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_421])]) ).

fof(f2215,plain,
    ( spl13_202
  <=> ! [X0,X1] :
        ( sK6 = relation_rng(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_202])]) ).

fof(f2316,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,function_inverse(sK0)))
        | ~ empty(X0) )
    | ~ spl13_157
    | ~ spl13_202 ),
    inference(resolution,[],[f2216,f1500]) ).

fof(f2216,plain,
    ( ! [X0,X1] :
        ( ~ relation(X1)
        | sK6 = relation_rng(relation_composition(X0,X1))
        | ~ empty(X0) )
    | ~ spl13_202 ),
    inference(avatar_component_clause,[],[f2215]) ).

fof(f6800,plain,
    ( ~ spl13_420
    | ~ spl13_15
    | ~ spl13_58
    | spl13_266 ),
    inference(avatar_split_clause,[],[f3712,f3694,f495,f274,f6797]) ).

fof(f6797,plain,
    ( spl13_420
  <=> relation(function_inverse(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_420])]) ).

fof(f274,plain,
    ( spl13_15
  <=> relation(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).

fof(f495,plain,
    ( spl13_58
  <=> ! [X0,X1] :
        ( relation(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).

fof(f3694,plain,
    ( spl13_266
  <=> relation(relation_composition(function_inverse(sK11),sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_266])]) ).

fof(f3712,plain,
    ( ~ relation(sK11)
    | ~ relation(function_inverse(sK11))
    | ~ spl13_58
    | spl13_266 ),
    inference(resolution,[],[f3696,f496]) ).

fof(f496,plain,
    ( ! [X0,X1] :
        ( relation(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ relation(X0) )
    | ~ spl13_58 ),
    inference(avatar_component_clause,[],[f495]) ).

fof(f3696,plain,
    ( ~ relation(relation_composition(function_inverse(sK11),sK11))
    | spl13_266 ),
    inference(avatar_component_clause,[],[f3694]) ).

fof(f6795,plain,
    ( spl13_419
    | ~ spl13_33
    | ~ spl13_178 ),
    inference(avatar_split_clause,[],[f1896,f1819,f363,f6793]) ).

fof(f6793,plain,
    ( spl13_419
  <=> ! [X0] :
        ( one_to_one(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_419])]) ).

fof(f1819,plain,
    ( spl13_178
  <=> ! [X0] :
        ( ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_178])]) ).

fof(f1896,plain,
    ( ! [X0] :
        ( one_to_one(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_178 ),
    inference(duplicate_literal_removal,[],[f1889]) ).

fof(f1889,plain,
    ( ! [X0] :
        ( one_to_one(relation_rng(X0))
        | ~ empty(X0)
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_178 ),
    inference(resolution,[],[f1820,f364]) ).

fof(f1820,plain,
    ( ! [X0] :
        ( ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_178 ),
    inference(avatar_component_clause,[],[f1819]) ).

fof(f6791,plain,
    ( spl13_418
    | ~ spl13_35
    | ~ spl13_177 ),
    inference(avatar_split_clause,[],[f1888,f1815,f371,f6789]) ).

fof(f6789,plain,
    ( spl13_418
  <=> ! [X0] :
        ( one_to_one(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_418])]) ).

fof(f1815,plain,
    ( spl13_177
  <=> ! [X0] :
        ( ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_177])]) ).

fof(f1888,plain,
    ( ! [X0] :
        ( one_to_one(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_177 ),
    inference(duplicate_literal_removal,[],[f1880]) ).

fof(f1880,plain,
    ( ! [X0] :
        ( one_to_one(relation_dom(X0))
        | ~ empty(X0)
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_177 ),
    inference(resolution,[],[f1816,f372]) ).

fof(f1816,plain,
    ( ! [X0] :
        ( ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_177 ),
    inference(avatar_component_clause,[],[f1815]) ).

fof(f6787,plain,
    ( ~ spl13_417
    | ~ spl13_15
    | ~ spl13_53
    | spl13_179 ),
    inference(avatar_split_clause,[],[f1833,f1823,f474,f274,f6784]) ).

fof(f6784,plain,
    ( spl13_417
  <=> empty(function_inverse(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_417])]) ).

fof(f474,plain,
    ( spl13_53
  <=> ! [X0,X1] :
        ( empty(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).

fof(f1823,plain,
    ( spl13_179
  <=> empty(relation_composition(function_inverse(sK11),sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_179])]) ).

fof(f1833,plain,
    ( ~ relation(sK11)
    | ~ empty(function_inverse(sK11))
    | ~ spl13_53
    | spl13_179 ),
    inference(resolution,[],[f1825,f475]) ).

fof(f475,plain,
    ( ! [X0,X1] :
        ( empty(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_53 ),
    inference(avatar_component_clause,[],[f474]) ).

fof(f1825,plain,
    ( ~ empty(relation_composition(function_inverse(sK11),sK11))
    | spl13_179 ),
    inference(avatar_component_clause,[],[f1823]) ).

fof(f6782,plain,
    ( spl13_416
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_173 ),
    inference(avatar_split_clause,[],[f1788,f1572,f683,f219,f6779]) ).

fof(f6779,plain,
    ( spl13_416
  <=> sK6 = relation_composition(sK11,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_416])]) ).

fof(f1572,plain,
    ( spl13_173
  <=> ! [X0] :
        ( sK6 = relation_composition(sK11,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_173])]) ).

fof(f1788,plain,
    ( sK6 = relation_composition(sK11,sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_173 ),
    inference(forward_demodulation,[],[f1780,f685]) ).

fof(f1780,plain,
    ( sK6 = relation_composition(sK11,empty_set)
    | ~ spl13_4
    | ~ spl13_173 ),
    inference(resolution,[],[f1573,f221]) ).

fof(f1573,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK11,X0) )
    | ~ spl13_173 ),
    inference(avatar_component_clause,[],[f1572]) ).

fof(f6777,plain,
    ( spl13_415
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_172 ),
    inference(avatar_split_clause,[],[f1774,f1568,f683,f219,f6774]) ).

fof(f6774,plain,
    ( spl13_415
  <=> sK6 = relation_composition(sK10,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_415])]) ).

fof(f1568,plain,
    ( spl13_172
  <=> ! [X0] :
        ( sK6 = relation_composition(sK10,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_172])]) ).

fof(f1774,plain,
    ( sK6 = relation_composition(sK10,sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_172 ),
    inference(forward_demodulation,[],[f1766,f685]) ).

fof(f1766,plain,
    ( sK6 = relation_composition(sK10,empty_set)
    | ~ spl13_4
    | ~ spl13_172 ),
    inference(resolution,[],[f1569,f221]) ).

fof(f1569,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK10,X0) )
    | ~ spl13_172 ),
    inference(avatar_component_clause,[],[f1568]) ).

fof(f6772,plain,
    ( spl13_414
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_171 ),
    inference(avatar_split_clause,[],[f1755,f1564,f683,f219,f6769]) ).

fof(f6769,plain,
    ( spl13_414
  <=> sK6 = relation_composition(sK9,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_414])]) ).

fof(f1564,plain,
    ( spl13_171
  <=> ! [X0] :
        ( sK6 = relation_composition(sK9,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_171])]) ).

fof(f1755,plain,
    ( sK6 = relation_composition(sK9,sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_171 ),
    inference(forward_demodulation,[],[f1747,f685]) ).

fof(f1747,plain,
    ( sK6 = relation_composition(sK9,empty_set)
    | ~ spl13_4
    | ~ spl13_171 ),
    inference(resolution,[],[f1565,f221]) ).

fof(f1565,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK9,X0) )
    | ~ spl13_171 ),
    inference(avatar_component_clause,[],[f1564]) ).

fof(f6767,plain,
    ( spl13_413
    | ~ spl13_157
    | ~ spl13_201 ),
    inference(avatar_split_clause,[],[f2294,f2211,f1499,f6765]) ).

fof(f6765,plain,
    ( spl13_413
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(function_inverse(sK0),X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_413])]) ).

fof(f2211,plain,
    ( spl13_201
  <=> ! [X0,X1] :
        ( sK6 = relation_rng(relation_composition(X0,X1))
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_201])]) ).

fof(f2294,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(function_inverse(sK0),X0))
        | ~ empty(X0) )
    | ~ spl13_157
    | ~ spl13_201 ),
    inference(resolution,[],[f2212,f1500]) ).

fof(f2212,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | sK6 = relation_rng(relation_composition(X0,X1))
        | ~ empty(X1) )
    | ~ spl13_201 ),
    inference(avatar_component_clause,[],[f2211]) ).

fof(f6763,plain,
    ( spl13_412
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_170 ),
    inference(avatar_split_clause,[],[f1741,f1560,f683,f219,f6760]) ).

fof(f6760,plain,
    ( spl13_412
  <=> sK6 = relation_composition(sK7,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_412])]) ).

fof(f1560,plain,
    ( spl13_170
  <=> ! [X0] :
        ( sK6 = relation_composition(sK7,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_170])]) ).

fof(f1741,plain,
    ( sK6 = relation_composition(sK7,sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_170 ),
    inference(forward_demodulation,[],[f1733,f685]) ).

fof(f1733,plain,
    ( sK6 = relation_composition(sK7,empty_set)
    | ~ spl13_4
    | ~ spl13_170 ),
    inference(resolution,[],[f1561,f221]) ).

fof(f1561,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK7,X0) )
    | ~ spl13_170 ),
    inference(avatar_component_clause,[],[f1560]) ).

fof(f6758,plain,
    ( spl13_411
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_169 ),
    inference(avatar_split_clause,[],[f1727,f1556,f683,f219,f6755]) ).

fof(f6755,plain,
    ( spl13_411
  <=> sK6 = relation_composition(sK6,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_411])]) ).

fof(f1556,plain,
    ( spl13_169
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,sK6)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_169])]) ).

fof(f1727,plain,
    ( sK6 = relation_composition(sK6,sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_169 ),
    inference(forward_demodulation,[],[f1719,f685]) ).

fof(f1719,plain,
    ( sK6 = relation_composition(empty_set,sK6)
    | ~ spl13_4
    | ~ spl13_169 ),
    inference(resolution,[],[f1557,f221]) ).

fof(f1557,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,sK6) )
    | ~ spl13_169 ),
    inference(avatar_component_clause,[],[f1556]) ).

fof(f6753,plain,
    ( spl13_410
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_168 ),
    inference(avatar_split_clause,[],[f1713,f1552,f683,f219,f6750]) ).

fof(f6750,plain,
    ( spl13_410
  <=> sK6 = relation_composition(sK6,sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_410])]) ).

fof(f1552,plain,
    ( spl13_168
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,sK11)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_168])]) ).

fof(f1713,plain,
    ( sK6 = relation_composition(sK6,sK11)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_168 ),
    inference(forward_demodulation,[],[f1705,f685]) ).

fof(f1705,plain,
    ( sK6 = relation_composition(empty_set,sK11)
    | ~ spl13_4
    | ~ spl13_168 ),
    inference(resolution,[],[f1553,f221]) ).

fof(f1553,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,sK11) )
    | ~ spl13_168 ),
    inference(avatar_component_clause,[],[f1552]) ).

fof(f6748,plain,
    ( spl13_409
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_167 ),
    inference(avatar_split_clause,[],[f1699,f1548,f683,f219,f6745]) ).

fof(f6745,plain,
    ( spl13_409
  <=> sK6 = relation_composition(sK6,sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_409])]) ).

fof(f1548,plain,
    ( spl13_167
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,sK10)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_167])]) ).

fof(f1699,plain,
    ( sK6 = relation_composition(sK6,sK10)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_167 ),
    inference(forward_demodulation,[],[f1691,f685]) ).

fof(f1691,plain,
    ( sK6 = relation_composition(empty_set,sK10)
    | ~ spl13_4
    | ~ spl13_167 ),
    inference(resolution,[],[f1549,f221]) ).

fof(f1549,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,sK10) )
    | ~ spl13_167 ),
    inference(avatar_component_clause,[],[f1548]) ).

fof(f6743,plain,
    ( spl13_408
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_166 ),
    inference(avatar_split_clause,[],[f1685,f1543,f683,f219,f6740]) ).

fof(f6740,plain,
    ( spl13_408
  <=> sK6 = relation_composition(sK6,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_408])]) ).

fof(f1543,plain,
    ( spl13_166
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,sK9)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_166])]) ).

fof(f1685,plain,
    ( sK6 = relation_composition(sK6,sK9)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_166 ),
    inference(forward_demodulation,[],[f1677,f685]) ).

fof(f1677,plain,
    ( sK6 = relation_composition(empty_set,sK9)
    | ~ spl13_4
    | ~ spl13_166 ),
    inference(resolution,[],[f1544,f221]) ).

fof(f1544,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,sK9) )
    | ~ spl13_166 ),
    inference(avatar_component_clause,[],[f1543]) ).

fof(f6738,plain,
    ( spl13_407
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_165 ),
    inference(avatar_split_clause,[],[f1671,f1539,f683,f219,f6735]) ).

fof(f6735,plain,
    ( spl13_407
  <=> sK6 = relation_composition(sK6,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_407])]) ).

fof(f1539,plain,
    ( spl13_165
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,sK7)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_165])]) ).

fof(f1671,plain,
    ( sK6 = relation_composition(sK6,sK7)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_165 ),
    inference(forward_demodulation,[],[f1663,f685]) ).

fof(f1663,plain,
    ( sK6 = relation_composition(empty_set,sK7)
    | ~ spl13_4
    | ~ spl13_165 ),
    inference(resolution,[],[f1540,f221]) ).

fof(f1540,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,sK7) )
    | ~ spl13_165 ),
    inference(avatar_component_clause,[],[f1539]) ).

fof(f6733,plain,
    ( spl13_406
    | ~ spl13_88
    | ~ spl13_148 ),
    inference(avatar_split_clause,[],[f1430,f1420,f730,f6731]) ).

fof(f6731,plain,
    ( spl13_406
  <=> ! [X0] :
        ( function(X0)
        | ~ empty(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_406])]) ).

fof(f730,plain,
    ( spl13_88
  <=> ! [X0] :
        ( ~ empty(X0)
        | function(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_88])]) ).

fof(f1420,plain,
    ( spl13_148
  <=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_148])]) ).

fof(f1430,plain,
    ( ! [X0] :
        ( function(X0)
        | ~ empty(identity_relation(X0)) )
    | ~ spl13_88
    | ~ spl13_148 ),
    inference(superposition,[],[f731,f1421]) ).

fof(f1421,plain,
    ( ! [X0] : relation_dom(identity_relation(X0)) = X0
    | ~ spl13_148 ),
    inference(avatar_component_clause,[],[f1420]) ).

fof(f731,plain,
    ( ! [X0] :
        ( function(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_88 ),
    inference(avatar_component_clause,[],[f730]) ).

fof(f6729,plain,
    ( spl13_405
    | ~ spl13_36
    | ~ spl13_148 ),
    inference(avatar_split_clause,[],[f1424,f1420,f375,f6727]) ).

fof(f6727,plain,
    ( spl13_405
  <=> ! [X0] :
        ( relation(X0)
        | ~ empty(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_405])]) ).

fof(f375,plain,
    ( spl13_36
  <=> ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).

fof(f1424,plain,
    ( ! [X0] :
        ( relation(X0)
        | ~ empty(identity_relation(X0)) )
    | ~ spl13_36
    | ~ spl13_148 ),
    inference(superposition,[],[f376,f1421]) ).

fof(f376,plain,
    ( ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_36 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f6725,plain,
    ( spl13_404
    | ~ spl13_35
    | ~ spl13_148 ),
    inference(avatar_split_clause,[],[f1423,f1420,f371,f6723]) ).

fof(f6723,plain,
    ( spl13_404
  <=> ! [X0] :
        ( empty(X0)
        | ~ empty(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_404])]) ).

fof(f1423,plain,
    ( ! [X0] :
        ( empty(X0)
        | ~ empty(identity_relation(X0)) )
    | ~ spl13_35
    | ~ spl13_148 ),
    inference(superposition,[],[f372,f1421]) ).

fof(f6721,plain,
    ( spl13_403
    | ~ spl13_33
    | ~ spl13_185 ),
    inference(avatar_split_clause,[],[f2266,f1906,f363,f6719]) ).

fof(f6719,plain,
    ( spl13_403
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_dom(relation_rng(X0)),sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_403])]) ).

fof(f1906,plain,
    ( spl13_185
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_dom(X0),sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_185])]) ).

fof(f2266,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_dom(relation_rng(X0)),sK0)
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_185 ),
    inference(resolution,[],[f1907,f364]) ).

fof(f1907,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_dom(X0),sK0) )
    | ~ spl13_185 ),
    inference(avatar_component_clause,[],[f1906]) ).

fof(f6717,plain,
    ( spl13_402
    | ~ spl13_160
    | ~ spl13_199 ),
    inference(avatar_split_clause,[],[f3909,f1962,f1512,f6714]) ).

fof(f6714,plain,
    ( spl13_402
  <=> sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) = apply(identity_relation(relation_dom(sK0)),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_402])]) ).

fof(f1962,plain,
    ( spl13_199
  <=> ! [X0,X1] :
        ( ~ in(X0,X1)
        | apply(identity_relation(X1),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_199])]) ).

fof(f3909,plain,
    ( sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) = apply(identity_relation(relation_dom(sK0)),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))))
    | ~ spl13_160
    | ~ spl13_199 ),
    inference(resolution,[],[f1514,f1963]) ).

fof(f1963,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | apply(identity_relation(X1),X0) = X0 )
    | ~ spl13_199 ),
    inference(avatar_component_clause,[],[f1962]) ).

fof(f6712,plain,
    ( spl13_401
    | ~ spl13_156
    | ~ spl13_199 ),
    inference(avatar_split_clause,[],[f3885,f1962,f1488,f6709]) ).

fof(f6709,plain,
    ( spl13_401
  <=> sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)) = apply(identity_relation(relation_rng(sK0)),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_401])]) ).

fof(f3885,plain,
    ( sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)) = apply(identity_relation(relation_rng(sK0)),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)))
    | ~ spl13_156
    | ~ spl13_199 ),
    inference(resolution,[],[f1490,f1963]) ).

fof(f6707,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_3
    | spl13_400
    | spl13_82
    | ~ spl13_263 ),
    inference(avatar_split_clause,[],[f3590,f3373,f692,f6704,f214,f209,f204]) ).

fof(f6704,plain,
    ( spl13_400
  <=> sK2(relation_rng(sK0)) = apply(sK0,apply(function_inverse(sK0),sK2(relation_rng(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_400])]) ).

fof(f692,plain,
    ( spl13_82
  <=> empty(relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_82])]) ).

fof(f3590,plain,
    ( sK2(relation_rng(sK0)) = apply(sK0,apply(function_inverse(sK0),sK2(relation_rng(sK0))))
    | ~ one_to_one(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | spl13_82
    | ~ spl13_263 ),
    inference(resolution,[],[f3374,f693]) ).

fof(f693,plain,
    ( ~ empty(relation_rng(sK0))
    | spl13_82 ),
    inference(avatar_component_clause,[],[f692]) ).

fof(f6702,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_3
    | spl13_399
    | spl13_82
    | ~ spl13_262 ),
    inference(avatar_split_clause,[],[f3521,f3369,f692,f6699,f214,f209,f204]) ).

fof(f6699,plain,
    ( spl13_399
  <=> sK2(relation_rng(sK0)) = apply(relation_composition(function_inverse(sK0),sK0),sK2(relation_rng(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_399])]) ).

fof(f3521,plain,
    ( sK2(relation_rng(sK0)) = apply(relation_composition(function_inverse(sK0),sK0),sK2(relation_rng(sK0)))
    | ~ one_to_one(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | spl13_82
    | ~ spl13_262 ),
    inference(resolution,[],[f3370,f693]) ).

fof(f6697,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_3
    | spl13_398
    | spl13_141
    | ~ spl13_261 ),
    inference(avatar_split_clause,[],[f3450,f3365,f1339,f6694,f214,f209,f204]) ).

fof(f6694,plain,
    ( spl13_398
  <=> sK2(relation_dom(sK0)) = apply(function_inverse(sK0),apply(sK0,sK2(relation_dom(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_398])]) ).

fof(f1339,plain,
    ( spl13_141
  <=> empty(relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_141])]) ).

fof(f3450,plain,
    ( sK2(relation_dom(sK0)) = apply(function_inverse(sK0),apply(sK0,sK2(relation_dom(sK0))))
    | ~ one_to_one(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | spl13_141
    | ~ spl13_261 ),
    inference(resolution,[],[f3366,f1340]) ).

fof(f1340,plain,
    ( ~ empty(relation_dom(sK0))
    | spl13_141 ),
    inference(avatar_component_clause,[],[f1339]) ).

fof(f6689,plain,
    ( ~ spl13_141
    | ~ spl13_38
    | ~ spl13_160 ),
    inference(avatar_split_clause,[],[f4222,f1512,f383,f1339]) ).

fof(f383,plain,
    ( spl13_38
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).

fof(f4222,plain,
    ( ~ empty(relation_dom(sK0))
    | ~ spl13_38
    | ~ spl13_160 ),
    inference(resolution,[],[f1514,f384]) ).

fof(f384,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | ~ empty(X1) )
    | ~ spl13_38 ),
    inference(avatar_component_clause,[],[f383]) ).

fof(f6674,plain,
    ( spl13_397
    | ~ spl13_26
    | ~ spl13_89
    | ~ spl13_141 ),
    inference(avatar_split_clause,[],[f6661,f1339,f735,f324,f6671]) ).

fof(f6671,plain,
    ( spl13_397
  <=> relation_composition(sK0,function_inverse(sK0)) = identity_relation(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_397])]) ).

fof(f735,plain,
    ( spl13_89
  <=> ! [X0] :
        ( sK6 = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_89])]) ).

fof(f6661,plain,
    ( relation_composition(sK0,function_inverse(sK0)) = identity_relation(sK6)
    | ~ spl13_26
    | ~ spl13_89
    | ~ spl13_141 ),
    inference(forward_demodulation,[],[f325,f6342]) ).

fof(f6342,plain,
    ( relation_dom(sK0) = sK6
    | ~ spl13_89
    | ~ spl13_141 ),
    inference(resolution,[],[f1341,f736]) ).

fof(f736,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = X0 )
    | ~ spl13_89 ),
    inference(avatar_component_clause,[],[f735]) ).

fof(f1341,plain,
    ( empty(relation_dom(sK0))
    | ~ spl13_141 ),
    inference(avatar_component_clause,[],[f1339]) ).

fof(f325,plain,
    ( relation_composition(sK0,function_inverse(sK0)) = identity_relation(relation_dom(sK0))
    | ~ spl13_26 ),
    inference(avatar_component_clause,[],[f324]) ).

fof(f6667,plain,
    ( spl13_396
    | ~ spl13_26
    | ~ spl13_89
    | ~ spl13_141
    | ~ spl13_258 ),
    inference(avatar_split_clause,[],[f6662,f3328,f1339,f735,f324,f6664]) ).

fof(f6664,plain,
    ( spl13_396
  <=> relation_composition(sK0,function_inverse(sK0)) = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_396])]) ).

fof(f3328,plain,
    ( spl13_258
  <=> sK6 = identity_relation(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_258])]) ).

fof(f6662,plain,
    ( relation_composition(sK0,function_inverse(sK0)) = sK6
    | ~ spl13_26
    | ~ spl13_89
    | ~ spl13_141
    | ~ spl13_258 ),
    inference(forward_demodulation,[],[f6661,f3330]) ).

fof(f3330,plain,
    ( sK6 = identity_relation(sK6)
    | ~ spl13_258 ),
    inference(avatar_component_clause,[],[f3328]) ).

fof(f6645,plain,
    ( ~ spl13_141
    | ~ spl13_38
    | ~ spl13_160 ),
    inference(avatar_split_clause,[],[f4222,f1512,f383,f1339]) ).

fof(f6336,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_3
    | spl13_395
    | spl13_141
    | ~ spl13_260 ),
    inference(avatar_split_clause,[],[f3378,f3361,f1339,f6333,f214,f209,f204]) ).

fof(f6333,plain,
    ( spl13_395
  <=> sK2(relation_dom(sK0)) = apply(relation_composition(sK0,function_inverse(sK0)),sK2(relation_dom(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_395])]) ).

fof(f3378,plain,
    ( sK2(relation_dom(sK0)) = apply(relation_composition(sK0,function_inverse(sK0)),sK2(relation_dom(sK0)))
    | ~ one_to_one(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | spl13_141
    | ~ spl13_260 ),
    inference(resolution,[],[f3362,f1340]) ).

fof(f6313,plain,
    ( ~ spl13_159
    | spl13_394
    | ~ spl13_158
    | ~ spl13_248 ),
    inference(avatar_split_clause,[],[f3119,f3081,f1504,f6311,f1508]) ).

fof(f6311,plain,
    ( spl13_394
  <=> ! [X0,X1] :
        ( relation_composition(function_inverse(relation_composition(sK0,function_inverse(sK0))),X0) = X1
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_394])]) ).

fof(f3081,plain,
    ( spl13_248
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(function_inverse(X1),X0) = X2
        | ~ empty(X2)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_248])]) ).

fof(f3119,plain,
    ( ! [X0,X1] :
        ( relation_composition(function_inverse(relation_composition(sK0,function_inverse(sK0))),X0) = X1
        | ~ empty(X1)
        | ~ function(relation_composition(sK0,function_inverse(sK0)))
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_248 ),
    inference(resolution,[],[f3082,f1505]) ).

fof(f1505,plain,
    ( relation(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_158 ),
    inference(avatar_component_clause,[],[f1504]) ).

fof(f3082,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | relation_composition(function_inverse(X1),X0) = X2
        | ~ empty(X2)
        | ~ function(X1)
        | ~ empty(X0) )
    | ~ spl13_248 ),
    inference(avatar_component_clause,[],[f3081]) ).

fof(f6291,plain,
    ( ~ spl13_155
    | spl13_393
    | ~ spl13_154
    | ~ spl13_248 ),
    inference(avatar_split_clause,[],[f3118,f3081,f1480,f6289,f1484]) ).

fof(f1484,plain,
    ( spl13_155
  <=> function(relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_155])]) ).

fof(f6289,plain,
    ( spl13_393
  <=> ! [X0,X1] :
        ( relation_composition(function_inverse(relation_composition(function_inverse(sK0),sK0)),X0) = X1
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_393])]) ).

fof(f1480,plain,
    ( spl13_154
  <=> relation(relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_154])]) ).

fof(f3118,plain,
    ( ! [X0,X1] :
        ( relation_composition(function_inverse(relation_composition(function_inverse(sK0),sK0)),X0) = X1
        | ~ empty(X1)
        | ~ function(relation_composition(function_inverse(sK0),sK0))
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_248 ),
    inference(resolution,[],[f3082,f1481]) ).

fof(f1481,plain,
    ( relation(relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_154 ),
    inference(avatar_component_clause,[],[f1480]) ).

fof(f6269,plain,
    ( ~ spl13_159
    | spl13_392
    | ~ spl13_158
    | ~ spl13_247 ),
    inference(avatar_split_clause,[],[f3094,f3077,f1504,f6267,f1508]) ).

fof(f6267,plain,
    ( spl13_392
  <=> ! [X0,X1] :
        ( relation_composition(X0,function_inverse(relation_composition(sK0,function_inverse(sK0)))) = X1
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_392])]) ).

fof(f3077,plain,
    ( spl13_247
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,function_inverse(X1)) = X2
        | ~ empty(X2)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_247])]) ).

fof(f3094,plain,
    ( ! [X0,X1] :
        ( relation_composition(X0,function_inverse(relation_composition(sK0,function_inverse(sK0)))) = X1
        | ~ empty(X1)
        | ~ function(relation_composition(sK0,function_inverse(sK0)))
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_247 ),
    inference(resolution,[],[f3078,f1505]) ).

fof(f3078,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | relation_composition(X0,function_inverse(X1)) = X2
        | ~ empty(X2)
        | ~ function(X1)
        | ~ empty(X0) )
    | ~ spl13_247 ),
    inference(avatar_component_clause,[],[f3077]) ).

fof(f6247,plain,
    ( ~ spl13_155
    | spl13_391
    | ~ spl13_154
    | ~ spl13_247 ),
    inference(avatar_split_clause,[],[f3093,f3077,f1480,f6245,f1484]) ).

fof(f6245,plain,
    ( spl13_391
  <=> ! [X0,X1] :
        ( relation_composition(X0,function_inverse(relation_composition(function_inverse(sK0),sK0))) = X1
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_391])]) ).

fof(f3093,plain,
    ( ! [X0,X1] :
        ( relation_composition(X0,function_inverse(relation_composition(function_inverse(sK0),sK0))) = X1
        | ~ empty(X1)
        | ~ function(relation_composition(function_inverse(sK0),sK0))
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_247 ),
    inference(resolution,[],[f3078,f1481]) ).

fof(f6243,plain,
    ( spl13_390
    | ~ spl13_35
    | ~ spl13_185 ),
    inference(avatar_split_clause,[],[f2265,f1906,f371,f6241]) ).

fof(f6241,plain,
    ( spl13_390
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_dom(relation_dom(X0)),sK0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_390])]) ).

fof(f2265,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_dom(relation_dom(X0)),sK0)
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_185 ),
    inference(resolution,[],[f1907,f372]) ).

fof(f6239,plain,
    ( spl13_389
    | ~ spl13_149
    | ~ spl13_160
    | ~ spl13_199 ),
    inference(avatar_split_clause,[],[f3913,f1962,f1512,f1435,f6236]) ).

fof(f6236,plain,
    ( spl13_389
  <=> sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) = apply(sK0,sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_389])]) ).

fof(f1435,plain,
    ( spl13_149
  <=> sK0 = identity_relation(relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_149])]) ).

fof(f3913,plain,
    ( sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) = apply(sK0,sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))))
    | ~ spl13_149
    | ~ spl13_160
    | ~ spl13_199 ),
    inference(forward_demodulation,[],[f3909,f1437]) ).

fof(f1437,plain,
    ( sK0 = identity_relation(relation_dom(sK0))
    | ~ spl13_149 ),
    inference(avatar_component_clause,[],[f1435]) ).

fof(f5976,plain,
    ( spl13_388
    | ~ spl13_158
    | ~ spl13_255 ),
    inference(avatar_split_clause,[],[f3297,f3159,f1504,f5974]) ).

fof(f5974,plain,
    ( spl13_388
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_388])]) ).

fof(f3159,plain,
    ( spl13_255
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_255])]) ).

fof(f3297,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ relation(X0) )
    | ~ spl13_158
    | ~ spl13_255 ),
    inference(resolution,[],[f3160,f1505]) ).

fof(f3160,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation(X2)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_255 ),
    inference(avatar_component_clause,[],[f3159]) ).

fof(f5972,plain,
    ( spl13_387
    | ~ spl13_154
    | ~ spl13_255 ),
    inference(avatar_split_clause,[],[f3296,f3159,f1480,f5970]) ).

fof(f5970,plain,
    ( spl13_387
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_387])]) ).

fof(f3296,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ relation(X0) )
    | ~ spl13_154
    | ~ spl13_255 ),
    inference(resolution,[],[f3160,f1481]) ).

fof(f5968,plain,
    ( spl13_386
    | ~ spl13_158
    | ~ spl13_254 ),
    inference(avatar_split_clause,[],[f3275,f3155,f1504,f5966]) ).

fof(f5966,plain,
    ( spl13_386
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_386])]) ).

fof(f3155,plain,
    ( spl13_254
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_254])]) ).

fof(f3275,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_254 ),
    inference(resolution,[],[f3156,f1505]) ).

fof(f3156,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation(X2)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_254 ),
    inference(avatar_component_clause,[],[f3155]) ).

fof(f5964,plain,
    ( spl13_385
    | ~ spl13_154
    | ~ spl13_254 ),
    inference(avatar_split_clause,[],[f3274,f3155,f1480,f5962]) ).

fof(f5962,plain,
    ( spl13_385
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_385])]) ).

fof(f3274,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_254 ),
    inference(resolution,[],[f3156,f1481]) ).

fof(f5950,plain,
    ( spl13_384
    | ~ spl13_158
    | ~ spl13_253 ),
    inference(avatar_split_clause,[],[f3253,f3151,f1504,f5948]) ).

fof(f5948,plain,
    ( spl13_384
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_384])]) ).

fof(f3151,plain,
    ( spl13_253
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_253])]) ).

fof(f3253,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_253 ),
    inference(resolution,[],[f3152,f1505]) ).

fof(f3152,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation(X1)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ empty(X0)
        | ~ empty(X2) )
    | ~ spl13_253 ),
    inference(avatar_component_clause,[],[f3151]) ).

fof(f5946,plain,
    ( spl13_383
    | ~ spl13_154
    | ~ spl13_253 ),
    inference(avatar_split_clause,[],[f3252,f3151,f1480,f5944]) ).

fof(f5944,plain,
    ( spl13_383
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(relation_composition(function_inverse(sK0),sK0),X0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_383])]) ).

fof(f3252,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(relation_composition(function_inverse(sK0),sK0),X0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_253 ),
    inference(resolution,[],[f3152,f1481]) ).

fof(f5942,plain,
    ( spl13_382
    | ~ spl13_158
    | ~ spl13_252 ),
    inference(avatar_split_clause,[],[f3231,f3147,f1504,f5940]) ).

fof(f5940,plain,
    ( spl13_382
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0)))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_382])]) ).

fof(f3147,plain,
    ( spl13_252
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_252])]) ).

fof(f3231,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0)))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_158
    | ~ spl13_252 ),
    inference(resolution,[],[f3148,f1505]) ).

fof(f3148,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation(X2)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_252 ),
    inference(avatar_component_clause,[],[f3147]) ).

fof(f5938,plain,
    ( spl13_381
    | ~ spl13_154
    | ~ spl13_252 ),
    inference(avatar_split_clause,[],[f3230,f3147,f1480,f5936]) ).

fof(f5936,plain,
    ( spl13_381
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_381])]) ).

fof(f3230,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_154
    | ~ spl13_252 ),
    inference(resolution,[],[f3148,f1481]) ).

fof(f5934,plain,
    ( spl13_380
    | ~ spl13_158
    | ~ spl13_251 ),
    inference(avatar_split_clause,[],[f3190,f3143,f1504,f5932]) ).

fof(f5932,plain,
    ( spl13_380
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0)))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_380])]) ).

fof(f3143,plain,
    ( spl13_251
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_251])]) ).

fof(f3190,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0)))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_158
    | ~ spl13_251 ),
    inference(resolution,[],[f3144,f1505]) ).

fof(f3144,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation(X2)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_251 ),
    inference(avatar_component_clause,[],[f3143]) ).

fof(f5930,plain,
    ( spl13_379
    | ~ spl13_154
    | ~ spl13_251 ),
    inference(avatar_split_clause,[],[f3189,f3143,f1480,f5928]) ).

fof(f5928,plain,
    ( spl13_379
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_379])]) ).

fof(f3189,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0))) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_154
    | ~ spl13_251 ),
    inference(resolution,[],[f3144,f1481]) ).

fof(f5926,plain,
    ( spl13_378
    | ~ spl13_158
    | ~ spl13_250 ),
    inference(avatar_split_clause,[],[f3168,f3139,f1504,f5924]) ).

fof(f5924,plain,
    ( spl13_378
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(relation_composition(sK0,function_inverse(sK0)),X1)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_378])]) ).

fof(f3139,plain,
    ( spl13_250
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_250])]) ).

fof(f3168,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(relation_composition(sK0,function_inverse(sK0)),X1)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_158
    | ~ spl13_250 ),
    inference(resolution,[],[f3140,f1505]) ).

fof(f3140,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation(X1)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ empty(X0)
        | ~ empty(X2) )
    | ~ spl13_250 ),
    inference(avatar_component_clause,[],[f3139]) ).

fof(f5922,plain,
    ( spl13_377
    | ~ spl13_154
    | ~ spl13_250 ),
    inference(avatar_split_clause,[],[f3167,f3139,f1480,f5920]) ).

fof(f5920,plain,
    ( spl13_377
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(relation_composition(function_inverse(sK0),sK0),X1)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_377])]) ).

fof(f3167,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(relation_composition(function_inverse(sK0),sK0),X1)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_154
    | ~ spl13_250 ),
    inference(resolution,[],[f3140,f1481]) ).

fof(f5900,plain,
    ( ~ spl13_159
    | spl13_376
    | ~ spl13_158
    | ~ spl13_231 ),
    inference(avatar_split_clause,[],[f2825,f2675,f1504,f5898,f1508]) ).

fof(f5898,plain,
    ( spl13_376
  <=> ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(function_inverse(relation_composition(sK0,function_inverse(sK0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_376])]) ).

fof(f2675,plain,
    ( spl13_231
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(function_inverse(X0),X1)
        | ~ empty(X1)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_231])]) ).

fof(f2825,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ~ function(relation_composition(sK0,function_inverse(sK0)))
        | sK6 = relation_composition(function_inverse(relation_composition(sK0,function_inverse(sK0))),X0) )
    | ~ spl13_158
    | ~ spl13_231 ),
    inference(resolution,[],[f2676,f1505]) ).

fof(f2676,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | ~ function(X0)
        | sK6 = relation_composition(function_inverse(X0),X1) )
    | ~ spl13_231 ),
    inference(avatar_component_clause,[],[f2675]) ).

fof(f5868,plain,
    ( ~ spl13_155
    | spl13_375
    | ~ spl13_154
    | ~ spl13_231 ),
    inference(avatar_split_clause,[],[f2824,f2675,f1480,f5866,f1484]) ).

fof(f5866,plain,
    ( spl13_375
  <=> ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(function_inverse(relation_composition(function_inverse(sK0),sK0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_375])]) ).

fof(f2824,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ~ function(relation_composition(function_inverse(sK0),sK0))
        | sK6 = relation_composition(function_inverse(relation_composition(function_inverse(sK0),sK0)),X0) )
    | ~ spl13_154
    | ~ spl13_231 ),
    inference(resolution,[],[f2676,f1481]) ).

fof(f5846,plain,
    ( ~ spl13_159
    | spl13_374
    | ~ spl13_158
    | ~ spl13_230 ),
    inference(avatar_split_clause,[],[f2800,f2671,f1504,f5844,f1508]) ).

fof(f5844,plain,
    ( spl13_374
  <=> ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,function_inverse(relation_composition(sK0,function_inverse(sK0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_374])]) ).

fof(f2671,plain,
    ( spl13_230
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(X0,function_inverse(X1))
        | ~ empty(X0)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_230])]) ).

fof(f2800,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ~ function(relation_composition(sK0,function_inverse(sK0)))
        | sK6 = relation_composition(X0,function_inverse(relation_composition(sK0,function_inverse(sK0)))) )
    | ~ spl13_158
    | ~ spl13_230 ),
    inference(resolution,[],[f2672,f1505]) ).

fof(f2672,plain,
    ( ! [X0,X1] :
        ( ~ relation(X1)
        | ~ empty(X0)
        | ~ function(X1)
        | sK6 = relation_composition(X0,function_inverse(X1)) )
    | ~ spl13_230 ),
    inference(avatar_component_clause,[],[f2671]) ).

fof(f5824,plain,
    ( ~ spl13_155
    | spl13_373
    | ~ spl13_154
    | ~ spl13_230 ),
    inference(avatar_split_clause,[],[f2799,f2671,f1480,f5822,f1484]) ).

fof(f5822,plain,
    ( spl13_373
  <=> ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,function_inverse(relation_composition(function_inverse(sK0),sK0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_373])]) ).

fof(f2799,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ~ function(relation_composition(function_inverse(sK0),sK0))
        | sK6 = relation_composition(X0,function_inverse(relation_composition(function_inverse(sK0),sK0))) )
    | ~ spl13_154
    | ~ spl13_230 ),
    inference(resolution,[],[f2672,f1481]) ).

fof(f5522,plain,
    ( spl13_372
    | ~ spl13_158
    | ~ spl13_246 ),
    inference(avatar_split_clause,[],[f3060,f2941,f1504,f5520]) ).

fof(f5520,plain,
    ( spl13_372
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(sK0,function_inverse(sK0))),X0)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_372])]) ).

fof(f2941,plain,
    ( spl13_246
  <=> ! [X2,X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X2)
        | ~ relation(X1)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_246])]) ).

fof(f3060,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(sK0,function_inverse(sK0))),X0)
        | ~ relation(X1) )
    | ~ spl13_158
    | ~ spl13_246 ),
    inference(resolution,[],[f2942,f1505]) ).

fof(f2942,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | ~ empty(X2)
        | sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ relation(X0) )
    | ~ spl13_246 ),
    inference(avatar_component_clause,[],[f2941]) ).

fof(f5518,plain,
    ( spl13_371
    | ~ spl13_154
    | ~ spl13_246 ),
    inference(avatar_split_clause,[],[f3059,f2941,f1480,f5516]) ).

fof(f5516,plain,
    ( spl13_371
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(function_inverse(sK0),sK0)),X0)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_371])]) ).

fof(f3059,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(function_inverse(sK0),sK0)),X0)
        | ~ relation(X1) )
    | ~ spl13_154
    | ~ spl13_246 ),
    inference(resolution,[],[f2942,f1481]) ).

fof(f5504,plain,
    ( spl13_370
    | ~ spl13_158
    | ~ spl13_245 ),
    inference(avatar_split_clause,[],[f3038,f2937,f1504,f5502]) ).

fof(f5502,plain,
    ( spl13_370
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(sK0,function_inverse(sK0))),X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_370])]) ).

fof(f2937,plain,
    ( spl13_245
  <=> ! [X2,X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X2)
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_245])]) ).

fof(f3038,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(sK0,function_inverse(sK0))),X0)
        | ~ empty(X1) )
    | ~ spl13_158
    | ~ spl13_245 ),
    inference(resolution,[],[f2938,f1505]) ).

fof(f2938,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | ~ empty(X2)
        | sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X0) )
    | ~ spl13_245 ),
    inference(avatar_component_clause,[],[f2937]) ).

fof(f5500,plain,
    ( spl13_369
    | ~ spl13_154
    | ~ spl13_245 ),
    inference(avatar_split_clause,[],[f3037,f2937,f1480,f5498]) ).

fof(f5498,plain,
    ( spl13_369
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(function_inverse(sK0),sK0)),X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_369])]) ).

fof(f3037,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,relation_composition(function_inverse(sK0),sK0)),X0)
        | ~ empty(X1) )
    | ~ spl13_154
    | ~ spl13_245 ),
    inference(resolution,[],[f2938,f1481]) ).

fof(f5496,plain,
    ( spl13_368
    | ~ spl13_158
    | ~ spl13_243 ),
    inference(avatar_split_clause,[],[f3016,f2929,f1504,f5494]) ).

fof(f5494,plain,
    ( spl13_368
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(relation_composition(sK0,function_inverse(sK0)),X1),X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_368])]) ).

fof(f2929,plain,
    ( spl13_243
  <=> ! [X2,X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X2)
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_243])]) ).

fof(f3016,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(relation_composition(sK0,function_inverse(sK0)),X1),X0)
        | ~ empty(X1) )
    | ~ spl13_158
    | ~ spl13_243 ),
    inference(resolution,[],[f2930,f1505]) ).

fof(f2930,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X2)
        | sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X1) )
    | ~ spl13_243 ),
    inference(avatar_component_clause,[],[f2929]) ).

fof(f5492,plain,
    ( spl13_367
    | ~ spl13_154
    | ~ spl13_243 ),
    inference(avatar_split_clause,[],[f3015,f2929,f1480,f5490]) ).

fof(f5490,plain,
    ( spl13_367
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(relation_composition(function_inverse(sK0),sK0),X1),X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_367])]) ).

fof(f3015,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(relation_composition(function_inverse(sK0),sK0),X1),X0)
        | ~ empty(X1) )
    | ~ spl13_154
    | ~ spl13_243 ),
    inference(resolution,[],[f2930,f1481]) ).

fof(f5488,plain,
    ( spl13_366
    | ~ spl13_158
    | ~ spl13_242 ),
    inference(avatar_split_clause,[],[f2994,f2925,f1504,f5486]) ).

fof(f5486,plain,
    ( spl13_366
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0))))
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_366])]) ).

fof(f2925,plain,
    ( spl13_242
  <=> ! [X2,X0,X1] :
        ( sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_242])]) ).

fof(f2994,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0))))
        | ~ relation(X1) )
    | ~ spl13_158
    | ~ spl13_242 ),
    inference(resolution,[],[f2926,f1505]) ).

fof(f2926,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X2)
        | ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ relation(X1) )
    | ~ spl13_242 ),
    inference(avatar_component_clause,[],[f2925]) ).

fof(f5484,plain,
    ( spl13_365
    | ~ spl13_154
    | ~ spl13_242 ),
    inference(avatar_split_clause,[],[f2993,f2925,f1480,f5482]) ).

fof(f5482,plain,
    ( spl13_365
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0)))
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_365])]) ).

fof(f2993,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0)))
        | ~ relation(X1) )
    | ~ spl13_154
    | ~ spl13_242 ),
    inference(resolution,[],[f2926,f1481]) ).

fof(f5480,plain,
    ( spl13_364
    | ~ spl13_158
    | ~ spl13_241 ),
    inference(avatar_split_clause,[],[f2972,f2921,f1504,f5478]) ).

fof(f5478,plain,
    ( spl13_364
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0))))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_364])]) ).

fof(f2921,plain,
    ( spl13_241
  <=> ! [X2,X0,X1] :
        ( sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_241])]) ).

fof(f2972,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(sK0,function_inverse(sK0))))
        | ~ empty(X1) )
    | ~ spl13_158
    | ~ spl13_241 ),
    inference(resolution,[],[f2922,f1505]) ).

fof(f2922,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X2)
        | ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X1) )
    | ~ spl13_241 ),
    inference(avatar_component_clause,[],[f2921]) ).

fof(f5476,plain,
    ( spl13_363
    | ~ spl13_154
    | ~ spl13_241 ),
    inference(avatar_split_clause,[],[f2971,f2921,f1480,f5474]) ).

fof(f5474,plain,
    ( spl13_363
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0)))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_363])]) ).

fof(f2971,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sK0),sK0)))
        | ~ empty(X1) )
    | ~ spl13_154
    | ~ spl13_241 ),
    inference(resolution,[],[f2922,f1481]) ).

fof(f5472,plain,
    ( spl13_362
    | ~ spl13_158
    | ~ spl13_240 ),
    inference(avatar_split_clause,[],[f2950,f2917,f1504,f5470]) ).

fof(f5470,plain,
    ( spl13_362
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(relation_composition(sK0,function_inverse(sK0)),X1))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_362])]) ).

fof(f2917,plain,
    ( spl13_240
  <=> ! [X2,X0,X1] :
        ( sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_240])]) ).

fof(f2950,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(relation_composition(sK0,function_inverse(sK0)),X1))
        | ~ empty(X1) )
    | ~ spl13_158
    | ~ spl13_240 ),
    inference(resolution,[],[f2918,f1505]) ).

fof(f2918,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X2) )
    | ~ spl13_240 ),
    inference(avatar_component_clause,[],[f2917]) ).

fof(f5468,plain,
    ( spl13_361
    | ~ spl13_154
    | ~ spl13_240 ),
    inference(avatar_split_clause,[],[f2949,f2917,f1480,f5466]) ).

fof(f5466,plain,
    ( spl13_361
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(relation_composition(function_inverse(sK0),sK0),X1))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_361])]) ).

fof(f2949,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(relation_composition(function_inverse(sK0),sK0),X1))
        | ~ empty(X1) )
    | ~ spl13_154
    | ~ spl13_240 ),
    inference(resolution,[],[f2918,f1481]) ).

fof(f5464,plain,
    ( spl13_360
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_312 ),
    inference(avatar_split_clause,[],[f5260,f4290,f683,f219,f5461]) ).

fof(f5461,plain,
    ( spl13_360
  <=> sK6 = relation_composition(sK6,function_inverse(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_360])]) ).

fof(f4290,plain,
    ( spl13_312
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,function_inverse(sK0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_312])]) ).

fof(f5260,plain,
    ( sK6 = relation_composition(sK6,function_inverse(sK0))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_312 ),
    inference(forward_demodulation,[],[f5248,f685]) ).

fof(f5248,plain,
    ( sK6 = relation_composition(empty_set,function_inverse(sK0))
    | ~ spl13_4
    | ~ spl13_312 ),
    inference(resolution,[],[f4291,f221]) ).

fof(f4291,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,function_inverse(sK0)) )
    | ~ spl13_312 ),
    inference(avatar_component_clause,[],[f4290]) ).

fof(f5085,plain,
    ( spl13_359
    | ~ spl13_1
    | ~ spl13_255 ),
    inference(avatar_split_clause,[],[f3302,f3159,f204,f5083]) ).

fof(f5083,plain,
    ( spl13_359
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,sK0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_359])]) ).

fof(f3302,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,sK0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ relation(X0) )
    | ~ spl13_1
    | ~ spl13_255 ),
    inference(resolution,[],[f3160,f206]) ).

fof(f206,plain,
    ( relation(sK0)
    | ~ spl13_1 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f5081,plain,
    ( spl13_358
    | ~ spl13_1
    | ~ spl13_254 ),
    inference(avatar_split_clause,[],[f3280,f3155,f204,f5079]) ).

fof(f5079,plain,
    ( spl13_358
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,sK0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_358])]) ).

fof(f3280,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(X0,sK0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_254 ),
    inference(resolution,[],[f3156,f206]) ).

fof(f5067,plain,
    ( spl13_357
    | ~ spl13_1
    | ~ spl13_253 ),
    inference(avatar_split_clause,[],[f3258,f3151,f204,f5065]) ).

fof(f5065,plain,
    ( spl13_357
  <=> ! [X2,X0,X1] :
        ( relation_composition(relation_composition(sK0,X0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_357])]) ).

fof(f3258,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(relation_composition(sK0,X0),X1) = X2
        | ~ empty(X2)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_253 ),
    inference(resolution,[],[f3152,f206]) ).

fof(f5063,plain,
    ( spl13_356
    | ~ spl13_1
    | ~ spl13_252 ),
    inference(avatar_split_clause,[],[f3236,f3147,f204,f5061]) ).

fof(f5061,plain,
    ( spl13_356
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,sK0)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_356])]) ).

fof(f3236,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,sK0)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_1
    | ~ spl13_252 ),
    inference(resolution,[],[f3148,f206]) ).

fof(f5059,plain,
    ( spl13_355
    | ~ spl13_1
    | ~ spl13_251 ),
    inference(avatar_split_clause,[],[f3195,f3143,f204,f5057]) ).

fof(f5057,plain,
    ( spl13_355
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,sK0)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_355])]) ).

fof(f3195,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(X1,sK0)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_251 ),
    inference(resolution,[],[f3144,f206]) ).

fof(f5055,plain,
    ( spl13_354
    | ~ spl13_1
    | ~ spl13_250 ),
    inference(avatar_split_clause,[],[f3173,f3139,f204,f5053]) ).

fof(f5053,plain,
    ( spl13_354
  <=> ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(sK0,X1)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_354])]) ).

fof(f3173,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X0,relation_composition(sK0,X1)) = X2
        | ~ empty(X2)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_250 ),
    inference(resolution,[],[f3140,f206]) ).

fof(f5051,plain,
    ( spl13_353
    | ~ spl13_158
    | ~ spl13_229 ),
    inference(avatar_split_clause,[],[f2778,f2667,f1504,f5049]) ).

fof(f5049,plain,
    ( spl13_353
  <=> ! [X0,X1] :
        ( relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_353])]) ).

fof(f2667,plain,
    ( spl13_229
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_composition(X1,X2)) = X0
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_229])]) ).

fof(f2778,plain,
    ( ! [X0,X1] :
        ( relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_229 ),
    inference(resolution,[],[f2668,f1505]) ).

fof(f2668,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X2)
        | relation_rng(relation_composition(X1,X2)) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_229 ),
    inference(avatar_component_clause,[],[f2667]) ).

fof(f5047,plain,
    ( spl13_352
    | ~ spl13_154
    | ~ spl13_229 ),
    inference(avatar_split_clause,[],[f2777,f2667,f1480,f5045]) ).

fof(f5045,plain,
    ( spl13_352
  <=> ! [X0,X1] :
        ( relation_rng(relation_composition(X0,relation_composition(function_inverse(sK0),sK0))) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_352])]) ).

fof(f2777,plain,
    ( ! [X0,X1] :
        ( relation_rng(relation_composition(X0,relation_composition(function_inverse(sK0),sK0))) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_229 ),
    inference(resolution,[],[f2668,f1481]) ).

fof(f5043,plain,
    ( spl13_351
    | ~ spl13_158
    | ~ spl13_228 ),
    inference(avatar_split_clause,[],[f2756,f2663,f1504,f5041]) ).

fof(f5041,plain,
    ( spl13_351
  <=> ! [X0,X1] :
        ( relation_rng(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_351])]) ).

fof(f2663,plain,
    ( spl13_228
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_composition(X1,X2)) = X0
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_228])]) ).

fof(f2756,plain,
    ( ! [X0,X1] :
        ( relation_rng(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_228 ),
    inference(resolution,[],[f2664,f1505]) ).

fof(f2664,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | relation_rng(relation_composition(X1,X2)) = X0
        | ~ empty(X0)
        | ~ empty(X2) )
    | ~ spl13_228 ),
    inference(avatar_component_clause,[],[f2663]) ).

fof(f5039,plain,
    ( spl13_350
    | ~ spl13_154
    | ~ spl13_228 ),
    inference(avatar_split_clause,[],[f2755,f2663,f1480,f5037]) ).

fof(f5037,plain,
    ( spl13_350
  <=> ! [X0,X1] :
        ( relation_rng(relation_composition(relation_composition(function_inverse(sK0),sK0),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_350])]) ).

fof(f2755,plain,
    ( ! [X0,X1] :
        ( relation_rng(relation_composition(relation_composition(function_inverse(sK0),sK0),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_228 ),
    inference(resolution,[],[f2664,f1481]) ).

fof(f5035,plain,
    ( spl13_349
    | ~ spl13_158
    | ~ spl13_227 ),
    inference(avatar_split_clause,[],[f2734,f2659,f1504,f5033]) ).

fof(f5033,plain,
    ( spl13_349
  <=> ! [X0,X1] :
        ( relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_349])]) ).

fof(f2659,plain,
    ( spl13_227
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_composition(X1,X2)) = X0
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_227])]) ).

fof(f2734,plain,
    ( ! [X0,X1] :
        ( relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_227 ),
    inference(resolution,[],[f2660,f1505]) ).

fof(f2660,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X2)
        | relation_dom(relation_composition(X1,X2)) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_227 ),
    inference(avatar_component_clause,[],[f2659]) ).

fof(f5031,plain,
    ( spl13_348
    | ~ spl13_154
    | ~ spl13_227 ),
    inference(avatar_split_clause,[],[f2733,f2659,f1480,f5029]) ).

fof(f5029,plain,
    ( spl13_348
  <=> ! [X0,X1] :
        ( relation_dom(relation_composition(X0,relation_composition(function_inverse(sK0),sK0))) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_348])]) ).

fof(f2733,plain,
    ( ! [X0,X1] :
        ( relation_dom(relation_composition(X0,relation_composition(function_inverse(sK0),sK0))) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_227 ),
    inference(resolution,[],[f2660,f1481]) ).

fof(f5027,plain,
    ( spl13_347
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_307 ),
    inference(avatar_split_clause,[],[f4923,f4226,f683,f219,f5024]) ).

fof(f5024,plain,
    ( spl13_347
  <=> sK6 = relation_composition(function_inverse(sK0),sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_347])]) ).

fof(f4226,plain,
    ( spl13_307
  <=> ! [X0] :
        ( sK6 = relation_composition(function_inverse(sK0),X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_307])]) ).

fof(f4923,plain,
    ( sK6 = relation_composition(function_inverse(sK0),sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_307 ),
    inference(forward_demodulation,[],[f4911,f685]) ).

fof(f4911,plain,
    ( sK6 = relation_composition(function_inverse(sK0),empty_set)
    | ~ spl13_4
    | ~ spl13_307 ),
    inference(resolution,[],[f4227,f221]) ).

fof(f4227,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(function_inverse(sK0),X0) )
    | ~ spl13_307 ),
    inference(avatar_component_clause,[],[f4226]) ).

fof(f5022,plain,
    ( spl13_346
    | ~ spl13_158
    | ~ spl13_226 ),
    inference(avatar_split_clause,[],[f2712,f2655,f1504,f5020]) ).

fof(f5020,plain,
    ( spl13_346
  <=> ! [X0,X1] :
        ( relation_dom(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_346])]) ).

fof(f2655,plain,
    ( spl13_226
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_composition(X1,X2)) = X0
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_226])]) ).

fof(f2712,plain,
    ( ! [X0,X1] :
        ( relation_dom(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_226 ),
    inference(resolution,[],[f2656,f1505]) ).

fof(f2656,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X1)
        | relation_dom(relation_composition(X1,X2)) = X0
        | ~ empty(X0)
        | ~ empty(X2) )
    | ~ spl13_226 ),
    inference(avatar_component_clause,[],[f2655]) ).

fof(f5018,plain,
    ( spl13_345
    | ~ spl13_154
    | ~ spl13_226 ),
    inference(avatar_split_clause,[],[f2711,f2655,f1480,f5016]) ).

fof(f5016,plain,
    ( spl13_345
  <=> ! [X0,X1] :
        ( relation_dom(relation_composition(relation_composition(function_inverse(sK0),sK0),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_345])]) ).

fof(f2711,plain,
    ( ! [X0,X1] :
        ( relation_dom(relation_composition(relation_composition(function_inverse(sK0),sK0),X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_226 ),
    inference(resolution,[],[f2656,f1481]) ).

fof(f5014,plain,
    ( spl13_344
    | ~ spl13_53
    | ~ spl13_143 ),
    inference(avatar_split_clause,[],[f1368,f1351,f474,f5012]) ).

fof(f5012,plain,
    ( spl13_344
  <=> ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_344])]) ).

fof(f1368,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_53
    | ~ spl13_143 ),
    inference(resolution,[],[f1352,f475]) ).

fof(f5010,plain,
    ( spl13_343
    | ~ spl13_56
    | ~ spl13_143 ),
    inference(avatar_split_clause,[],[f1367,f1351,f487,f5008]) ).

fof(f5008,plain,
    ( spl13_343
  <=> ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_343])]) ).

fof(f487,plain,
    ( spl13_56
  <=> ! [X0,X1] :
        ( empty(relation_composition(X1,X0))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).

fof(f1367,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_56
    | ~ spl13_143 ),
    inference(resolution,[],[f1352,f488]) ).

fof(f488,plain,
    ( ! [X0,X1] :
        ( empty(relation_composition(X1,X0))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_56 ),
    inference(avatar_component_clause,[],[f487]) ).

fof(f5006,plain,
    ( spl13_342
    | ~ spl13_53
    | ~ spl13_142 ),
    inference(avatar_split_clause,[],[f1355,f1347,f474,f5004]) ).

fof(f5004,plain,
    ( spl13_342
  <=> ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_342])]) ).

fof(f1355,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_53
    | ~ spl13_142 ),
    inference(resolution,[],[f1348,f475]) ).

fof(f5002,plain,
    ( spl13_341
    | ~ spl13_56
    | ~ spl13_142 ),
    inference(avatar_split_clause,[],[f1354,f1347,f487,f5000]) ).

fof(f5000,plain,
    ( spl13_341
  <=> ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_341])]) ).

fof(f1354,plain,
    ( ! [X2,X0,X1] :
        ( relation_composition(X1,X2) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_56
    | ~ spl13_142 ),
    inference(resolution,[],[f1348,f488]) ).

fof(f4908,plain,
    ( spl13_340
    | ~ spl13_122
    | ~ spl13_158 ),
    inference(avatar_split_clause,[],[f1836,f1504,f1106,f4906]) ).

fof(f4906,plain,
    ( spl13_340
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(sK0,function_inverse(sK0))) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_340])]) ).

fof(f1106,plain,
    ( spl13_122
  <=> ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X1,X0) = X2
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_122])]) ).

fof(f1836,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(sK0,function_inverse(sK0))) = X1
        | ~ empty(X1) )
    | ~ spl13_122
    | ~ spl13_158 ),
    inference(resolution,[],[f1505,f1107]) ).

fof(f1107,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X1,X0) = X2
        | ~ empty(X2) )
    | ~ spl13_122 ),
    inference(avatar_component_clause,[],[f1106]) ).

fof(f4904,plain,
    ( spl13_339
    | ~ spl13_123
    | ~ spl13_158 ),
    inference(avatar_split_clause,[],[f1835,f1504,f1110,f4902]) ).

fof(f4902,plain,
    ( spl13_339
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(sK0,function_inverse(sK0)),X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_339])]) ).

fof(f1110,plain,
    ( spl13_123
  <=> ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X0,X1) = X2
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_123])]) ).

fof(f1835,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(sK0,function_inverse(sK0)),X0) = X1
        | ~ empty(X1) )
    | ~ spl13_123
    | ~ spl13_158 ),
    inference(resolution,[],[f1505,f1111]) ).

fof(f1111,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X0,X1) = X2
        | ~ empty(X2) )
    | ~ spl13_123 ),
    inference(avatar_component_clause,[],[f1110]) ).

fof(f4900,plain,
    ( spl13_338
    | ~ spl13_122
    | ~ spl13_154 ),
    inference(avatar_split_clause,[],[f1619,f1480,f1106,f4898]) ).

fof(f4898,plain,
    ( spl13_338
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(function_inverse(sK0),sK0)) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_338])]) ).

fof(f1619,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(function_inverse(sK0),sK0)) = X1
        | ~ empty(X1) )
    | ~ spl13_122
    | ~ spl13_154 ),
    inference(resolution,[],[f1481,f1107]) ).

fof(f4896,plain,
    ( spl13_337
    | ~ spl13_123
    | ~ spl13_154 ),
    inference(avatar_split_clause,[],[f1618,f1480,f1110,f4894]) ).

fof(f4894,plain,
    ( spl13_337
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(function_inverse(sK0),sK0),X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_337])]) ).

fof(f1618,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(function_inverse(sK0),sK0),X0) = X1
        | ~ empty(X1) )
    | ~ spl13_123
    | ~ spl13_154 ),
    inference(resolution,[],[f1481,f1111]) ).

fof(f4748,plain,
    ( spl13_336
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_287 ),
    inference(avatar_split_clause,[],[f4112,f3857,f683,f219,f4745]) ).

fof(f4745,plain,
    ( spl13_336
  <=> sK6 = relation_composition(sK6,relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_336])]) ).

fof(f3857,plain,
    ( spl13_287
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_287])]) ).

fof(f4112,plain,
    ( sK6 = relation_composition(sK6,relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_287 ),
    inference(forward_demodulation,[],[f4100,f685]) ).

fof(f4100,plain,
    ( sK6 = relation_composition(empty_set,relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_4
    | ~ spl13_287 ),
    inference(resolution,[],[f3858,f221]) ).

fof(f3858,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(sK0,function_inverse(sK0))) )
    | ~ spl13_287 ),
    inference(avatar_component_clause,[],[f3857]) ).

fof(f4513,plain,
    ( spl13_335
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_286 ),
    inference(avatar_split_clause,[],[f4094,f3853,f683,f219,f4510]) ).

fof(f4510,plain,
    ( spl13_335
  <=> sK6 = relation_composition(relation_composition(sK0,function_inverse(sK0)),sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_335])]) ).

fof(f3853,plain,
    ( spl13_286
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_286])]) ).

fof(f4094,plain,
    ( sK6 = relation_composition(relation_composition(sK0,function_inverse(sK0)),sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_286 ),
    inference(forward_demodulation,[],[f4082,f685]) ).

fof(f4082,plain,
    ( sK6 = relation_composition(relation_composition(sK0,function_inverse(sK0)),empty_set)
    | ~ spl13_4
    | ~ spl13_286 ),
    inference(resolution,[],[f3854,f221]) ).

fof(f3854,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(sK0,function_inverse(sK0)),X0) )
    | ~ spl13_286 ),
    inference(avatar_component_clause,[],[f3853]) ).

fof(f4420,plain,
    ( spl13_334
    | ~ spl13_1
    | ~ spl13_246 ),
    inference(avatar_split_clause,[],[f3065,f2941,f204,f4418]) ).

fof(f4418,plain,
    ( spl13_334
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,sK0),X0)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_334])]) ).

fof(f3065,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,sK0),X0)
        | ~ relation(X1) )
    | ~ spl13_1
    | ~ spl13_246 ),
    inference(resolution,[],[f2942,f206]) ).

fof(f4416,plain,
    ( spl13_333
    | ~ spl13_1
    | ~ spl13_245 ),
    inference(avatar_split_clause,[],[f3043,f2937,f204,f4414]) ).

fof(f4414,plain,
    ( spl13_333
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,sK0),X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_333])]) ).

fof(f3043,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(X1,sK0),X0)
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_245 ),
    inference(resolution,[],[f2938,f206]) ).

fof(f4412,plain,
    ( spl13_332
    | ~ spl13_1
    | ~ spl13_243 ),
    inference(avatar_split_clause,[],[f3021,f2929,f204,f4410]) ).

fof(f4410,plain,
    ( spl13_332
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(sK0,X1),X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_332])]) ).

fof(f3021,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(sK0,X1),X0)
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_243 ),
    inference(resolution,[],[f2930,f206]) ).

fof(f4408,plain,
    ( spl13_331
    | ~ spl13_1
    | ~ spl13_242 ),
    inference(avatar_split_clause,[],[f2999,f2925,f204,f4406]) ).

fof(f4406,plain,
    ( spl13_331
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,sK0))
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_331])]) ).

fof(f2999,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,sK0))
        | ~ relation(X1) )
    | ~ spl13_1
    | ~ spl13_242 ),
    inference(resolution,[],[f2926,f206]) ).

fof(f4404,plain,
    ( spl13_330
    | ~ spl13_1
    | ~ spl13_241 ),
    inference(avatar_split_clause,[],[f2977,f2921,f204,f4402]) ).

fof(f4402,plain,
    ( spl13_330
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,sK0))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_330])]) ).

fof(f2977,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(X1,sK0))
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_241 ),
    inference(resolution,[],[f2922,f206]) ).

fof(f4400,plain,
    ( spl13_329
    | ~ spl13_1
    | ~ spl13_240 ),
    inference(avatar_split_clause,[],[f2955,f2917,f204,f4398]) ).

fof(f4398,plain,
    ( spl13_329
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(sK0,X1))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_329])]) ).

fof(f2955,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(sK0,X1))
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_240 ),
    inference(resolution,[],[f2918,f206]) ).

fof(f4396,plain,
    ( spl13_328
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_285 ),
    inference(avatar_split_clause,[],[f4076,f3849,f683,f219,f4393]) ).

fof(f4393,plain,
    ( spl13_328
  <=> sK6 = relation_composition(sK6,relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_328])]) ).

fof(f3849,plain,
    ( spl13_285
  <=> ! [X0] :
        ( sK6 = relation_composition(X0,relation_composition(function_inverse(sK0),sK0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_285])]) ).

fof(f4076,plain,
    ( sK6 = relation_composition(sK6,relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_285 ),
    inference(forward_demodulation,[],[f4064,f685]) ).

fof(f4064,plain,
    ( sK6 = relation_composition(empty_set,relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_4
    | ~ spl13_285 ),
    inference(resolution,[],[f3850,f221]) ).

fof(f3850,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(X0,relation_composition(function_inverse(sK0),sK0)) )
    | ~ spl13_285 ),
    inference(avatar_component_clause,[],[f3849]) ).

fof(f4391,plain,
    ( spl13_327
    | ~ spl13_158
    | ~ spl13_205 ),
    inference(avatar_split_clause,[],[f2365,f2227,f1504,f4389]) ).

fof(f4389,plain,
    ( spl13_327
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_327])]) ).

fof(f2365,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))))
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_205 ),
    inference(resolution,[],[f2228,f1505]) ).

fof(f4387,plain,
    ( spl13_326
    | ~ spl13_154
    | ~ spl13_205 ),
    inference(avatar_split_clause,[],[f2364,f2227,f1480,f4385]) ).

fof(f4385,plain,
    ( spl13_326
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_326])]) ).

fof(f2364,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)))
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_205 ),
    inference(resolution,[],[f2228,f1481]) ).

fof(f4383,plain,
    ( spl13_325
    | ~ spl13_158
    | ~ spl13_204 ),
    inference(avatar_split_clause,[],[f2343,f2223,f1504,f4381]) ).

fof(f4381,plain,
    ( spl13_325
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_325])]) ).

fof(f2343,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0))
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_204 ),
    inference(resolution,[],[f2224,f1505]) ).

fof(f4379,plain,
    ( spl13_324
    | ~ spl13_154
    | ~ spl13_204 ),
    inference(avatar_split_clause,[],[f2342,f2223,f1480,f4377]) ).

fof(f4377,plain,
    ( spl13_324
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(relation_composition(function_inverse(sK0),sK0),X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_324])]) ).

fof(f2342,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(relation_composition(function_inverse(sK0),sK0),X0))
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_204 ),
    inference(resolution,[],[f2224,f1481]) ).

fof(f4375,plain,
    ( spl13_323
    | ~ spl13_158
    | ~ spl13_202 ),
    inference(avatar_split_clause,[],[f2321,f2215,f1504,f4373]) ).

fof(f4373,plain,
    ( spl13_323
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_323])]) ).

fof(f2321,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))))
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_202 ),
    inference(resolution,[],[f2216,f1505]) ).

fof(f4371,plain,
    ( spl13_322
    | ~ spl13_154
    | ~ spl13_202 ),
    inference(avatar_split_clause,[],[f2320,f2215,f1480,f4369]) ).

fof(f4369,plain,
    ( spl13_322
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_322])]) ).

fof(f2320,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,relation_composition(function_inverse(sK0),sK0)))
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_202 ),
    inference(resolution,[],[f2216,f1481]) ).

fof(f4367,plain,
    ( spl13_321
    | ~ spl13_158
    | ~ spl13_201 ),
    inference(avatar_split_clause,[],[f2299,f2211,f1504,f4365]) ).

fof(f4365,plain,
    ( spl13_321
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_321])]) ).

fof(f2299,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(relation_composition(sK0,function_inverse(sK0)),X0))
        | ~ empty(X0) )
    | ~ spl13_158
    | ~ spl13_201 ),
    inference(resolution,[],[f2212,f1505]) ).

fof(f4363,plain,
    ( spl13_320
    | ~ spl13_154
    | ~ spl13_201 ),
    inference(avatar_split_clause,[],[f2298,f2211,f1480,f4361]) ).

fof(f4361,plain,
    ( spl13_320
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(relation_composition(function_inverse(sK0),sK0),X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_320])]) ).

fof(f2298,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(relation_composition(function_inverse(sK0),sK0),X0))
        | ~ empty(X0) )
    | ~ spl13_154
    | ~ spl13_201 ),
    inference(resolution,[],[f2212,f1481]) ).

fof(f4359,plain,
    ( spl13_319
    | ~ spl13_143
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f1477,f1459,f1351,f4357]) ).

fof(f4357,plain,
    ( spl13_319
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK2(powerset(X0)) = relation_composition(sK0,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_319])]) ).

fof(f1477,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK2(powerset(X0)) = relation_composition(sK0,X1)
        | ~ empty(X1) )
    | ~ spl13_143
    | ~ spl13_152 ),
    inference(resolution,[],[f1460,f1352]) ).

fof(f4355,plain,
    ( spl13_318
    | ~ spl13_142
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f1476,f1459,f1347,f4353]) ).

fof(f4353,plain,
    ( spl13_318
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sK2(powerset(X0)) = relation_composition(X1,sK0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_318])]) ).

fof(f1476,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sK2(powerset(X0)) = relation_composition(X1,sK0)
        | ~ empty(X1) )
    | ~ spl13_142
    | ~ spl13_152 ),
    inference(resolution,[],[f1460,f1348]) ).

fof(f4351,plain,
    ( spl13_317
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_284 ),
    inference(avatar_split_clause,[],[f4058,f3845,f683,f219,f4348]) ).

fof(f4348,plain,
    ( spl13_317
  <=> sK6 = relation_composition(relation_composition(function_inverse(sK0),sK0),sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_317])]) ).

fof(f3845,plain,
    ( spl13_284
  <=> ! [X0] :
        ( sK6 = relation_composition(relation_composition(function_inverse(sK0),sK0),X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_284])]) ).

fof(f4058,plain,
    ( sK6 = relation_composition(relation_composition(function_inverse(sK0),sK0),sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_284 ),
    inference(forward_demodulation,[],[f4046,f685]) ).

fof(f4046,plain,
    ( sK6 = relation_composition(relation_composition(function_inverse(sK0),sK0),empty_set)
    | ~ spl13_4
    | ~ spl13_284 ),
    inference(resolution,[],[f3846,f221]) ).

fof(f3846,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(relation_composition(function_inverse(sK0),sK0),X0) )
    | ~ spl13_284 ),
    inference(avatar_component_clause,[],[f3845]) ).

fof(f4346,plain,
    ( spl13_316
    | ~ spl13_53
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f1322,f1118,f474,f4344]) ).

fof(f4344,plain,
    ( spl13_316
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(sK0,relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_316])]) ).

fof(f1322,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(sK0,relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_53
    | ~ spl13_124 ),
    inference(resolution,[],[f1119,f475]) ).

fof(f4342,plain,
    ( spl13_315
    | ~ spl13_56
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f1321,f1118,f487,f4340]) ).

fof(f4340,plain,
    ( spl13_315
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(sK0,relation_composition(X0,X1))
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_315])]) ).

fof(f1321,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(sK0,relation_composition(X0,X1))
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_56
    | ~ spl13_124 ),
    inference(resolution,[],[f1119,f488]) ).

fof(f4338,plain,
    ( spl13_314
    | ~ spl13_53
    | ~ spl13_117 ),
    inference(avatar_split_clause,[],[f1206,f1079,f474,f4336]) ).

fof(f4336,plain,
    ( spl13_314
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),sK0)
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_314])]) ).

fof(f1206,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),sK0)
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_53
    | ~ spl13_117 ),
    inference(resolution,[],[f1080,f475]) ).

fof(f4334,plain,
    ( spl13_313
    | ~ spl13_56
    | ~ spl13_117 ),
    inference(avatar_split_clause,[],[f1205,f1079,f487,f4332]) ).

fof(f4332,plain,
    ( spl13_313
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),sK0)
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_313])]) ).

fof(f1205,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),sK0)
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_56
    | ~ spl13_117 ),
    inference(resolution,[],[f1080,f488]) ).

fof(f4292,plain,
    ( spl13_312
    | ~ spl13_113
    | ~ spl13_157 ),
    inference(avatar_split_clause,[],[f1762,f1499,f1023,f4290]) ).

fof(f1023,plain,
    ( spl13_113
  <=> ! [X0,X1] :
        ( relation_composition(X1,X0) = sK6
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_113])]) ).

fof(f1762,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,function_inverse(sK0))
        | ~ empty(X0) )
    | ~ spl13_113
    | ~ spl13_157 ),
    inference(resolution,[],[f1500,f1024]) ).

fof(f1024,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | relation_composition(X1,X0) = sK6
        | ~ empty(X1) )
    | ~ spl13_113 ),
    inference(avatar_component_clause,[],[f1023]) ).

fof(f4252,plain,
    ( ~ spl13_311
    | ~ spl13_40
    | ~ spl13_160 ),
    inference(avatar_split_clause,[],[f3912,f1512,f407,f4249]) ).

fof(f4249,plain,
    ( spl13_311
  <=> in(relation_dom(sK0),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_311])]) ).

fof(f407,plain,
    ( spl13_40
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).

fof(f3912,plain,
    ( ~ in(relation_dom(sK0),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))))
    | ~ spl13_40
    | ~ spl13_160 ),
    inference(resolution,[],[f1514,f408]) ).

fof(f408,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) )
    | ~ spl13_40 ),
    inference(avatar_component_clause,[],[f407]) ).

fof(f4247,plain,
    ( ~ spl13_310
    | ~ spl13_40
    | ~ spl13_156 ),
    inference(avatar_split_clause,[],[f3888,f1488,f407,f4244]) ).

fof(f4244,plain,
    ( spl13_310
  <=> in(relation_rng(sK0),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_310])]) ).

fof(f3888,plain,
    ( ~ in(relation_rng(sK0),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)))
    | ~ spl13_40
    | ~ spl13_156 ),
    inference(resolution,[],[f1490,f408]) ).

fof(f4242,plain,
    ( ~ spl13_309
    | ~ spl13_149
    | spl13_306 ),
    inference(avatar_split_clause,[],[f4234,f4209,f1435,f4239]) ).

fof(f4239,plain,
    ( spl13_309
  <=> relation_rng(sK0) = relation_dom(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_309])]) ).

fof(f4209,plain,
    ( spl13_306
  <=> relation_dom(sK0) = relation_rng(identity_relation(relation_dom(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_306])]) ).

fof(f4234,plain,
    ( relation_rng(sK0) != relation_dom(sK0)
    | ~ spl13_149
    | spl13_306 ),
    inference(superposition,[],[f4210,f1437]) ).

fof(f4210,plain,
    ( relation_dom(sK0) != relation_rng(identity_relation(relation_dom(sK0)))
    | spl13_306 ),
    inference(avatar_component_clause,[],[f4209]) ).

fof(f4233,plain,
    ( spl13_149
    | ~ spl13_1
    | ~ spl13_2
    | spl13_308
    | ~ spl13_3
    | ~ spl13_139 ),
    inference(avatar_split_clause,[],[f1316,f1299,f214,f4230,f209,f204,f1435]) ).

fof(f4230,plain,
    ( spl13_308
  <=> sK4(relation_dom(sK0),sK0) = apply(relation_composition(sK0,function_inverse(sK0)),sK4(relation_dom(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_308])]) ).

fof(f1299,plain,
    ( spl13_139
  <=> ! [X0] :
        ( sK4(relation_dom(X0),X0) = apply(relation_composition(X0,function_inverse(X0)),sK4(relation_dom(X0),X0))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_139])]) ).

fof(f1316,plain,
    ( sK4(relation_dom(sK0),sK0) = apply(relation_composition(sK0,function_inverse(sK0)),sK4(relation_dom(sK0),sK0))
    | ~ function(sK0)
    | ~ relation(sK0)
    | sK0 = identity_relation(relation_dom(sK0))
    | ~ spl13_3
    | ~ spl13_139 ),
    inference(resolution,[],[f1300,f216]) ).

fof(f216,plain,
    ( one_to_one(sK0)
    | ~ spl13_3 ),
    inference(avatar_component_clause,[],[f214]) ).

fof(f1300,plain,
    ( ! [X0] :
        ( ~ one_to_one(X0)
        | sK4(relation_dom(X0),X0) = apply(relation_composition(X0,function_inverse(X0)),sK4(relation_dom(X0),X0))
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 )
    | ~ spl13_139 ),
    inference(avatar_component_clause,[],[f1299]) ).

fof(f4228,plain,
    ( spl13_307
    | ~ spl13_114
    | ~ spl13_157 ),
    inference(avatar_split_clause,[],[f1761,f1499,f1027,f4226]) ).

fof(f1027,plain,
    ( spl13_114
  <=> ! [X0,X1] :
        ( relation_composition(X0,X1) = sK6
        | ~ relation(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_114])]) ).

fof(f1761,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(function_inverse(sK0),X0)
        | ~ empty(X0) )
    | ~ spl13_114
    | ~ spl13_157 ),
    inference(resolution,[],[f1500,f1028]) ).

fof(f1028,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | relation_composition(X0,X1) = sK6
        | ~ empty(X1) )
    | ~ spl13_114 ),
    inference(avatar_component_clause,[],[f1027]) ).

fof(f4212,plain,
    ( spl13_306
    | ~ spl13_26
    | ~ spl13_77 ),
    inference(avatar_split_clause,[],[f4191,f663,f324,f4209]) ).

fof(f663,plain,
    ( spl13_77
  <=> relation_dom(sK0) = relation_rng(relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).

fof(f4191,plain,
    ( relation_dom(sK0) = relation_rng(identity_relation(relation_dom(sK0)))
    | ~ spl13_26
    | ~ spl13_77 ),
    inference(superposition,[],[f665,f325]) ).

fof(f665,plain,
    ( relation_dom(sK0) = relation_rng(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_77 ),
    inference(avatar_component_clause,[],[f663]) ).

fof(f4188,plain,
    ( spl13_295
    | ~ spl13_26
    | ~ spl13_149 ),
    inference(avatar_split_clause,[],[f4187,f1435,f324,f3927]) ).

fof(f3927,plain,
    ( spl13_295
  <=> sK0 = relation_composition(sK0,function_inverse(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_295])]) ).

fof(f4187,plain,
    ( sK0 = relation_composition(sK0,function_inverse(sK0))
    | ~ spl13_26
    | ~ spl13_149 ),
    inference(forward_demodulation,[],[f325,f1437]) ).

fof(f4186,plain,
    ( spl13_305
    | ~ spl13_41
    | ~ spl13_160 ),
    inference(avatar_split_clause,[],[f3911,f1512,f411,f4183]) ).

fof(f4183,plain,
    ( spl13_305
  <=> element(sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))),relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_305])]) ).

fof(f411,plain,
    ( spl13_41
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).

fof(f3911,plain,
    ( element(sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))),relation_dom(sK0))
    | ~ spl13_41
    | ~ spl13_160 ),
    inference(resolution,[],[f1514,f412]) ).

fof(f412,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | element(X0,X1) )
    | ~ spl13_41 ),
    inference(avatar_component_clause,[],[f411]) ).

fof(f4171,plain,
    ( ~ spl13_304
    | ~ spl13_27
    | spl13_156 ),
    inference(avatar_split_clause,[],[f3865,f1488,f328,f4168]) ).

fof(f4168,plain,
    ( spl13_304
  <=> in(sK4(relation_rng(sK0),identity_relation(relation_rng(sK0))),relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_304])]) ).

fof(f3865,plain,
    ( ~ in(sK4(relation_rng(sK0),identity_relation(relation_rng(sK0))),relation_rng(sK0))
    | ~ spl13_27
    | spl13_156 ),
    inference(superposition,[],[f1489,f329]) ).

fof(f1489,plain,
    ( ~ in(sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)),relation_rng(sK0))
    | spl13_156 ),
    inference(avatar_component_clause,[],[f1488]) ).

fof(f4166,plain,
    ( ~ spl13_303
    | ~ spl13_27
    | spl13_289 ),
    inference(avatar_split_clause,[],[f4136,f3890,f328,f4163]) ).

fof(f4163,plain,
    ( spl13_303
  <=> one_to_one(identity_relation(relation_rng(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_303])]) ).

fof(f3890,plain,
    ( spl13_289
  <=> one_to_one(relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_289])]) ).

fof(f4136,plain,
    ( ~ one_to_one(identity_relation(relation_rng(sK0)))
    | ~ spl13_27
    | spl13_289 ),
    inference(superposition,[],[f3892,f329]) ).

fof(f3892,plain,
    ( ~ one_to_one(relation_composition(function_inverse(sK0),sK0))
    | spl13_289 ),
    inference(avatar_component_clause,[],[f3890]) ).

fof(f4161,plain,
    ( ~ spl13_302
    | ~ spl13_27
    | spl13_81 ),
    inference(avatar_split_clause,[],[f3863,f688,f328,f4158]) ).

fof(f4158,plain,
    ( spl13_302
  <=> empty(identity_relation(relation_rng(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_302])]) ).

fof(f688,plain,
    ( spl13_81
  <=> empty(relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).

fof(f3863,plain,
    ( ~ empty(identity_relation(relation_rng(sK0)))
    | ~ spl13_27
    | spl13_81 ),
    inference(superposition,[],[f690,f329]) ).

fof(f690,plain,
    ( ~ empty(relation_composition(function_inverse(sK0),sK0))
    | spl13_81 ),
    inference(avatar_component_clause,[],[f688]) ).

fof(f4130,plain,
    ( spl13_301
    | ~ spl13_41
    | ~ spl13_156 ),
    inference(avatar_split_clause,[],[f3887,f1488,f411,f4127]) ).

fof(f4127,plain,
    ( spl13_301
  <=> element(sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)),relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_301])]) ).

fof(f3887,plain,
    ( element(sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)),relation_rng(sK0))
    | ~ spl13_41
    | ~ spl13_156 ),
    inference(resolution,[],[f1490,f412]) ).

fof(f3951,plain,
    ( spl13_300
    | ~ spl13_1
    | ~ spl13_229 ),
    inference(avatar_split_clause,[],[f2783,f2667,f204,f3949]) ).

fof(f3949,plain,
    ( spl13_300
  <=> ! [X0,X1] :
        ( relation_rng(relation_composition(X0,sK0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_300])]) ).

fof(f2783,plain,
    ( ! [X0,X1] :
        ( relation_rng(relation_composition(X0,sK0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_229 ),
    inference(resolution,[],[f2668,f206]) ).

fof(f3947,plain,
    ( spl13_299
    | ~ spl13_1
    | ~ spl13_228 ),
    inference(avatar_split_clause,[],[f2761,f2663,f204,f3945]) ).

fof(f3945,plain,
    ( spl13_299
  <=> ! [X0,X1] :
        ( relation_rng(relation_composition(sK0,X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_299])]) ).

fof(f2761,plain,
    ( ! [X0,X1] :
        ( relation_rng(relation_composition(sK0,X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_228 ),
    inference(resolution,[],[f2664,f206]) ).

fof(f3943,plain,
    ( spl13_298
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_277 ),
    inference(avatar_split_clause,[],[f3813,f3778,f683,f219,f3940]) ).

fof(f3940,plain,
    ( spl13_298
  <=> sK6 = relation_composition(sK0,sK2(powerset(sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_298])]) ).

fof(f3778,plain,
    ( spl13_277
  <=> ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK0,sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_277])]) ).

fof(f3813,plain,
    ( sK6 = relation_composition(sK0,sK2(powerset(sK6)))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_277 ),
    inference(forward_demodulation,[],[f3801,f685]) ).

fof(f3801,plain,
    ( sK6 = relation_composition(sK0,sK2(powerset(empty_set)))
    | ~ spl13_4
    | ~ spl13_277 ),
    inference(resolution,[],[f3779,f221]) ).

fof(f3779,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK0,sK2(powerset(X0))) )
    | ~ spl13_277 ),
    inference(avatar_component_clause,[],[f3778]) ).

fof(f3938,plain,
    ( spl13_297
    | ~ spl13_1
    | ~ spl13_227 ),
    inference(avatar_split_clause,[],[f2739,f2659,f204,f3936]) ).

fof(f3936,plain,
    ( spl13_297
  <=> ! [X0,X1] :
        ( relation_dom(relation_composition(X0,sK0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_297])]) ).

fof(f2739,plain,
    ( ! [X0,X1] :
        ( relation_dom(relation_composition(X0,sK0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_227 ),
    inference(resolution,[],[f2660,f206]) ).

fof(f3934,plain,
    ( spl13_296
    | ~ spl13_1
    | ~ spl13_226 ),
    inference(avatar_split_clause,[],[f2717,f2655,f204,f3932]) ).

fof(f3932,plain,
    ( spl13_296
  <=> ! [X0,X1] :
        ( relation_dom(relation_composition(sK0,X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_296])]) ).

fof(f2717,plain,
    ( ! [X0,X1] :
        ( relation_dom(relation_composition(sK0,X0)) = X1
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_226 ),
    inference(resolution,[],[f2656,f206]) ).

fof(f3930,plain,
    ( ~ spl13_158
    | ~ spl13_159
    | ~ spl13_294
    | spl13_295
    | ~ spl13_73
    | ~ spl13_76
    | ~ spl13_149 ),
    inference(avatar_split_clause,[],[f3903,f1435,f651,f625,f3927,f3923,f1508,f1504]) ).

fof(f3903,plain,
    ( sK0 = relation_composition(sK0,function_inverse(sK0))
    | sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))) != apply(relation_composition(sK0,function_inverse(sK0)),sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))))
    | ~ function(relation_composition(sK0,function_inverse(sK0)))
    | ~ relation(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_73
    | ~ spl13_76
    | ~ spl13_149 ),
    inference(forward_demodulation,[],[f661,f1437]) ).

fof(f3921,plain,
    ( ~ spl13_158
    | ~ spl13_159
    | ~ spl13_292
    | spl13_293
    | ~ spl13_71
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f659,f651,f613,f3919,f3915,f1508,f1504]) ).

fof(f3915,plain,
    ( spl13_292
  <=> one_to_one(relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_292])]) ).

fof(f3919,plain,
    ( spl13_293
  <=> ! [X0] :
        ( ~ in(X0,relation_dom(sK0))
        | apply(function_inverse(relation_composition(sK0,function_inverse(sK0))),apply(relation_composition(sK0,function_inverse(sK0)),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_293])]) ).

fof(f613,plain,
    ( spl13_71
  <=> ! [X0,X1] :
        ( apply(function_inverse(X1),apply(X1,X0)) = X0
        | ~ in(X0,relation_dom(X1))
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).

fof(f659,plain,
    ( ! [X0] :
        ( ~ in(X0,relation_dom(sK0))
        | apply(function_inverse(relation_composition(sK0,function_inverse(sK0))),apply(relation_composition(sK0,function_inverse(sK0)),X0)) = X0
        | ~ one_to_one(relation_composition(sK0,function_inverse(sK0)))
        | ~ function(relation_composition(sK0,function_inverse(sK0)))
        | ~ relation(relation_composition(sK0,function_inverse(sK0))) )
    | ~ spl13_71
    | ~ spl13_76 ),
    inference(superposition,[],[f614,f653]) ).

fof(f614,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,relation_dom(X1))
        | apply(function_inverse(X1),apply(X1,X0)) = X0
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_71 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f3902,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_157
    | ~ spl13_283
    | ~ spl13_62
    | spl13_159 ),
    inference(avatar_split_clause,[],[f1521,f1508,f564,f3839,f1499,f209,f204]) ).

fof(f3839,plain,
    ( spl13_283
  <=> function(function_inverse(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_283])]) ).

fof(f564,plain,
    ( spl13_62
  <=> ! [X0,X1] :
        ( function(relation_composition(X0,X1))
        | ~ function(X1)
        | ~ relation(X1)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).

fof(f1521,plain,
    ( ~ function(function_inverse(sK0))
    | ~ relation(function_inverse(sK0))
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_62
    | spl13_159 ),
    inference(resolution,[],[f1510,f565]) ).

fof(f565,plain,
    ( ! [X0,X1] :
        ( function(relation_composition(X0,X1))
        | ~ function(X1)
        | ~ relation(X1)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_62 ),
    inference(avatar_component_clause,[],[f564]) ).

fof(f1510,plain,
    ( ~ function(relation_composition(sK0,function_inverse(sK0)))
    | spl13_159 ),
    inference(avatar_component_clause,[],[f1508]) ).

fof(f3901,plain,
    ( ~ spl13_154
    | ~ spl13_155
    | spl13_27
    | ~ spl13_291
    | ~ spl13_73
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f639,f629,f625,f3898,f328,f1484,f1480]) ).

fof(f629,plain,
    ( spl13_74
  <=> relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).

fof(f639,plain,
    ( sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)) != apply(relation_composition(function_inverse(sK0),sK0),sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)))
    | relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
    | ~ function(relation_composition(function_inverse(sK0),sK0))
    | ~ relation(relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_73
    | ~ spl13_74 ),
    inference(superposition,[],[f626,f631]) ).

fof(f631,plain,
    ( relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_74 ),
    inference(avatar_component_clause,[],[f629]) ).

fof(f3896,plain,
    ( ~ spl13_154
    | ~ spl13_155
    | ~ spl13_289
    | spl13_290
    | ~ spl13_71
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f637,f629,f613,f3894,f3890,f1484,f1480]) ).

fof(f3894,plain,
    ( spl13_290
  <=> ! [X0] :
        ( ~ in(X0,relation_rng(sK0))
        | apply(function_inverse(relation_composition(function_inverse(sK0),sK0)),apply(relation_composition(function_inverse(sK0),sK0),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_290])]) ).

fof(f637,plain,
    ( ! [X0] :
        ( ~ in(X0,relation_rng(sK0))
        | apply(function_inverse(relation_composition(function_inverse(sK0),sK0)),apply(relation_composition(function_inverse(sK0),sK0),X0)) = X0
        | ~ one_to_one(relation_composition(function_inverse(sK0),sK0))
        | ~ function(relation_composition(function_inverse(sK0),sK0))
        | ~ relation(relation_composition(function_inverse(sK0),sK0)) )
    | ~ spl13_71
    | ~ spl13_74 ),
    inference(superposition,[],[f614,f631]) ).

fof(f3882,plain,
    ( spl13_288
    | ~ spl13_27
    | ~ spl13_75 ),
    inference(avatar_split_clause,[],[f3862,f641,f328,f3879]) ).

fof(f3879,plain,
    ( spl13_288
  <=> relation_rng(sK0) = relation_rng(identity_relation(relation_rng(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_288])]) ).

fof(f641,plain,
    ( spl13_75
  <=> relation_rng(sK0) = relation_rng(relation_composition(function_inverse(sK0),sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).

fof(f3862,plain,
    ( relation_rng(sK0) = relation_rng(identity_relation(relation_rng(sK0)))
    | ~ spl13_27
    | ~ spl13_75 ),
    inference(superposition,[],[f643,f329]) ).

fof(f643,plain,
    ( relation_rng(sK0) = relation_rng(relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_75 ),
    inference(avatar_component_clause,[],[f641]) ).

fof(f3860,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_47
    | spl13_283 ),
    inference(avatar_split_clause,[],[f3843,f3839,f436,f209,f204]) ).

fof(f436,plain,
    ( spl13_47
  <=> ! [X0] :
        ( function(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).

fof(f3843,plain,
    ( ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_47
    | spl13_283 ),
    inference(resolution,[],[f3841,f437]) ).

fof(f437,plain,
    ( ! [X0] :
        ( function(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_47 ),
    inference(avatar_component_clause,[],[f436]) ).

fof(f3841,plain,
    ( ~ function(function_inverse(sK0))
    | spl13_283 ),
    inference(avatar_component_clause,[],[f3839]) ).

fof(f3859,plain,
    ( spl13_287
    | ~ spl13_113
    | ~ spl13_158 ),
    inference(avatar_split_clause,[],[f1838,f1504,f1023,f3857]) ).

fof(f1838,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))
        | ~ empty(X0) )
    | ~ spl13_113
    | ~ spl13_158 ),
    inference(resolution,[],[f1505,f1024]) ).

fof(f3855,plain,
    ( spl13_286
    | ~ spl13_114
    | ~ spl13_158 ),
    inference(avatar_split_clause,[],[f1837,f1504,f1027,f3853]) ).

fof(f1837,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)
        | ~ empty(X0) )
    | ~ spl13_114
    | ~ spl13_158 ),
    inference(resolution,[],[f1505,f1028]) ).

fof(f3851,plain,
    ( spl13_285
    | ~ spl13_113
    | ~ spl13_154 ),
    inference(avatar_split_clause,[],[f1621,f1480,f1023,f3849]) ).

fof(f1621,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,relation_composition(function_inverse(sK0),sK0))
        | ~ empty(X0) )
    | ~ spl13_113
    | ~ spl13_154 ),
    inference(resolution,[],[f1481,f1024]) ).

fof(f3847,plain,
    ( spl13_284
    | ~ spl13_114
    | ~ spl13_154 ),
    inference(avatar_split_clause,[],[f1620,f1480,f1027,f3845]) ).

fof(f1620,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_composition(function_inverse(sK0),sK0),X0)
        | ~ empty(X0) )
    | ~ spl13_114
    | ~ spl13_154 ),
    inference(resolution,[],[f1481,f1028]) ).

fof(f3842,plain,
    ( ~ spl13_157
    | ~ spl13_283
    | ~ spl13_1
    | ~ spl13_2
    | ~ spl13_62
    | spl13_155 ),
    inference(avatar_split_clause,[],[f1497,f1484,f564,f209,f204,f3839,f1499]) ).

fof(f1497,plain,
    ( ~ function(sK0)
    | ~ relation(sK0)
    | ~ function(function_inverse(sK0))
    | ~ relation(function_inverse(sK0))
    | ~ spl13_62
    | spl13_155 ),
    inference(resolution,[],[f1486,f565]) ).

fof(f1486,plain,
    ( ~ function(relation_composition(function_inverse(sK0),sK0))
    | spl13_155 ),
    inference(avatar_component_clause,[],[f1484]) ).

fof(f3837,plain,
    ( spl13_282
    | ~ spl13_33
    | ~ spl13_143 ),
    inference(avatar_split_clause,[],[f1371,f1351,f363,f3835]) ).

fof(f3835,plain,
    ( spl13_282
  <=> ! [X0,X1] :
        ( relation_rng(X1) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_282])]) ).

fof(f1371,plain,
    ( ! [X0,X1] :
        ( relation_rng(X1) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_33
    | ~ spl13_143 ),
    inference(resolution,[],[f1352,f364]) ).

fof(f3833,plain,
    ( spl13_281
    | ~ spl13_35
    | ~ spl13_143 ),
    inference(avatar_split_clause,[],[f1370,f1351,f371,f3831]) ).

fof(f3831,plain,
    ( spl13_281
  <=> ! [X0,X1] :
        ( relation_dom(X1) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_281])]) ).

fof(f1370,plain,
    ( ! [X0,X1] :
        ( relation_dom(X1) = relation_composition(sK0,X0)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_35
    | ~ spl13_143 ),
    inference(resolution,[],[f1352,f372]) ).

fof(f3829,plain,
    ( spl13_280
    | ~ spl13_33
    | ~ spl13_142 ),
    inference(avatar_split_clause,[],[f1358,f1347,f363,f3827]) ).

fof(f3827,plain,
    ( spl13_280
  <=> ! [X0,X1] :
        ( relation_rng(X1) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_280])]) ).

fof(f1358,plain,
    ( ! [X0,X1] :
        ( relation_rng(X1) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_33
    | ~ spl13_142 ),
    inference(resolution,[],[f1348,f364]) ).

fof(f3825,plain,
    ( spl13_279
    | ~ spl13_35
    | ~ spl13_142 ),
    inference(avatar_split_clause,[],[f1357,f1347,f371,f3823]) ).

fof(f3823,plain,
    ( spl13_279
  <=> ! [X0,X1] :
        ( relation_dom(X1) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_279])]) ).

fof(f1357,plain,
    ( ! [X0,X1] :
        ( relation_dom(X1) = relation_composition(X0,sK0)
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_35
    | ~ spl13_142 ),
    inference(resolution,[],[f1348,f372]) ).

fof(f3821,plain,
    ( spl13_278
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_276 ),
    inference(avatar_split_clause,[],[f3795,f3774,f683,f219,f3818]) ).

fof(f3818,plain,
    ( spl13_278
  <=> sK6 = relation_composition(sK2(powerset(sK6)),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_278])]) ).

fof(f3774,plain,
    ( spl13_276
  <=> ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK2(powerset(X0)),sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_276])]) ).

fof(f3795,plain,
    ( sK6 = relation_composition(sK2(powerset(sK6)),sK0)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_276 ),
    inference(forward_demodulation,[],[f3783,f685]) ).

fof(f3783,plain,
    ( sK6 = relation_composition(sK2(powerset(empty_set)),sK0)
    | ~ spl13_4
    | ~ spl13_276 ),
    inference(resolution,[],[f3775,f221]) ).

fof(f3775,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK2(powerset(X0)),sK0) )
    | ~ spl13_276 ),
    inference(avatar_component_clause,[],[f3774]) ).

fof(f3780,plain,
    ( spl13_277
    | ~ spl13_124
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f1475,f1459,f1118,f3778]) ).

fof(f1475,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK0,sK2(powerset(X0))) )
    | ~ spl13_124
    | ~ spl13_152 ),
    inference(resolution,[],[f1460,f1119]) ).

fof(f3776,plain,
    ( spl13_276
    | ~ spl13_117
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f1474,f1459,f1079,f3774]) ).

fof(f1474,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | sK6 = relation_composition(sK2(powerset(X0)),sK0) )
    | ~ spl13_117
    | ~ spl13_152 ),
    inference(resolution,[],[f1460,f1080]) ).

fof(f3772,plain,
    ( ~ spl13_275
    | ~ spl13_33
    | spl13_180 ),
    inference(avatar_split_clause,[],[f1831,f1827,f363,f3769]) ).

fof(f3769,plain,
    ( spl13_275
  <=> empty(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_275])]) ).

fof(f1827,plain,
    ( spl13_180
  <=> empty(relation_rng(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_180])]) ).

fof(f1831,plain,
    ( ~ empty(sK11)
    | ~ spl13_33
    | spl13_180 ),
    inference(resolution,[],[f1828,f364]) ).

fof(f1828,plain,
    ( ~ empty(relation_rng(sK11))
    | spl13_180 ),
    inference(avatar_component_clause,[],[f1827]) ).

fof(f3767,plain,
    ( ~ spl13_274
    | ~ spl13_264
    | spl13_272 ),
    inference(avatar_split_clause,[],[f3733,f3725,f3682,f3764]) ).

fof(f3764,plain,
    ( spl13_274
  <=> sK11 = relation_composition(sK11,function_inverse(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_274])]) ).

fof(f3682,plain,
    ( spl13_264
  <=> sK11 = identity_relation(relation_dom(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_264])]) ).

fof(f3725,plain,
    ( spl13_272
  <=> relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_272])]) ).

fof(f3733,plain,
    ( sK11 != relation_composition(sK11,function_inverse(sK11))
    | ~ spl13_264
    | spl13_272 ),
    inference(forward_demodulation,[],[f3726,f3684]) ).

fof(f3684,plain,
    ( sK11 = identity_relation(relation_dom(sK11))
    | ~ spl13_264 ),
    inference(avatar_component_clause,[],[f3682]) ).

fof(f3726,plain,
    ( relation_composition(sK11,function_inverse(sK11)) != identity_relation(relation_dom(sK11))
    | spl13_272 ),
    inference(avatar_component_clause,[],[f3725]) ).

fof(f3732,plain,
    ( ~ spl13_270
    | ~ spl13_271
    | spl13_272
    | spl13_273
    | ~ spl13_68
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f1195,f1188,f597,f3729,f3725,f3721,f3717]) ).

fof(f3717,plain,
    ( spl13_270
  <=> relation(relation_composition(sK11,function_inverse(sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_270])]) ).

fof(f3721,plain,
    ( spl13_271
  <=> function(relation_composition(sK11,function_inverse(sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_271])]) ).

fof(f3729,plain,
    ( spl13_273
  <=> in(sK4(relation_dom(sK11),relation_composition(sK11,function_inverse(sK11))),relation_dom(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_273])]) ).

fof(f597,plain,
    ( spl13_68
  <=> ! [X1] :
        ( identity_relation(relation_dom(X1)) = X1
        | in(sK4(relation_dom(X1),X1),relation_dom(X1))
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).

fof(f1188,plain,
    ( spl13_127
  <=> relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_127])]) ).

fof(f1195,plain,
    ( in(sK4(relation_dom(sK11),relation_composition(sK11,function_inverse(sK11))),relation_dom(sK11))
    | relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11))
    | ~ function(relation_composition(sK11,function_inverse(sK11)))
    | ~ relation(relation_composition(sK11,function_inverse(sK11)))
    | ~ spl13_68
    | ~ spl13_127 ),
    inference(superposition,[],[f598,f1190]) ).

fof(f1190,plain,
    ( relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11)))
    | ~ spl13_127 ),
    inference(avatar_component_clause,[],[f1188]) ).

fof(f598,plain,
    ( ! [X1] :
        ( in(sK4(relation_dom(X1),X1),relation_dom(X1))
        | identity_relation(relation_dom(X1)) = X1
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_68 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f3709,plain,
    ( ~ spl13_266
    | ~ spl13_267
    | spl13_268
    | spl13_269
    | ~ spl13_68
    | ~ spl13_125 ),
    inference(avatar_split_clause,[],[f1171,f1164,f597,f3706,f3702,f3698,f3694]) ).

fof(f3698,plain,
    ( spl13_267
  <=> function(relation_composition(function_inverse(sK11),sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_267])]) ).

fof(f3702,plain,
    ( spl13_268
  <=> relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_268])]) ).

fof(f3706,plain,
    ( spl13_269
  <=> in(sK4(relation_rng(sK11),relation_composition(function_inverse(sK11),sK11)),relation_rng(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_269])]) ).

fof(f1164,plain,
    ( spl13_125
  <=> relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_125])]) ).

fof(f1171,plain,
    ( in(sK4(relation_rng(sK11),relation_composition(function_inverse(sK11),sK11)),relation_rng(sK11))
    | relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11))
    | ~ function(relation_composition(function_inverse(sK11),sK11))
    | ~ relation(relation_composition(function_inverse(sK11),sK11))
    | ~ spl13_68
    | ~ spl13_125 ),
    inference(superposition,[],[f598,f1166]) ).

fof(f1166,plain,
    ( relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11))
    | ~ spl13_125 ),
    inference(avatar_component_clause,[],[f1164]) ).

fof(f3689,plain,
    ( spl13_264
    | ~ spl13_15
    | ~ spl13_16
    | spl13_265
    | ~ spl13_17
    | ~ spl13_138 ),
    inference(avatar_split_clause,[],[f1303,f1295,f284,f3686,f279,f274,f3682]) ).

fof(f279,plain,
    ( spl13_16
  <=> function(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).

fof(f3686,plain,
    ( spl13_265
  <=> sK4(relation_dom(sK11),sK11) = apply(function_inverse(sK11),apply(sK11,sK4(relation_dom(sK11),sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_265])]) ).

fof(f284,plain,
    ( spl13_17
  <=> one_to_one(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).

fof(f1295,plain,
    ( spl13_138
  <=> ! [X0] :
        ( sK4(relation_dom(X0),X0) = apply(function_inverse(X0),apply(X0,sK4(relation_dom(X0),X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_138])]) ).

fof(f1303,plain,
    ( sK4(relation_dom(sK11),sK11) = apply(function_inverse(sK11),apply(sK11,sK4(relation_dom(sK11),sK11)))
    | ~ function(sK11)
    | ~ relation(sK11)
    | sK11 = identity_relation(relation_dom(sK11))
    | ~ spl13_17
    | ~ spl13_138 ),
    inference(resolution,[],[f1296,f286]) ).

fof(f286,plain,
    ( one_to_one(sK11)
    | ~ spl13_17 ),
    inference(avatar_component_clause,[],[f284]) ).

fof(f1296,plain,
    ( ! [X0] :
        ( ~ one_to_one(X0)
        | sK4(relation_dom(X0),X0) = apply(function_inverse(X0),apply(X0,sK4(relation_dom(X0),X0)))
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 )
    | ~ spl13_138 ),
    inference(avatar_component_clause,[],[f1295]) ).

fof(f3375,plain,
    ( spl13_263
    | ~ spl13_69
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f932,f895,f605,f3373]) ).

fof(f605,plain,
    ( spl13_69
  <=> ! [X0,X1] :
        ( apply(X1,apply(function_inverse(X1),X0)) = X0
        | ~ in(X0,relation_rng(X1))
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_69])]) ).

fof(f895,plain,
    ( spl13_101
  <=> ! [X0] :
        ( empty(X0)
        | in(sK2(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_101])]) ).

fof(f932,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | sK2(relation_rng(X0)) = apply(X0,apply(function_inverse(X0),sK2(relation_rng(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_69
    | ~ spl13_101 ),
    inference(resolution,[],[f896,f606]) ).

fof(f606,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,relation_rng(X1))
        | apply(X1,apply(function_inverse(X1),X0)) = X0
        | ~ one_to_one(X1)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_69 ),
    inference(avatar_component_clause,[],[f605]) ).

fof(f896,plain,
    ( ! [X0] :
        ( in(sK2(X0),X0)
        | empty(X0) )
    | ~ spl13_101 ),
    inference(avatar_component_clause,[],[f895]) ).

fof(f3371,plain,
    ( spl13_262
    | ~ spl13_70
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f931,f895,f609,f3369]) ).

fof(f931,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | sK2(relation_rng(X0)) = apply(relation_composition(function_inverse(X0),X0),sK2(relation_rng(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_70
    | ~ spl13_101 ),
    inference(resolution,[],[f896,f610]) ).

fof(f3367,plain,
    ( spl13_261
    | ~ spl13_71
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f930,f895,f613,f3365]) ).

fof(f930,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | sK2(relation_dom(X0)) = apply(function_inverse(X0),apply(X0,sK2(relation_dom(X0))))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_71
    | ~ spl13_101 ),
    inference(resolution,[],[f896,f614]) ).

fof(f3363,plain,
    ( spl13_260
    | ~ spl13_72
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f929,f895,f617,f3361]) ).

fof(f929,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | sK2(relation_dom(X0)) = apply(relation_composition(X0,function_inverse(X0)),sK2(relation_dom(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_72
    | ~ spl13_101 ),
    inference(resolution,[],[f896,f618]) ).

fof(f3336,plain,
    ( ~ spl13_55
    | ~ spl13_42
    | spl13_259
    | spl13_258
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94
    | ~ spl13_100
    | ~ spl13_139 ),
    inference(avatar_split_clause,[],[f1320,f1299,f886,f859,f683,f219,f3328,f3333,f415,f482]) ).

fof(f482,plain,
    ( spl13_55
  <=> relation(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).

fof(f415,plain,
    ( spl13_42
  <=> function(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).

fof(f3333,plain,
    ( spl13_259
  <=> sK4(sK6,sK6) = apply(relation_composition(sK6,function_inverse(sK6)),sK4(sK6,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_259])]) ).

fof(f859,plain,
    ( spl13_94
  <=> ! [X0] :
        ( relation_dom(X0) = sK6
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_94])]) ).

fof(f886,plain,
    ( spl13_100
  <=> one_to_one(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_100])]) ).

fof(f1320,plain,
    ( sK6 = identity_relation(sK6)
    | sK4(sK6,sK6) = apply(relation_composition(sK6,function_inverse(sK6)),sK4(sK6,sK6))
    | ~ function(sK6)
    | ~ relation(sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94
    | ~ spl13_100
    | ~ spl13_139 ),
    inference(forward_demodulation,[],[f1319,f922]) ).

fof(f922,plain,
    ( sK6 = relation_dom(sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94 ),
    inference(forward_demodulation,[],[f915,f685]) ).

fof(f915,plain,
    ( sK6 = relation_dom(empty_set)
    | ~ spl13_4
    | ~ spl13_94 ),
    inference(resolution,[],[f860,f221]) ).

fof(f860,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_dom(X0) = sK6 )
    | ~ spl13_94 ),
    inference(avatar_component_clause,[],[f859]) ).

fof(f1319,plain,
    ( sK4(sK6,sK6) = apply(relation_composition(sK6,function_inverse(sK6)),sK4(sK6,sK6))
    | ~ function(sK6)
    | ~ relation(sK6)
    | sK6 = identity_relation(relation_dom(sK6))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94
    | ~ spl13_100
    | ~ spl13_139 ),
    inference(forward_demodulation,[],[f1318,f922]) ).

fof(f1318,plain,
    ( sK4(relation_dom(sK6),sK6) = apply(relation_composition(sK6,function_inverse(sK6)),sK4(relation_dom(sK6),sK6))
    | ~ function(sK6)
    | ~ relation(sK6)
    | sK6 = identity_relation(relation_dom(sK6))
    | ~ spl13_100
    | ~ spl13_139 ),
    inference(resolution,[],[f1300,f888]) ).

fof(f888,plain,
    ( one_to_one(sK6)
    | ~ spl13_100 ),
    inference(avatar_component_clause,[],[f886]) ).

fof(f3331,plain,
    ( ~ spl13_55
    | ~ spl13_42
    | spl13_257
    | spl13_258
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94
    | ~ spl13_100
    | ~ spl13_138 ),
    inference(avatar_split_clause,[],[f1306,f1295,f886,f859,f683,f219,f3328,f3324,f415,f482]) ).

fof(f3324,plain,
    ( spl13_257
  <=> sK4(sK6,sK6) = apply(function_inverse(sK6),apply(sK6,sK4(sK6,sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_257])]) ).

fof(f1306,plain,
    ( sK6 = identity_relation(sK6)
    | sK4(sK6,sK6) = apply(function_inverse(sK6),apply(sK6,sK4(sK6,sK6)))
    | ~ function(sK6)
    | ~ relation(sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94
    | ~ spl13_100
    | ~ spl13_138 ),
    inference(forward_demodulation,[],[f1305,f922]) ).

fof(f1305,plain,
    ( sK4(sK6,sK6) = apply(function_inverse(sK6),apply(sK6,sK4(sK6,sK6)))
    | ~ function(sK6)
    | ~ relation(sK6)
    | sK6 = identity_relation(relation_dom(sK6))
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94
    | ~ spl13_100
    | ~ spl13_138 ),
    inference(forward_demodulation,[],[f1304,f922]) ).

fof(f1304,plain,
    ( sK4(relation_dom(sK6),sK6) = apply(function_inverse(sK6),apply(sK6,sK4(relation_dom(sK6),sK6)))
    | ~ function(sK6)
    | ~ relation(sK6)
    | sK6 = identity_relation(relation_dom(sK6))
    | ~ spl13_100
    | ~ spl13_138 ),
    inference(resolution,[],[f1296,f888]) ).

fof(f3316,plain,
    ( spl13_256
    | ~ spl13_62
    | ~ spl13_134 ),
    inference(avatar_split_clause,[],[f1282,f1253,f564,f3314]) ).

fof(f3314,plain,
    ( spl13_256
  <=> ! [X0,X1] :
        ( ~ relation(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1))
        | ~ function(X1)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_256])]) ).

fof(f1253,plain,
    ( spl13_134
  <=> ! [X0,X1] :
        ( ~ relation(X0)
        | ~ relation(X1)
        | ~ function(relation_composition(X1,X0))
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_134])]) ).

fof(f1282,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1))
        | ~ function(X1)
        | ~ function(X0) )
    | ~ spl13_62
    | ~ spl13_134 ),
    inference(duplicate_literal_removal,[],[f1281]) ).

fof(f1281,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1))
        | ~ function(X1)
        | ~ relation(X1)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_62
    | ~ spl13_134 ),
    inference(resolution,[],[f1254,f565]) ).

fof(f1254,plain,
    ( ! [X0,X1] :
        ( ~ function(relation_composition(X1,X0))
        | ~ relation(X1)
        | ~ relation(X0)
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) )
    | ~ spl13_134 ),
    inference(avatar_component_clause,[],[f1253]) ).

fof(f3161,plain,
    ( spl13_255
    | ~ spl13_58
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1147,f1110,f495,f3159]) ).

fof(f1147,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ relation(X1) )
    | ~ spl13_58
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f496]) ).

fof(f3157,plain,
    ( spl13_254
    | ~ spl13_54
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1146,f1110,f478,f3155]) ).

fof(f478,plain,
    ( spl13_54
  <=> ! [X0,X1] :
        ( relation(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).

fof(f1146,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_54
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f479]) ).

fof(f479,plain,
    ( ! [X0,X1] :
        ( relation(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_54 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f3153,plain,
    ( spl13_253
    | ~ spl13_57
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1145,f1110,f491,f3151]) ).

fof(f491,plain,
    ( spl13_57
  <=> ! [X0,X1] :
        ( relation(relation_composition(X1,X0))
        | ~ relation(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).

fof(f1145,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_composition(X1,X2),X0) = X3
        | ~ empty(X3)
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_57
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f492]) ).

fof(f492,plain,
    ( ! [X0,X1] :
        ( relation(relation_composition(X1,X0))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_57 ),
    inference(avatar_component_clause,[],[f491]) ).

fof(f3149,plain,
    ( spl13_252
    | ~ spl13_58
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1128,f1106,f495,f3147]) ).

fof(f1128,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ relation(X1) )
    | ~ spl13_58
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f496]) ).

fof(f3145,plain,
    ( spl13_251
    | ~ spl13_54
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1127,f1106,f478,f3143]) ).

fof(f1127,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_54
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f479]) ).

fof(f3141,plain,
    ( spl13_250
    | ~ spl13_57
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1126,f1106,f491,f3139]) ).

fof(f1126,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_composition(X1,X2)) = X3
        | ~ empty(X3)
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_57
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f492]) ).

fof(f3087,plain,
    ( spl13_249
    | ~ spl13_1
    | ~ spl13_205 ),
    inference(avatar_split_clause,[],[f2370,f2227,f204,f3085]) ).

fof(f3085,plain,
    ( spl13_249
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,sK0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_249])]) ).

fof(f2370,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(X0,sK0))
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_205 ),
    inference(resolution,[],[f2228,f206]) ).

fof(f3083,plain,
    ( spl13_248
    | ~ spl13_46
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1144,f1110,f432,f3081]) ).

fof(f432,plain,
    ( spl13_46
  <=> ! [X0] :
        ( relation(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).

fof(f1144,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(function_inverse(X1),X0) = X2
        | ~ empty(X2)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_46
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f433]) ).

fof(f433,plain,
    ( ! [X0] :
        ( relation(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_46 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f3079,plain,
    ( spl13_247
    | ~ spl13_46
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1125,f1106,f432,f3077]) ).

fof(f1125,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,function_inverse(X1)) = X2
        | ~ empty(X2)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_46
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f433]) ).

fof(f2943,plain,
    ( spl13_246
    | ~ spl13_58
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1061,f1027,f495,f2941]) ).

fof(f1061,plain,
    ( ! [X2,X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X2)
        | ~ relation(X1)
        | ~ relation(X0) )
    | ~ spl13_58
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f496]) ).

fof(f2939,plain,
    ( spl13_245
    | ~ spl13_54
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1060,f1027,f478,f2937]) ).

fof(f1060,plain,
    ( ! [X2,X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X2)
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_54
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f479]) ).

fof(f2935,plain,
    ( spl13_244
    | ~ spl13_1
    | ~ spl13_204 ),
    inference(avatar_split_clause,[],[f2348,f2223,f204,f2933]) ).

fof(f2933,plain,
    ( spl13_244
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_composition(sK0,X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_244])]) ).

fof(f2348,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_composition(sK0,X0))
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_204 ),
    inference(resolution,[],[f2224,f206]) ).

fof(f2931,plain,
    ( spl13_243
    | ~ spl13_57
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1059,f1027,f491,f2929]) ).

fof(f1059,plain,
    ( ! [X2,X0,X1] :
        ( sK6 = relation_composition(relation_composition(X0,X1),X2)
        | ~ empty(X2)
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_57
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f492]) ).

fof(f2927,plain,
    ( spl13_242
    | ~ spl13_58
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1042,f1023,f495,f2925]) ).

fof(f1042,plain,
    ( ! [X2,X0,X1] :
        ( sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ relation(X1) )
    | ~ spl13_58
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f496]) ).

fof(f2923,plain,
    ( spl13_241
    | ~ spl13_54
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1041,f1023,f478,f2921]) ).

fof(f1041,plain,
    ( ! [X2,X0,X1] :
        ( sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X0)
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_54
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f479]) ).

fof(f2919,plain,
    ( spl13_240
    | ~ spl13_57
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1040,f1023,f491,f2917]) ).

fof(f1040,plain,
    ( ! [X2,X0,X1] :
        ( sK6 = relation_composition(X0,relation_composition(X1,X2))
        | ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_57
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f492]) ).

fof(f2847,plain,
    ( spl13_239
    | ~ spl13_1
    | ~ spl13_202 ),
    inference(avatar_split_clause,[],[f2326,f2215,f204,f2845]) ).

fof(f2845,plain,
    ( spl13_239
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,sK0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_239])]) ).

fof(f2326,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(X0,sK0))
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_202 ),
    inference(resolution,[],[f2216,f206]) ).

fof(f2705,plain,
    ( spl13_238
    | ~ spl13_108
    | ~ spl13_133 ),
    inference(avatar_split_clause,[],[f1278,f1249,f964,f2703]) ).

fof(f2703,plain,
    ( spl13_238
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_238])]) ).

fof(f964,plain,
    ( spl13_108
  <=> ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | function(relation_composition(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_108])]) ).

fof(f1249,plain,
    ( spl13_133
  <=> ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | ~ function(relation_composition(X0,X1))
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_133])]) ).

fof(f1278,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) )
    | ~ spl13_108
    | ~ spl13_133 ),
    inference(duplicate_literal_removal,[],[f1274]) ).

fof(f1274,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0))
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_108
    | ~ spl13_133 ),
    inference(resolution,[],[f1250,f965]) ).

fof(f965,plain,
    ( ! [X0,X1] :
        ( function(relation_composition(X0,X1))
        | ~ empty(X1)
        | ~ relation(X0) )
    | ~ spl13_108 ),
    inference(avatar_component_clause,[],[f964]) ).

fof(f1250,plain,
    ( ! [X0,X1] :
        ( ~ function(relation_composition(X0,X1))
        | ~ empty(X1)
        | ~ relation(X0)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1)) )
    | ~ spl13_133 ),
    inference(avatar_component_clause,[],[f1249]) ).

fof(f2701,plain,
    ( spl13_237
    | ~ spl13_106
    | ~ spl13_132 ),
    inference(avatar_split_clause,[],[f1273,f1245,f955,f2699]) ).

fof(f2699,plain,
    ( spl13_237
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_237])]) ).

fof(f955,plain,
    ( spl13_106
  <=> ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | function(relation_composition(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_106])]) ).

fof(f1245,plain,
    ( spl13_132
  <=> ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | ~ function(relation_composition(X1,X0))
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_132])]) ).

fof(f1273,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1)) )
    | ~ spl13_106
    | ~ spl13_132 ),
    inference(duplicate_literal_removal,[],[f1270]) ).

fof(f1270,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ relation(X1)
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1))
        | ~ empty(X0)
        | ~ relation(X1) )
    | ~ spl13_106
    | ~ spl13_132 ),
    inference(resolution,[],[f1246,f956]) ).

fof(f956,plain,
    ( ! [X0,X1] :
        ( function(relation_composition(X1,X0))
        | ~ empty(X1)
        | ~ relation(X0) )
    | ~ spl13_106 ),
    inference(avatar_component_clause,[],[f955]) ).

fof(f1246,plain,
    ( ! [X0,X1] :
        ( ~ function(relation_composition(X1,X0))
        | ~ empty(X1)
        | ~ relation(X0)
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) )
    | ~ spl13_132 ),
    inference(avatar_component_clause,[],[f1245]) ).

fof(f2697,plain,
    ( spl13_236
    | ~ spl13_34
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1151,f1110,f367,f2695]) ).

fof(f2695,plain,
    ( spl13_236
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_rng(X1),X0) = X2
        | ~ empty(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_236])]) ).

fof(f367,plain,
    ( spl13_34
  <=> ! [X0] :
        ( relation(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).

fof(f1151,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_rng(X1),X0) = X2
        | ~ empty(X2)
        | ~ empty(X1) )
    | ~ spl13_34
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f368]) ).

fof(f368,plain,
    ( ! [X0] :
        ( relation(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_34 ),
    inference(avatar_component_clause,[],[f367]) ).

fof(f2693,plain,
    ( spl13_235
    | ~ spl13_36
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1150,f1110,f375,f2691]) ).

fof(f2691,plain,
    ( spl13_235
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_dom(X1),X0) = X2
        | ~ empty(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_235])]) ).

fof(f1150,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(relation_dom(X1),X0) = X2
        | ~ empty(X2)
        | ~ empty(X1) )
    | ~ spl13_36
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f376]) ).

fof(f2689,plain,
    ( spl13_234
    | ~ spl13_1
    | ~ spl13_201 ),
    inference(avatar_split_clause,[],[f2304,f2211,f204,f2687]) ).

fof(f2687,plain,
    ( spl13_234
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_composition(sK0,X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_234])]) ).

fof(f2304,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_composition(sK0,X0))
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_201 ),
    inference(resolution,[],[f2212,f206]) ).

fof(f2685,plain,
    ( spl13_233
    | ~ spl13_34
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1132,f1106,f367,f2683]) ).

fof(f2683,plain,
    ( spl13_233
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_rng(X1)) = X2
        | ~ empty(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_233])]) ).

fof(f1132,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_rng(X1)) = X2
        | ~ empty(X2)
        | ~ empty(X1) )
    | ~ spl13_34
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f368]) ).

fof(f2681,plain,
    ( spl13_232
    | ~ spl13_36
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1131,f1106,f375,f2679]) ).

fof(f2679,plain,
    ( spl13_232
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_dom(X1)) = X2
        | ~ empty(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_232])]) ).

fof(f1131,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,relation_dom(X1)) = X2
        | ~ empty(X2)
        | ~ empty(X1) )
    | ~ spl13_36
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f376]) ).

fof(f2677,plain,
    ( spl13_231
    | ~ spl13_46
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1058,f1027,f432,f2675]) ).

fof(f1058,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(function_inverse(X0),X1)
        | ~ empty(X1)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_46
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f433]) ).

fof(f2673,plain,
    ( spl13_230
    | ~ spl13_46
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1039,f1023,f432,f2671]) ).

fof(f1039,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(X0,function_inverse(X1))
        | ~ empty(X0)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl13_46
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f433]) ).

fof(f2669,plain,
    ( spl13_229
    | ~ spl13_53
    | ~ spl13_105 ),
    inference(avatar_split_clause,[],[f998,f951,f474,f2667]) ).

fof(f951,plain,
    ( spl13_105
  <=> ! [X0,X1] :
        ( relation_rng(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_105])]) ).

fof(f998,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_composition(X1,X2)) = X0
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_53
    | ~ spl13_105 ),
    inference(resolution,[],[f952,f475]) ).

fof(f952,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | ~ empty(X0)
        | relation_rng(X1) = X0 )
    | ~ spl13_105 ),
    inference(avatar_component_clause,[],[f951]) ).

fof(f2665,plain,
    ( spl13_228
    | ~ spl13_56
    | ~ spl13_105 ),
    inference(avatar_split_clause,[],[f997,f951,f487,f2663]) ).

fof(f997,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_composition(X1,X2)) = X0
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_56
    | ~ spl13_105 ),
    inference(resolution,[],[f952,f488]) ).

fof(f2661,plain,
    ( spl13_227
    | ~ spl13_53
    | ~ spl13_104 ),
    inference(avatar_split_clause,[],[f980,f947,f474,f2659]) ).

fof(f947,plain,
    ( spl13_104
  <=> ! [X0,X1] :
        ( relation_dom(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_104])]) ).

fof(f980,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_composition(X1,X2)) = X0
        | ~ relation(X2)
        | ~ empty(X1) )
    | ~ spl13_53
    | ~ spl13_104 ),
    inference(resolution,[],[f948,f475]) ).

fof(f948,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | ~ empty(X0)
        | relation_dom(X1) = X0 )
    | ~ spl13_104 ),
    inference(avatar_component_clause,[],[f947]) ).

fof(f2657,plain,
    ( spl13_226
    | ~ spl13_56
    | ~ spl13_104 ),
    inference(avatar_split_clause,[],[f979,f947,f487,f2655]) ).

fof(f979,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_composition(X1,X2)) = X0
        | ~ relation(X1)
        | ~ empty(X2) )
    | ~ spl13_56
    | ~ spl13_104 ),
    inference(resolution,[],[f948,f488]) ).

fof(f2642,plain,
    ( spl13_225
    | ~ spl13_146
    | ~ spl13_224 ),
    inference(avatar_split_clause,[],[f2618,f2614,f1390,f2639]) ).

fof(f2639,plain,
    ( spl13_225
  <=> sK6 = relation_dom(relation_composition(function_inverse(sK6),sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_225])]) ).

fof(f1390,plain,
    ( spl13_146
  <=> sK6 = relation_rng(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_146])]) ).

fof(f2614,plain,
    ( spl13_224
  <=> relation_rng(sK6) = relation_dom(relation_composition(function_inverse(sK6),sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_224])]) ).

fof(f2618,plain,
    ( sK6 = relation_dom(relation_composition(function_inverse(sK6),sK6))
    | ~ spl13_146
    | ~ spl13_224 ),
    inference(forward_demodulation,[],[f2616,f1392]) ).

fof(f1392,plain,
    ( sK6 = relation_rng(sK6)
    | ~ spl13_146 ),
    inference(avatar_component_clause,[],[f1390]) ).

fof(f2616,plain,
    ( relation_rng(sK6) = relation_dom(relation_composition(function_inverse(sK6),sK6))
    | ~ spl13_224 ),
    inference(avatar_component_clause,[],[f2614]) ).

fof(f2617,plain,
    ( ~ spl13_55
    | ~ spl13_42
    | spl13_224
    | ~ spl13_63
    | ~ spl13_100 ),
    inference(avatar_split_clause,[],[f893,f886,f568,f2614,f415,f482]) ).

fof(f568,plain,
    ( spl13_63
  <=> ! [X0] :
        ( relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).

fof(f893,plain,
    ( relation_rng(sK6) = relation_dom(relation_composition(function_inverse(sK6),sK6))
    | ~ function(sK6)
    | ~ relation(sK6)
    | ~ spl13_63
    | ~ spl13_100 ),
    inference(resolution,[],[f888,f569]) ).

fof(f569,plain,
    ( ! [X0] :
        ( ~ one_to_one(X0)
        | relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_63 ),
    inference(avatar_component_clause,[],[f568]) ).

fof(f2606,plain,
    ( spl13_223
    | ~ spl13_146
    | ~ spl13_222 ),
    inference(avatar_split_clause,[],[f2601,f2597,f1390,f2603]) ).

fof(f2603,plain,
    ( spl13_223
  <=> sK6 = relation_rng(relation_composition(function_inverse(sK6),sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_223])]) ).

fof(f2597,plain,
    ( spl13_222
  <=> relation_rng(sK6) = relation_rng(relation_composition(function_inverse(sK6),sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_222])]) ).

fof(f2601,plain,
    ( sK6 = relation_rng(relation_composition(function_inverse(sK6),sK6))
    | ~ spl13_146
    | ~ spl13_222 ),
    inference(forward_demodulation,[],[f2599,f1392]) ).

fof(f2599,plain,
    ( relation_rng(sK6) = relation_rng(relation_composition(function_inverse(sK6),sK6))
    | ~ spl13_222 ),
    inference(avatar_component_clause,[],[f2597]) ).

fof(f2600,plain,
    ( ~ spl13_55
    | ~ spl13_42
    | spl13_222
    | ~ spl13_64
    | ~ spl13_100 ),
    inference(avatar_split_clause,[],[f892,f886,f572,f2597,f415,f482]) ).

fof(f572,plain,
    ( spl13_64
  <=> ! [X0] :
        ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).

fof(f892,plain,
    ( relation_rng(sK6) = relation_rng(relation_composition(function_inverse(sK6),sK6))
    | ~ function(sK6)
    | ~ relation(sK6)
    | ~ spl13_64
    | ~ spl13_100 ),
    inference(resolution,[],[f888,f573]) ).

fof(f573,plain,
    ( ! [X0] :
        ( ~ one_to_one(X0)
        | relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_64 ),
    inference(avatar_component_clause,[],[f572]) ).

fof(f2584,plain,
    ( spl13_221
    | ~ spl13_147
    | ~ spl13_220 ),
    inference(avatar_split_clause,[],[f2579,f2575,f1395,f2581]) ).

fof(f2581,plain,
    ( spl13_221
  <=> sK6 = relation_dom(relation_composition(sK6,function_inverse(sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_221])]) ).

fof(f1395,plain,
    ( spl13_147
  <=> sK6 = relation_dom(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_147])]) ).

fof(f2575,plain,
    ( spl13_220
  <=> relation_dom(sK6) = relation_dom(relation_composition(sK6,function_inverse(sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_220])]) ).

fof(f2579,plain,
    ( sK6 = relation_dom(relation_composition(sK6,function_inverse(sK6)))
    | ~ spl13_147
    | ~ spl13_220 ),
    inference(forward_demodulation,[],[f2577,f1397]) ).

fof(f1397,plain,
    ( sK6 = relation_dom(sK6)
    | ~ spl13_147 ),
    inference(avatar_component_clause,[],[f1395]) ).

fof(f2577,plain,
    ( relation_dom(sK6) = relation_dom(relation_composition(sK6,function_inverse(sK6)))
    | ~ spl13_220 ),
    inference(avatar_component_clause,[],[f2575]) ).

fof(f2578,plain,
    ( ~ spl13_55
    | ~ spl13_42
    | spl13_220
    | ~ spl13_65
    | ~ spl13_100 ),
    inference(avatar_split_clause,[],[f891,f886,f576,f2575,f415,f482]) ).

fof(f576,plain,
    ( spl13_65
  <=> ! [X0] :
        ( relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).

fof(f891,plain,
    ( relation_dom(sK6) = relation_dom(relation_composition(sK6,function_inverse(sK6)))
    | ~ function(sK6)
    | ~ relation(sK6)
    | ~ spl13_65
    | ~ spl13_100 ),
    inference(resolution,[],[f888,f577]) ).

fof(f577,plain,
    ( ! [X0] :
        ( ~ one_to_one(X0)
        | relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0)))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_65 ),
    inference(avatar_component_clause,[],[f576]) ).

fof(f2567,plain,
    ( spl13_219
    | ~ spl13_147
    | ~ spl13_218 ),
    inference(avatar_split_clause,[],[f2562,f2558,f1395,f2564]) ).

fof(f2564,plain,
    ( spl13_219
  <=> sK6 = relation_rng(relation_composition(sK6,function_inverse(sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_219])]) ).

fof(f2558,plain,
    ( spl13_218
  <=> relation_dom(sK6) = relation_rng(relation_composition(sK6,function_inverse(sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_218])]) ).

fof(f2562,plain,
    ( sK6 = relation_rng(relation_composition(sK6,function_inverse(sK6)))
    | ~ spl13_147
    | ~ spl13_218 ),
    inference(forward_demodulation,[],[f2560,f1397]) ).

fof(f2560,plain,
    ( relation_dom(sK6) = relation_rng(relation_composition(sK6,function_inverse(sK6)))
    | ~ spl13_218 ),
    inference(avatar_component_clause,[],[f2558]) ).

fof(f2561,plain,
    ( ~ spl13_55
    | ~ spl13_42
    | spl13_218
    | ~ spl13_66
    | ~ spl13_100 ),
    inference(avatar_split_clause,[],[f890,f886,f580,f2558,f415,f482]) ).

fof(f580,plain,
    ( spl13_66
  <=> ! [X0] :
        ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).

fof(f890,plain,
    ( relation_dom(sK6) = relation_rng(relation_composition(sK6,function_inverse(sK6)))
    | ~ function(sK6)
    | ~ relation(sK6)
    | ~ spl13_66
    | ~ spl13_100 ),
    inference(resolution,[],[f888,f581]) ).

fof(f581,plain,
    ( ! [X0] :
        ( ~ one_to_one(X0)
        | relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_66 ),
    inference(avatar_component_clause,[],[f580]) ).

fof(f2505,plain,
    ( spl13_217
    | ~ spl13_35
    | ~ spl13_130 ),
    inference(avatar_split_clause,[],[f1233,f1229,f371,f2503]) ).

fof(f2503,plain,
    ( spl13_217
  <=> ! [X0] :
        ( ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_217])]) ).

fof(f1229,plain,
    ( spl13_130
  <=> ! [X0] :
        ( identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0)
        | ~ empty(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_130])]) ).

fof(f1233,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_130 ),
    inference(resolution,[],[f1230,f372]) ).

fof(f1230,plain,
    ( ! [X0] :
        ( ~ empty(relation_dom(X0))
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 )
    | ~ spl13_130 ),
    inference(avatar_component_clause,[],[f1229]) ).

fof(f2292,plain,
    ( spl13_216
    | ~ spl13_47
    | ~ spl13_131 ),
    inference(avatar_split_clause,[],[f1243,f1239,f436,f2290]) ).

fof(f2290,plain,
    ( spl13_216
  <=> ! [X0] :
        ( ~ empty(function_inverse(X0))
        | one_to_one(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_216])]) ).

fof(f1239,plain,
    ( spl13_131
  <=> ! [X0] :
        ( ~ function(function_inverse(X0))
        | ~ empty(function_inverse(X0))
        | one_to_one(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_131])]) ).

fof(f1243,plain,
    ( ! [X0] :
        ( ~ empty(function_inverse(X0))
        | one_to_one(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_47
    | ~ spl13_131 ),
    inference(duplicate_literal_removal,[],[f1242]) ).

fof(f1242,plain,
    ( ! [X0] :
        ( ~ empty(function_inverse(X0))
        | one_to_one(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_47
    | ~ spl13_131 ),
    inference(resolution,[],[f1240,f437]) ).

fof(f1240,plain,
    ( ! [X0] :
        ( ~ function(function_inverse(X0))
        | ~ empty(function_inverse(X0))
        | one_to_one(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_131 ),
    inference(avatar_component_clause,[],[f1239]) ).

fof(f2288,plain,
    ( spl13_215
    | ~ spl13_22
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1148,f1110,f308,f2286]) ).

fof(f2286,plain,
    ( spl13_215
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(identity_relation(X1),X0) = X2
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_215])]) ).

fof(f308,plain,
    ( spl13_22
  <=> ! [X0] : relation(identity_relation(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).

fof(f1148,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(identity_relation(X1),X0) = X2
        | ~ empty(X2) )
    | ~ spl13_22
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f309]) ).

fof(f309,plain,
    ( ! [X0] : relation(identity_relation(X0))
    | ~ spl13_22 ),
    inference(avatar_component_clause,[],[f308]) ).

fof(f2284,plain,
    ( spl13_214
    | ~ spl13_22
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1129,f1106,f308,f2282]) ).

fof(f2282,plain,
    ( spl13_214
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,identity_relation(X1)) = X2
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_214])]) ).

fof(f1129,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,identity_relation(X1)) = X2
        | ~ empty(X2) )
    | ~ spl13_22
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f309]) ).

fof(f2261,plain,
    ( spl13_213
    | ~ spl13_40
    | ~ spl13_119 ),
    inference(avatar_split_clause,[],[f1096,f1088,f407,f2259]) ).

fof(f2259,plain,
    ( spl13_213
  <=> ! [X0] :
        ( empty(powerset(X0))
        | empty(X0)
        | ~ in(powerset(X0),sK1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_213])]) ).

fof(f1088,plain,
    ( spl13_119
  <=> ! [X0] :
        ( empty(powerset(X0))
        | in(sK1(X0),powerset(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_119])]) ).

fof(f1096,plain,
    ( ! [X0] :
        ( empty(powerset(X0))
        | empty(X0)
        | ~ in(powerset(X0),sK1(X0)) )
    | ~ spl13_40
    | ~ spl13_119 ),
    inference(resolution,[],[f1089,f408]) ).

fof(f1089,plain,
    ( ! [X0] :
        ( in(sK1(X0),powerset(X0))
        | empty(powerset(X0))
        | empty(X0) )
    | ~ spl13_119 ),
    inference(avatar_component_clause,[],[f1088]) ).

fof(f2257,plain,
    ( spl13_212
    | ~ spl13_40
    | ~ spl13_118 ),
    inference(avatar_split_clause,[],[f1093,f1084,f407,f2255]) ).

fof(f2255,plain,
    ( spl13_212
  <=> ! [X0,X1] :
        ( empty(powerset(X0))
        | ~ subset(X1,X0)
        | ~ in(powerset(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_212])]) ).

fof(f1084,plain,
    ( spl13_118
  <=> ! [X0,X1] :
        ( empty(powerset(X0))
        | in(X1,powerset(X0))
        | ~ subset(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_118])]) ).

fof(f1093,plain,
    ( ! [X0,X1] :
        ( empty(powerset(X0))
        | ~ subset(X1,X0)
        | ~ in(powerset(X0),X1) )
    | ~ spl13_40
    | ~ spl13_118 ),
    inference(resolution,[],[f1085,f408]) ).

fof(f1085,plain,
    ( ! [X0,X1] :
        ( in(X1,powerset(X0))
        | empty(powerset(X0))
        | ~ subset(X1,X0) )
    | ~ spl13_118 ),
    inference(avatar_component_clause,[],[f1084]) ).

fof(f2253,plain,
    ( spl13_211
    | ~ spl13_101
    | ~ spl13_116 ),
    inference(avatar_split_clause,[],[f1082,f1035,f895,f2251]) ).

fof(f2251,plain,
    ( spl13_211
  <=> ! [X0] :
        ( element(sK2(sK1(X0)),X0)
        | empty(X0)
        | empty(sK1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_211])]) ).

fof(f1035,plain,
    ( spl13_116
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK1(X1))
        | empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_116])]) ).

fof(f1082,plain,
    ( ! [X0] :
        ( element(sK2(sK1(X0)),X0)
        | empty(X0)
        | empty(sK1(X0)) )
    | ~ spl13_101
    | ~ spl13_116 ),
    inference(resolution,[],[f1036,f896]) ).

fof(f1036,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK1(X1))
        | element(X0,X1)
        | empty(X1) )
    | ~ spl13_116 ),
    inference(avatar_component_clause,[],[f1035]) ).

fof(f2249,plain,
    ( spl13_210
    | ~ spl13_34
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1065,f1027,f367,f2247]) ).

fof(f2247,plain,
    ( spl13_210
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(relation_rng(X0),X1)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_210])]) ).

fof(f1065,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(relation_rng(X0),X1)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_34
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f368]) ).

fof(f2245,plain,
    ( spl13_209
    | ~ spl13_36
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1064,f1027,f375,f2243]) ).

fof(f2243,plain,
    ( spl13_209
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(relation_dom(X0),X1)
        | ~ empty(X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_209])]) ).

fof(f1064,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(relation_dom(X0),X1)
        | ~ empty(X1)
        | ~ empty(X0) )
    | ~ spl13_36
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f376]) ).

fof(f2241,plain,
    ( spl13_208
    | ~ spl13_34
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1046,f1023,f367,f2239]) ).

fof(f2239,plain,
    ( spl13_208
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(X0,relation_rng(X1))
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_208])]) ).

fof(f1046,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(X0,relation_rng(X1))
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_34
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f368]) ).

fof(f2237,plain,
    ( spl13_207
    | ~ spl13_36
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1045,f1023,f375,f2235]) ).

fof(f2235,plain,
    ( spl13_207
  <=> ! [X0,X1] :
        ( sK6 = relation_composition(X0,relation_dom(X1))
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_207])]) ).

fof(f1045,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(X0,relation_dom(X1))
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_36
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f376]) ).

fof(f2233,plain,
    ( spl13_206
    | ~ spl13_101
    | ~ spl13_110 ),
    inference(avatar_split_clause,[],[f1016,f972,f895,f2231]) ).

fof(f2231,plain,
    ( spl13_206
  <=> ! [X0] :
        ( element(sK2(sK2(powerset(X0))),X0)
        | empty(sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_206])]) ).

fof(f972,plain,
    ( spl13_110
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK2(powerset(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_110])]) ).

fof(f1016,plain,
    ( ! [X0] :
        ( element(sK2(sK2(powerset(X0))),X0)
        | empty(sK2(powerset(X0))) )
    | ~ spl13_101
    | ~ spl13_110 ),
    inference(resolution,[],[f973,f896]) ).

fof(f973,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK2(powerset(X1)))
        | element(X0,X1) )
    | ~ spl13_110 ),
    inference(avatar_component_clause,[],[f972]) ).

fof(f2229,plain,
    ( spl13_205
    | ~ spl13_53
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f914,f859,f474,f2227]) ).

fof(f914,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_dom(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_53
    | ~ spl13_94 ),
    inference(resolution,[],[f860,f475]) ).

fof(f2225,plain,
    ( spl13_204
    | ~ spl13_56
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f913,f859,f487,f2223]) ).

fof(f913,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_dom(relation_composition(X0,X1))
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_56
    | ~ spl13_94 ),
    inference(resolution,[],[f860,f488]) ).

fof(f2221,plain,
    ( spl13_203
    | ~ spl13_33
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f1325,f1118,f363,f2219]) ).

fof(f2219,plain,
    ( spl13_203
  <=> ! [X0] :
        ( sK6 = relation_composition(sK0,relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_203])]) ).

fof(f1325,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK0,relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_124 ),
    inference(resolution,[],[f1119,f364]) ).

fof(f2217,plain,
    ( spl13_202
    | ~ spl13_53
    | ~ spl13_93 ),
    inference(avatar_split_clause,[],[f901,f855,f474,f2215]) ).

fof(f855,plain,
    ( spl13_93
  <=> ! [X0] :
        ( relation_rng(X0) = sK6
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_93])]) ).

fof(f901,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_rng(relation_composition(X0,X1))
        | ~ relation(X1)
        | ~ empty(X0) )
    | ~ spl13_53
    | ~ spl13_93 ),
    inference(resolution,[],[f856,f475]) ).

fof(f856,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_rng(X0) = sK6 )
    | ~ spl13_93 ),
    inference(avatar_component_clause,[],[f855]) ).

fof(f2213,plain,
    ( spl13_201
    | ~ spl13_56
    | ~ spl13_93 ),
    inference(avatar_split_clause,[],[f900,f855,f487,f2211]) ).

fof(f900,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_rng(relation_composition(X0,X1))
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_56
    | ~ spl13_93 ),
    inference(resolution,[],[f856,f488]) ).

fof(f2106,plain,
    ( spl13_200
    | ~ spl13_35
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f1324,f1118,f371,f2104]) ).

fof(f1324,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK0,relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_124 ),
    inference(resolution,[],[f1119,f372]) ).

fof(f1964,plain,
    ( spl13_199
    | ~ spl13_23
    | ~ spl13_129 ),
    inference(avatar_split_clause,[],[f1232,f1225,f312,f1962]) ).

fof(f312,plain,
    ( spl13_23
  <=> ! [X0] : function(identity_relation(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).

fof(f1225,plain,
    ( spl13_129
  <=> ! [X0,X1] :
        ( ~ in(X0,X1)
        | ~ function(identity_relation(X1))
        | apply(identity_relation(X1),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_129])]) ).

fof(f1232,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | apply(identity_relation(X1),X0) = X0 )
    | ~ spl13_23
    | ~ spl13_129 ),
    inference(resolution,[],[f1226,f313]) ).

fof(f313,plain,
    ( ! [X0] : function(identity_relation(X0))
    | ~ spl13_23 ),
    inference(avatar_component_clause,[],[f312]) ).

fof(f1226,plain,
    ( ! [X0,X1] :
        ( ~ function(identity_relation(X1))
        | ~ in(X0,X1)
        | apply(identity_relation(X1),X0) = X0 )
    | ~ spl13_129 ),
    inference(avatar_component_clause,[],[f1225]) ).

fof(f1960,plain,
    ( spl13_198
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1160,f1110,f683,f224,f1958]) ).

fof(f1958,plain,
    ( spl13_198
  <=> ! [X0,X1] :
        ( relation_composition(sK6,X0) = X1
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_198])]) ).

fof(f224,plain,
    ( spl13_5
  <=> relation(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

fof(f1160,plain,
    ( ! [X0,X1] :
        ( relation_composition(sK6,X0) = X1
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_123 ),
    inference(forward_demodulation,[],[f1149,f685]) ).

fof(f1149,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(empty_set,X0) = X1
        | ~ empty(X1) )
    | ~ spl13_5
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f226]) ).

fof(f226,plain,
    ( relation(empty_set)
    | ~ spl13_5 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f1956,plain,
    ( spl13_197
    | ~ spl13_15
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1158,f1110,f274,f1954]) ).

fof(f1954,plain,
    ( spl13_197
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK11,X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_197])]) ).

fof(f1158,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK11,X0) = X1
        | ~ empty(X1) )
    | ~ spl13_15
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f276]) ).

fof(f276,plain,
    ( relation(sK11)
    | ~ spl13_15 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f1952,plain,
    ( spl13_196
    | ~ spl13_33
    | ~ spl13_117 ),
    inference(avatar_split_clause,[],[f1209,f1079,f363,f1950]) ).

fof(f1209,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_rng(X0),sK0)
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_117 ),
    inference(resolution,[],[f1080,f364]) ).

fof(f1948,plain,
    ( spl13_195
    | ~ spl13_13
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1157,f1110,f264,f1946]) ).

fof(f1946,plain,
    ( spl13_195
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK10,X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_195])]) ).

fof(f264,plain,
    ( spl13_13
  <=> relation(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).

fof(f1157,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK10,X0) = X1
        | ~ empty(X1) )
    | ~ spl13_13
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f266]) ).

fof(f266,plain,
    ( relation(sK10)
    | ~ spl13_13 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f1944,plain,
    ( spl13_194
    | ~ spl13_12
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1156,f1110,f259,f1942]) ).

fof(f1942,plain,
    ( spl13_194
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK9,X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_194])]) ).

fof(f259,plain,
    ( spl13_12
  <=> relation(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).

fof(f1156,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK9,X0) = X1
        | ~ empty(X1) )
    | ~ spl13_12
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f261]) ).

fof(f261,plain,
    ( relation(sK9)
    | ~ spl13_12 ),
    inference(avatar_component_clause,[],[f259]) ).

fof(f1940,plain,
    ( spl13_193
    | ~ spl13_9
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1154,f1110,f244,f1938]) ).

fof(f1938,plain,
    ( spl13_193
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK7,X0) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_193])]) ).

fof(f244,plain,
    ( spl13_9
  <=> relation(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

fof(f1154,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK7,X0) = X1
        | ~ empty(X1) )
    | ~ spl13_9
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f246]) ).

fof(f246,plain,
    ( relation(sK7)
    | ~ spl13_9 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f1936,plain,
    ( spl13_192
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1141,f1106,f683,f224,f1934]) ).

fof(f1934,plain,
    ( spl13_192
  <=> ! [X0,X1] :
        ( relation_composition(X0,sK6) = X1
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_192])]) ).

fof(f1141,plain,
    ( ! [X0,X1] :
        ( relation_composition(X0,sK6) = X1
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_122 ),
    inference(forward_demodulation,[],[f1130,f685]) ).

fof(f1130,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,empty_set) = X1
        | ~ empty(X1) )
    | ~ spl13_5
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f226]) ).

fof(f1932,plain,
    ( spl13_191
    | ~ spl13_15
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1139,f1106,f274,f1930]) ).

fof(f1930,plain,
    ( spl13_191
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK11) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_191])]) ).

fof(f1139,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK11) = X1
        | ~ empty(X1) )
    | ~ spl13_15
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f276]) ).

fof(f1928,plain,
    ( spl13_190
    | ~ spl13_13
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1138,f1106,f264,f1926]) ).

fof(f1926,plain,
    ( spl13_190
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK10) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_190])]) ).

fof(f1138,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK10) = X1
        | ~ empty(X1) )
    | ~ spl13_13
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f266]) ).

fof(f1924,plain,
    ( spl13_189
    | ~ spl13_12
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1137,f1106,f259,f1922]) ).

fof(f1922,plain,
    ( spl13_189
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK9) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_189])]) ).

fof(f1137,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK9) = X1
        | ~ empty(X1) )
    | ~ spl13_12
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f261]) ).

fof(f1920,plain,
    ( spl13_188
    | ~ spl13_9
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1135,f1106,f244,f1918]) ).

fof(f1918,plain,
    ( spl13_188
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK7) = X1
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_188])]) ).

fof(f1135,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK7) = X1
        | ~ empty(X1) )
    | ~ spl13_9
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f246]) ).

fof(f1916,plain,
    ( spl13_187
    | ~ spl13_33
    | ~ spl13_105 ),
    inference(avatar_split_clause,[],[f1001,f951,f363,f1914]) ).

fof(f1914,plain,
    ( spl13_187
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_rng(X1)) = X0
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_187])]) ).

fof(f1001,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_rng(X1)) = X0
        | ~ empty(X1) )
    | ~ spl13_33
    | ~ spl13_105 ),
    inference(resolution,[],[f952,f364]) ).

fof(f1912,plain,
    ( spl13_186
    | ~ spl13_35
    | ~ spl13_105 ),
    inference(avatar_split_clause,[],[f1000,f951,f371,f1910]) ).

fof(f1910,plain,
    ( spl13_186
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_dom(X1)) = X0
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_186])]) ).

fof(f1000,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_rng(relation_dom(X1)) = X0
        | ~ empty(X1) )
    | ~ spl13_35
    | ~ spl13_105 ),
    inference(resolution,[],[f952,f372]) ).

fof(f1908,plain,
    ( spl13_185
    | ~ spl13_35
    | ~ spl13_117 ),
    inference(avatar_split_clause,[],[f1208,f1079,f371,f1906]) ).

fof(f1208,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(relation_dom(X0),sK0)
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_117 ),
    inference(resolution,[],[f1080,f372]) ).

fof(f1904,plain,
    ( spl13_184
    | ~ spl13_33
    | ~ spl13_104 ),
    inference(avatar_split_clause,[],[f983,f947,f363,f1902]) ).

fof(f1902,plain,
    ( spl13_184
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_rng(X1)) = X0
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_184])]) ).

fof(f983,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_rng(X1)) = X0
        | ~ empty(X1) )
    | ~ spl13_33
    | ~ spl13_104 ),
    inference(resolution,[],[f948,f364]) ).

fof(f1900,plain,
    ( spl13_183
    | ~ spl13_35
    | ~ spl13_104 ),
    inference(avatar_split_clause,[],[f982,f947,f371,f1898]) ).

fof(f1898,plain,
    ( spl13_183
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_dom(X1)) = X0
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_183])]) ).

fof(f982,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_dom(relation_dom(X1)) = X0
        | ~ empty(X1) )
    | ~ spl13_35
    | ~ spl13_104 ),
    inference(resolution,[],[f948,f372]) ).

fof(f1848,plain,
    ( ~ spl13_181
    | spl13_182
    | ~ spl13_35
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f1192,f1188,f371,f1845,f1841]) ).

fof(f1841,plain,
    ( spl13_181
  <=> empty(relation_composition(sK11,function_inverse(sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_181])]) ).

fof(f1845,plain,
    ( spl13_182
  <=> empty(relation_dom(sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_182])]) ).

fof(f1192,plain,
    ( empty(relation_dom(sK11))
    | ~ empty(relation_composition(sK11,function_inverse(sK11)))
    | ~ spl13_35
    | ~ spl13_127 ),
    inference(superposition,[],[f372,f1190]) ).

fof(f1834,plain,
    ( ~ spl13_1
    | ~ spl13_157
    | ~ spl13_58
    | spl13_158 ),
    inference(avatar_split_clause,[],[f1518,f1504,f495,f1499,f204]) ).

fof(f1518,plain,
    ( ~ relation(function_inverse(sK0))
    | ~ relation(sK0)
    | ~ spl13_58
    | spl13_158 ),
    inference(resolution,[],[f1506,f496]) ).

fof(f1506,plain,
    ( ~ relation(relation_composition(sK0,function_inverse(sK0)))
    | spl13_158 ),
    inference(avatar_component_clause,[],[f1504]) ).

fof(f1830,plain,
    ( ~ spl13_179
    | spl13_180
    | ~ spl13_35
    | ~ spl13_125 ),
    inference(avatar_split_clause,[],[f1168,f1164,f371,f1827,f1823]) ).

fof(f1168,plain,
    ( empty(relation_rng(sK11))
    | ~ empty(relation_composition(function_inverse(sK11),sK11))
    | ~ spl13_35
    | ~ spl13_125 ),
    inference(superposition,[],[f372,f1166]) ).

fof(f1821,plain,
    ( spl13_178
    | ~ spl13_87
    | ~ spl13_121 ),
    inference(avatar_split_clause,[],[f1124,f1102,f726,f1819]) ).

fof(f726,plain,
    ( spl13_87
  <=> ! [X0] :
        ( ~ empty(X0)
        | function(relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_87])]) ).

fof(f1102,plain,
    ( spl13_121
  <=> ! [X0] :
        ( ~ function(relation_rng(X0))
        | ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_121])]) ).

fof(f1124,plain,
    ( ! [X0] :
        ( ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_87
    | ~ spl13_121 ),
    inference(duplicate_literal_removal,[],[f1121]) ).

fof(f1121,plain,
    ( ! [X0] :
        ( ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0)
        | ~ empty(X0) )
    | ~ spl13_87
    | ~ spl13_121 ),
    inference(resolution,[],[f1103,f727]) ).

fof(f727,plain,
    ( ! [X0] :
        ( function(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_87 ),
    inference(avatar_component_clause,[],[f726]) ).

fof(f1103,plain,
    ( ! [X0] :
        ( ~ function(relation_rng(X0))
        | ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_121 ),
    inference(avatar_component_clause,[],[f1102]) ).

fof(f1817,plain,
    ( spl13_177
    | ~ spl13_88
    | ~ spl13_120 ),
    inference(avatar_split_clause,[],[f1116,f1098,f730,f1815]) ).

fof(f1098,plain,
    ( spl13_120
  <=> ! [X0] :
        ( ~ function(relation_dom(X0))
        | ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_120])]) ).

fof(f1116,plain,
    ( ! [X0] :
        ( ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_88
    | ~ spl13_120 ),
    inference(duplicate_literal_removal,[],[f1113]) ).

fof(f1113,plain,
    ( ! [X0] :
        ( ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0)
        | ~ empty(X0) )
    | ~ spl13_88
    | ~ spl13_120 ),
    inference(resolution,[],[f1099,f731]) ).

fof(f1099,plain,
    ( ! [X0] :
        ( ~ function(relation_dom(X0))
        | ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_120 ),
    inference(avatar_component_clause,[],[f1098]) ).

fof(f1813,plain,
    ( spl13_176
    | ~ spl13_22
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1062,f1027,f308,f1811]) ).

fof(f1062,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(identity_relation(X0),X1)
        | ~ empty(X1) )
    | ~ spl13_22
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f309]) ).

fof(f1809,plain,
    ( spl13_175
    | ~ spl13_22
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1043,f1023,f308,f1807]) ).

fof(f1043,plain,
    ( ! [X0,X1] :
        ( sK6 = relation_composition(X0,identity_relation(X1))
        | ~ empty(X0) )
    | ~ spl13_22
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f309]) ).

fof(f1617,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | ~ spl13_46
    | spl13_157 ),
    inference(avatar_split_clause,[],[f1546,f1499,f432,f209,f204]) ).

fof(f1546,plain,
    ( ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_46
    | spl13_157 ),
    inference(resolution,[],[f1501,f433]) ).

fof(f1501,plain,
    ( ~ relation(function_inverse(sK0))
    | spl13_157 ),
    inference(avatar_component_clause,[],[f1499]) ).

fof(f1578,plain,
    ( spl13_174
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1074,f1027,f683,f224,f1576]) ).

fof(f1576,plain,
    ( spl13_174
  <=> ! [X0] :
        ( sK6 = relation_composition(sK6,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_174])]) ).

fof(f1074,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK6,X0)
        | ~ empty(X0) )
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_114 ),
    inference(forward_demodulation,[],[f1063,f685]) ).

fof(f1063,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(empty_set,X0)
        | ~ empty(X0) )
    | ~ spl13_5
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f226]) ).

fof(f1574,plain,
    ( spl13_173
    | ~ spl13_15
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1072,f1027,f274,f1572]) ).

fof(f1072,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK11,X0)
        | ~ empty(X0) )
    | ~ spl13_15
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f276]) ).

fof(f1570,plain,
    ( spl13_172
    | ~ spl13_13
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1071,f1027,f264,f1568]) ).

fof(f1071,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK10,X0)
        | ~ empty(X0) )
    | ~ spl13_13
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f266]) ).

fof(f1566,plain,
    ( spl13_171
    | ~ spl13_12
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1070,f1027,f259,f1564]) ).

fof(f1070,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK9,X0)
        | ~ empty(X0) )
    | ~ spl13_12
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f261]) ).

fof(f1562,plain,
    ( spl13_170
    | ~ spl13_9
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1068,f1027,f244,f1560]) ).

fof(f1068,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK7,X0)
        | ~ empty(X0) )
    | ~ spl13_9
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f246]) ).

fof(f1558,plain,
    ( spl13_169
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1055,f1023,f683,f224,f1556]) ).

fof(f1055,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,sK6)
        | ~ empty(X0) )
    | ~ spl13_5
    | ~ spl13_80
    | ~ spl13_113 ),
    inference(forward_demodulation,[],[f1044,f685]) ).

fof(f1044,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,empty_set)
        | ~ empty(X0) )
    | ~ spl13_5
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f226]) ).

fof(f1554,plain,
    ( spl13_168
    | ~ spl13_15
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1053,f1023,f274,f1552]) ).

fof(f1053,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,sK11)
        | ~ empty(X0) )
    | ~ spl13_15
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f276]) ).

fof(f1550,plain,
    ( spl13_167
    | ~ spl13_13
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1052,f1023,f264,f1548]) ).

fof(f1052,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,sK10)
        | ~ empty(X0) )
    | ~ spl13_13
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f266]) ).

fof(f1545,plain,
    ( spl13_166
    | ~ spl13_12
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1051,f1023,f259,f1543]) ).

fof(f1051,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,sK9)
        | ~ empty(X0) )
    | ~ spl13_12
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f261]) ).

fof(f1541,plain,
    ( spl13_165
    | ~ spl13_9
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1049,f1023,f244,f1539]) ).

fof(f1049,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,sK7)
        | ~ empty(X0) )
    | ~ spl13_9
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f246]) ).

fof(f1537,plain,
    ( spl13_164
    | ~ spl13_33
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f917,f859,f363,f1535]) ).

fof(f1535,plain,
    ( spl13_164
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_164])]) ).

fof(f917,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_94 ),
    inference(resolution,[],[f860,f364]) ).

fof(f1533,plain,
    ( spl13_163
    | ~ spl13_35
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f916,f859,f371,f1531]) ).

fof(f1531,plain,
    ( spl13_163
  <=> ! [X0] :
        ( sK6 = relation_dom(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_163])]) ).

fof(f916,plain,
    ( ! [X0] :
        ( sK6 = relation_dom(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_94 ),
    inference(resolution,[],[f860,f372]) ).

fof(f1529,plain,
    ( spl13_162
    | ~ spl13_33
    | ~ spl13_93 ),
    inference(avatar_split_clause,[],[f904,f855,f363,f1527]) ).

fof(f1527,plain,
    ( spl13_162
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_162])]) ).

fof(f904,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_33
    | ~ spl13_93 ),
    inference(resolution,[],[f856,f364]) ).

fof(f1525,plain,
    ( spl13_161
    | ~ spl13_35
    | ~ spl13_93 ),
    inference(avatar_split_clause,[],[f903,f855,f371,f1523]) ).

fof(f1523,plain,
    ( spl13_161
  <=> ! [X0] :
        ( sK6 = relation_rng(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_161])]) ).

fof(f903,plain,
    ( ! [X0] :
        ( sK6 = relation_rng(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_35
    | ~ spl13_93 ),
    inference(resolution,[],[f856,f372]) ).

fof(f1515,plain,
    ( ~ spl13_158
    | ~ spl13_159
    | spl13_26
    | spl13_160
    | ~ spl13_68
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f658,f651,f597,f1512,f324,f1508,f1504]) ).

fof(f658,plain,
    ( in(sK4(relation_dom(sK0),relation_composition(sK0,function_inverse(sK0))),relation_dom(sK0))
    | relation_composition(sK0,function_inverse(sK0)) = identity_relation(relation_dom(sK0))
    | ~ function(relation_composition(sK0,function_inverse(sK0)))
    | ~ relation(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_68
    | ~ spl13_76 ),
    inference(superposition,[],[f598,f653]) ).

fof(f1502,plain,
    ( ~ spl13_157
    | ~ spl13_1
    | ~ spl13_58
    | spl13_154 ),
    inference(avatar_split_clause,[],[f1494,f1480,f495,f204,f1499]) ).

fof(f1494,plain,
    ( ~ relation(sK0)
    | ~ relation(function_inverse(sK0))
    | ~ spl13_58
    | spl13_154 ),
    inference(resolution,[],[f1482,f496]) ).

fof(f1482,plain,
    ( ~ relation(relation_composition(function_inverse(sK0),sK0))
    | spl13_154 ),
    inference(avatar_component_clause,[],[f1480]) ).

fof(f1491,plain,
    ( ~ spl13_154
    | ~ spl13_155
    | spl13_27
    | spl13_156
    | ~ spl13_68
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f636,f629,f597,f1488,f328,f1484,f1480]) ).

fof(f636,plain,
    ( in(sK4(relation_rng(sK0),relation_composition(function_inverse(sK0),sK0)),relation_rng(sK0))
    | relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
    | ~ function(relation_composition(function_inverse(sK0),sK0))
    | ~ relation(relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_68
    | ~ spl13_74 ),
    inference(superposition,[],[f598,f631]) ).

fof(f1465,plain,
    ( spl13_153
    | ~ spl13_23
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1038,f1019,f312,f1463]) ).

fof(f1463,plain,
    ( spl13_153
  <=> ! [X0] :
        ( ~ empty(identity_relation(X0))
        | one_to_one(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_153])]) ).

fof(f1019,plain,
    ( spl13_112
  <=> ! [X0] :
        ( ~ function(identity_relation(X0))
        | ~ empty(identity_relation(X0))
        | one_to_one(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_112])]) ).

fof(f1038,plain,
    ( ! [X0] :
        ( ~ empty(identity_relation(X0))
        | one_to_one(identity_relation(X0)) )
    | ~ spl13_23
    | ~ spl13_112 ),
    inference(resolution,[],[f1020,f313]) ).

fof(f1020,plain,
    ( ! [X0] :
        ( ~ function(identity_relation(X0))
        | ~ empty(identity_relation(X0))
        | one_to_one(identity_relation(X0)) )
    | ~ spl13_112 ),
    inference(avatar_component_clause,[],[f1019]) ).

fof(f1461,plain,
    ( spl13_152
    | ~ spl13_101
    | ~ spl13_103 ),
    inference(avatar_split_clause,[],[f945,f939,f895,f1459]) ).

fof(f939,plain,
    ( spl13_103
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_103])]) ).

fof(f945,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty(sK2(powerset(X0))) )
    | ~ spl13_101
    | ~ spl13_103 ),
    inference(resolution,[],[f940,f896]) ).

fof(f940,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,sK2(powerset(X0)))
        | ~ empty(X0) )
    | ~ spl13_103 ),
    inference(avatar_component_clause,[],[f939]) ).

fof(f1457,plain,
    ( spl13_151
    | ~ spl13_40
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f928,f895,f407,f1455]) ).

fof(f1455,plain,
    ( spl13_151
  <=> ! [X0] :
        ( empty(X0)
        | ~ in(X0,sK2(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_151])]) ).

fof(f928,plain,
    ( ! [X0] :
        ( empty(X0)
        | ~ in(X0,sK2(X0)) )
    | ~ spl13_40
    | ~ spl13_101 ),
    inference(resolution,[],[f896,f408]) ).

fof(f1442,plain,
    ( spl13_149
    | ~ spl13_1
    | ~ spl13_2
    | spl13_150
    | ~ spl13_3
    | ~ spl13_138 ),
    inference(avatar_split_clause,[],[f1302,f1295,f214,f1439,f209,f204,f1435]) ).

fof(f1439,plain,
    ( spl13_150
  <=> sK4(relation_dom(sK0),sK0) = apply(function_inverse(sK0),apply(sK0,sK4(relation_dom(sK0),sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_150])]) ).

fof(f1302,plain,
    ( sK4(relation_dom(sK0),sK0) = apply(function_inverse(sK0),apply(sK0,sK4(relation_dom(sK0),sK0)))
    | ~ function(sK0)
    | ~ relation(sK0)
    | sK0 = identity_relation(relation_dom(sK0))
    | ~ spl13_3
    | ~ spl13_138 ),
    inference(resolution,[],[f1296,f216]) ).

fof(f1422,plain,
    ( spl13_148
    | ~ spl13_23
    | ~ spl13_111 ),
    inference(avatar_split_clause,[],[f1017,f976,f312,f1420]) ).

fof(f976,plain,
    ( spl13_111
  <=> ! [X0] :
        ( ~ function(identity_relation(X0))
        | relation_dom(identity_relation(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_111])]) ).

fof(f1017,plain,
    ( ! [X0] : relation_dom(identity_relation(X0)) = X0
    | ~ spl13_23
    | ~ spl13_111 ),
    inference(resolution,[],[f977,f313]) ).

fof(f977,plain,
    ( ! [X0] :
        ( ~ function(identity_relation(X0))
        | relation_dom(identity_relation(X0)) = X0 )
    | ~ spl13_111 ),
    inference(avatar_component_clause,[],[f976]) ).

fof(f1398,plain,
    ( spl13_147
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f922,f859,f683,f219,f1395]) ).

fof(f1393,plain,
    ( spl13_146
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_93 ),
    inference(avatar_split_clause,[],[f909,f855,f683,f219,f1390]) ).

fof(f909,plain,
    ( sK6 = relation_rng(sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_93 ),
    inference(forward_demodulation,[],[f902,f685]) ).

fof(f902,plain,
    ( sK6 = relation_rng(empty_set)
    | ~ spl13_4
    | ~ spl13_93 ),
    inference(resolution,[],[f856,f221]) ).

fof(f1388,plain,
    ( spl13_145
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f1330,f1118,f683,f219,f1385]) ).

fof(f1385,plain,
    ( spl13_145
  <=> sK6 = relation_composition(sK0,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_145])]) ).

fof(f1330,plain,
    ( sK6 = relation_composition(sK0,sK6)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_124 ),
    inference(forward_demodulation,[],[f1323,f685]) ).

fof(f1323,plain,
    ( sK6 = relation_composition(sK0,empty_set)
    | ~ spl13_4
    | ~ spl13_124 ),
    inference(resolution,[],[f1119,f221]) ).

fof(f1383,plain,
    ( spl13_144
    | ~ spl13_37
    | ~ spl13_86 ),
    inference(avatar_split_clause,[],[f723,f720,f379,f1381]) ).

fof(f1381,plain,
    ( spl13_144
  <=> ! [X0] : element(sK6,powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_144])]) ).

fof(f379,plain,
    ( spl13_37
  <=> ! [X0] : element(sK3(X0),powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).

fof(f720,plain,
    ( spl13_86
  <=> ! [X0] : sK3(X0) = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_86])]) ).

fof(f723,plain,
    ( ! [X0] : element(sK6,powerset(X0))
    | ~ spl13_37
    | ~ spl13_86 ),
    inference(superposition,[],[f380,f721]) ).

fof(f721,plain,
    ( ! [X0] : sK3(X0) = sK6
    | ~ spl13_86 ),
    inference(avatar_component_clause,[],[f720]) ).

fof(f380,plain,
    ( ! [X0] : element(sK3(X0),powerset(X0))
    | ~ spl13_37 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f1353,plain,
    ( spl13_143
    | ~ spl13_1
    | ~ spl13_123 ),
    inference(avatar_split_clause,[],[f1152,f1110,f204,f1351]) ).

fof(f1152,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(sK0,X0) = X1
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_123 ),
    inference(resolution,[],[f1111,f206]) ).

fof(f1349,plain,
    ( spl13_142
    | ~ spl13_1
    | ~ spl13_122 ),
    inference(avatar_split_clause,[],[f1133,f1106,f204,f1347]) ).

fof(f1133,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | relation_composition(X0,sK0) = X1
        | ~ empty(X1) )
    | ~ spl13_1
    | ~ spl13_122 ),
    inference(resolution,[],[f1107,f206]) ).

fof(f1342,plain,
    ( ~ spl13_140
    | spl13_141
    | ~ spl13_35
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f655,f651,f371,f1339,f1335]) ).

fof(f1335,plain,
    ( spl13_140
  <=> empty(relation_composition(sK0,function_inverse(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_140])]) ).

fof(f655,plain,
    ( empty(relation_dom(sK0))
    | ~ empty(relation_composition(sK0,function_inverse(sK0)))
    | ~ spl13_35
    | ~ spl13_76 ),
    inference(superposition,[],[f372,f653]) ).

fof(f1301,plain,
    ( spl13_139
    | ~ spl13_68
    | ~ spl13_72 ),
    inference(avatar_split_clause,[],[f623,f617,f597,f1299]) ).

fof(f623,plain,
    ( ! [X0] :
        ( sK4(relation_dom(X0),X0) = apply(relation_composition(X0,function_inverse(X0)),sK4(relation_dom(X0),X0))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 )
    | ~ spl13_68
    | ~ spl13_72 ),
    inference(duplicate_literal_removal,[],[f622]) ).

fof(f622,plain,
    ( ! [X0] :
        ( sK4(relation_dom(X0),X0) = apply(relation_composition(X0,function_inverse(X0)),sK4(relation_dom(X0),X0))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_68
    | ~ spl13_72 ),
    inference(resolution,[],[f618,f598]) ).

fof(f1297,plain,
    ( spl13_138
    | ~ spl13_68
    | ~ spl13_71 ),
    inference(avatar_split_clause,[],[f621,f613,f597,f1295]) ).

fof(f621,plain,
    ( ! [X0] :
        ( sK4(relation_dom(X0),X0) = apply(function_inverse(X0),apply(X0,sK4(relation_dom(X0),X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0 )
    | ~ spl13_68
    | ~ spl13_71 ),
    inference(duplicate_literal_removal,[],[f620]) ).

fof(f620,plain,
    ( ! [X0] :
        ( sK4(relation_dom(X0),X0) = apply(function_inverse(X0),apply(X0,sK4(relation_dom(X0),X0)))
        | ~ one_to_one(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_68
    | ~ spl13_71 ),
    inference(resolution,[],[f614,f598]) ).

fof(f1268,plain,
    ( spl13_137
    | ~ spl13_40
    | ~ spl13_68 ),
    inference(avatar_split_clause,[],[f601,f597,f407,f1266]) ).

fof(f1266,plain,
    ( spl13_137
  <=> ! [X0] :
        ( identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0)
        | ~ in(relation_dom(X0),sK4(relation_dom(X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_137])]) ).

fof(f601,plain,
    ( ! [X0] :
        ( identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0)
        | ~ in(relation_dom(X0),sK4(relation_dom(X0),X0)) )
    | ~ spl13_40
    | ~ spl13_68 ),
    inference(resolution,[],[f598,f408]) ).

fof(f1264,plain,
    ( spl13_136
    | ~ spl13_41
    | ~ spl13_68 ),
    inference(avatar_split_clause,[],[f600,f597,f411,f1262]) ).

fof(f1262,plain,
    ( spl13_136
  <=> ! [X0] :
        ( identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0)
        | element(sK4(relation_dom(X0),X0),relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_136])]) ).

fof(f600,plain,
    ( ! [X0] :
        ( identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0)
        | element(sK4(relation_dom(X0),X0),relation_dom(X0)) )
    | ~ spl13_41
    | ~ spl13_68 ),
    inference(resolution,[],[f598,f412]) ).

fof(f1260,plain,
    ( spl13_135
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_117 ),
    inference(avatar_split_clause,[],[f1214,f1079,f683,f219,f1257]) ).

fof(f1257,plain,
    ( spl13_135
  <=> sK6 = relation_composition(sK6,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_135])]) ).

fof(f1214,plain,
    ( sK6 = relation_composition(sK6,sK0)
    | ~ spl13_4
    | ~ spl13_80
    | ~ spl13_117 ),
    inference(forward_demodulation,[],[f1207,f685]) ).

fof(f1207,plain,
    ( sK6 = relation_composition(empty_set,sK0)
    | ~ spl13_4
    | ~ spl13_117 ),
    inference(resolution,[],[f1080,f221]) ).

fof(f1255,plain,
    ( spl13_134
    | ~ spl13_51
    | ~ spl13_58 ),
    inference(avatar_split_clause,[],[f537,f495,f466,f1253]) ).

fof(f466,plain,
    ( spl13_51
  <=> ! [X0] :
        ( one_to_one(X0)
        | ~ function(X0)
        | ~ empty(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).

fof(f537,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ relation(X1)
        | ~ function(relation_composition(X1,X0))
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) )
    | ~ spl13_51
    | ~ spl13_58 ),
    inference(resolution,[],[f496,f467]) ).

fof(f467,plain,
    ( ! [X0] :
        ( ~ relation(X0)
        | ~ function(X0)
        | ~ empty(X0)
        | one_to_one(X0) )
    | ~ spl13_51 ),
    inference(avatar_component_clause,[],[f466]) ).

fof(f1251,plain,
    ( spl13_133
    | ~ spl13_51
    | ~ spl13_57 ),
    inference(avatar_split_clause,[],[f536,f491,f466,f1249]) ).

fof(f536,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | ~ function(relation_composition(X0,X1))
        | ~ empty(relation_composition(X0,X1))
        | one_to_one(relation_composition(X0,X1)) )
    | ~ spl13_51
    | ~ spl13_57 ),
    inference(resolution,[],[f492,f467]) ).

fof(f1247,plain,
    ( spl13_132
    | ~ spl13_51
    | ~ spl13_54 ),
    inference(avatar_split_clause,[],[f530,f478,f466,f1245]) ).

fof(f530,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | ~ function(relation_composition(X1,X0))
        | ~ empty(relation_composition(X1,X0))
        | one_to_one(relation_composition(X1,X0)) )
    | ~ spl13_51
    | ~ spl13_54 ),
    inference(resolution,[],[f479,f467]) ).

fof(f1241,plain,
    ( spl13_131
    | ~ spl13_46
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f498,f466,f432,f1239]) ).

fof(f498,plain,
    ( ! [X0] :
        ( ~ function(function_inverse(X0))
        | ~ empty(function_inverse(X0))
        | one_to_one(function_inverse(X0))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl13_46
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f433]) ).

fof(f1231,plain,
    ( spl13_130
    | ~ spl13_38
    | ~ spl13_68 ),
    inference(avatar_split_clause,[],[f602,f597,f383,f1229]) ).

fof(f602,plain,
    ( ! [X0] :
        ( identity_relation(relation_dom(X0)) = X0
        | ~ function(X0)
        | ~ relation(X0)
        | ~ empty(relation_dom(X0)) )
    | ~ spl13_38
    | ~ spl13_68 ),
    inference(resolution,[],[f598,f384]) ).

fof(f1227,plain,
    ( spl13_129
    | ~ spl13_22
    | ~ spl13_67 ),
    inference(avatar_split_clause,[],[f595,f592,f308,f1225]) ).

fof(f592,plain,
    ( spl13_67
  <=> ! [X0,X3] :
        ( apply(identity_relation(X0),X3) = X3
        | ~ in(X3,X0)
        | ~ function(identity_relation(X0))
        | ~ relation(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).

fof(f595,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | ~ function(identity_relation(X1))
        | apply(identity_relation(X1),X0) = X0 )
    | ~ spl13_22
    | ~ spl13_67 ),
    inference(resolution,[],[f593,f309]) ).

fof(f593,plain,
    ( ! [X3,X0] :
        ( ~ relation(identity_relation(X0))
        | ~ in(X3,X0)
        | ~ function(identity_relation(X0))
        | apply(identity_relation(X0),X3) = X3 )
    | ~ spl13_67 ),
    inference(avatar_component_clause,[],[f592]) ).

fof(f1204,plain,
    ( ~ spl13_15
    | ~ spl13_16
    | spl13_128
    | ~ spl13_17
    | ~ spl13_66 ),
    inference(avatar_split_clause,[],[f590,f580,f284,f1201,f279,f274]) ).

fof(f1201,plain,
    ( spl13_128
  <=> relation_dom(sK11) = relation_rng(relation_composition(sK11,function_inverse(sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_128])]) ).

fof(f590,plain,
    ( relation_dom(sK11) = relation_rng(relation_composition(sK11,function_inverse(sK11)))
    | ~ function(sK11)
    | ~ relation(sK11)
    | ~ spl13_17
    | ~ spl13_66 ),
    inference(resolution,[],[f581,f286]) ).

fof(f1191,plain,
    ( ~ spl13_15
    | ~ spl13_16
    | spl13_127
    | ~ spl13_17
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f588,f576,f284,f1188,f279,f274]) ).

fof(f588,plain,
    ( relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11)))
    | ~ function(sK11)
    | ~ relation(sK11)
    | ~ spl13_17
    | ~ spl13_65 ),
    inference(resolution,[],[f577,f286]) ).

fof(f1180,plain,
    ( ~ spl13_15
    | ~ spl13_16
    | spl13_126
    | ~ spl13_17
    | ~ spl13_64 ),
    inference(avatar_split_clause,[],[f586,f572,f284,f1177,f279,f274]) ).

fof(f1177,plain,
    ( spl13_126
  <=> relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_126])]) ).

fof(f586,plain,
    ( relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11))
    | ~ function(sK11)
    | ~ relation(sK11)
    | ~ spl13_17
    | ~ spl13_64 ),
    inference(resolution,[],[f573,f286]) ).

fof(f1167,plain,
    ( ~ spl13_15
    | ~ spl13_16
    | spl13_125
    | ~ spl13_17
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f584,f568,f284,f1164,f279,f274]) ).

fof(f584,plain,
    ( relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11))
    | ~ function(sK11)
    | ~ relation(sK11)
    | ~ spl13_17
    | ~ spl13_63 ),
    inference(resolution,[],[f569,f286]) ).

fof(f1120,plain,
    ( spl13_124
    | ~ spl13_1
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f1066,f1027,f204,f1118]) ).

fof(f1066,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(sK0,X0)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_114 ),
    inference(resolution,[],[f1028,f206]) ).

fof(f1112,plain,
    ( spl13_123
    | ~ spl13_49
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f531,f487,f444,f1110]) ).

fof(f444,plain,
    ( spl13_49
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).

fof(f531,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X0,X1) = X2
        | ~ empty(X2) )
    | ~ spl13_49
    | ~ spl13_56 ),
    inference(resolution,[],[f488,f445]) ).

fof(f445,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) )
    | ~ spl13_49 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f1108,plain,
    ( spl13_122
    | ~ spl13_49
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f525,f474,f444,f1106]) ).

fof(f525,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X1,X0) = X2
        | ~ empty(X2) )
    | ~ spl13_49
    | ~ spl13_53 ),
    inference(resolution,[],[f475,f445]) ).

fof(f1104,plain,
    ( spl13_121
    | ~ spl13_34
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f502,f466,f367,f1102]) ).

fof(f502,plain,
    ( ! [X0] :
        ( ~ function(relation_rng(X0))
        | ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl13_34
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f368]) ).

fof(f1100,plain,
    ( spl13_120
    | ~ spl13_36
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f501,f466,f375,f1098]) ).

fof(f501,plain,
    ( ! [X0] :
        ( ~ function(relation_dom(X0))
        | ~ empty(relation_dom(X0))
        | one_to_one(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl13_36
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f376]) ).

fof(f1090,plain,
    ( spl13_119
    | ~ spl13_43
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f520,f470,f420,f1088]) ).

fof(f420,plain,
    ( spl13_43
  <=> ! [X0] :
        ( element(sK1(X0),powerset(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).

fof(f470,plain,
    ( spl13_52
  <=> ! [X0,X1] :
        ( in(X0,X1)
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).

fof(f520,plain,
    ( ! [X0] :
        ( empty(powerset(X0))
        | in(sK1(X0),powerset(X0))
        | empty(X0) )
    | ~ spl13_43
    | ~ spl13_52 ),
    inference(resolution,[],[f471,f421]) ).

fof(f421,plain,
    ( ! [X0] :
        ( element(sK1(X0),powerset(X0))
        | empty(X0) )
    | ~ spl13_43 ),
    inference(avatar_component_clause,[],[f420]) ).

fof(f471,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,X1)
        | empty(X1)
        | in(X0,X1) )
    | ~ spl13_52 ),
    inference(avatar_component_clause,[],[f470]) ).

fof(f1086,plain,
    ( spl13_118
    | ~ spl13_48
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f519,f470,f440,f1084]) ).

fof(f440,plain,
    ( spl13_48
  <=> ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).

fof(f519,plain,
    ( ! [X0,X1] :
        ( empty(powerset(X0))
        | in(X1,powerset(X0))
        | ~ subset(X1,X0) )
    | ~ spl13_48
    | ~ spl13_52 ),
    inference(resolution,[],[f471,f441]) ).

fof(f441,plain,
    ( ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
    | ~ spl13_48 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f1081,plain,
    ( spl13_117
    | ~ spl13_1
    | ~ spl13_113 ),
    inference(avatar_split_clause,[],[f1047,f1023,f204,f1079]) ).

fof(f1047,plain,
    ( ! [X0] :
        ( sK6 = relation_composition(X0,sK0)
        | ~ empty(X0) )
    | ~ spl13_1
    | ~ spl13_113 ),
    inference(resolution,[],[f1024,f206]) ).

fof(f1037,plain,
    ( spl13_116
    | ~ spl13_43
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f553,f549,f420,f1035]) ).

fof(f549,plain,
    ( spl13_60
  <=> ! [X2,X0,X1] :
        ( element(X0,X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).

fof(f553,plain,
    ( ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK1(X1))
        | empty(X1) )
    | ~ spl13_43
    | ~ spl13_60 ),
    inference(resolution,[],[f550,f421]) ).

fof(f550,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | element(X0,X2)
        | ~ in(X0,X1) )
    | ~ spl13_60 ),
    inference(avatar_component_clause,[],[f549]) ).

fof(f1033,plain,
    ( spl13_115
    | ~ spl13_48
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f552,f549,f440,f1031]) ).

fof(f1031,plain,
    ( spl13_115
  <=> ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_115])]) ).

fof(f552,plain,
    ( ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) )
    | ~ spl13_48
    | ~ spl13_60 ),
    inference(resolution,[],[f550,f441]) ).

fof(f1029,plain,
    ( spl13_114
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f535,f487,f359,f234,f1027]) ).

fof(f234,plain,
    ( spl13_7
  <=> empty(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f359,plain,
    ( spl13_32
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).

fof(f535,plain,
    ( ! [X0,X1] :
        ( relation_composition(X0,X1) = sK6
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_56 ),
    inference(forward_demodulation,[],[f532,f393]) ).

fof(f393,plain,
    ( empty_set = sK6
    | ~ spl13_7
    | ~ spl13_32 ),
    inference(resolution,[],[f360,f236]) ).

fof(f236,plain,
    ( empty(sK6)
    | ~ spl13_7 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f360,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = X0 )
    | ~ spl13_32 ),
    inference(avatar_component_clause,[],[f359]) ).

fof(f532,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X0,X1) = empty_set )
    | ~ spl13_32
    | ~ spl13_56 ),
    inference(resolution,[],[f488,f360]) ).

fof(f1025,plain,
    ( spl13_113
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f529,f474,f359,f234,f1023]) ).

fof(f529,plain,
    ( ! [X0,X1] :
        ( relation_composition(X1,X0) = sK6
        | ~ relation(X0)
        | ~ empty(X1) )
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_53 ),
    inference(forward_demodulation,[],[f526,f393]) ).

fof(f526,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | relation_composition(X1,X0) = empty_set )
    | ~ spl13_32
    | ~ spl13_53 ),
    inference(resolution,[],[f475,f360]) ).

fof(f1021,plain,
    ( spl13_112
    | ~ spl13_22
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f499,f466,f308,f1019]) ).

fof(f499,plain,
    ( ! [X0] :
        ( ~ function(identity_relation(X0))
        | ~ empty(identity_relation(X0))
        | one_to_one(identity_relation(X0)) )
    | ~ spl13_22
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f309]) ).

fof(f978,plain,
    ( spl13_111
    | ~ spl13_22
    | ~ spl13_61 ),
    inference(avatar_split_clause,[],[f562,f559,f308,f976]) ).

fof(f559,plain,
    ( spl13_61
  <=> ! [X0] :
        ( relation_dom(identity_relation(X0)) = X0
        | ~ function(identity_relation(X0))
        | ~ relation(identity_relation(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).

fof(f562,plain,
    ( ! [X0] :
        ( ~ function(identity_relation(X0))
        | relation_dom(identity_relation(X0)) = X0 )
    | ~ spl13_22
    | ~ spl13_61 ),
    inference(resolution,[],[f560,f309]) ).

fof(f560,plain,
    ( ! [X0] :
        ( ~ relation(identity_relation(X0))
        | ~ function(identity_relation(X0))
        | relation_dom(identity_relation(X0)) = X0 )
    | ~ spl13_61 ),
    inference(avatar_component_clause,[],[f559]) ).

fof(f974,plain,
    ( spl13_110
    | ~ spl13_30
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f554,f549,f341,f972]) ).

fof(f341,plain,
    ( spl13_30
  <=> ! [X0] : element(sK2(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).

fof(f554,plain,
    ( ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK2(powerset(X1))) )
    | ~ spl13_30
    | ~ spl13_60 ),
    inference(resolution,[],[f550,f342]) ).

fof(f342,plain,
    ( ! [X0] : element(sK2(X0),X0)
    | ~ spl13_30 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f970,plain,
    ( spl13_109
    | ~ spl13_48
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f542,f539,f440,f968]) ).

fof(f968,plain,
    ( spl13_109
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_109])]) ).

fof(f539,plain,
    ( spl13_59
  <=> ! [X2,X0,X1] :
        ( ~ empty(X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).

fof(f542,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) )
    | ~ spl13_48
    | ~ spl13_59 ),
    inference(resolution,[],[f540,f441]) ).

fof(f540,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | ~ empty(X2)
        | ~ in(X0,X1) )
    | ~ spl13_59 ),
    inference(avatar_component_clause,[],[f539]) ).

fof(f966,plain,
    ( spl13_108
    | ~ spl13_28
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f534,f487,f333,f964]) ).

fof(f534,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | function(relation_composition(X0,X1)) )
    | ~ spl13_28
    | ~ spl13_56 ),
    inference(resolution,[],[f488,f334]) ).

fof(f962,plain,
    ( ~ spl13_107
    | ~ spl13_1
    | ~ spl13_53
    | spl13_81 ),
    inference(avatar_split_clause,[],[f899,f688,f474,f204,f959]) ).

fof(f959,plain,
    ( spl13_107
  <=> empty(function_inverse(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_107])]) ).

fof(f899,plain,
    ( ~ relation(sK0)
    | ~ empty(function_inverse(sK0))
    | ~ spl13_53
    | spl13_81 ),
    inference(resolution,[],[f690,f475]) ).

fof(f957,plain,
    ( spl13_106
    | ~ spl13_28
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f528,f474,f333,f955]) ).

fof(f528,plain,
    ( ! [X0,X1] :
        ( ~ relation(X0)
        | ~ empty(X1)
        | function(relation_composition(X1,X0)) )
    | ~ spl13_28
    | ~ spl13_53 ),
    inference(resolution,[],[f475,f334]) ).

fof(f953,plain,
    ( spl13_105
    | ~ spl13_33
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f457,f444,f363,f951]) ).

fof(f457,plain,
    ( ! [X0,X1] :
        ( relation_rng(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_33
    | ~ spl13_49 ),
    inference(resolution,[],[f445,f364]) ).

fof(f949,plain,
    ( spl13_104
    | ~ spl13_35
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f456,f444,f371,f947]) ).

fof(f456,plain,
    ( ! [X0,X1] :
        ( relation_dom(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl13_35
    | ~ spl13_49 ),
    inference(resolution,[],[f445,f372]) ).

fof(f941,plain,
    ( spl13_103
    | ~ spl13_30
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f544,f539,f341,f939]) ).

fof(f544,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK2(powerset(X0))) )
    | ~ spl13_30
    | ~ spl13_59 ),
    inference(resolution,[],[f540,f342]) ).

fof(f937,plain,
    ( spl13_102
    | ~ spl13_7
    | ~ spl13_24
    | ~ spl13_32
    | ~ spl13_37
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f524,f470,f379,f359,f316,f234,f935]) ).

fof(f935,plain,
    ( spl13_102
  <=> ! [X0] :
        ( in(sK6,powerset(X0))
        | empty(powerset(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_102])]) ).

fof(f316,plain,
    ( spl13_24
  <=> ! [X0] : empty(sK3(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).

fof(f524,plain,
    ( ! [X0] :
        ( in(sK6,powerset(X0))
        | empty(powerset(X0)) )
    | ~ spl13_7
    | ~ spl13_24
    | ~ spl13_32
    | ~ spl13_37
    | ~ spl13_52 ),
    inference(forward_demodulation,[],[f523,f393]) ).

fof(f523,plain,
    ( ! [X0] :
        ( in(empty_set,powerset(X0))
        | empty(powerset(X0)) )
    | ~ spl13_24
    | ~ spl13_32
    | ~ spl13_37
    | ~ spl13_52 ),
    inference(forward_demodulation,[],[f522,f392]) ).

fof(f392,plain,
    ( ! [X0] : empty_set = sK3(X0)
    | ~ spl13_24
    | ~ spl13_32 ),
    inference(resolution,[],[f360,f317]) ).

fof(f317,plain,
    ( ! [X0] : empty(sK3(X0))
    | ~ spl13_24 ),
    inference(avatar_component_clause,[],[f316]) ).

fof(f522,plain,
    ( ! [X0] :
        ( empty(powerset(X0))
        | in(sK3(X0),powerset(X0)) )
    | ~ spl13_37
    | ~ spl13_52 ),
    inference(resolution,[],[f471,f380]) ).

fof(f897,plain,
    ( spl13_101
    | ~ spl13_30
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f521,f470,f341,f895]) ).

fof(f521,plain,
    ( ! [X0] :
        ( empty(X0)
        | in(sK2(X0),X0) )
    | ~ spl13_30
    | ~ spl13_52 ),
    inference(resolution,[],[f471,f342]) ).

fof(f889,plain,
    ( ~ spl13_42
    | ~ spl13_7
    | spl13_100
    | ~ spl13_5
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f512,f466,f359,f234,f224,f886,f234,f415]) ).

fof(f512,plain,
    ( one_to_one(sK6)
    | ~ empty(sK6)
    | ~ function(sK6)
    | ~ spl13_5
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_51 ),
    inference(forward_demodulation,[],[f511,f393]) ).

fof(f511,plain,
    ( ~ empty(sK6)
    | ~ function(sK6)
    | one_to_one(empty_set)
    | ~ spl13_5
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_51 ),
    inference(forward_demodulation,[],[f510,f393]) ).

fof(f510,plain,
    ( ~ function(sK6)
    | ~ empty(empty_set)
    | one_to_one(empty_set)
    | ~ spl13_5
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_51 ),
    inference(forward_demodulation,[],[f500,f393]) ).

fof(f500,plain,
    ( ~ function(empty_set)
    | ~ empty(empty_set)
    | one_to_one(empty_set)
    | ~ spl13_5
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f226]) ).

fof(f884,plain,
    ( spl13_98
    | ~ spl13_99
    | ~ spl13_14
    | ~ spl13_13
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f507,f466,f264,f269,f881,f877]) ).

fof(f877,plain,
    ( spl13_98
  <=> one_to_one(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_98])]) ).

fof(f881,plain,
    ( spl13_99
  <=> empty(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_99])]) ).

fof(f269,plain,
    ( spl13_14
  <=> function(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).

fof(f507,plain,
    ( ~ function(sK10)
    | ~ empty(sK10)
    | one_to_one(sK10)
    | ~ spl13_13
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f266]) ).

fof(f875,plain,
    ( spl13_95
    | ~ spl13_96
    | ~ spl13_97
    | ~ spl13_12
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f506,f466,f259,f872,f868,f864]) ).

fof(f864,plain,
    ( spl13_95
  <=> one_to_one(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_95])]) ).

fof(f868,plain,
    ( spl13_96
  <=> empty(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_96])]) ).

fof(f872,plain,
    ( spl13_97
  <=> function(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_97])]) ).

fof(f506,plain,
    ( ~ function(sK9)
    | ~ empty(sK9)
    | one_to_one(sK9)
    | ~ spl13_12
    | ~ spl13_51 ),
    inference(resolution,[],[f467,f261]) ).

fof(f861,plain,
    ( spl13_94
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_35 ),
    inference(avatar_split_clause,[],[f405,f371,f359,f234,f859]) ).

fof(f405,plain,
    ( ! [X0] :
        ( relation_dom(X0) = sK6
        | ~ empty(X0) )
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_35 ),
    inference(forward_demodulation,[],[f402,f393]) ).

fof(f402,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = relation_dom(X0) )
    | ~ spl13_32
    | ~ spl13_35 ),
    inference(resolution,[],[f372,f360]) ).

fof(f857,plain,
    ( spl13_93
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_33 ),
    inference(avatar_split_clause,[],[f401,f363,f359,f234,f855]) ).

fof(f401,plain,
    ( ! [X0] :
        ( relation_rng(X0) = sK6
        | ~ empty(X0) )
    | ~ spl13_7
    | ~ spl13_32
    | ~ spl13_33 ),
    inference(forward_demodulation,[],[f398,f393]) ).

fof(f398,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = relation_rng(X0) )
    | ~ spl13_32
    | ~ spl13_33 ),
    inference(resolution,[],[f364,f360]) ).

fof(f787,plain,
    ( spl13_89
    | ~ spl13_32
    | ~ spl13_80 ),
    inference(avatar_split_clause,[],[f755,f683,f359,f735]) ).

fof(f755,plain,
    ( ! [X0] :
        ( sK6 = X0
        | ~ empty(X0) )
    | ~ spl13_32
    | ~ spl13_80 ),
    inference(forward_demodulation,[],[f360,f685]) ).

fof(f777,plain,
    ( ~ spl13_92
    | ~ spl13_33
    | spl13_82 ),
    inference(avatar_split_clause,[],[f733,f692,f363,f774]) ).

fof(f774,plain,
    ( spl13_92
  <=> empty(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_92])]) ).

fof(f733,plain,
    ( ~ empty(sK0)
    | ~ spl13_33
    | spl13_82 ),
    inference(resolution,[],[f693,f364]) ).

fof(f754,plain,
    ( ~ spl13_4
    | ~ spl13_90 ),
    inference(avatar_contradiction_clause,[],[f745]) ).

fof(f745,plain,
    ( $false
    | ~ spl13_4
    | ~ spl13_90 ),
    inference(resolution,[],[f740,f221]) ).

fof(f740,plain,
    ( ! [X0] : ~ empty(X0)
    | ~ spl13_90 ),
    inference(avatar_component_clause,[],[f739]) ).

fof(f739,plain,
    ( spl13_90
  <=> ! [X0] : ~ empty(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_90])]) ).

fof(f753,plain,
    ( ~ spl13_24
    | ~ spl13_90 ),
    inference(avatar_contradiction_clause,[],[f746]) ).

fof(f746,plain,
    ( $false
    | ~ spl13_24
    | ~ spl13_90 ),
    inference(resolution,[],[f740,f317]) ).

fof(f752,plain,
    ( ~ spl13_7
    | ~ spl13_90 ),
    inference(avatar_contradiction_clause,[],[f747]) ).

fof(f747,plain,
    ( $false
    | ~ spl13_7
    | ~ spl13_90 ),
    inference(resolution,[],[f740,f236]) ).

fof(f751,plain,
    ( ~ spl13_10
    | ~ spl13_90 ),
    inference(avatar_contradiction_clause,[],[f748]) ).

fof(f748,plain,
    ( $false
    | ~ spl13_10
    | ~ spl13_90 ),
    inference(resolution,[],[f740,f251]) ).

fof(f251,plain,
    ( empty(sK8)
    | ~ spl13_10 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f249,plain,
    ( spl13_10
  <=> empty(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

fof(f750,plain,
    ( ~ spl13_19
    | ~ spl13_90 ),
    inference(avatar_contradiction_clause,[],[f749]) ).

fof(f749,plain,
    ( $false
    | ~ spl13_19
    | ~ spl13_90 ),
    inference(resolution,[],[f740,f296]) ).

fof(f296,plain,
    ( empty(sK12)
    | ~ spl13_19 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f294,plain,
    ( spl13_19
  <=> empty(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).

fof(f744,plain,
    ( spl13_90
    | spl13_91
    | ~ spl13_7
    | ~ spl13_24
    | ~ spl13_32
    | ~ spl13_37
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f547,f539,f379,f359,f316,f234,f742,f739]) ).

fof(f742,plain,
    ( spl13_91
  <=> ! [X1] : ~ in(X1,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_91])]) ).

fof(f547,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,sK6)
        | ~ empty(X0) )
    | ~ spl13_7
    | ~ spl13_24
    | ~ spl13_32
    | ~ spl13_37
    | ~ spl13_59 ),
    inference(forward_demodulation,[],[f546,f393]) ).

fof(f546,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,empty_set)
        | ~ empty(X0) )
    | ~ spl13_24
    | ~ spl13_32
    | ~ spl13_37
    | ~ spl13_59 ),
    inference(forward_demodulation,[],[f545,f392]) ).

fof(f545,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK3(X0)) )
    | ~ spl13_37
    | ~ spl13_59 ),
    inference(resolution,[],[f540,f380]) ).

fof(f737,plain,
    ( spl13_89
    | ~ spl13_7
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f459,f444,f234,f735]) ).

fof(f459,plain,
    ( ! [X0] :
        ( sK6 = X0
        | ~ empty(X0) )
    | ~ spl13_7
    | ~ spl13_49 ),
    inference(resolution,[],[f445,f236]) ).

fof(f732,plain,
    ( spl13_88
    | ~ spl13_28
    | ~ spl13_35 ),
    inference(avatar_split_clause,[],[f404,f371,f333,f730]) ).

fof(f404,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(relation_dom(X0)) )
    | ~ spl13_28
    | ~ spl13_35 ),
    inference(resolution,[],[f372,f334]) ).

fof(f728,plain,
    ( spl13_87
    | ~ spl13_28
    | ~ spl13_33 ),
    inference(avatar_split_clause,[],[f400,f363,f333,f726]) ).

fof(f400,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(relation_rng(X0)) )
    | ~ spl13_28
    | ~ spl13_33 ),
    inference(resolution,[],[f364,f334]) ).

fof(f722,plain,
    ( spl13_86
    | ~ spl13_80
    | ~ spl13_85 ),
    inference(avatar_split_clause,[],[f718,f715,f683,f720]) ).

fof(f715,plain,
    ( spl13_85
  <=> ! [X0] : empty_set = sK3(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_85])]) ).

fof(f718,plain,
    ( ! [X0] : sK3(X0) = sK6
    | ~ spl13_80
    | ~ spl13_85 ),
    inference(forward_demodulation,[],[f716,f685]) ).

fof(f716,plain,
    ( ! [X0] : empty_set = sK3(X0)
    | ~ spl13_85 ),
    inference(avatar_component_clause,[],[f715]) ).

fof(f717,plain,
    ( spl13_85
    | ~ spl13_24
    | ~ spl13_32 ),
    inference(avatar_split_clause,[],[f392,f359,f316,f715]) ).

fof(f705,plain,
    ( spl13_84
    | ~ spl13_7
    | ~ spl13_19
    | ~ spl13_32 ),
    inference(avatar_split_clause,[],[f397,f359,f294,f234,f702]) ).

fof(f702,plain,
    ( spl13_84
  <=> sK6 = sK12 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_84])]) ).

fof(f397,plain,
    ( sK6 = sK12
    | ~ spl13_7
    | ~ spl13_19
    | ~ spl13_32 ),
    inference(forward_demodulation,[],[f395,f393]) ).

fof(f395,plain,
    ( empty_set = sK12
    | ~ spl13_19
    | ~ spl13_32 ),
    inference(resolution,[],[f360,f296]) ).

fof(f700,plain,
    ( spl13_83
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_32 ),
    inference(avatar_split_clause,[],[f396,f359,f249,f234,f697]) ).

fof(f697,plain,
    ( spl13_83
  <=> sK6 = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_83])]) ).

fof(f396,plain,
    ( sK6 = sK8
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_32 ),
    inference(forward_demodulation,[],[f394,f393]) ).

fof(f394,plain,
    ( empty_set = sK8
    | ~ spl13_10
    | ~ spl13_32 ),
    inference(resolution,[],[f360,f251]) ).

fof(f695,plain,
    ( ~ spl13_81
    | spl13_82
    | ~ spl13_35
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f633,f629,f371,f692,f688]) ).

fof(f633,plain,
    ( empty(relation_rng(sK0))
    | ~ empty(relation_composition(function_inverse(sK0),sK0))
    | ~ spl13_35
    | ~ spl13_74 ),
    inference(superposition,[],[f372,f631]) ).

fof(f686,plain,
    ( spl13_80
    | ~ spl13_7
    | ~ spl13_32 ),
    inference(avatar_split_clause,[],[f393,f359,f234,f683]) ).

fof(f680,plain,
    ( spl13_79
    | ~ spl13_24
    | ~ spl13_29 ),
    inference(avatar_split_clause,[],[f350,f337,f316,f678]) ).

fof(f678,plain,
    ( spl13_79
  <=> ! [X0] : relation(sK3(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_79])]) ).

fof(f350,plain,
    ( ! [X0] : relation(sK3(X0))
    | ~ spl13_24
    | ~ spl13_29 ),
    inference(resolution,[],[f338,f317]) ).

fof(f675,plain,
    ( spl13_78
    | ~ spl13_24
    | ~ spl13_28 ),
    inference(avatar_split_clause,[],[f345,f333,f316,f673]) ).

fof(f673,plain,
    ( spl13_78
  <=> ! [X0] : function(sK3(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).

fof(f345,plain,
    ( ! [X0] : function(sK3(X0))
    | ~ spl13_24
    | ~ spl13_28 ),
    inference(resolution,[],[f334,f317]) ).

fof(f666,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_77
    | ~ spl13_3
    | ~ spl13_66 ),
    inference(avatar_split_clause,[],[f589,f580,f214,f663,f209,f204]) ).

fof(f589,plain,
    ( relation_dom(sK0) = relation_rng(relation_composition(sK0,function_inverse(sK0)))
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_3
    | ~ spl13_66 ),
    inference(resolution,[],[f581,f216]) ).

fof(f654,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_76
    | ~ spl13_3
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f587,f576,f214,f651,f209,f204]) ).

fof(f587,plain,
    ( relation_dom(sK0) = relation_dom(relation_composition(sK0,function_inverse(sK0)))
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_3
    | ~ spl13_65 ),
    inference(resolution,[],[f577,f216]) ).

fof(f644,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_75
    | ~ spl13_3
    | ~ spl13_64 ),
    inference(avatar_split_clause,[],[f585,f572,f214,f641,f209,f204]) ).

fof(f585,plain,
    ( relation_rng(sK0) = relation_rng(relation_composition(function_inverse(sK0),sK0))
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_3
    | ~ spl13_64 ),
    inference(resolution,[],[f573,f216]) ).

fof(f632,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_74
    | ~ spl13_3
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f583,f568,f214,f629,f209,f204]) ).

fof(f583,plain,
    ( relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),sK0))
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl13_3
    | ~ spl13_63 ),
    inference(resolution,[],[f569,f216]) ).

fof(f627,plain,
    spl13_73,
    inference(avatar_split_clause,[],[f199,f625]) ).

fof(f199,plain,
    ! [X1] :
      ( identity_relation(relation_dom(X1)) = X1
      | sK4(relation_dom(X1),X1) != apply(X1,sK4(relation_dom(X1),X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f177]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( identity_relation(X0) = X1
      | sK4(X0,X1) != apply(X1,sK4(X0,X1))
      | relation_dom(X1) != X0
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ( sK4(X0,X1) != apply(X1,sK4(X0,X1))
            & in(sK4(X0,X1),X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X3] :
                ( apply(X1,X3) = X3
                | ~ in(X3,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f105,f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( apply(X1,X2) != X2
          & in(X2,X0) )
     => ( sK4(X0,X1) != apply(X1,sK4(X0,X1))
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X3] :
                ( apply(X1,X3) = X3
                | ~ in(X3,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X2] :
                ( apply(X1,X2) = X2
                | ~ in(X2,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X2] :
                ( apply(X1,X2) = X2
                | ~ in(X2,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( apply(X1,X2) = X2
              | ~ in(X2,X0) )
          & relation_dom(X1) = X0 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( apply(X1,X2) = X2
              | ~ in(X2,X0) )
          & relation_dom(X1) = X0 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( in(X2,X0)
             => apply(X1,X2) = X2 )
          & relation_dom(X1) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).

fof(f619,plain,
    spl13_72,
    inference(avatar_split_clause,[],[f173,f617]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
        & apply(function_inverse(X1),apply(X1,X0)) = X0 )
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
        & apply(function_inverse(X1),apply(X1,X0)) = X0 )
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( in(X0,relation_dom(X1))
          & one_to_one(X1) )
       => ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
          & apply(function_inverse(X1),apply(X1,X0)) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).

fof(f615,plain,
    spl13_71,
    inference(avatar_split_clause,[],[f172,f613]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( apply(function_inverse(X1),apply(X1,X0)) = X0
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f611,plain,
    spl13_70,
    inference(avatar_split_clause,[],[f171,f609]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( in(X0,relation_rng(X1))
          & one_to_one(X1) )
       => ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
          & apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).

fof(f607,plain,
    spl13_69,
    inference(avatar_split_clause,[],[f170,f605]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( apply(X1,apply(function_inverse(X1),X0)) = X0
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f599,plain,
    spl13_68,
    inference(avatar_split_clause,[],[f200,f597]) ).

fof(f200,plain,
    ! [X1] :
      ( identity_relation(relation_dom(X1)) = X1
      | in(sK4(relation_dom(X1),X1),relation_dom(X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f176]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( identity_relation(X0) = X1
      | in(sK4(X0,X1),X0)
      | relation_dom(X1) != X0
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f594,plain,
    spl13_67,
    inference(avatar_split_clause,[],[f201,f592]) ).

fof(f201,plain,
    ! [X3,X0] :
      ( apply(identity_relation(X0),X3) = X3
      | ~ in(X3,X0)
      | ~ function(identity_relation(X0))
      | ~ relation(identity_relation(X0)) ),
    inference(equality_resolution,[],[f175]) ).

fof(f175,plain,
    ! [X3,X0,X1] :
      ( apply(X1,X3) = X3
      | ~ in(X3,X0)
      | identity_relation(X0) != X1
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f582,plain,
    spl13_66,
    inference(avatar_split_clause,[],[f153,f580]) ).

fof(f153,plain,
    ! [X0] :
      ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
        & relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
        & relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
          & relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).

fof(f578,plain,
    spl13_65,
    inference(avatar_split_clause,[],[f152,f576]) ).

fof(f152,plain,
    ! [X0] :
      ( relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0)))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f574,plain,
    spl13_64,
    inference(avatar_split_clause,[],[f151,f572]) ).

fof(f151,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
        & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
        & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
          & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).

fof(f570,plain,
    spl13_63,
    inference(avatar_split_clause,[],[f150,f568]) ).

fof(f150,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f566,plain,
    spl13_62,
    inference(avatar_split_clause,[],[f169,f564]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( function(relation_composition(X0,X1))
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1)
        & function(X0)
        & relation(X0) )
     => ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

fof(f561,plain,
    spl13_61,
    inference(avatar_split_clause,[],[f202,f559]) ).

fof(f202,plain,
    ! [X0] :
      ( relation_dom(identity_relation(X0)) = X0
      | ~ function(identity_relation(X0))
      | ~ relation(identity_relation(X0)) ),
    inference(equality_resolution,[],[f174]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( relation_dom(X1) = X0
      | identity_relation(X0) != X1
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f551,plain,
    spl13_60,
    inference(avatar_split_clause,[],[f182,f549]) ).

fof(f182,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(f541,plain,
    spl13_59,
    inference(avatar_split_clause,[],[f183,f539]) ).

fof(f183,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f497,plain,
    spl13_58,
    inference(avatar_split_clause,[],[f178,f495]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(relation_composition(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(f493,plain,
    spl13_57,
    inference(avatar_split_clause,[],[f167,f491]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X1,X0))
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( relation(relation_composition(X1,X0))
        & empty(relation_composition(X1,X0)) )
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( relation(relation_composition(X1,X0))
        & empty(relation_composition(X1,X0)) )
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & empty(X0) )
     => ( relation(relation_composition(X1,X0))
        & empty(relation_composition(X1,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).

fof(f489,plain,
    spl13_56,
    inference(avatar_split_clause,[],[f166,f487]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( empty(relation_composition(X1,X0))
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f485,plain,
    ( spl13_55
    | ~ spl13_7
    | ~ spl13_29 ),
    inference(avatar_split_clause,[],[f351,f337,f234,f482]) ).

fof(f351,plain,
    ( relation(sK6)
    | ~ spl13_7
    | ~ spl13_29 ),
    inference(resolution,[],[f338,f236]) ).

fof(f480,plain,
    spl13_54,
    inference(avatar_split_clause,[],[f165,f478]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( relation(relation_composition(X0,X1))
        & empty(relation_composition(X0,X1)) )
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ( relation(relation_composition(X0,X1))
        & empty(relation_composition(X0,X1)) )
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & empty(X0) )
     => ( relation(relation_composition(X0,X1))
        & empty(relation_composition(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).

fof(f476,plain,
    spl13_53,
    inference(avatar_split_clause,[],[f164,f474]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( empty(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f472,plain,
    spl13_52,
    inference(avatar_split_clause,[],[f163,f470]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f468,plain,
    spl13_51,
    inference(avatar_split_clause,[],[f156,f466]) ).

fof(f156,plain,
    ! [X0] :
      ( one_to_one(X0)
      | ~ function(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ( one_to_one(X0)
        & function(X0)
        & relation(X0) )
      | ~ function(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ( one_to_one(X0)
        & function(X0)
        & relation(X0) )
      | ~ function(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ( function(X0)
        & empty(X0)
        & relation(X0) )
     => ( one_to_one(X0)
        & function(X0)
        & relation(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).

fof(f451,plain,
    ( spl13_50
    | ~ spl13_10
    | ~ spl13_28 ),
    inference(avatar_split_clause,[],[f347,f333,f249,f448]) ).

fof(f448,plain,
    ( spl13_50
  <=> function(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).

fof(f347,plain,
    ( function(sK8)
    | ~ spl13_10
    | ~ spl13_28 ),
    inference(resolution,[],[f334,f251]) ).

fof(f446,plain,
    spl13_49,
    inference(avatar_split_clause,[],[f180,f444]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f442,plain,
    spl13_48,
    inference(avatar_split_clause,[],[f179,f440]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => element(X0,powerset(X1)) ),
    inference(unused_predicate_definition_removal,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f438,plain,
    spl13_47,
    inference(avatar_split_clause,[],[f149,f436]) ).

fof(f149,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(function_inverse(X0))
        & relation(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(f434,plain,
    spl13_46,
    inference(avatar_split_clause,[],[f148,f432]) ).

fof(f148,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f430,plain,
    spl13_45,
    inference(avatar_split_clause,[],[f147,f428]) ).

fof(f428,plain,
    ( spl13_45
  <=> ! [X0] :
        ( ~ empty(relation_dom(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).

fof(f147,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(f426,plain,
    spl13_44,
    inference(avatar_split_clause,[],[f146,f424]) ).

fof(f424,plain,
    ( spl13_44
  <=> ! [X0] :
        ( ~ empty(relation_rng(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).

fof(f146,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

fof(f422,plain,
    spl13_43,
    inference(avatar_split_clause,[],[f137,f420]) ).

fof(f137,plain,
    ! [X0] :
      ( element(sK1(X0),powerset(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ( ~ empty(sK1(X0))
        & element(sK1(X0),powerset(X0)) )
      | empty(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f53,f97]) ).

fof(f97,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
     => ( ~ empty(sK1(X0))
        & element(sK1(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
      | empty(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ~ empty(X0)
     => ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

fof(f418,plain,
    ( spl13_42
    | ~ spl13_7
    | ~ spl13_28 ),
    inference(avatar_split_clause,[],[f346,f333,f234,f415]) ).

fof(f346,plain,
    ( function(sK6)
    | ~ spl13_7
    | ~ spl13_28 ),
    inference(resolution,[],[f334,f236]) ).

fof(f413,plain,
    spl13_41,
    inference(avatar_split_clause,[],[f162,f411]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(f409,plain,
    spl13_40,
    inference(avatar_split_clause,[],[f161,f407]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f390,plain,
    ( spl13_39
    | ~ spl13_4
    | ~ spl13_28 ),
    inference(avatar_split_clause,[],[f344,f333,f219,f387]) ).

fof(f387,plain,
    ( spl13_39
  <=> function(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).

fof(f344,plain,
    ( function(empty_set)
    | ~ spl13_4
    | ~ spl13_28 ),
    inference(resolution,[],[f334,f221]) ).

fof(f385,plain,
    spl13_38,
    inference(avatar_split_clause,[],[f181,f383]) ).

fof(f181,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f381,plain,
    spl13_37,
    inference(avatar_split_clause,[],[f158,f379]) ).

fof(f158,plain,
    ! [X0] : element(sK3(X0),powerset(X0)),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( empty(sK3(X0))
      & element(sK3(X0),powerset(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ? [X1] :
          ( empty(X1)
          & element(X1,powerset(X0)) )
     => ( empty(sK3(X0))
        & element(sK3(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,axiom,
    ! [X0] :
    ? [X1] :
      ( empty(X1)
      & element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

fof(f377,plain,
    spl13_36,
    inference(avatar_split_clause,[],[f145,f375]) ).

fof(f145,plain,
    ! [X0] :
      ( relation(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

fof(f373,plain,
    spl13_35,
    inference(avatar_split_clause,[],[f144,f371]) ).

fof(f144,plain,
    ! [X0] :
      ( empty(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f369,plain,
    spl13_34,
    inference(avatar_split_clause,[],[f143,f367]) ).

fof(f143,plain,
    ! [X0] :
      ( relation(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

fof(f365,plain,
    spl13_33,
    inference(avatar_split_clause,[],[f142,f363]) ).

fof(f142,plain,
    ! [X0] :
      ( empty(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f361,plain,
    spl13_32,
    inference(avatar_split_clause,[],[f141,f359]) ).

fof(f141,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f357,plain,
    spl13_31,
    inference(avatar_split_clause,[],[f138,f355]) ).

fof(f355,plain,
    ( spl13_31
  <=> ! [X0] :
        ( ~ empty(sK1(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ empty(sK1(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f343,plain,
    spl13_30,
    inference(avatar_split_clause,[],[f157,f341]) ).

fof(f157,plain,
    ! [X0] : element(sK2(X0),X0),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] : element(sK2(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f8,f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f8,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f339,plain,
    spl13_29,
    inference(avatar_split_clause,[],[f140,f337]) ).

fof(f140,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f335,plain,
    spl13_28,
    inference(avatar_split_clause,[],[f139,f333]) ).

fof(f139,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( empty(X0)
     => function(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

fof(f331,plain,
    ( ~ spl13_26
    | ~ spl13_27 ),
    inference(avatar_split_clause,[],[f127,f328,f324]) ).

fof(f127,plain,
    ( relation_composition(function_inverse(sK0),sK0) != identity_relation(relation_rng(sK0))
    | relation_composition(sK0,function_inverse(sK0)) != identity_relation(relation_dom(sK0)) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ( ( relation_composition(function_inverse(sK0),sK0) != identity_relation(relation_rng(sK0))
      | relation_composition(sK0,function_inverse(sK0)) != identity_relation(relation_dom(sK0)) )
    & one_to_one(sK0)
    & function(sK0)
    & relation(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f52,f95]) ).

fof(f95,plain,
    ( ? [X0] :
        ( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
          | relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( ( relation_composition(function_inverse(sK0),sK0) != identity_relation(relation_rng(sK0))
        | relation_composition(sK0,function_inverse(sK0)) != identity_relation(relation_dom(sK0)) )
      & one_to_one(sK0)
      & function(sK0)
      & relation(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ? [X0] :
      ( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
        | relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ? [X0] :
      ( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
        | relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( one_to_one(X0)
         => ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
            & relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
    inference(negated_conjecture,[],[f42]) ).

fof(f42,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
          & relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).

fof(f322,plain,
    spl13_25,
    inference(avatar_split_clause,[],[f160,f320]) ).

fof(f320,plain,
    ( spl13_25
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).

fof(f160,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f318,plain,
    spl13_24,
    inference(avatar_split_clause,[],[f159,f316]) ).

fof(f159,plain,
    ! [X0] : empty(sK3(X0)),
    inference(cnf_transformation,[],[f102]) ).

fof(f314,plain,
    spl13_23,
    inference(avatar_split_clause,[],[f136,f312]) ).

fof(f136,plain,
    ! [X0] : function(identity_relation(X0)),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( function(identity_relation(X0))
      & relation(identity_relation(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(f310,plain,
    spl13_22,
    inference(avatar_split_clause,[],[f134,f308]) ).

fof(f134,plain,
    ! [X0] : relation(identity_relation(X0)),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : relation(identity_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).

fof(f306,plain,
    spl13_21,
    inference(avatar_split_clause,[],[f133,f304]) ).

fof(f304,plain,
    ( spl13_21
  <=> ! [X0] : ~ empty(powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).

fof(f133,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(f302,plain,
    spl13_20,
    inference(avatar_split_clause,[],[f198,f299]) ).

fof(f299,plain,
    ( spl13_20
  <=> function(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).

fof(f198,plain,
    function(sK12),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ( function(sK12)
    & empty(sK12)
    & relation(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f25,f122]) ).

fof(f122,plain,
    ( ? [X0] :
        ( function(X0)
        & empty(X0)
        & relation(X0) )
   => ( function(sK12)
      & empty(sK12)
      & relation(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,axiom,
    ? [X0] :
      ( function(X0)
      & empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(f297,plain,
    spl13_19,
    inference(avatar_split_clause,[],[f197,f294]) ).

fof(f197,plain,
    empty(sK12),
    inference(cnf_transformation,[],[f123]) ).

fof(f292,plain,
    spl13_18,
    inference(avatar_split_clause,[],[f196,f289]) ).

fof(f289,plain,
    ( spl13_18
  <=> relation(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).

fof(f196,plain,
    relation(sK12),
    inference(cnf_transformation,[],[f123]) ).

fof(f287,plain,
    spl13_17,
    inference(avatar_split_clause,[],[f195,f284]) ).

fof(f195,plain,
    one_to_one(sK11),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ( one_to_one(sK11)
    & function(sK11)
    & relation(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f29,f120]) ).

fof(f120,plain,
    ( ? [X0] :
        ( one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( one_to_one(sK11)
      & function(sK11)
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,axiom,
    ? [X0] :
      ( one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

fof(f282,plain,
    spl13_16,
    inference(avatar_split_clause,[],[f194,f279]) ).

fof(f194,plain,
    function(sK11),
    inference(cnf_transformation,[],[f121]) ).

fof(f277,plain,
    spl13_15,
    inference(avatar_split_clause,[],[f193,f274]) ).

fof(f193,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f121]) ).

fof(f272,plain,
    spl13_14,
    inference(avatar_split_clause,[],[f192,f269]) ).

fof(f192,plain,
    function(sK10),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ( function(sK10)
    & relation(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f21,f118]) ).

fof(f118,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK10)
      & relation(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,axiom,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

fof(f267,plain,
    spl13_13,
    inference(avatar_split_clause,[],[f191,f264]) ).

fof(f191,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f119]) ).

fof(f262,plain,
    spl13_12,
    inference(avatar_split_clause,[],[f190,f259]) ).

fof(f190,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    relation(sK9),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f50,f116]) ).

fof(f116,plain,
    ( ? [X0] : relation(X0)
   => relation(sK9) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ? [X0] : relation(X0),
    inference(pure_predicate_removal,[],[f30]) ).

fof(f30,axiom,
    ? [X0] :
      ( relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).

fof(f257,plain,
    spl13_11,
    inference(avatar_split_clause,[],[f189,f254]) ).

fof(f254,plain,
    ( spl13_11
  <=> relation(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).

fof(f189,plain,
    relation(sK8),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ( relation(sK8)
    & empty(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f22,f114]) ).

fof(f114,plain,
    ( ? [X0] :
        ( relation(X0)
        & empty(X0) )
   => ( relation(sK8)
      & empty(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,axiom,
    ? [X0] :
      ( relation(X0)
      & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(f252,plain,
    spl13_10,
    inference(avatar_split_clause,[],[f188,f249]) ).

fof(f188,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f115]) ).

fof(f247,plain,
    spl13_9,
    inference(avatar_split_clause,[],[f187,f244]) ).

fof(f187,plain,
    relation(sK7),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ( relation(sK7)
    & ~ empty(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f26,f112]) ).

fof(f112,plain,
    ( ? [X0] :
        ( relation(X0)
        & ~ empty(X0) )
   => ( relation(sK7)
      & ~ empty(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,axiom,
    ? [X0] :
      ( relation(X0)
      & ~ empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

fof(f242,plain,
    ~ spl13_8,
    inference(avatar_split_clause,[],[f186,f239]) ).

fof(f239,plain,
    ( spl13_8
  <=> empty(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

fof(f186,plain,
    ~ empty(sK7),
    inference(cnf_transformation,[],[f113]) ).

fof(f237,plain,
    spl13_7,
    inference(avatar_split_clause,[],[f185,f234]) ).

fof(f185,plain,
    empty(sK6),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    empty(sK6),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f24,f110]) ).

fof(f110,plain,
    ( ? [X0] : empty(X0)
   => empty(sK6) ),
    introduced(choice_axiom,[]) ).

fof(f24,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f232,plain,
    ~ spl13_6,
    inference(avatar_split_clause,[],[f184,f229]) ).

fof(f229,plain,
    ( spl13_6
  <=> empty(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f184,plain,
    ~ empty(sK5),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ~ empty(sK5),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f28,f108]) ).

fof(f108,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK5) ),
    introduced(choice_axiom,[]) ).

fof(f28,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f227,plain,
    spl13_5,
    inference(avatar_split_clause,[],[f130,f224]) ).

fof(f130,plain,
    relation(empty_set),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f222,plain,
    spl13_4,
    inference(avatar_split_clause,[],[f128,f219]) ).

fof(f128,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f217,plain,
    spl13_3,
    inference(avatar_split_clause,[],[f126,f214]) ).

fof(f126,plain,
    one_to_one(sK0),
    inference(cnf_transformation,[],[f96]) ).

fof(f212,plain,
    spl13_2,
    inference(avatar_split_clause,[],[f125,f209]) ).

fof(f125,plain,
    function(sK0),
    inference(cnf_transformation,[],[f96]) ).

fof(f207,plain,
    spl13_1,
    inference(avatar_split_clause,[],[f124,f204]) ).

fof(f124,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n011.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon Apr 29 21:04:01 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (15453)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.35  % (15460)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)
% 0.17/0.36  % (15456)WARNING: value z3 for option sas not known
% 0.17/0.36  % (15455)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.36  % (15457)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.36  % (15459)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)
% 0.17/0.37  % (15458)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)
% 0.17/0.37  % (15454)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.37  % (15456)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)
% 0.17/0.38  TRYING [1]
% 0.17/0.38  TRYING [2]
% 0.17/0.38  TRYING [3]
% 0.17/0.39  TRYING [4]
% 0.17/0.40  TRYING [1]
% 0.17/0.40  TRYING [2]
% 0.17/0.41  TRYING [5]
% 0.17/0.44  TRYING [3]
% 0.17/0.47  TRYING [6]
% 0.17/0.51  TRYING [4]
% 0.17/0.57  TRYING [7]
% 1.35/0.66  TRYING [5]
% 2.12/0.86  TRYING [8]
% 2.53/1.00  % (15458)First to succeed.
% 2.74/1.02  % (15458)Refutation found. Thanks to Tanya!
% 2.74/1.02  % SZS status Theorem for theBenchmark
% 2.74/1.02  % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.03  % (15458)------------------------------
% 2.74/1.03  % (15458)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.74/1.03  % (15458)Termination reason: Refutation
% 2.74/1.03  
% 2.74/1.03  % (15458)Memory used [KB]: 4269
% 2.74/1.03  % (15458)Time elapsed: 0.673 s
% 2.74/1.03  % (15458)Instructions burned: 641 (million)
% 2.74/1.03  % (15458)------------------------------
% 2.74/1.03  % (15458)------------------------------
% 2.74/1.03  % (15453)Success in time 0.689 s
% 2.74/1.03  15454 Aborted by signal SIGHUP on /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.74/1.03  % (15454)------------------------------
% 2.74/1.03  % (15454)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.74/1.03  % (15454)Termination reason: Unknown
% 2.74/1.03  % (15454)Termination phase: Finite model building SAT solving
% 2.74/1.03  
% 2.74/1.03  % (15454)Memory used [KB]: 3290
%------------------------------------------------------------------------------