TSTP Solution File: SEU290+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n017.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 : Sat Sep  2 00:12:21 EDT 2023

% Result   : Theorem 0.15s 0.37s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  291
% Syntax   : Number of formulae    :  922 ( 151 unt;   0 def)
%            Number of atoms       : 2764 ( 272 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives : 3189 (1347   ~;1377   |; 178   &)
%                                         ( 239 <=>;  48  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :  236 ( 234 usr; 221 prp; 0-3 aty)
%            Number of functors    :   31 (  31 usr;  15 con; 0-3 aty)
%            Number of variables   : 1033 (; 971   !;  62   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1793,plain,
    $false,
    inference(avatar_sat_refutation,[],[f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f343,f348,f353,f358,f363,f368,f373,f378,f383,f388,f393,f398,f402,f406,f410,f414,f418,f422,f426,f430,f434,f438,f449,f459,f463,f467,f471,f476,f480,f484,f488,f492,f514,f520,f524,f528,f532,f536,f540,f544,f548,f553,f580,f584,f588,f592,f596,f600,f625,f629,f633,f637,f641,f645,f649,f653,f686,f701,f705,f709,f720,f724,f739,f743,f755,f760,f764,f774,f779,f783,f788,f793,f799,f803,f808,f815,f825,f829,f833,f837,f841,f845,f850,f857,f865,f870,f876,f881,f887,f892,f897,f902,f909,f927,f937,f942,f951,f956,f961,f966,f971,f975,f981,f985,f989,f993,f1000,f1007,f1008,f1009,f1010,f1011,f1012,f1043,f1044,f1096,f1108,f1112,f1116,f1125,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1224,f1228,f1232,f1246,f1250,f1254,f1259,f1263,f1267,f1271,f1275,f1279,f1336,f1340,f1344,f1348,f1362,f1369,f1373,f1377,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1445,f1463,f1467,f1471,f1475,f1479,f1507,f1511,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1594,f1606,f1613,f1617,f1627,f1636,f1644,f1659,f1664,f1665,f1674,f1678,f1682,f1686,f1690,f1694,f1719,f1729,f1733,f1739,f1754,f1758,f1762,f1766,f1770,f1792]) ).

fof(f1792,plain,
    ( ~ spl27_2
    | spl27_202
    | ~ spl27_212 ),
    inference(avatar_split_clause,[],[f1740,f1716,f1633,f245]) ).

fof(f245,plain,
    ( spl27_2
  <=> in(sK5,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).

fof(f1633,plain,
    ( spl27_202
  <=> in(sK5,relation_dom(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_202])]) ).

fof(f1716,plain,
    ( spl27_212
  <=> sK3 = relation_dom(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_212])]) ).

fof(f1740,plain,
    ( ~ in(sK5,sK3)
    | spl27_202
    | ~ spl27_212 ),
    inference(superposition,[],[f1635,f1718]) ).

fof(f1718,plain,
    ( sK3 = relation_dom(sK6)
    | ~ spl27_212 ),
    inference(avatar_component_clause,[],[f1716]) ).

fof(f1635,plain,
    ( ~ in(sK5,relation_dom(sK6))
    | spl27_202 ),
    inference(avatar_component_clause,[],[f1633]) ).

fof(f1770,plain,
    ( spl27_220
    | ~ spl27_130
    | ~ spl27_175 ),
    inference(avatar_split_clause,[],[f1456,f1413,f998,f1768]) ).

fof(f1768,plain,
    ( spl27_220
  <=> ! [X12] :
        ( sP0(X12,sK18)
        | ~ empty(relation_dom(X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_220])]) ).

fof(f998,plain,
    ( spl27_130
  <=> ! [X8] : ~ in(X8,sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_130])]) ).

fof(f1413,plain,
    ( spl27_175
  <=> ! [X4,X5] :
        ( in(sK8(X4,X5),X5)
        | sP0(X4,X5)
        | ~ empty(relation_dom(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_175])]) ).

fof(f1456,plain,
    ( ! [X12] :
        ( sP0(X12,sK18)
        | ~ empty(relation_dom(X12)) )
    | ~ spl27_130
    | ~ spl27_175 ),
    inference(resolution,[],[f1414,f999]) ).

fof(f999,plain,
    ( ! [X8] : ~ in(X8,sK18)
    | ~ spl27_130 ),
    inference(avatar_component_clause,[],[f998]) ).

fof(f1414,plain,
    ( ! [X4,X5] :
        ( in(sK8(X4,X5),X5)
        | sP0(X4,X5)
        | ~ empty(relation_dom(X4)) )
    | ~ spl27_175 ),
    inference(avatar_component_clause,[],[f1413]) ).

fof(f1766,plain,
    ( spl27_219
    | ~ spl27_140
    | ~ spl27_151 ),
    inference(avatar_split_clause,[],[f1242,f1230,f1136,f1764]) ).

fof(f1764,plain,
    ( spl27_219
  <=> ! [X4] :
        ( ~ empty(X4)
        | empty(sK11(powerset(X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_219])]) ).

fof(f1136,plain,
    ( spl27_140
  <=> ! [X3] :
        ( empty(X3)
        | in(sK11(X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_140])]) ).

fof(f1230,plain,
    ( spl27_151
  <=> ! [X6,X5] :
        ( ~ empty(X5)
        | ~ in(X6,sK11(powerset(X5))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_151])]) ).

fof(f1242,plain,
    ( ! [X4] :
        ( ~ empty(X4)
        | empty(sK11(powerset(X4))) )
    | ~ spl27_140
    | ~ spl27_151 ),
    inference(resolution,[],[f1231,f1137]) ).

fof(f1137,plain,
    ( ! [X3] :
        ( in(sK11(X3),X3)
        | empty(X3) )
    | ~ spl27_140 ),
    inference(avatar_component_clause,[],[f1136]) ).

fof(f1231,plain,
    ( ! [X6,X5] :
        ( ~ in(X6,sK11(powerset(X5)))
        | ~ empty(X5) )
    | ~ spl27_151 ),
    inference(avatar_component_clause,[],[f1230]) ).

fof(f1762,plain,
    ( spl27_218
    | ~ spl27_73
    | ~ spl27_146 ),
    inference(avatar_split_clause,[],[f1211,f1160,f639,f1760]) ).

fof(f1760,plain,
    ( spl27_218
  <=> ! [X2,X3] : sP2(X2,sK16(X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_218])]) ).

fof(f639,plain,
    ( spl27_73
  <=> ! [X2,X0,X1] :
        ( sP2(X0,X2,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_73])]) ).

fof(f1160,plain,
    ( spl27_146
  <=> ! [X4,X5] : relation_of2_as_subset(sK16(X4,X5),X4,X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_146])]) ).

fof(f1211,plain,
    ( ! [X2,X3] : sP2(X2,sK16(X2,X3),X3)
    | ~ spl27_73
    | ~ spl27_146 ),
    inference(resolution,[],[f1161,f640]) ).

fof(f640,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation_of2_as_subset(X2,X0,X1)
        | sP2(X0,X2,X1) )
    | ~ spl27_73 ),
    inference(avatar_component_clause,[],[f639]) ).

fof(f1161,plain,
    ( ! [X4,X5] : relation_of2_as_subset(sK16(X4,X5),X4,X5)
    | ~ spl27_146 ),
    inference(avatar_component_clause,[],[f1160]) ).

fof(f1758,plain,
    ( spl27_217
    | ~ spl27_73
    | ~ spl27_145 ),
    inference(avatar_split_clause,[],[f1209,f1156,f639,f1756]) ).

fof(f1756,plain,
    ( spl27_217
  <=> ! [X2,X3] : sP2(X2,sK15(X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_217])]) ).

fof(f1156,plain,
    ( spl27_145
  <=> ! [X2,X3] : relation_of2_as_subset(sK15(X2,X3),X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_145])]) ).

fof(f1209,plain,
    ( ! [X2,X3] : sP2(X2,sK15(X2,X3),X3)
    | ~ spl27_73
    | ~ spl27_145 ),
    inference(resolution,[],[f1157,f640]) ).

fof(f1157,plain,
    ( ! [X2,X3] : relation_of2_as_subset(sK15(X2,X3),X2,X3)
    | ~ spl27_145 ),
    inference(avatar_component_clause,[],[f1156]) ).

fof(f1754,plain,
    ( spl27_216
    | ~ spl27_73
    | ~ spl27_144 ),
    inference(avatar_split_clause,[],[f1207,f1152,f639,f1752]) ).

fof(f1752,plain,
    ( spl27_216
  <=> ! [X2,X3] : sP2(X2,sK14(X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_216])]) ).

fof(f1152,plain,
    ( spl27_144
  <=> ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_144])]) ).

fof(f1207,plain,
    ( ! [X2,X3] : sP2(X2,sK14(X2,X3),X3)
    | ~ spl27_73
    | ~ spl27_144 ),
    inference(resolution,[],[f1153,f640]) ).

fof(f1153,plain,
    ( ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1)
    | ~ spl27_144 ),
    inference(avatar_component_clause,[],[f1152]) ).

fof(f1739,plain,
    ( spl27_215
    | ~ spl27_55
    | ~ spl27_140 ),
    inference(avatar_split_clause,[],[f1199,f1136,f522,f1737]) ).

fof(f1737,plain,
    ( spl27_215
  <=> ! [X2] :
        ( empty(X2)
        | ~ in(X2,sK11(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_215])]) ).

fof(f522,plain,
    ( spl27_55
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_55])]) ).

fof(f1199,plain,
    ( ! [X2] :
        ( empty(X2)
        | ~ in(X2,sK11(X2)) )
    | ~ spl27_55
    | ~ spl27_140 ),
    inference(resolution,[],[f1137,f523]) ).

fof(f523,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) )
    | ~ spl27_55 ),
    inference(avatar_component_clause,[],[f522]) ).

fof(f1733,plain,
    ( spl27_214
    | ~ spl27_126
    | ~ spl27_153 ),
    inference(avatar_split_clause,[],[f1283,f1248,f983,f1731]) ).

fof(f1731,plain,
    ( spl27_214
  <=> ! [X0] :
        ( sP1(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_214])]) ).

fof(f983,plain,
    ( spl27_126
  <=> ! [X2] :
        ( ~ empty(X2)
        | function(relation_dom(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_126])]) ).

fof(f1248,plain,
    ( spl27_153
  <=> ! [X1] :
        ( ~ function(relation_dom(X1))
        | sP1(relation_dom(X1))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_153])]) ).

fof(f1283,plain,
    ( ! [X0] :
        ( sP1(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl27_126
    | ~ spl27_153 ),
    inference(duplicate_literal_removal,[],[f1282]) ).

fof(f1282,plain,
    ( ! [X0] :
        ( sP1(relation_dom(X0))
        | ~ empty(X0)
        | ~ empty(X0) )
    | ~ spl27_126
    | ~ spl27_153 ),
    inference(resolution,[],[f1249,f984]) ).

fof(f984,plain,
    ( ! [X2] :
        ( function(relation_dom(X2))
        | ~ empty(X2) )
    | ~ spl27_126 ),
    inference(avatar_component_clause,[],[f983]) ).

fof(f1249,plain,
    ( ! [X1] :
        ( ~ function(relation_dom(X1))
        | sP1(relation_dom(X1))
        | ~ empty(X1) )
    | ~ spl27_153 ),
    inference(avatar_component_clause,[],[f1248]) ).

fof(f1729,plain,
    ( spl27_213
    | ~ spl27_125
    | ~ spl27_152 ),
    inference(avatar_split_clause,[],[f1281,f1244,f979,f1727]) ).

fof(f1727,plain,
    ( spl27_213
  <=> ! [X0] :
        ( sP1(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_213])]) ).

fof(f979,plain,
    ( spl27_125
  <=> ! [X2] :
        ( ~ empty(X2)
        | function(relation_rng(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_125])]) ).

fof(f1244,plain,
    ( spl27_152
  <=> ! [X0] :
        ( ~ function(relation_rng(X0))
        | sP1(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_152])]) ).

fof(f1281,plain,
    ( ! [X0] :
        ( sP1(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl27_125
    | ~ spl27_152 ),
    inference(duplicate_literal_removal,[],[f1280]) ).

fof(f1280,plain,
    ( ! [X0] :
        ( sP1(relation_rng(X0))
        | ~ empty(X0)
        | ~ empty(X0) )
    | ~ spl27_125
    | ~ spl27_152 ),
    inference(resolution,[],[f1245,f980]) ).

fof(f980,plain,
    ( ! [X2] :
        ( function(relation_rng(X2))
        | ~ empty(X2) )
    | ~ spl27_125 ),
    inference(avatar_component_clause,[],[f979]) ).

fof(f1245,plain,
    ( ! [X0] :
        ( ~ function(relation_rng(X0))
        | sP1(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl27_152 ),
    inference(avatar_component_clause,[],[f1244]) ).

fof(f1719,plain,
    ( spl27_212
    | ~ spl27_105
    | ~ spl27_203 ),
    inference(avatar_split_clause,[],[f1645,f1641,f862,f1716]) ).

fof(f862,plain,
    ( spl27_105
  <=> relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_105])]) ).

fof(f1641,plain,
    ( spl27_203
  <=> sK3 = relation_dom_as_subset(sK3,sK4,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_203])]) ).

fof(f1645,plain,
    ( sK3 = relation_dom(sK6)
    | ~ spl27_105
    | ~ spl27_203 ),
    inference(superposition,[],[f1643,f864]) ).

fof(f864,plain,
    ( relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6)
    | ~ spl27_105 ),
    inference(avatar_component_clause,[],[f862]) ).

fof(f1643,plain,
    ( sK3 = relation_dom_as_subset(sK3,sK4,sK6)
    | ~ spl27_203 ),
    inference(avatar_component_clause,[],[f1641]) ).

fof(f1694,plain,
    ( spl27_211
    | ~ spl27_42
    | ~ spl27_156 ),
    inference(avatar_split_clause,[],[f1285,f1261,f436,f1692]) ).

fof(f1692,plain,
    ( spl27_211
  <=> ! [X0,X1] : sP1(sK16(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_211])]) ).

fof(f436,plain,
    ( spl27_42
  <=> ! [X0,X1] : function(sK16(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_42])]) ).

fof(f1261,plain,
    ( spl27_156
  <=> ! [X4,X5] :
        ( ~ function(sK16(X4,X5))
        | sP1(sK16(X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_156])]) ).

fof(f1285,plain,
    ( ! [X0,X1] : sP1(sK16(X0,X1))
    | ~ spl27_42
    | ~ spl27_156 ),
    inference(resolution,[],[f1262,f437]) ).

fof(f437,plain,
    ( ! [X0,X1] : function(sK16(X0,X1))
    | ~ spl27_42 ),
    inference(avatar_component_clause,[],[f436]) ).

fof(f1262,plain,
    ( ! [X4,X5] :
        ( ~ function(sK16(X4,X5))
        | sP1(sK16(X4,X5)) )
    | ~ spl27_156 ),
    inference(avatar_component_clause,[],[f1261]) ).

fof(f1690,plain,
    ( spl27_210
    | ~ spl27_40
    | ~ spl27_154 ),
    inference(avatar_split_clause,[],[f1284,f1252,f428,f1688]) ).

fof(f1688,plain,
    ( spl27_210
  <=> ! [X0,X1] : sP1(sK15(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_210])]) ).

fof(f428,plain,
    ( spl27_40
  <=> ! [X0,X1] : function(sK15(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_40])]) ).

fof(f1252,plain,
    ( spl27_154
  <=> ! [X2,X3] :
        ( ~ function(sK15(X2,X3))
        | sP1(sK15(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_154])]) ).

fof(f1284,plain,
    ( ! [X0,X1] : sP1(sK15(X0,X1))
    | ~ spl27_40
    | ~ spl27_154 ),
    inference(resolution,[],[f1253,f429]) ).

fof(f429,plain,
    ( ! [X0,X1] : function(sK15(X0,X1))
    | ~ spl27_40 ),
    inference(avatar_component_clause,[],[f428]) ).

fof(f1253,plain,
    ( ! [X2,X3] :
        ( ~ function(sK15(X2,X3))
        | sP1(sK15(X2,X3)) )
    | ~ spl27_154 ),
    inference(avatar_component_clause,[],[f1252]) ).

fof(f1686,plain,
    ( spl27_209
    | ~ spl27_35
    | ~ spl27_150 ),
    inference(avatar_split_clause,[],[f1236,f1226,f408,f1684]) ).

fof(f1684,plain,
    ( spl27_209
  <=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_209])]) ).

fof(f408,plain,
    ( spl27_35
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).

fof(f1226,plain,
    ( spl27_150
  <=> ! [X2,X0,X1] :
        ( relation(X0)
        | ~ subset(X0,cartesian_product2(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_150])]) ).

fof(f1236,plain,
    ( ! [X0,X1] : relation(cartesian_product2(X0,X1))
    | ~ spl27_35
    | ~ spl27_150 ),
    inference(resolution,[],[f1227,f409]) ).

fof(f409,plain,
    ( ! [X0] : subset(X0,X0)
    | ~ spl27_35 ),
    inference(avatar_component_clause,[],[f408]) ).

fof(f1227,plain,
    ( ! [X2,X0,X1] :
        ( ~ subset(X0,cartesian_product2(X1,X2))
        | relation(X0) )
    | ~ spl27_150 ),
    inference(avatar_component_clause,[],[f1226]) ).

fof(f1682,plain,
    ( spl27_208
    | ~ spl27_144
    | ~ spl27_148 ),
    inference(avatar_split_clause,[],[f1218,f1168,f1152,f1680]) ).

fof(f1680,plain,
    ( spl27_208
  <=> ! [X2,X3] : relation(sK14(X2,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_208])]) ).

fof(f1168,plain,
    ( spl27_148
  <=> ! [X2,X0,X1] :
        ( ~ relation_of2_as_subset(X0,X1,X2)
        | relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_148])]) ).

fof(f1218,plain,
    ( ! [X2,X3] : relation(sK14(X2,X3))
    | ~ spl27_144
    | ~ spl27_148 ),
    inference(resolution,[],[f1169,f1153]) ).

fof(f1169,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation_of2_as_subset(X0,X1,X2)
        | relation(X0) )
    | ~ spl27_148 ),
    inference(avatar_component_clause,[],[f1168]) ).

fof(f1678,plain,
    ( spl27_207
    | ~ spl27_57
    | ~ spl27_148 ),
    inference(avatar_split_clause,[],[f1217,f1168,f530,f1676]) ).

fof(f1676,plain,
    ( spl27_207
  <=> ! [X0,X1] : relation(sK13(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_207])]) ).

fof(f530,plain,
    ( spl27_57
  <=> ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_57])]) ).

fof(f1217,plain,
    ( ! [X0,X1] : relation(sK13(X0,X1))
    | ~ spl27_57
    | ~ spl27_148 ),
    inference(resolution,[],[f1169,f531]) ).

fof(f531,plain,
    ( ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1)
    | ~ spl27_57 ),
    inference(avatar_component_clause,[],[f530]) ).

fof(f1674,plain,
    ( spl27_206
    | ~ spl27_7
    | ~ spl27_109
    | ~ spl27_134 ),
    inference(avatar_split_clause,[],[f1192,f1110,f884,f270,f1671]) ).

fof(f1671,plain,
    ( spl27_206
  <=> sK18 = relation_dom(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_206])]) ).

fof(f270,plain,
    ( spl27_7
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).

fof(f884,plain,
    ( spl27_109
  <=> empty_set = sK18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_109])]) ).

fof(f1110,plain,
    ( spl27_134
  <=> ! [X0] :
        ( relation_dom(X0) = sK18
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_134])]) ).

fof(f1192,plain,
    ( sK18 = relation_dom(sK18)
    | ~ spl27_7
    | ~ spl27_109
    | ~ spl27_134 ),
    inference(forward_demodulation,[],[f1184,f886]) ).

fof(f886,plain,
    ( empty_set = sK18
    | ~ spl27_109 ),
    inference(avatar_component_clause,[],[f884]) ).

fof(f1184,plain,
    ( sK18 = relation_dom(empty_set)
    | ~ spl27_7
    | ~ spl27_134 ),
    inference(resolution,[],[f1111,f272]) ).

fof(f272,plain,
    ( empty(empty_set)
    | ~ spl27_7 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f1111,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_dom(X0) = sK18 )
    | ~ spl27_134 ),
    inference(avatar_component_clause,[],[f1110]) ).

fof(f1665,plain,
    ( ~ spl27_165
    | ~ spl27_147
    | spl27_201 ),
    inference(avatar_split_clause,[],[f1637,f1629,f1164,f1359]) ).

fof(f1359,plain,
    ( spl27_165
  <=> sP1(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_165])]) ).

fof(f1164,plain,
    ( spl27_147
  <=> ! [X0] :
        ( sP0(X0,relation_rng(X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_147])]) ).

fof(f1629,plain,
    ( spl27_201
  <=> sP0(sK6,relation_rng(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_201])]) ).

fof(f1637,plain,
    ( ~ sP1(sK6)
    | ~ spl27_147
    | spl27_201 ),
    inference(resolution,[],[f1631,f1165]) ).

fof(f1165,plain,
    ( ! [X0] :
        ( sP0(X0,relation_rng(X0))
        | ~ sP1(X0) )
    | ~ spl27_147 ),
    inference(avatar_component_clause,[],[f1164]) ).

fof(f1631,plain,
    ( ~ sP0(sK6,relation_rng(sK6))
    | spl27_201 ),
    inference(avatar_component_clause,[],[f1629]) ).

fof(f1664,plain,
    ( spl27_205
    | ~ spl27_7
    | ~ spl27_109
    | ~ spl27_133 ),
    inference(avatar_split_clause,[],[f1179,f1106,f884,f270,f1661]) ).

fof(f1661,plain,
    ( spl27_205
  <=> sK18 = relation_rng(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_205])]) ).

fof(f1106,plain,
    ( spl27_133
  <=> ! [X0] :
        ( relation_rng(X0) = sK18
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_133])]) ).

fof(f1179,plain,
    ( sK18 = relation_rng(sK18)
    | ~ spl27_7
    | ~ spl27_109
    | ~ spl27_133 ),
    inference(forward_demodulation,[],[f1171,f886]) ).

fof(f1171,plain,
    ( sK18 = relation_rng(empty_set)
    | ~ spl27_7
    | ~ spl27_133 ),
    inference(resolution,[],[f1107,f272]) ).

fof(f1107,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_rng(X0) = sK18 )
    | ~ spl27_133 ),
    inference(avatar_component_clause,[],[f1106]) ).

fof(f1659,plain,
    ( spl27_204
    | ~ spl27_51
    | ~ spl27_124 ),
    inference(avatar_split_clause,[],[f976,f973,f486,f1657]) ).

fof(f1657,plain,
    ( spl27_204
  <=> ! [X0] : element(sK18,powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_204])]) ).

fof(f486,plain,
    ( spl27_51
  <=> ! [X0] : element(sK12(X0),powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_51])]) ).

fof(f973,plain,
    ( spl27_124
  <=> ! [X0] : sK12(X0) = sK18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_124])]) ).

fof(f976,plain,
    ( ! [X0] : element(sK18,powerset(X0))
    | ~ spl27_51
    | ~ spl27_124 ),
    inference(superposition,[],[f487,f974]) ).

fof(f974,plain,
    ( ! [X0] : sK12(X0) = sK18
    | ~ spl27_124 ),
    inference(avatar_component_clause,[],[f973]) ).

fof(f487,plain,
    ( ! [X0] : element(sK12(X0),powerset(X0))
    | ~ spl27_51 ),
    inference(avatar_component_clause,[],[f486]) ).

fof(f1644,plain,
    ( spl27_117
    | ~ spl27_4
    | spl27_203
    | ~ spl27_93
    | ~ spl27_97 ),
    inference(avatar_split_clause,[],[f858,f823,f796,f1641,f255,f939]) ).

fof(f939,plain,
    ( spl27_117
  <=> sK4 = sK18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_117])]) ).

fof(f255,plain,
    ( spl27_4
  <=> quasi_total(sK6,sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).

fof(f796,plain,
    ( spl27_93
  <=> sP2(sK3,sK6,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_93])]) ).

fof(f823,plain,
    ( spl27_97
  <=> ! [X2,X0,X1] :
        ( sK18 = X2
        | relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_97])]) ).

fof(f858,plain,
    ( sK3 = relation_dom_as_subset(sK3,sK4,sK6)
    | ~ quasi_total(sK6,sK3,sK4)
    | sK4 = sK18
    | ~ spl27_93
    | ~ spl27_97 ),
    inference(resolution,[],[f798,f824]) ).

fof(f824,plain,
    ( ! [X2,X0,X1] :
        ( ~ sP2(X0,X1,X2)
        | relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | sK18 = X2 )
    | ~ spl27_97 ),
    inference(avatar_component_clause,[],[f823]) ).

fof(f798,plain,
    ( sP2(sK3,sK6,sK4)
    | ~ spl27_93 ),
    inference(avatar_component_clause,[],[f796]) ).

fof(f1636,plain,
    ( ~ spl27_201
    | ~ spl27_202
    | spl27_6
    | ~ spl27_183 ),
    inference(avatar_split_clause,[],[f1495,f1477,f265,f1633,f1629]) ).

fof(f265,plain,
    ( spl27_6
  <=> in(apply(sK6,sK5),relation_rng(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).

fof(f1477,plain,
    ( spl27_183
  <=> ! [X2,X0,X1] :
        ( in(apply(X0,X1),X2)
        | ~ in(X1,relation_dom(X0))
        | ~ sP0(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_183])]) ).

fof(f1495,plain,
    ( ~ in(sK5,relation_dom(sK6))
    | ~ sP0(sK6,relation_rng(sK6))
    | spl27_6
    | ~ spl27_183 ),
    inference(resolution,[],[f1478,f267]) ).

fof(f267,plain,
    ( ~ in(apply(sK6,sK5),relation_rng(sK6))
    | spl27_6 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f1478,plain,
    ( ! [X2,X0,X1] :
        ( in(apply(X0,X1),X2)
        | ~ in(X1,relation_dom(X0))
        | ~ sP0(X0,X2) )
    | ~ spl27_183 ),
    inference(avatar_component_clause,[],[f1477]) ).

fof(f1627,plain,
    ( spl27_200
    | ~ spl27_5
    | ~ spl27_181 ),
    inference(avatar_split_clause,[],[f1482,f1469,f260,f1625]) ).

fof(f1625,plain,
    ( spl27_200
  <=> ! [X0] :
        ( ~ in(X0,sK6)
        | element(X0,cartesian_product2(sK3,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_200])]) ).

fof(f260,plain,
    ( spl27_5
  <=> relation_of2_as_subset(sK6,sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).

fof(f1469,plain,
    ( spl27_181
  <=> ! [X5,X4,X6,X3] :
        ( element(X3,cartesian_product2(X4,X5))
        | ~ in(X3,X6)
        | ~ relation_of2_as_subset(X6,X4,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_181])]) ).

fof(f1482,plain,
    ( ! [X0] :
        ( ~ in(X0,sK6)
        | element(X0,cartesian_product2(sK3,sK4)) )
    | ~ spl27_5
    | ~ spl27_181 ),
    inference(resolution,[],[f1470,f262]) ).

fof(f262,plain,
    ( relation_of2_as_subset(sK6,sK3,sK4)
    | ~ spl27_5 ),
    inference(avatar_component_clause,[],[f260]) ).

fof(f1470,plain,
    ( ! [X3,X6,X4,X5] :
        ( ~ relation_of2_as_subset(X6,X4,X5)
        | ~ in(X3,X6)
        | element(X3,cartesian_product2(X4,X5)) )
    | ~ spl27_181 ),
    inference(avatar_component_clause,[],[f1469]) ).

fof(f1617,plain,
    ( spl27_199
    | ~ spl27_55
    | ~ spl27_89 ),
    inference(avatar_split_clause,[],[f820,f777,f522,f1615]) ).

fof(f1615,plain,
    ( spl27_199
  <=> ! [X2,X3] :
        ( sK8(X2,X3) = apply(X2,sK9(X2,X3))
        | sP0(X2,X3)
        | ~ in(X3,sK8(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_199])]) ).

fof(f777,plain,
    ( spl27_89
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | sK8(X0,X1) = apply(X0,sK9(X0,X1))
        | in(sK8(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_89])]) ).

fof(f820,plain,
    ( ! [X2,X3] :
        ( sK8(X2,X3) = apply(X2,sK9(X2,X3))
        | sP0(X2,X3)
        | ~ in(X3,sK8(X2,X3)) )
    | ~ spl27_55
    | ~ spl27_89 ),
    inference(resolution,[],[f778,f523]) ).

fof(f778,plain,
    ( ! [X0,X1] :
        ( in(sK8(X0,X1),X1)
        | sK8(X0,X1) = apply(X0,sK9(X0,X1))
        | sP0(X0,X1) )
    | ~ spl27_89 ),
    inference(avatar_component_clause,[],[f777]) ).

fof(f1613,plain,
    ( spl27_198
    | ~ spl27_56
    | ~ spl27_89 ),
    inference(avatar_split_clause,[],[f819,f777,f526,f1611]) ).

fof(f1611,plain,
    ( spl27_198
  <=> ! [X0,X1] :
        ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
        | sP0(X0,X1)
        | element(sK8(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_198])]) ).

fof(f526,plain,
    ( spl27_56
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_56])]) ).

fof(f819,plain,
    ( ! [X0,X1] :
        ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
        | sP0(X0,X1)
        | element(sK8(X0,X1),X1) )
    | ~ spl27_56
    | ~ spl27_89 ),
    inference(resolution,[],[f778,f527]) ).

fof(f527,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | element(X0,X1) )
    | ~ spl27_56 ),
    inference(avatar_component_clause,[],[f526]) ).

fof(f1606,plain,
    ( spl27_197
    | ~ spl27_71
    | ~ spl27_81 ),
    inference(avatar_split_clause,[],[f728,f718,f631,f1604]) ).

fof(f1604,plain,
    ( spl27_197
  <=> ! [X11,X12,X10] :
        ( ~ relation_of2_as_subset(X10,X11,X12)
        | empty(powerset(cartesian_product2(X11,X12)))
        | in(X10,powerset(cartesian_product2(X11,X12))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_197])]) ).

fof(f631,plain,
    ( spl27_71
  <=> ! [X0,X1] :
        ( in(X0,X1)
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_71])]) ).

fof(f718,plain,
    ( spl27_81
  <=> ! [X2,X0,X1] :
        ( element(X2,powerset(cartesian_product2(X0,X1)))
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_81])]) ).

fof(f728,plain,
    ( ! [X10,X11,X12] :
        ( ~ relation_of2_as_subset(X10,X11,X12)
        | empty(powerset(cartesian_product2(X11,X12)))
        | in(X10,powerset(cartesian_product2(X11,X12))) )
    | ~ spl27_71
    | ~ spl27_81 ),
    inference(resolution,[],[f719,f632]) ).

fof(f632,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,X1)
        | empty(X1)
        | in(X0,X1) )
    | ~ spl27_71 ),
    inference(avatar_component_clause,[],[f631]) ).

fof(f719,plain,
    ( ! [X2,X0,X1] :
        ( element(X2,powerset(cartesian_product2(X0,X1)))
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_81 ),
    inference(avatar_component_clause,[],[f718]) ).

fof(f1594,plain,
    ( spl27_195
    | ~ spl27_196
    | ~ spl27_5
    | ~ spl27_171 ),
    inference(avatar_split_clause,[],[f1424,f1397,f260,f1591,f1588]) ).

fof(f1588,plain,
    ( spl27_195
  <=> ! [X0] : ~ in(X0,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_195])]) ).

fof(f1591,plain,
    ( spl27_196
  <=> empty(cartesian_product2(sK3,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_196])]) ).

fof(f1397,plain,
    ( spl27_171
  <=> ! [X6,X4,X5,X3] :
        ( ~ relation_of2_as_subset(X3,X4,X5)
        | ~ empty(cartesian_product2(X4,X5))
        | ~ in(X6,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_171])]) ).

fof(f1424,plain,
    ( ! [X0] :
        ( ~ empty(cartesian_product2(sK3,sK4))
        | ~ in(X0,sK6) )
    | ~ spl27_5
    | ~ spl27_171 ),
    inference(resolution,[],[f1398,f262]) ).

fof(f1398,plain,
    ( ! [X3,X6,X4,X5] :
        ( ~ relation_of2_as_subset(X3,X4,X5)
        | ~ empty(cartesian_product2(X4,X5))
        | ~ in(X6,X3) )
    | ~ spl27_171 ),
    inference(avatar_component_clause,[],[f1397]) ).

fof(f1561,plain,
    ( spl27_194
    | ~ spl27_102 ),
    inference(avatar_split_clause,[],[f853,f843,f1559]) ).

fof(f1559,plain,
    ( spl27_194
  <=> ! [X0,X1] :
        ( sK18 = X0
        | sK18 != X1
        | quasi_total(sK18,X0,X1)
        | ~ relation_of2_as_subset(sK18,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_194])]) ).

fof(f843,plain,
    ( spl27_102
  <=> ! [X2,X0,X1] :
        ( sK18 != X1
        | sK18 = X0
        | sK18 != X2
        | quasi_total(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_102])]) ).

fof(f853,plain,
    ( ! [X0,X1] :
        ( sK18 = X0
        | sK18 != X1
        | quasi_total(sK18,X0,X1)
        | ~ relation_of2_as_subset(sK18,X0,X1) )
    | ~ spl27_102 ),
    inference(equality_resolution,[],[f844]) ).

fof(f844,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X2
        | sK18 = X0
        | sK18 != X1
        | quasi_total(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_102 ),
    inference(avatar_component_clause,[],[f843]) ).

fof(f1557,plain,
    ( spl27_193
    | ~ spl27_101 ),
    inference(avatar_split_clause,[],[f852,f839,f1555]) ).

fof(f1555,plain,
    ( spl27_193
  <=> ! [X0,X1] :
        ( sK18 = X0
        | sK18 = X1
        | ~ quasi_total(X1,X0,sK18)
        | ~ relation_of2_as_subset(X1,X0,sK18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_193])]) ).

fof(f839,plain,
    ( spl27_101
  <=> ! [X2,X0,X1] :
        ( sK18 != X1
        | sK18 = X0
        | sK18 = X2
        | ~ quasi_total(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_101])]) ).

fof(f852,plain,
    ( ! [X0,X1] :
        ( sK18 = X0
        | sK18 = X1
        | ~ quasi_total(X1,X0,sK18)
        | ~ relation_of2_as_subset(X1,X0,sK18) )
    | ~ spl27_101 ),
    inference(equality_resolution,[],[f840]) ).

fof(f840,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X1
        | sK18 = X0
        | sK18 = X2
        | ~ quasi_total(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_101 ),
    inference(avatar_component_clause,[],[f839]) ).

fof(f1553,plain,
    ( spl27_192
    | ~ spl27_98 ),
    inference(avatar_split_clause,[],[f851,f827,f1551]) ).

fof(f1551,plain,
    ( spl27_192
  <=> ! [X0,X1] :
        ( sK18 = relation_dom_as_subset(sK18,X0,X1)
        | ~ quasi_total(X1,sK18,X0)
        | ~ sP2(sK18,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_192])]) ).

fof(f827,plain,
    ( spl27_98
  <=> ! [X2,X0,X1] :
        ( sK18 != X0
        | relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_98])]) ).

fof(f851,plain,
    ( ! [X0,X1] :
        ( sK18 = relation_dom_as_subset(sK18,X0,X1)
        | ~ quasi_total(X1,sK18,X0)
        | ~ sP2(sK18,X1,X0) )
    | ~ spl27_98 ),
    inference(equality_resolution,[],[f828]) ).

fof(f828,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X0
        | relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_98 ),
    inference(avatar_component_clause,[],[f827]) ).

fof(f1549,plain,
    ( spl27_191
    | ~ spl27_52
    | ~ spl27_89 ),
    inference(avatar_split_clause,[],[f821,f777,f490,f1547]) ).

fof(f1547,plain,
    ( spl27_191
  <=> ! [X4,X5] :
        ( sK8(X4,X5) = apply(X4,sK9(X4,X5))
        | sP0(X4,X5)
        | ~ empty(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_191])]) ).

fof(f490,plain,
    ( spl27_52
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_52])]) ).

fof(f821,plain,
    ( ! [X4,X5] :
        ( sK8(X4,X5) = apply(X4,sK9(X4,X5))
        | sP0(X4,X5)
        | ~ empty(X5) )
    | ~ spl27_52
    | ~ spl27_89 ),
    inference(resolution,[],[f778,f491]) ).

fof(f491,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | ~ empty(X1) )
    | ~ spl27_52 ),
    inference(avatar_component_clause,[],[f490]) ).

fof(f1545,plain,
    ( spl27_190
    | ~ spl27_55
    | ~ spl27_87 ),
    inference(avatar_split_clause,[],[f769,f762,f522,f1543]) ).

fof(f1543,plain,
    ( spl27_190
  <=> ! [X2,X3] :
        ( in(sK9(X2,X3),relation_dom(X2))
        | sP0(X2,X3)
        | ~ in(X3,sK8(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_190])]) ).

fof(f762,plain,
    ( spl27_87
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | in(sK9(X0,X1),relation_dom(X0))
        | in(sK8(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_87])]) ).

fof(f769,plain,
    ( ! [X2,X3] :
        ( in(sK9(X2,X3),relation_dom(X2))
        | sP0(X2,X3)
        | ~ in(X3,sK8(X2,X3)) )
    | ~ spl27_55
    | ~ spl27_87 ),
    inference(resolution,[],[f763,f523]) ).

fof(f763,plain,
    ( ! [X0,X1] :
        ( in(sK9(X0,X1),relation_dom(X0))
        | in(sK8(X0,X1),X1)
        | sP0(X0,X1) )
    | ~ spl27_87 ),
    inference(avatar_component_clause,[],[f762]) ).

fof(f1541,plain,
    ( spl27_189
    | ~ spl27_56
    | ~ spl27_87 ),
    inference(avatar_split_clause,[],[f768,f762,f526,f1539]) ).

fof(f1539,plain,
    ( spl27_189
  <=> ! [X0,X1] :
        ( in(sK9(X0,X1),relation_dom(X0))
        | sP0(X0,X1)
        | element(sK8(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_189])]) ).

fof(f768,plain,
    ( ! [X0,X1] :
        ( in(sK9(X0,X1),relation_dom(X0))
        | sP0(X0,X1)
        | element(sK8(X0,X1),X1) )
    | ~ spl27_56
    | ~ spl27_87 ),
    inference(resolution,[],[f763,f527]) ).

fof(f1537,plain,
    ( spl27_188
    | ~ spl27_55
    | ~ spl27_87 ),
    inference(avatar_split_clause,[],[f766,f762,f522,f1535]) ).

fof(f1535,plain,
    ( spl27_188
  <=> ! [X2,X3] :
        ( in(sK8(X2,X3),X3)
        | sP0(X2,X3)
        | ~ in(relation_dom(X2),sK9(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_188])]) ).

fof(f766,plain,
    ( ! [X2,X3] :
        ( in(sK8(X2,X3),X3)
        | sP0(X2,X3)
        | ~ in(relation_dom(X2),sK9(X2,X3)) )
    | ~ spl27_55
    | ~ spl27_87 ),
    inference(resolution,[],[f763,f523]) ).

fof(f1533,plain,
    ( spl27_187
    | ~ spl27_56
    | ~ spl27_87 ),
    inference(avatar_split_clause,[],[f765,f762,f526,f1531]) ).

fof(f1531,plain,
    ( spl27_187
  <=> ! [X0,X1] :
        ( in(sK8(X0,X1),X1)
        | sP0(X0,X1)
        | element(sK9(X0,X1),relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_187])]) ).

fof(f765,plain,
    ( ! [X0,X1] :
        ( in(sK8(X0,X1),X1)
        | sP0(X0,X1)
        | element(sK9(X0,X1),relation_dom(X0)) )
    | ~ spl27_56
    | ~ spl27_87 ),
    inference(resolution,[],[f763,f527]) ).

fof(f1529,plain,
    ( spl27_186
    | ~ spl27_71
    | ~ spl27_84 ),
    inference(avatar_split_clause,[],[f751,f741,f631,f1527]) ).

fof(f1527,plain,
    ( spl27_186
  <=> ! [X16,X17,X15] :
        ( ~ relation_of2(X15,X16,X17)
        | empty(powerset(X16))
        | in(relation_dom_as_subset(X16,X17,X15),powerset(X16)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_186])]) ).

fof(f741,plain,
    ( spl27_84
  <=> ! [X2,X0,X1] :
        ( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
        | ~ relation_of2(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_84])]) ).

fof(f751,plain,
    ( ! [X16,X17,X15] :
        ( ~ relation_of2(X15,X16,X17)
        | empty(powerset(X16))
        | in(relation_dom_as_subset(X16,X17,X15),powerset(X16)) )
    | ~ spl27_71
    | ~ spl27_84 ),
    inference(resolution,[],[f742,f632]) ).

fof(f742,plain,
    ( ! [X2,X0,X1] :
        ( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
        | ~ relation_of2(X2,X0,X1) )
    | ~ spl27_84 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f1511,plain,
    ( spl27_185
    | ~ spl27_74
    | ~ spl27_84 ),
    inference(avatar_split_clause,[],[f750,f741,f643,f1509]) ).

fof(f1509,plain,
    ( spl27_185
  <=> ! [X11,X13,X14,X12] :
        ( ~ relation_of2(X11,cartesian_product2(X12,X13),X14)
        | relation(relation_dom_as_subset(cartesian_product2(X12,X13),X14,X11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_185])]) ).

fof(f643,plain,
    ( spl27_74
  <=> ! [X2,X0,X1] :
        ( relation(X2)
        | ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_74])]) ).

fof(f750,plain,
    ( ! [X11,X14,X12,X13] :
        ( ~ relation_of2(X11,cartesian_product2(X12,X13),X14)
        | relation(relation_dom_as_subset(cartesian_product2(X12,X13),X14,X11)) )
    | ~ spl27_74
    | ~ spl27_84 ),
    inference(resolution,[],[f742,f644]) ).

fof(f644,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X2,powerset(cartesian_product2(X0,X1)))
        | relation(X2) )
    | ~ spl27_74 ),
    inference(avatar_component_clause,[],[f643]) ).

fof(f1507,plain,
    ( spl27_184
    | ~ spl27_82
    | ~ spl27_84 ),
    inference(avatar_split_clause,[],[f747,f741,f722,f1505]) ).

fof(f1505,plain,
    ( spl27_184
  <=> ! [X0,X3,X2,X1] :
        ( ~ relation_of2(X0,X1,X2)
        | element(X3,X1)
        | ~ in(X3,relation_dom_as_subset(X1,X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_184])]) ).

fof(f722,plain,
    ( spl27_82
  <=> ! [X2,X0,X1] :
        ( element(X0,X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_82])]) ).

fof(f747,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ relation_of2(X0,X1,X2)
        | element(X3,X1)
        | ~ in(X3,relation_dom_as_subset(X1,X2,X0)) )
    | ~ spl27_82
    | ~ spl27_84 ),
    inference(resolution,[],[f742,f723]) ).

fof(f723,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | element(X0,X2)
        | ~ in(X0,X1) )
    | ~ spl27_82 ),
    inference(avatar_component_clause,[],[f722]) ).

fof(f1479,plain,
    ( spl27_183
    | ~ spl27_88 ),
    inference(avatar_split_clause,[],[f775,f772,f1477]) ).

fof(f772,plain,
    ( spl27_88
  <=> ! [X5,X0,X6,X1] :
        ( in(X5,X1)
        | apply(X0,X6) != X5
        | ~ in(X6,relation_dom(X0))
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_88])]) ).

fof(f775,plain,
    ( ! [X2,X0,X1] :
        ( in(apply(X0,X1),X2)
        | ~ in(X1,relation_dom(X0))
        | ~ sP0(X0,X2) )
    | ~ spl27_88 ),
    inference(equality_resolution,[],[f773]) ).

fof(f773,plain,
    ( ! [X0,X1,X6,X5] :
        ( apply(X0,X6) != X5
        | in(X5,X1)
        | ~ in(X6,relation_dom(X0))
        | ~ sP0(X0,X1) )
    | ~ spl27_88 ),
    inference(avatar_component_clause,[],[f772]) ).

fof(f1475,plain,
    ( spl27_182
    | ~ spl27_80
    | ~ spl27_84 ),
    inference(avatar_split_clause,[],[f748,f741,f707,f1473]) ).

fof(f1473,plain,
    ( spl27_182
  <=> ! [X6,X4,X5,X7] :
        ( ~ relation_of2(X4,X5,X6)
        | ~ empty(X5)
        | ~ in(X7,relation_dom_as_subset(X5,X6,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_182])]) ).

fof(f707,plain,
    ( spl27_80
  <=> ! [X2,X0,X1] :
        ( ~ empty(X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_80])]) ).

fof(f748,plain,
    ( ! [X6,X7,X4,X5] :
        ( ~ relation_of2(X4,X5,X6)
        | ~ empty(X5)
        | ~ in(X7,relation_dom_as_subset(X5,X6,X4)) )
    | ~ spl27_80
    | ~ spl27_84 ),
    inference(resolution,[],[f742,f708]) ).

fof(f708,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | ~ empty(X2)
        | ~ in(X0,X1) )
    | ~ spl27_80 ),
    inference(avatar_component_clause,[],[f707]) ).

fof(f1471,plain,
    ( spl27_181
    | ~ spl27_81
    | ~ spl27_82 ),
    inference(avatar_split_clause,[],[f730,f722,f718,f1469]) ).

fof(f730,plain,
    ( ! [X3,X6,X4,X5] :
        ( element(X3,cartesian_product2(X4,X5))
        | ~ in(X3,X6)
        | ~ relation_of2_as_subset(X6,X4,X5) )
    | ~ spl27_81
    | ~ spl27_82 ),
    inference(resolution,[],[f723,f719]) ).

fof(f1467,plain,
    ( spl27_180
    | ~ spl27_41
    | ~ spl27_70 ),
    inference(avatar_split_clause,[],[f658,f627,f432,f1465]) ).

fof(f1465,plain,
    ( spl27_180
  <=> ! [X4,X5] :
        ( ~ function(sK16(X4,X5))
        | ~ empty(sK16(X4,X5))
        | one_to_one(sK16(X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_180])]) ).

fof(f432,plain,
    ( spl27_41
  <=> ! [X0,X1] : relation(sK16(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_41])]) ).

fof(f627,plain,
    ( spl27_70
  <=> ! [X0] :
        ( one_to_one(X0)
        | ~ function(X0)
        | ~ empty(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_70])]) ).

fof(f658,plain,
    ( ! [X4,X5] :
        ( ~ function(sK16(X4,X5))
        | ~ empty(sK16(X4,X5))
        | one_to_one(sK16(X4,X5)) )
    | ~ spl27_41
    | ~ spl27_70 ),
    inference(resolution,[],[f628,f433]) ).

fof(f433,plain,
    ( ! [X0,X1] : relation(sK16(X0,X1))
    | ~ spl27_41 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f628,plain,
    ( ! [X0] :
        ( ~ relation(X0)
        | ~ function(X0)
        | ~ empty(X0)
        | one_to_one(X0) )
    | ~ spl27_70 ),
    inference(avatar_component_clause,[],[f627]) ).

fof(f1463,plain,
    ( spl27_179
    | ~ spl27_39
    | ~ spl27_70 ),
    inference(avatar_split_clause,[],[f657,f627,f424,f1461]) ).

fof(f1461,plain,
    ( spl27_179
  <=> ! [X2,X3] :
        ( ~ function(sK15(X2,X3))
        | ~ empty(sK15(X2,X3))
        | one_to_one(sK15(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_179])]) ).

fof(f424,plain,
    ( spl27_39
  <=> ! [X0,X1] : relation(sK15(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_39])]) ).

fof(f657,plain,
    ( ! [X2,X3] :
        ( ~ function(sK15(X2,X3))
        | ~ empty(sK15(X2,X3))
        | one_to_one(sK15(X2,X3)) )
    | ~ spl27_39
    | ~ spl27_70 ),
    inference(resolution,[],[f628,f425]) ).

fof(f425,plain,
    ( ! [X0,X1] : relation(sK15(X0,X1))
    | ~ spl27_39 ),
    inference(avatar_component_clause,[],[f424]) ).

fof(f1445,plain,
    ( spl27_177
    | ~ spl27_178
    | ~ spl27_1
    | ~ spl27_70
    | ~ spl27_155 ),
    inference(avatar_split_clause,[],[f1305,f1256,f627,f240,f1442,f1438]) ).

fof(f1438,plain,
    ( spl27_177
  <=> one_to_one(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_177])]) ).

fof(f1442,plain,
    ( spl27_178
  <=> empty(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_178])]) ).

fof(f240,plain,
    ( spl27_1
  <=> function(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).

fof(f1256,plain,
    ( spl27_155
  <=> relation(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_155])]) ).

fof(f1305,plain,
    ( ~ function(sK6)
    | ~ empty(sK6)
    | one_to_one(sK6)
    | ~ spl27_70
    | ~ spl27_155 ),
    inference(resolution,[],[f1258,f628]) ).

fof(f1258,plain,
    ( relation(sK6)
    | ~ spl27_155 ),
    inference(avatar_component_clause,[],[f1256]) ).

fof(f1419,plain,
    ( spl27_176
    | ~ spl27_52
    | ~ spl27_87 ),
    inference(avatar_split_clause,[],[f770,f762,f490,f1417]) ).

fof(f1417,plain,
    ( spl27_176
  <=> ! [X4,X5] :
        ( in(sK9(X4,X5),relation_dom(X4))
        | sP0(X4,X5)
        | ~ empty(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_176])]) ).

fof(f770,plain,
    ( ! [X4,X5] :
        ( in(sK9(X4,X5),relation_dom(X4))
        | sP0(X4,X5)
        | ~ empty(X5) )
    | ~ spl27_52
    | ~ spl27_87 ),
    inference(resolution,[],[f763,f491]) ).

fof(f1415,plain,
    ( spl27_175
    | ~ spl27_52
    | ~ spl27_87 ),
    inference(avatar_split_clause,[],[f767,f762,f490,f1413]) ).

fof(f767,plain,
    ( ! [X4,X5] :
        ( in(sK8(X4,X5),X5)
        | sP0(X4,X5)
        | ~ empty(relation_dom(X4)) )
    | ~ spl27_52
    | ~ spl27_87 ),
    inference(resolution,[],[f763,f491]) ).

fof(f1411,plain,
    ( spl27_174
    | ~ spl27_60
    | ~ spl27_83 ),
    inference(avatar_split_clause,[],[f746,f737,f542,f1409]) ).

fof(f1409,plain,
    ( spl27_174
  <=> ! [X4,X5] : relation_dom_as_subset(X4,X5,sK16(X4,X5)) = relation_dom(sK16(X4,X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_174])]) ).

fof(f542,plain,
    ( spl27_60
  <=> ! [X0,X1] : relation_of2(sK16(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_60])]) ).

fof(f737,plain,
    ( spl27_83
  <=> ! [X2,X0,X1] :
        ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
        | ~ relation_of2(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_83])]) ).

fof(f746,plain,
    ( ! [X4,X5] : relation_dom_as_subset(X4,X5,sK16(X4,X5)) = relation_dom(sK16(X4,X5))
    | ~ spl27_60
    | ~ spl27_83 ),
    inference(resolution,[],[f738,f543]) ).

fof(f543,plain,
    ( ! [X0,X1] : relation_of2(sK16(X0,X1),X0,X1)
    | ~ spl27_60 ),
    inference(avatar_component_clause,[],[f542]) ).

fof(f738,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation_of2(X2,X0,X1)
        | relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) )
    | ~ spl27_83 ),
    inference(avatar_component_clause,[],[f737]) ).

fof(f1407,plain,
    ( spl27_173
    | ~ spl27_59
    | ~ spl27_83 ),
    inference(avatar_split_clause,[],[f745,f737,f538,f1405]) ).

fof(f1405,plain,
    ( spl27_173
  <=> ! [X2,X3] : relation_dom_as_subset(X2,X3,sK15(X2,X3)) = relation_dom(sK15(X2,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_173])]) ).

fof(f538,plain,
    ( spl27_59
  <=> ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_59])]) ).

fof(f745,plain,
    ( ! [X2,X3] : relation_dom_as_subset(X2,X3,sK15(X2,X3)) = relation_dom(sK15(X2,X3))
    | ~ spl27_59
    | ~ spl27_83 ),
    inference(resolution,[],[f738,f539]) ).

fof(f539,plain,
    ( ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1)
    | ~ spl27_59 ),
    inference(avatar_component_clause,[],[f538]) ).

fof(f1403,plain,
    ( spl27_172
    | ~ spl27_58
    | ~ spl27_83 ),
    inference(avatar_split_clause,[],[f744,f737,f534,f1401]) ).

fof(f1401,plain,
    ( spl27_172
  <=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK14(X0,X1)) = relation_dom(sK14(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_172])]) ).

fof(f534,plain,
    ( spl27_58
  <=> ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_58])]) ).

fof(f744,plain,
    ( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK14(X0,X1)) = relation_dom(sK14(X0,X1))
    | ~ spl27_58
    | ~ spl27_83 ),
    inference(resolution,[],[f738,f535]) ).

fof(f535,plain,
    ( ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1)
    | ~ spl27_58 ),
    inference(avatar_component_clause,[],[f534]) ).

fof(f1399,plain,
    ( spl27_171
    | ~ spl27_80
    | ~ spl27_81 ),
    inference(avatar_split_clause,[],[f726,f718,f707,f1397]) ).

fof(f726,plain,
    ( ! [X3,X6,X4,X5] :
        ( ~ relation_of2_as_subset(X3,X4,X5)
        | ~ empty(cartesian_product2(X4,X5))
        | ~ in(X6,X3) )
    | ~ spl27_80
    | ~ spl27_81 ),
    inference(resolution,[],[f719,f708]) ).

fof(f1395,plain,
    ( spl27_170
    | ~ spl27_50
    | ~ spl27_70 ),
    inference(avatar_split_clause,[],[f656,f627,f482,f1393]) ).

fof(f1393,plain,
    ( spl27_170
  <=> ! [X1] :
        ( ~ function(relation_dom(X1))
        | ~ empty(relation_dom(X1))
        | one_to_one(relation_dom(X1))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_170])]) ).

fof(f482,plain,
    ( spl27_50
  <=> ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_50])]) ).

fof(f656,plain,
    ( ! [X1] :
        ( ~ function(relation_dom(X1))
        | ~ empty(relation_dom(X1))
        | one_to_one(relation_dom(X1))
        | ~ empty(X1) )
    | ~ spl27_50
    | ~ spl27_70 ),
    inference(resolution,[],[f628,f483]) ).

fof(f483,plain,
    ( ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl27_50 ),
    inference(avatar_component_clause,[],[f482]) ).

fof(f1391,plain,
    ( spl27_169
    | ~ spl27_47
    | ~ spl27_70 ),
    inference(avatar_split_clause,[],[f655,f627,f469,f1389]) ).

fof(f1389,plain,
    ( spl27_169
  <=> ! [X0] :
        ( ~ function(relation_rng(X0))
        | ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_169])]) ).

fof(f469,plain,
    ( spl27_47
  <=> ! [X0] :
        ( relation(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_47])]) ).

fof(f655,plain,
    ( ! [X0] :
        ( ~ function(relation_rng(X0))
        | ~ empty(relation_rng(X0))
        | one_to_one(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl27_47
    | ~ spl27_70 ),
    inference(resolution,[],[f628,f470]) ).

fof(f470,plain,
    ( ! [X0] :
        ( relation(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl27_47 ),
    inference(avatar_component_clause,[],[f469]) ).

fof(f1377,plain,
    ( spl27_168
    | ~ spl27_66
    | ~ spl27_84 ),
    inference(avatar_split_clause,[],[f749,f741,f590,f1375]) ).

fof(f1375,plain,
    ( spl27_168
  <=> ! [X9,X8,X10] :
        ( ~ relation_of2(X8,X9,X10)
        | subset(relation_dom_as_subset(X9,X10,X8),X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_168])]) ).

fof(f590,plain,
    ( spl27_66
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_66])]) ).

fof(f749,plain,
    ( ! [X10,X8,X9] :
        ( ~ relation_of2(X8,X9,X10)
        | subset(relation_dom_as_subset(X9,X10,X8),X9) )
    | ~ spl27_66
    | ~ spl27_84 ),
    inference(resolution,[],[f742,f591]) ).

fof(f591,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,powerset(X1))
        | subset(X0,X1) )
    | ~ spl27_66 ),
    inference(avatar_component_clause,[],[f590]) ).

fof(f1373,plain,
    ( spl27_167
    | ~ spl27_63
    | ~ spl27_71 ),
    inference(avatar_split_clause,[],[f677,f631,f578,f1371]) ).

fof(f1371,plain,
    ( spl27_167
  <=> ! [X2] :
        ( empty(powerset(X2))
        | in(sK7(X2),powerset(X2))
        | empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_167])]) ).

fof(f578,plain,
    ( spl27_63
  <=> ! [X0] :
        ( element(sK7(X0),powerset(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_63])]) ).

fof(f677,plain,
    ( ! [X2] :
        ( empty(powerset(X2))
        | in(sK7(X2),powerset(X2))
        | empty(X2) )
    | ~ spl27_63
    | ~ spl27_71 ),
    inference(resolution,[],[f632,f579]) ).

fof(f579,plain,
    ( ! [X0] :
        ( element(sK7(X0),powerset(X0))
        | empty(X0) )
    | ~ spl27_63 ),
    inference(avatar_component_clause,[],[f578]) ).

fof(f1369,plain,
    ( spl27_166
    | ~ spl27_67
    | ~ spl27_71 ),
    inference(avatar_split_clause,[],[f676,f631,f594,f1367]) ).

fof(f1367,plain,
    ( spl27_166
  <=> ! [X0,X1] :
        ( empty(powerset(X0))
        | in(X1,powerset(X0))
        | ~ subset(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_166])]) ).

fof(f594,plain,
    ( spl27_67
  <=> ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_67])]) ).

fof(f676,plain,
    ( ! [X0,X1] :
        ( empty(powerset(X0))
        | in(X1,powerset(X0))
        | ~ subset(X1,X0) )
    | ~ spl27_67
    | ~ spl27_71 ),
    inference(resolution,[],[f632,f595]) ).

fof(f595,plain,
    ( ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
    | ~ spl27_67 ),
    inference(avatar_component_clause,[],[f594]) ).

fof(f1362,plain,
    ( spl27_165
    | ~ spl27_1
    | ~ spl27_54
    | ~ spl27_155 ),
    inference(avatar_split_clause,[],[f1306,f1256,f518,f240,f1359]) ).

fof(f518,plain,
    ( spl27_54
  <=> ! [X0] :
        ( sP1(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_54])]) ).

fof(f1306,plain,
    ( ~ function(sK6)
    | sP1(sK6)
    | ~ spl27_54
    | ~ spl27_155 ),
    inference(resolution,[],[f1258,f519]) ).

fof(f519,plain,
    ( ! [X0] :
        ( ~ relation(X0)
        | ~ function(X0)
        | sP1(X0) )
    | ~ spl27_54 ),
    inference(avatar_component_clause,[],[f518]) ).

fof(f1348,plain,
    ( spl27_164
    | ~ spl27_63
    | ~ spl27_82 ),
    inference(avatar_split_clause,[],[f731,f722,f578,f1346]) ).

fof(f1346,plain,
    ( spl27_164
  <=> ! [X8,X7] :
        ( element(X7,X8)
        | ~ in(X7,sK7(X8))
        | empty(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_164])]) ).

fof(f731,plain,
    ( ! [X8,X7] :
        ( element(X7,X8)
        | ~ in(X7,sK7(X8))
        | empty(X8) )
    | ~ spl27_63
    | ~ spl27_82 ),
    inference(resolution,[],[f723,f579]) ).

fof(f1344,plain,
    ( spl27_163
    | ~ spl27_67
    | ~ spl27_82 ),
    inference(avatar_split_clause,[],[f729,f722,f594,f1342]) ).

fof(f1342,plain,
    ( spl27_163
  <=> ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_163])]) ).

fof(f729,plain,
    ( ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) )
    | ~ spl27_67
    | ~ spl27_82 ),
    inference(resolution,[],[f723,f595]) ).

fof(f1340,plain,
    ( spl27_162
    | ~ spl27_66
    | ~ spl27_81 ),
    inference(avatar_split_clause,[],[f727,f718,f590,f1338]) ).

fof(f1338,plain,
    ( spl27_162
  <=> ! [X9,X8,X7] :
        ( ~ relation_of2_as_subset(X7,X8,X9)
        | subset(X7,cartesian_product2(X8,X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_162])]) ).

fof(f727,plain,
    ( ! [X8,X9,X7] :
        ( ~ relation_of2_as_subset(X7,X8,X9)
        | subset(X7,cartesian_product2(X8,X9)) )
    | ~ spl27_66
    | ~ spl27_81 ),
    inference(resolution,[],[f719,f591]) ).

fof(f1336,plain,
    ( spl27_161
    | ~ spl27_63
    | ~ spl27_74 ),
    inference(avatar_split_clause,[],[f690,f643,f578,f1334]) ).

fof(f1334,plain,
    ( spl27_161
  <=> ! [X4,X3] :
        ( relation(sK7(cartesian_product2(X3,X4)))
        | empty(cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_161])]) ).

fof(f690,plain,
    ( ! [X3,X4] :
        ( relation(sK7(cartesian_product2(X3,X4)))
        | empty(cartesian_product2(X3,X4)) )
    | ~ spl27_63
    | ~ spl27_74 ),
    inference(resolution,[],[f644,f579]) ).

fof(f1279,plain,
    ( spl27_160
    | ~ spl27_38
    | ~ spl27_82 ),
    inference(avatar_split_clause,[],[f732,f722,f420,f1277]) ).

fof(f1277,plain,
    ( spl27_160
  <=> ! [X9,X10] :
        ( element(X9,X10)
        | ~ in(X9,sK11(powerset(X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_160])]) ).

fof(f420,plain,
    ( spl27_38
  <=> ! [X0] : element(sK11(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_38])]) ).

fof(f732,plain,
    ( ! [X10,X9] :
        ( element(X9,X10)
        | ~ in(X9,sK11(powerset(X10))) )
    | ~ spl27_38
    | ~ spl27_82 ),
    inference(resolution,[],[f723,f421]) ).

fof(f421,plain,
    ( ! [X0] : element(sK11(X0),X0)
    | ~ spl27_38 ),
    inference(avatar_component_clause,[],[f420]) ).

fof(f1275,plain,
    ( spl27_159
    | ~ spl27_67
    | ~ spl27_80 ),
    inference(avatar_split_clause,[],[f711,f707,f594,f1273]) ).

fof(f1273,plain,
    ( spl27_159
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_159])]) ).

fof(f711,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) )
    | ~ spl27_67
    | ~ spl27_80 ),
    inference(resolution,[],[f708,f595]) ).

fof(f1271,plain,
    ( spl27_158
    | ~ spl27_49
    | ~ spl27_68 ),
    inference(avatar_split_clause,[],[f611,f598,f478,f1269]) ).

fof(f1269,plain,
    ( spl27_158
  <=> ! [X4,X3] :
        ( relation_dom(X4) = X3
        | ~ empty(X3)
        | ~ empty(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_158])]) ).

fof(f478,plain,
    ( spl27_49
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_49])]) ).

fof(f598,plain,
    ( spl27_68
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_68])]) ).

fof(f611,plain,
    ( ! [X3,X4] :
        ( relation_dom(X4) = X3
        | ~ empty(X3)
        | ~ empty(X4) )
    | ~ spl27_49
    | ~ spl27_68 ),
    inference(resolution,[],[f599,f479]) ).

fof(f479,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl27_49 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f599,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) )
    | ~ spl27_68 ),
    inference(avatar_component_clause,[],[f598]) ).

fof(f1267,plain,
    ( spl27_157
    | ~ spl27_46
    | ~ spl27_68 ),
    inference(avatar_split_clause,[],[f610,f598,f465,f1265]) ).

fof(f1265,plain,
    ( spl27_157
  <=> ! [X2,X1] :
        ( relation_rng(X2) = X1
        | ~ empty(X1)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_157])]) ).

fof(f465,plain,
    ( spl27_46
  <=> ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_46])]) ).

fof(f610,plain,
    ( ! [X2,X1] :
        ( relation_rng(X2) = X1
        | ~ empty(X1)
        | ~ empty(X2) )
    | ~ spl27_46
    | ~ spl27_68 ),
    inference(resolution,[],[f599,f466]) ).

fof(f466,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl27_46 ),
    inference(avatar_component_clause,[],[f465]) ).

fof(f1263,plain,
    ( spl27_156
    | ~ spl27_41
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f558,f518,f432,f1261]) ).

fof(f558,plain,
    ( ! [X4,X5] :
        ( ~ function(sK16(X4,X5))
        | sP1(sK16(X4,X5)) )
    | ~ spl27_41
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f433]) ).

fof(f1259,plain,
    ( spl27_155
    | ~ spl27_5
    | ~ spl27_148 ),
    inference(avatar_split_clause,[],[f1216,f1168,f260,f1256]) ).

fof(f1216,plain,
    ( relation(sK6)
    | ~ spl27_5
    | ~ spl27_148 ),
    inference(resolution,[],[f1169,f262]) ).

fof(f1254,plain,
    ( spl27_154
    | ~ spl27_39
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f557,f518,f424,f1252]) ).

fof(f557,plain,
    ( ! [X2,X3] :
        ( ~ function(sK15(X2,X3))
        | sP1(sK15(X2,X3)) )
    | ~ spl27_39
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f425]) ).

fof(f1250,plain,
    ( spl27_153
    | ~ spl27_50
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f556,f518,f482,f1248]) ).

fof(f556,plain,
    ( ! [X1] :
        ( ~ function(relation_dom(X1))
        | sP1(relation_dom(X1))
        | ~ empty(X1) )
    | ~ spl27_50
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f483]) ).

fof(f1246,plain,
    ( spl27_152
    | ~ spl27_47
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f555,f518,f469,f1244]) ).

fof(f555,plain,
    ( ! [X0] :
        ( ~ function(relation_rng(X0))
        | sP1(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl27_47
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f470]) ).

fof(f1232,plain,
    ( spl27_151
    | ~ spl27_38
    | ~ spl27_80 ),
    inference(avatar_split_clause,[],[f713,f707,f420,f1230]) ).

fof(f713,plain,
    ( ! [X6,X5] :
        ( ~ empty(X5)
        | ~ in(X6,sK11(powerset(X5))) )
    | ~ spl27_38
    | ~ spl27_80 ),
    inference(resolution,[],[f708,f421]) ).

fof(f1228,plain,
    ( spl27_150
    | ~ spl27_67
    | ~ spl27_74 ),
    inference(avatar_split_clause,[],[f689,f643,f594,f1226]) ).

fof(f689,plain,
    ( ! [X2,X0,X1] :
        ( relation(X0)
        | ~ subset(X0,cartesian_product2(X1,X2)) )
    | ~ spl27_67
    | ~ spl27_74 ),
    inference(resolution,[],[f644,f595]) ).

fof(f1224,plain,
    ( spl27_149
    | ~ spl27_11
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_71 ),
    inference(avatar_split_clause,[],[f681,f631,f486,f461,f404,f290,f1222]) ).

fof(f1222,plain,
    ( spl27_149
  <=> ! [X4] :
        ( in(sK18,powerset(X4))
        | empty(powerset(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_149])]) ).

fof(f290,plain,
    ( spl27_11
  <=> empty(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).

fof(f404,plain,
    ( spl27_34
  <=> ! [X0] : empty(sK12(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).

fof(f461,plain,
    ( spl27_45
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_45])]) ).

fof(f681,plain,
    ( ! [X4] :
        ( in(sK18,powerset(X4))
        | empty(powerset(X4)) )
    | ~ spl27_11
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_71 ),
    inference(forward_demodulation,[],[f680,f495]) ).

fof(f495,plain,
    ( empty_set = sK18
    | ~ spl27_11
    | ~ spl27_45 ),
    inference(resolution,[],[f462,f292]) ).

fof(f292,plain,
    ( empty(sK18)
    | ~ spl27_11 ),
    inference(avatar_component_clause,[],[f290]) ).

fof(f462,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = X0 )
    | ~ spl27_45 ),
    inference(avatar_component_clause,[],[f461]) ).

fof(f680,plain,
    ( ! [X4] :
        ( in(empty_set,powerset(X4))
        | empty(powerset(X4)) )
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_71 ),
    inference(forward_demodulation,[],[f679,f494]) ).

fof(f494,plain,
    ( ! [X0] : empty_set = sK12(X0)
    | ~ spl27_34
    | ~ spl27_45 ),
    inference(resolution,[],[f462,f405]) ).

fof(f405,plain,
    ( ! [X0] : empty(sK12(X0))
    | ~ spl27_34 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f679,plain,
    ( ! [X4] :
        ( empty(powerset(X4))
        | in(sK12(X4),powerset(X4)) )
    | ~ spl27_51
    | ~ spl27_71 ),
    inference(resolution,[],[f632,f487]) ).

fof(f1170,plain,
    ( spl27_148
    | ~ spl27_74
    | ~ spl27_81 ),
    inference(avatar_split_clause,[],[f725,f718,f643,f1168]) ).

fof(f725,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation_of2_as_subset(X0,X1,X2)
        | relation(X0) )
    | ~ spl27_74
    | ~ spl27_81 ),
    inference(resolution,[],[f719,f644]) ).

fof(f1166,plain,
    ( spl27_147
    | ~ spl27_78 ),
    inference(avatar_split_clause,[],[f710,f699,f1164]) ).

fof(f699,plain,
    ( spl27_78
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | relation_rng(X0) != X1
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_78])]) ).

fof(f710,plain,
    ( ! [X0] :
        ( sP0(X0,relation_rng(X0))
        | ~ sP1(X0) )
    | ~ spl27_78 ),
    inference(equality_resolution,[],[f700]) ).

fof(f700,plain,
    ( ! [X0,X1] :
        ( relation_rng(X0) != X1
        | sP0(X0,X1)
        | ~ sP1(X0) )
    | ~ spl27_78 ),
    inference(avatar_component_clause,[],[f699]) ).

fof(f1162,plain,
    ( spl27_146
    | ~ spl27_60
    | ~ spl27_76 ),
    inference(avatar_split_clause,[],[f697,f651,f542,f1160]) ).

fof(f651,plain,
    ( spl27_76
  <=> ! [X2,X0,X1] :
        ( relation_of2_as_subset(X2,X0,X1)
        | ~ relation_of2(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_76])]) ).

fof(f697,plain,
    ( ! [X4,X5] : relation_of2_as_subset(sK16(X4,X5),X4,X5)
    | ~ spl27_60
    | ~ spl27_76 ),
    inference(resolution,[],[f652,f543]) ).

fof(f652,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation_of2(X2,X0,X1)
        | relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_76 ),
    inference(avatar_component_clause,[],[f651]) ).

fof(f1158,plain,
    ( spl27_145
    | ~ spl27_59
    | ~ spl27_76 ),
    inference(avatar_split_clause,[],[f696,f651,f538,f1156]) ).

fof(f696,plain,
    ( ! [X2,X3] : relation_of2_as_subset(sK15(X2,X3),X2,X3)
    | ~ spl27_59
    | ~ spl27_76 ),
    inference(resolution,[],[f652,f539]) ).

fof(f1154,plain,
    ( spl27_144
    | ~ spl27_58
    | ~ spl27_76 ),
    inference(avatar_split_clause,[],[f695,f651,f534,f1152]) ).

fof(f695,plain,
    ( ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1)
    | ~ spl27_58
    | ~ spl27_76 ),
    inference(resolution,[],[f652,f535]) ).

fof(f1150,plain,
    ( spl27_143
    | ~ spl27_57
    | ~ spl27_75 ),
    inference(avatar_split_clause,[],[f694,f647,f530,f1148]) ).

fof(f1148,plain,
    ( spl27_143
  <=> ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_143])]) ).

fof(f647,plain,
    ( spl27_75
  <=> ! [X2,X0,X1] :
        ( relation_of2(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_75])]) ).

fof(f694,plain,
    ( ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1)
    | ~ spl27_57
    | ~ spl27_75 ),
    inference(resolution,[],[f648,f531]) ).

fof(f648,plain,
    ( ! [X2,X0,X1] :
        ( ~ relation_of2_as_subset(X2,X0,X1)
        | relation_of2(X2,X0,X1) )
    | ~ spl27_75 ),
    inference(avatar_component_clause,[],[f647]) ).

fof(f1146,plain,
    ( spl27_142
    | ~ spl27_38
    | ~ spl27_74 ),
    inference(avatar_split_clause,[],[f691,f643,f420,f1144]) ).

fof(f1144,plain,
    ( spl27_142
  <=> ! [X6,X5] : relation(sK11(powerset(cartesian_product2(X5,X6)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_142])]) ).

fof(f691,plain,
    ( ! [X6,X5] : relation(sK11(powerset(cartesian_product2(X5,X6))))
    | ~ spl27_38
    | ~ spl27_74 ),
    inference(resolution,[],[f644,f421]) ).

fof(f1142,plain,
    ( spl27_141
    | ~ spl27_57
    | ~ spl27_73 ),
    inference(avatar_split_clause,[],[f688,f639,f530,f1140]) ).

fof(f1140,plain,
    ( spl27_141
  <=> ! [X0,X1] : sP2(X0,sK13(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_141])]) ).

fof(f688,plain,
    ( ! [X0,X1] : sP2(X0,sK13(X0,X1),X1)
    | ~ spl27_57
    | ~ spl27_73 ),
    inference(resolution,[],[f640,f531]) ).

fof(f1138,plain,
    ( spl27_140
    | ~ spl27_38
    | ~ spl27_71 ),
    inference(avatar_split_clause,[],[f678,f631,f420,f1136]) ).

fof(f678,plain,
    ( ! [X3] :
        ( empty(X3)
        | in(sK11(X3),X3) )
    | ~ spl27_38
    | ~ spl27_71 ),
    inference(resolution,[],[f632,f421]) ).

fof(f1134,plain,
    ( spl27_138
    | ~ spl27_139
    | ~ spl27_22
    | ~ spl27_21
    | ~ spl27_70 ),
    inference(avatar_split_clause,[],[f663,f627,f340,f345,f1131,f1127]) ).

fof(f1127,plain,
    ( spl27_138
  <=> one_to_one(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_138])]) ).

fof(f1131,plain,
    ( spl27_139
  <=> empty(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_139])]) ).

fof(f345,plain,
    ( spl27_22
  <=> function(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_22])]) ).

fof(f340,plain,
    ( spl27_21
  <=> relation(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_21])]) ).

fof(f663,plain,
    ( ~ function(sK23)
    | ~ empty(sK23)
    | one_to_one(sK23)
    | ~ spl27_21
    | ~ spl27_70 ),
    inference(resolution,[],[f628,f342]) ).

fof(f342,plain,
    ( relation(sK23)
    | ~ spl27_21 ),
    inference(avatar_component_clause,[],[f340]) ).

fof(f1125,plain,
    ( spl27_136
    | ~ spl27_137
    | ~ spl27_20
    | ~ spl27_18
    | ~ spl27_70 ),
    inference(avatar_split_clause,[],[f662,f627,f325,f335,f1122,f1118]) ).

fof(f1118,plain,
    ( spl27_136
  <=> one_to_one(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_136])]) ).

fof(f1122,plain,
    ( spl27_137
  <=> empty(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_137])]) ).

fof(f335,plain,
    ( spl27_20
  <=> function(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_20])]) ).

fof(f325,plain,
    ( spl27_18
  <=> relation(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).

fof(f662,plain,
    ( ~ function(sK22)
    | ~ empty(sK22)
    | one_to_one(sK22)
    | ~ spl27_18
    | ~ spl27_70 ),
    inference(resolution,[],[f628,f327]) ).

fof(f327,plain,
    ( relation(sK22)
    | ~ spl27_18 ),
    inference(avatar_component_clause,[],[f325]) ).

fof(f1116,plain,
    ( spl27_135
    | ~ spl27_63
    | ~ spl27_66 ),
    inference(avatar_split_clause,[],[f605,f590,f578,f1114]) ).

fof(f1114,plain,
    ( spl27_135
  <=> ! [X2] :
        ( subset(sK7(X2),X2)
        | empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_135])]) ).

fof(f605,plain,
    ( ! [X2] :
        ( subset(sK7(X2),X2)
        | empty(X2) )
    | ~ spl27_63
    | ~ spl27_66 ),
    inference(resolution,[],[f591,f579]) ).

fof(f1112,plain,
    ( spl27_134
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_49 ),
    inference(avatar_split_clause,[],[f509,f478,f461,f290,f1110]) ).

fof(f509,plain,
    ( ! [X0] :
        ( relation_dom(X0) = sK18
        | ~ empty(X0) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_49 ),
    inference(forward_demodulation,[],[f506,f495]) ).

fof(f506,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = relation_dom(X0) )
    | ~ spl27_45
    | ~ spl27_49 ),
    inference(resolution,[],[f479,f462]) ).

fof(f1108,plain,
    ( spl27_133
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_46 ),
    inference(avatar_split_clause,[],[f505,f465,f461,f290,f1106]) ).

fof(f505,plain,
    ( ! [X0] :
        ( relation_rng(X0) = sK18
        | ~ empty(X0) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_46 ),
    inference(forward_demodulation,[],[f502,f495]) ).

fof(f502,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = relation_rng(X0) )
    | ~ spl27_45
    | ~ spl27_46 ),
    inference(resolution,[],[f466,f462]) ).

fof(f1096,plain,
    ( spl27_132
    | ~ spl27_28
    | ~ spl27_111 ),
    inference(avatar_split_clause,[],[f918,f894,f375,f1093]) ).

fof(f1093,plain,
    ( spl27_132
  <=> one_to_one(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_132])]) ).

fof(f375,plain,
    ( spl27_28
  <=> one_to_one(sK25) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_28])]) ).

fof(f894,plain,
    ( spl27_111
  <=> sK18 = sK25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_111])]) ).

fof(f918,plain,
    ( one_to_one(sK18)
    | ~ spl27_28
    | ~ spl27_111 ),
    inference(superposition,[],[f377,f896]) ).

fof(f896,plain,
    ( sK18 = sK25
    | ~ spl27_111 ),
    inference(avatar_component_clause,[],[f894]) ).

fof(f377,plain,
    ( one_to_one(sK25)
    | ~ spl27_28 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f1044,plain,
    ( spl27_128
    | ~ spl27_45
    | ~ spl27_109 ),
    inference(avatar_split_clause,[],[f1013,f884,f461,f991]) ).

fof(f991,plain,
    ( spl27_128
  <=> ! [X7] :
        ( sK18 = X7
        | ~ empty(X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_128])]) ).

fof(f1013,plain,
    ( ! [X0] :
        ( sK18 = X0
        | ~ empty(X0) )
    | ~ spl27_45
    | ~ spl27_109 ),
    inference(forward_demodulation,[],[f462,f886]) ).

fof(f1043,plain,
    ( spl27_131
    | ~ spl27_9
    | ~ spl27_109 ),
    inference(avatar_split_clause,[],[f911,f884,f280,f1040]) ).

fof(f1040,plain,
    ( spl27_131
  <=> relation_empty_yielding(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_131])]) ).

fof(f280,plain,
    ( spl27_9
  <=> relation_empty_yielding(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).

fof(f911,plain,
    ( relation_empty_yielding(sK18)
    | ~ spl27_9
    | ~ spl27_109 ),
    inference(superposition,[],[f282,f886]) ).

fof(f282,plain,
    ( relation_empty_yielding(empty_set)
    | ~ spl27_9 ),
    inference(avatar_component_clause,[],[f280]) ).

fof(f1012,plain,
    ( ~ spl27_7
    | ~ spl27_129 ),
    inference(avatar_contradiction_clause,[],[f1001]) ).

fof(f1001,plain,
    ( $false
    | ~ spl27_7
    | ~ spl27_129 ),
    inference(resolution,[],[f996,f272]) ).

fof(f996,plain,
    ( ! [X7] : ~ empty(X7)
    | ~ spl27_129 ),
    inference(avatar_component_clause,[],[f995]) ).

fof(f995,plain,
    ( spl27_129
  <=> ! [X7] : ~ empty(X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_129])]) ).

fof(f1011,plain,
    ( ~ spl27_34
    | ~ spl27_129 ),
    inference(avatar_contradiction_clause,[],[f1002]) ).

fof(f1002,plain,
    ( $false
    | ~ spl27_34
    | ~ spl27_129 ),
    inference(resolution,[],[f996,f405]) ).

fof(f1010,plain,
    ( ~ spl27_11
    | ~ spl27_129 ),
    inference(avatar_contradiction_clause,[],[f1003]) ).

fof(f1003,plain,
    ( $false
    | ~ spl27_11
    | ~ spl27_129 ),
    inference(resolution,[],[f996,f292]) ).

fof(f1009,plain,
    ( ~ spl27_14
    | ~ spl27_129 ),
    inference(avatar_contradiction_clause,[],[f1004]) ).

fof(f1004,plain,
    ( $false
    | ~ spl27_14
    | ~ spl27_129 ),
    inference(resolution,[],[f996,f307]) ).

fof(f307,plain,
    ( empty(sK20)
    | ~ spl27_14 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f305,plain,
    ( spl27_14
  <=> empty(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).

fof(f1008,plain,
    ( ~ spl27_29
    | ~ spl27_129 ),
    inference(avatar_contradiction_clause,[],[f1005]) ).

fof(f1005,plain,
    ( $false
    | ~ spl27_29
    | ~ spl27_129 ),
    inference(resolution,[],[f996,f382]) ).

fof(f382,plain,
    ( empty(sK25)
    | ~ spl27_29 ),
    inference(avatar_component_clause,[],[f380]) ).

fof(f380,plain,
    ( spl27_29
  <=> empty(sK25) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).

fof(f1007,plain,
    ( ~ spl27_31
    | ~ spl27_129 ),
    inference(avatar_contradiction_clause,[],[f1006]) ).

fof(f1006,plain,
    ( $false
    | ~ spl27_31
    | ~ spl27_129 ),
    inference(resolution,[],[f996,f392]) ).

fof(f392,plain,
    ( empty(sK26)
    | ~ spl27_31 ),
    inference(avatar_component_clause,[],[f390]) ).

fof(f390,plain,
    ( spl27_31
  <=> empty(sK26) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_31])]) ).

fof(f1000,plain,
    ( spl27_129
    | spl27_130
    | ~ spl27_11
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_80 ),
    inference(avatar_split_clause,[],[f716,f707,f486,f461,f404,f290,f998,f995]) ).

fof(f716,plain,
    ( ! [X8,X7] :
        ( ~ in(X8,sK18)
        | ~ empty(X7) )
    | ~ spl27_11
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_80 ),
    inference(forward_demodulation,[],[f715,f495]) ).

fof(f715,plain,
    ( ! [X8,X7] :
        ( ~ in(X8,empty_set)
        | ~ empty(X7) )
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_80 ),
    inference(forward_demodulation,[],[f714,f494]) ).

fof(f714,plain,
    ( ! [X8,X7] :
        ( ~ empty(X7)
        | ~ in(X8,sK12(X7)) )
    | ~ spl27_51
    | ~ spl27_80 ),
    inference(resolution,[],[f708,f487]) ).

fof(f993,plain,
    ( spl27_128
    | ~ spl27_11
    | ~ spl27_68 ),
    inference(avatar_split_clause,[],[f613,f598,f290,f991]) ).

fof(f613,plain,
    ( ! [X7] :
        ( sK18 = X7
        | ~ empty(X7) )
    | ~ spl27_11
    | ~ spl27_68 ),
    inference(resolution,[],[f599,f292]) ).

fof(f989,plain,
    ( spl27_127
    | ~ spl27_38
    | ~ spl27_66 ),
    inference(avatar_split_clause,[],[f603,f590,f420,f987]) ).

fof(f987,plain,
    ( spl27_127
  <=> ! [X0] : subset(sK11(powerset(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_127])]) ).

fof(f603,plain,
    ( ! [X0] : subset(sK11(powerset(X0)),X0)
    | ~ spl27_38
    | ~ spl27_66 ),
    inference(resolution,[],[f591,f421]) ).

fof(f985,plain,
    ( spl27_126
    | ~ spl27_36
    | ~ spl27_49 ),
    inference(avatar_split_clause,[],[f508,f478,f412,f983]) ).

fof(f412,plain,
    ( spl27_36
  <=> ! [X0] :
        ( function(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_36])]) ).

fof(f508,plain,
    ( ! [X2] :
        ( ~ empty(X2)
        | function(relation_dom(X2)) )
    | ~ spl27_36
    | ~ spl27_49 ),
    inference(resolution,[],[f479,f413]) ).

fof(f413,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(X0) )
    | ~ spl27_36 ),
    inference(avatar_component_clause,[],[f412]) ).

fof(f981,plain,
    ( spl27_125
    | ~ spl27_36
    | ~ spl27_46 ),
    inference(avatar_split_clause,[],[f504,f465,f412,f979]) ).

fof(f504,plain,
    ( ! [X2] :
        ( ~ empty(X2)
        | function(relation_rng(X2)) )
    | ~ spl27_36
    | ~ spl27_46 ),
    inference(resolution,[],[f466,f413]) ).

fof(f975,plain,
    ( spl27_124
    | ~ spl27_109
    | ~ spl27_114 ),
    inference(avatar_split_clause,[],[f928,f925,f884,f973]) ).

fof(f925,plain,
    ( spl27_114
  <=> ! [X0] : empty_set = sK12(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_114])]) ).

fof(f928,plain,
    ( ! [X0] : sK12(X0) = sK18
    | ~ spl27_109
    | ~ spl27_114 ),
    inference(forward_demodulation,[],[f926,f886]) ).

fof(f926,plain,
    ( ! [X0] : empty_set = sK12(X0)
    | ~ spl27_114 ),
    inference(avatar_component_clause,[],[f925]) ).

fof(f971,plain,
    ( ~ spl27_48
    | spl27_123
    | ~ spl27_8
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f568,f518,f461,f290,f275,f968,f473]) ).

fof(f473,plain,
    ( spl27_48
  <=> function(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_48])]) ).

fof(f968,plain,
    ( spl27_123
  <=> sP1(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_123])]) ).

fof(f275,plain,
    ( spl27_8
  <=> relation(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_8])]) ).

fof(f568,plain,
    ( sP1(sK18)
    | ~ function(sK18)
    | ~ spl27_8
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_54 ),
    inference(forward_demodulation,[],[f567,f495]) ).

fof(f567,plain,
    ( ~ function(sK18)
    | sP1(empty_set)
    | ~ spl27_8
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_54 ),
    inference(forward_demodulation,[],[f554,f495]) ).

fof(f554,plain,
    ( ~ function(empty_set)
    | sP1(empty_set)
    | ~ spl27_8
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f277]) ).

fof(f277,plain,
    ( relation(empty_set)
    | ~ spl27_8 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f966,plain,
    ( spl27_122
    | ~ spl27_24
    | ~ spl27_23
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f564,f518,f350,f355,f963]) ).

fof(f963,plain,
    ( spl27_122
  <=> sP1(sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_122])]) ).

fof(f355,plain,
    ( spl27_24
  <=> function(sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_24])]) ).

fof(f350,plain,
    ( spl27_23
  <=> relation(sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_23])]) ).

fof(f564,plain,
    ( ~ function(sK24)
    | sP1(sK24)
    | ~ spl27_23
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f352]) ).

fof(f352,plain,
    ( relation(sK24)
    | ~ spl27_23 ),
    inference(avatar_component_clause,[],[f350]) ).

fof(f961,plain,
    ( spl27_121
    | ~ spl27_22
    | ~ spl27_21
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f563,f518,f340,f345,f958]) ).

fof(f958,plain,
    ( spl27_121
  <=> sP1(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_121])]) ).

fof(f563,plain,
    ( ~ function(sK23)
    | sP1(sK23)
    | ~ spl27_21
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f342]) ).

fof(f956,plain,
    ( spl27_120
    | ~ spl27_20
    | ~ spl27_18
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f562,f518,f325,f335,f953]) ).

fof(f953,plain,
    ( spl27_120
  <=> sP1(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_120])]) ).

fof(f562,plain,
    ( ~ function(sK22)
    | sP1(sK22)
    | ~ spl27_18
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f327]) ).

fof(f951,plain,
    ( spl27_118
    | ~ spl27_119
    | ~ spl27_16
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f561,f518,f315,f948,f944]) ).

fof(f944,plain,
    ( spl27_118
  <=> sP1(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_118])]) ).

fof(f948,plain,
    ( spl27_119
  <=> function(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_119])]) ).

fof(f315,plain,
    ( spl27_16
  <=> relation(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).

fof(f561,plain,
    ( ~ function(sK21)
    | sP1(sK21)
    | ~ spl27_16
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f317]) ).

fof(f317,plain,
    ( relation(sK21)
    | ~ spl27_16 ),
    inference(avatar_component_clause,[],[f315]) ).

fof(f942,plain,
    ( ~ spl27_117
    | spl27_3
    | ~ spl27_109 ),
    inference(avatar_split_clause,[],[f914,f884,f250,f939]) ).

fof(f250,plain,
    ( spl27_3
  <=> empty_set = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).

fof(f914,plain,
    ( sK4 != sK18
    | spl27_3
    | ~ spl27_109 ),
    inference(superposition,[],[f252,f886]) ).

fof(f252,plain,
    ( empty_set != sK4
    | spl27_3 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f937,plain,
    ( spl27_115
    | ~ spl27_116
    | ~ spl27_13
    | ~ spl27_54 ),
    inference(avatar_split_clause,[],[f559,f518,f300,f934,f930]) ).

fof(f930,plain,
    ( spl27_115
  <=> sP1(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_115])]) ).

fof(f934,plain,
    ( spl27_116
  <=> function(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_116])]) ).

fof(f300,plain,
    ( spl27_13
  <=> relation(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).

fof(f559,plain,
    ( ~ function(sK19)
    | sP1(sK19)
    | ~ spl27_13
    | ~ spl27_54 ),
    inference(resolution,[],[f519,f302]) ).

fof(f302,plain,
    ( relation(sK19)
    | ~ spl27_13 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f927,plain,
    ( spl27_114
    | ~ spl27_34
    | ~ spl27_45 ),
    inference(avatar_split_clause,[],[f494,f461,f404,f925]) ).

fof(f909,plain,
    ( spl27_113
    | ~ spl27_11
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_66 ),
    inference(avatar_split_clause,[],[f607,f590,f486,f461,f404,f290,f907]) ).

fof(f907,plain,
    ( spl27_113
  <=> ! [X1] : subset(sK18,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_113])]) ).

fof(f607,plain,
    ( ! [X1] : subset(sK18,X1)
    | ~ spl27_11
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_66 ),
    inference(forward_demodulation,[],[f606,f495]) ).

fof(f606,plain,
    ( ! [X1] : subset(empty_set,X1)
    | ~ spl27_34
    | ~ spl27_45
    | ~ spl27_51
    | ~ spl27_66 ),
    inference(forward_demodulation,[],[f604,f494]) ).

fof(f604,plain,
    ( ! [X1] : subset(sK12(X1),X1)
    | ~ spl27_51
    | ~ spl27_66 ),
    inference(resolution,[],[f591,f487]) ).

fof(f902,plain,
    ( spl27_112
    | ~ spl27_11
    | ~ spl27_31
    | ~ spl27_45 ),
    inference(avatar_split_clause,[],[f501,f461,f390,f290,f899]) ).

fof(f899,plain,
    ( spl27_112
  <=> sK18 = sK26 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_112])]) ).

fof(f501,plain,
    ( sK18 = sK26
    | ~ spl27_11
    | ~ spl27_31
    | ~ spl27_45 ),
    inference(forward_demodulation,[],[f498,f495]) ).

fof(f498,plain,
    ( empty_set = sK26
    | ~ spl27_31
    | ~ spl27_45 ),
    inference(resolution,[],[f462,f392]) ).

fof(f897,plain,
    ( spl27_111
    | ~ spl27_11
    | ~ spl27_29
    | ~ spl27_45 ),
    inference(avatar_split_clause,[],[f500,f461,f380,f290,f894]) ).

fof(f500,plain,
    ( sK18 = sK25
    | ~ spl27_11
    | ~ spl27_29
    | ~ spl27_45 ),
    inference(forward_demodulation,[],[f497,f495]) ).

fof(f497,plain,
    ( empty_set = sK25
    | ~ spl27_29
    | ~ spl27_45 ),
    inference(resolution,[],[f462,f382]) ).

fof(f892,plain,
    ( spl27_110
    | ~ spl27_11
    | ~ spl27_14
    | ~ spl27_45 ),
    inference(avatar_split_clause,[],[f499,f461,f305,f290,f889]) ).

fof(f889,plain,
    ( spl27_110
  <=> sK18 = sK20 ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_110])]) ).

fof(f499,plain,
    ( sK18 = sK20
    | ~ spl27_11
    | ~ spl27_14
    | ~ spl27_45 ),
    inference(forward_demodulation,[],[f496,f495]) ).

fof(f496,plain,
    ( empty_set = sK20
    | ~ spl27_14
    | ~ spl27_45 ),
    inference(resolution,[],[f462,f307]) ).

fof(f887,plain,
    ( spl27_109
    | ~ spl27_11
    | ~ spl27_45 ),
    inference(avatar_split_clause,[],[f495,f461,f290,f884]) ).

fof(f881,plain,
    ( spl27_108
    | ~ spl27_34
    | ~ spl27_37 ),
    inference(avatar_split_clause,[],[f451,f416,f404,f879]) ).

fof(f879,plain,
    ( spl27_108
  <=> ! [X0] : relation(sK12(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_108])]) ).

fof(f416,plain,
    ( spl27_37
  <=> ! [X0] :
        ( relation(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_37])]) ).

fof(f451,plain,
    ( ! [X0] : relation(sK12(X0))
    | ~ spl27_34
    | ~ spl27_37 ),
    inference(resolution,[],[f417,f405]) ).

fof(f417,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation(X0) )
    | ~ spl27_37 ),
    inference(avatar_component_clause,[],[f416]) ).

fof(f876,plain,
    ( spl27_107
    | ~ spl27_34
    | ~ spl27_36 ),
    inference(avatar_split_clause,[],[f440,f412,f404,f874]) ).

fof(f874,plain,
    ( spl27_107
  <=> ! [X0] : function(sK12(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_107])]) ).

fof(f440,plain,
    ( ! [X0] : function(sK12(X0))
    | ~ spl27_34
    | ~ spl27_36 ),
    inference(resolution,[],[f413,f405]) ).

fof(f870,plain,
    ( spl27_106
    | ~ spl27_11
    | ~ spl27_37 ),
    inference(avatar_split_clause,[],[f452,f416,f290,f867]) ).

fof(f867,plain,
    ( spl27_106
  <=> relation(sK18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_106])]) ).

fof(f452,plain,
    ( relation(sK18)
    | ~ spl27_11
    | ~ spl27_37 ),
    inference(resolution,[],[f417,f292]) ).

fof(f865,plain,
    ( spl27_105
    | ~ spl27_83
    | ~ spl27_103 ),
    inference(avatar_split_clause,[],[f859,f847,f737,f862]) ).

fof(f847,plain,
    ( spl27_103
  <=> relation_of2(sK6,sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_103])]) ).

fof(f859,plain,
    ( relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6)
    | ~ spl27_83
    | ~ spl27_103 ),
    inference(resolution,[],[f849,f738]) ).

fof(f849,plain,
    ( relation_of2(sK6,sK3,sK4)
    | ~ spl27_103 ),
    inference(avatar_component_clause,[],[f847]) ).

fof(f857,plain,
    spl27_104,
    inference(avatar_split_clause,[],[f175,f855]) ).

fof(f855,plain,
    ( spl27_104
  <=> ! [X0,X1,X3] :
        ( sP0(X0,X1)
        | apply(X0,X3) != sK8(X0,X1)
        | ~ in(X3,relation_dom(X0))
        | ~ in(sK8(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_104])]) ).

fof(f175,plain,
    ! [X3,X0,X1] :
      ( sP0(X0,X1)
      | apply(X0,X3) != sK8(X0,X1)
      | ~ in(X3,relation_dom(X0))
      | ~ in(sK8(X0,X1),X1) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ! [X3] :
                ( apply(X0,X3) != sK8(X0,X1)
                | ~ in(X3,relation_dom(X0)) )
            | ~ in(sK8(X0,X1),X1) )
          & ( ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
              & in(sK9(X0,X1),relation_dom(X0)) )
            | in(sK8(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( apply(X0,X6) != X5
                  | ~ in(X6,relation_dom(X0)) ) )
            & ( ( apply(X0,sK10(X0,X5)) = X5
                & in(sK10(X0,X5),relation_dom(X0)) )
              | ~ in(X5,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f102,f105,f104,f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( apply(X0,X3) != X2
                | ~ in(X3,relation_dom(X0)) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( apply(X0,X4) = X2
                & in(X4,relation_dom(X0)) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( apply(X0,X3) != sK8(X0,X1)
              | ~ in(X3,relation_dom(X0)) )
          | ~ in(sK8(X0,X1),X1) )
        & ( ? [X4] :
              ( apply(X0,X4) = sK8(X0,X1)
              & in(X4,relation_dom(X0)) )
          | in(sK8(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( apply(X0,X4) = sK8(X0,X1)
          & in(X4,relation_dom(X0)) )
     => ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
        & in(sK9(X0,X1),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( apply(X0,X7) = X5
          & in(X7,relation_dom(X0)) )
     => ( apply(X0,sK10(X0,X5)) = X5
        & in(sK10(X0,X5),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ! [X3] :
                  ( apply(X0,X3) != X2
                  | ~ in(X3,relation_dom(X0)) )
              | ~ in(X2,X1) )
            & ( ? [X4] :
                  ( apply(X0,X4) = X2
                  & in(X4,relation_dom(X0)) )
              | in(X2,X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( apply(X0,X6) != X5
                  | ~ in(X6,relation_dom(X0)) ) )
            & ( ? [X7] :
                  ( apply(X0,X7) = X5
                  & in(X7,relation_dom(X0)) )
              | ~ in(X5,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ! [X3] :
                  ( apply(X0,X3) != X2
                  | ~ in(X3,relation_dom(X0)) )
              | ~ in(X2,X1) )
            & ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ! [X3] :
                  ( apply(X0,X3) != X2
                  | ~ in(X3,relation_dom(X0)) ) )
            & ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( apply(X0,X3) = X2
              & in(X3,relation_dom(X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f850,plain,
    ( spl27_103
    | ~ spl27_5
    | ~ spl27_75 ),
    inference(avatar_split_clause,[],[f693,f647,f260,f847]) ).

fof(f693,plain,
    ( relation_of2(sK6,sK3,sK4)
    | ~ spl27_5
    | ~ spl27_75 ),
    inference(resolution,[],[f648,f262]) ).

fof(f845,plain,
    ( spl27_102
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_96 ),
    inference(avatar_split_clause,[],[f818,f813,f461,f290,f843]) ).

fof(f813,plain,
    ( spl27_96
  <=> ! [X2,X0,X1] :
        ( quasi_total(X2,X0,X1)
        | empty_set != X2
        | empty_set = X0
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_96])]) ).

fof(f818,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X1
        | sK18 = X0
        | sK18 != X2
        | quasi_total(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_96 ),
    inference(forward_demodulation,[],[f817,f495]) ).

fof(f817,plain,
    ( ! [X2,X0,X1] :
        ( sK18 = X0
        | sK18 != X2
        | quasi_total(X2,X0,X1)
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_96 ),
    inference(forward_demodulation,[],[f816,f495]) ).

fof(f816,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X2
        | quasi_total(X2,X0,X1)
        | empty_set = X0
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_96 ),
    inference(forward_demodulation,[],[f814,f495]) ).

fof(f814,plain,
    ( ! [X2,X0,X1] :
        ( quasi_total(X2,X0,X1)
        | empty_set != X2
        | empty_set = X0
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_96 ),
    inference(avatar_component_clause,[],[f813]) ).

fof(f841,plain,
    ( spl27_101
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_95 ),
    inference(avatar_split_clause,[],[f811,f806,f461,f290,f839]) ).

fof(f806,plain,
    ( spl27_95
  <=> ! [X2,X0,X1] :
        ( empty_set = X2
        | ~ quasi_total(X2,X0,X1)
        | empty_set = X0
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_95])]) ).

fof(f811,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X1
        | sK18 = X0
        | sK18 = X2
        | ~ quasi_total(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_95 ),
    inference(forward_demodulation,[],[f810,f495]) ).

fof(f810,plain,
    ( ! [X2,X0,X1] :
        ( sK18 = X0
        | sK18 = X2
        | ~ quasi_total(X2,X0,X1)
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_95 ),
    inference(forward_demodulation,[],[f809,f495]) ).

fof(f809,plain,
    ( ! [X2,X0,X1] :
        ( sK18 = X2
        | ~ quasi_total(X2,X0,X1)
        | empty_set = X0
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_95 ),
    inference(forward_demodulation,[],[f807,f495]) ).

fof(f807,plain,
    ( ! [X2,X0,X1] :
        ( empty_set = X2
        | ~ quasi_total(X2,X0,X1)
        | empty_set = X0
        | empty_set != X1
        | ~ relation_of2_as_subset(X2,X0,X1) )
    | ~ spl27_95 ),
    inference(avatar_component_clause,[],[f806]) ).

fof(f837,plain,
    ( spl27_100
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_94 ),
    inference(avatar_split_clause,[],[f804,f801,f461,f290,f835]) ).

fof(f835,plain,
    ( spl27_100
  <=> ! [X2,X0,X1] :
        ( sK18 != X0
        | quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_100])]) ).

fof(f801,plain,
    ( spl27_94
  <=> ! [X2,X0,X1] :
        ( quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | empty_set != X0
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_94])]) ).

fof(f804,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X0
        | quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_94 ),
    inference(forward_demodulation,[],[f802,f495]) ).

fof(f802,plain,
    ( ! [X2,X0,X1] :
        ( quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | empty_set != X0
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_94 ),
    inference(avatar_component_clause,[],[f801]) ).

fof(f833,plain,
    ( spl27_99
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_92 ),
    inference(avatar_split_clause,[],[f794,f791,f461,f290,f831]) ).

fof(f831,plain,
    ( spl27_99
  <=> ! [X2,X0,X1] :
        ( sK18 = X2
        | quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_99])]) ).

fof(f791,plain,
    ( spl27_92
  <=> ! [X2,X0,X1] :
        ( quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | empty_set = X2
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_92])]) ).

fof(f794,plain,
    ( ! [X2,X0,X1] :
        ( sK18 = X2
        | quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_92 ),
    inference(forward_demodulation,[],[f792,f495]) ).

fof(f792,plain,
    ( ! [X2,X0,X1] :
        ( quasi_total(X1,X0,X2)
        | relation_dom_as_subset(X0,X2,X1) != X0
        | empty_set = X2
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_92 ),
    inference(avatar_component_clause,[],[f791]) ).

fof(f829,plain,
    ( spl27_98
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_91 ),
    inference(avatar_split_clause,[],[f789,f786,f461,f290,f827]) ).

fof(f786,plain,
    ( spl27_91
  <=> ! [X2,X0,X1] :
        ( relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | empty_set != X0
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_91])]) ).

fof(f789,plain,
    ( ! [X2,X0,X1] :
        ( sK18 != X0
        | relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_91 ),
    inference(forward_demodulation,[],[f787,f495]) ).

fof(f787,plain,
    ( ! [X2,X0,X1] :
        ( relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | empty_set != X0
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_91 ),
    inference(avatar_component_clause,[],[f786]) ).

fof(f825,plain,
    ( spl27_97
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_90 ),
    inference(avatar_split_clause,[],[f784,f781,f461,f290,f823]) ).

fof(f781,plain,
    ( spl27_90
  <=> ! [X2,X0,X1] :
        ( relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | empty_set = X2
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_90])]) ).

fof(f784,plain,
    ( ! [X2,X0,X1] :
        ( sK18 = X2
        | relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_11
    | ~ spl27_45
    | ~ spl27_90 ),
    inference(forward_demodulation,[],[f782,f495]) ).

fof(f782,plain,
    ( ! [X2,X0,X1] :
        ( relation_dom_as_subset(X0,X2,X1) = X0
        | ~ quasi_total(X1,X0,X2)
        | empty_set = X2
        | ~ sP2(X0,X1,X2) )
    | ~ spl27_90 ),
    inference(avatar_component_clause,[],[f781]) ).

fof(f815,plain,
    spl27_96,
    inference(avatar_split_clause,[],[f208,f813]) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( quasi_total(X2,X0,X1)
      | empty_set != X2
      | empty_set = X0
      | empty_set != X1
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ( ( ( ( quasi_total(X2,X0,X1)
              | empty_set != X2 )
            & ( empty_set = X2
              | ~ quasi_total(X2,X0,X1) ) )
          | empty_set = X0
          | empty_set != X1 )
        & sP2(X0,X2,X1) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(nnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & sP2(X0,X2,X1) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(definition_folding,[],[f84,f94]) ).

fof(f94,plain,
    ! [X0,X2,X1] :
      ( ( quasi_total(X2,X0,X1)
      <=> relation_dom_as_subset(X0,X1,X2) = X0 )
      | ( empty_set != X0
        & empty_set = X1 )
      | ~ sP2(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(flattening,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => ( ( empty_set = X1
         => ( ( quasi_total(X2,X0,X1)
            <=> empty_set = X2 )
            | empty_set = X0 ) )
        & ( ( empty_set = X1
           => empty_set = X0 )
         => ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',d1_funct_2) ).

fof(f808,plain,
    spl27_95,
    inference(avatar_split_clause,[],[f207,f806]) ).

fof(f207,plain,
    ! [X2,X0,X1] :
      ( empty_set = X2
      | ~ quasi_total(X2,X0,X1)
      | empty_set = X0
      | empty_set != X1
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f803,plain,
    spl27_94,
    inference(avatar_split_clause,[],[f205,f801]) ).

fof(f205,plain,
    ! [X2,X0,X1] :
      ( quasi_total(X1,X0,X2)
      | relation_dom_as_subset(X0,X2,X1) != X0
      | empty_set != X0
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( ( ( quasi_total(X1,X0,X2)
          | relation_dom_as_subset(X0,X2,X1) != X0 )
        & ( relation_dom_as_subset(X0,X2,X1) = X0
          | ~ quasi_total(X1,X0,X2) ) )
      | ( empty_set != X0
        & empty_set = X2 )
      | ~ sP2(X0,X1,X2) ),
    inference(rectify,[],[f120]) ).

fof(f120,plain,
    ! [X0,X2,X1] :
      ( ( ( quasi_total(X2,X0,X1)
          | relation_dom_as_subset(X0,X1,X2) != X0 )
        & ( relation_dom_as_subset(X0,X1,X2) = X0
          | ~ quasi_total(X2,X0,X1) ) )
      | ( empty_set != X0
        & empty_set = X1 )
      | ~ sP2(X0,X2,X1) ),
    inference(nnf_transformation,[],[f94]) ).

fof(f799,plain,
    ( spl27_93
    | ~ spl27_5
    | ~ spl27_73 ),
    inference(avatar_split_clause,[],[f687,f639,f260,f796]) ).

fof(f687,plain,
    ( sP2(sK3,sK6,sK4)
    | ~ spl27_5
    | ~ spl27_73 ),
    inference(resolution,[],[f640,f262]) ).

fof(f793,plain,
    spl27_92,
    inference(avatar_split_clause,[],[f204,f791]) ).

fof(f204,plain,
    ! [X2,X0,X1] :
      ( quasi_total(X1,X0,X2)
      | relation_dom_as_subset(X0,X2,X1) != X0
      | empty_set = X2
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f788,plain,
    spl27_91,
    inference(avatar_split_clause,[],[f203,f786]) ).

fof(f203,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X2,X1) = X0
      | ~ quasi_total(X1,X0,X2)
      | empty_set != X0
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f783,plain,
    spl27_90,
    inference(avatar_split_clause,[],[f202,f781]) ).

fof(f202,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X2,X1) = X0
      | ~ quasi_total(X1,X0,X2)
      | empty_set = X2
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f779,plain,
    spl27_89,
    inference(avatar_split_clause,[],[f174,f777]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK8(X0,X1) = apply(X0,sK9(X0,X1))
      | in(sK8(X0,X1),X1) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f774,plain,
    spl27_88,
    inference(avatar_split_clause,[],[f172,f772]) ).

fof(f172,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | apply(X0,X6) != X5
      | ~ in(X6,relation_dom(X0))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f764,plain,
    spl27_87,
    inference(avatar_split_clause,[],[f173,f762]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | in(sK9(X0,X1),relation_dom(X0))
      | in(sK8(X0,X1),X1) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f760,plain,
    spl27_86,
    inference(avatar_split_clause,[],[f171,f758]) ).

fof(f758,plain,
    ( spl27_86
  <=> ! [X5,X0,X1] :
        ( apply(X0,sK10(X0,X5)) = X5
        | ~ in(X5,X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_86])]) ).

fof(f171,plain,
    ! [X0,X1,X5] :
      ( apply(X0,sK10(X0,X5)) = X5
      | ~ in(X5,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f755,plain,
    spl27_85,
    inference(avatar_split_clause,[],[f170,f753]) ).

fof(f753,plain,
    ( spl27_85
  <=> ! [X5,X0,X1] :
        ( in(sK10(X0,X5),relation_dom(X0))
        | ~ in(X5,X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_85])]) ).

fof(f170,plain,
    ! [X0,X1,X5] :
      ( in(sK10(X0,X5),relation_dom(X0))
      | ~ in(X5,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f743,plain,
    spl27_84,
    inference(avatar_split_clause,[],[f210,f741]) ).

fof(f210,plain,
    ! [X2,X0,X1] :
      ( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
      | ~ relation_of2(X2,X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( relation_of2(X2,X0,X1)
     => element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',dt_k4_relset_1) ).

fof(f739,plain,
    spl27_83,
    inference(avatar_split_clause,[],[f209,f737]) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0,X1,X2] :
      ( relation_of2(X2,X0,X1)
     => relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',redefinition_k4_relset_1) ).

fof(f724,plain,
    spl27_82,
    inference(avatar_split_clause,[],[f212,f722]) ).

fof(f212,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t4_subset) ).

fof(f720,plain,
    spl27_81,
    inference(avatar_split_clause,[],[f201,f718]) ).

fof(f201,plain,
    ! [X2,X0,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => element(X2,powerset(cartesian_product2(X0,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',dt_m2_relset_1) ).

fof(f709,plain,
    spl27_80,
    inference(avatar_split_clause,[],[f215,f707]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t5_subset) ).

fof(f705,plain,
    spl27_79,
    inference(avatar_split_clause,[],[f169,f703]) ).

fof(f703,plain,
    ( spl27_79
  <=> ! [X0,X1] :
        ( relation_rng(X0) = X1
        | ~ sP0(X0,X1)
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_79])]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( relation_rng(X0) = X1
      | ~ sP0(X0,X1)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ~ sP0(X0,X1) )
          & ( sP0(X0,X1)
            | relation_rng(X0) != X1 ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> sP0(X0,X1) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f701,plain,
    spl27_78,
    inference(avatar_split_clause,[],[f168,f699]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | relation_rng(X0) != X1
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f686,plain,
    ( spl27_77
    | ~ spl27_2
    | ~ spl27_56 ),
    inference(avatar_split_clause,[],[f576,f526,f245,f683]) ).

fof(f683,plain,
    ( spl27_77
  <=> element(sK5,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_77])]) ).

fof(f576,plain,
    ( element(sK5,sK3)
    | ~ spl27_2
    | ~ spl27_56 ),
    inference(resolution,[],[f527,f247]) ).

fof(f247,plain,
    ( in(sK5,sK3)
    | ~ spl27_2 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f653,plain,
    spl27_76,
    inference(avatar_split_clause,[],[f214,f651]) ).

fof(f214,plain,
    ! [X2,X0,X1] :
      ( relation_of2_as_subset(X2,X0,X1)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2_as_subset(X2,X0,X1)
        | ~ relation_of2(X2,X0,X1) )
      & ( relation_of2(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',redefinition_m2_relset_1) ).

fof(f649,plain,
    spl27_75,
    inference(avatar_split_clause,[],[f213,f647]) ).

fof(f213,plain,
    ! [X2,X0,X1] :
      ( relation_of2(X2,X0,X1)
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f645,plain,
    spl27_74,
    inference(avatar_split_clause,[],[f211,f643]) ).

fof(f211,plain,
    ! [X2,X0,X1] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
     => relation(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc1_relset_1) ).

fof(f641,plain,
    spl27_73,
    inference(avatar_split_clause,[],[f206,f639]) ).

fof(f206,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X2,X1)
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f637,plain,
    spl27_72,
    inference(avatar_split_clause,[],[f187,f635]) ).

fof(f635,plain,
    ( spl27_72
  <=> ! [X0,X1] :
        ( ~ empty(cartesian_product2(X0,X1))
        | empty(X1)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_72])]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( ~ empty(cartesian_product2(X0,X1))
      | empty(X1)
      | empty(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ~ empty(cartesian_product2(X0,X1))
      | empty(X1)
      | empty(X0) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ empty(cartesian_product2(X0,X1))
      | empty(X1)
      | empty(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( ( ~ empty(X1)
        & ~ empty(X0) )
     => ~ empty(cartesian_product2(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc4_subset_1) ).

fof(f633,plain,
    spl27_71,
    inference(avatar_split_clause,[],[f186,f631]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t2_subset) ).

fof(f629,plain,
    spl27_70,
    inference(avatar_split_clause,[],[f179,f627]) ).

fof(f179,plain,
    ! [X0] :
      ( one_to_one(X0)
      | ~ function(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ( one_to_one(X0)
        & function(X0)
        & relation(X0) )
      | ~ function(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ( one_to_one(X0)
        & function(X0)
        & relation(X0) )
      | ~ function(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & empty(X0)
        & relation(X0) )
     => ( one_to_one(X0)
        & function(X0)
        & relation(X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc2_funct_1) ).

fof(f625,plain,
    ( ~ spl27_69
    | ~ spl27_2
    | ~ spl27_55 ),
    inference(avatar_split_clause,[],[f575,f522,f245,f622]) ).

fof(f622,plain,
    ( spl27_69
  <=> in(sK3,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_69])]) ).

fof(f575,plain,
    ( ~ in(sK3,sK5)
    | ~ spl27_2
    | ~ spl27_55 ),
    inference(resolution,[],[f523,f247]) ).

fof(f600,plain,
    spl27_68,
    inference(avatar_split_clause,[],[f190,f598]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t8_boole) ).

fof(f596,plain,
    spl27_67,
    inference(avatar_split_clause,[],[f189,f594]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t3_subset) ).

fof(f592,plain,
    spl27_66,
    inference(avatar_split_clause,[],[f188,f590]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f588,plain,
    spl27_65,
    inference(avatar_split_clause,[],[f167,f586]) ).

fof(f586,plain,
    ( spl27_65
  <=> ! [X0] :
        ( ~ empty(relation_dom(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_65])]) ).

fof(f167,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc5_relat_1) ).

fof(f584,plain,
    spl27_64,
    inference(avatar_split_clause,[],[f166,f582]) ).

fof(f582,plain,
    ( spl27_64
  <=> ! [X0] :
        ( ~ empty(relation_rng(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_64])]) ).

fof(f166,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc6_relat_1) ).

fof(f580,plain,
    spl27_63,
    inference(avatar_split_clause,[],[f157,f578]) ).

fof(f157,plain,
    ! [X0] :
      ( element(sK7(X0),powerset(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ( ~ empty(sK7(X0))
        & element(sK7(X0),powerset(X0)) )
      | empty(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f60,f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
     => ( ~ empty(sK7(X0))
        & element(sK7(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
      | empty(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0] :
      ( ~ empty(X0)
     => ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_subset_1) ).

fof(f553,plain,
    ( ~ spl27_62
    | ~ spl27_2
    | ~ spl27_52 ),
    inference(avatar_split_clause,[],[f516,f490,f245,f550]) ).

fof(f550,plain,
    ( spl27_62
  <=> empty(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_62])]) ).

fof(f516,plain,
    ( ~ empty(sK3)
    | ~ spl27_2
    | ~ spl27_52 ),
    inference(resolution,[],[f491,f247]) ).

fof(f548,plain,
    spl27_61,
    inference(avatar_split_clause,[],[f200,f546]) ).

fof(f546,plain,
    ( spl27_61
  <=> ! [X0,X1] : quasi_total(sK16(X0,X1),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_61])]) ).

fof(f200,plain,
    ! [X0,X1] : quasi_total(sK16(X0,X1),X0,X1),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( quasi_total(sK16(X0,X1),X0,X1)
      & function(sK16(X0,X1))
      & relation(sK16(X0,X1))
      & relation_of2(sK16(X0,X1),X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f31,f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( quasi_total(X2,X0,X1)
          & function(X2)
          & relation(X2)
          & relation_of2(X2,X0,X1) )
     => ( quasi_total(sK16(X0,X1),X0,X1)
        & function(sK16(X0,X1))
        & relation(sK16(X0,X1))
        & relation_of2(sK16(X0,X1),X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,axiom,
    ! [X0,X1] :
    ? [X2] :
      ( quasi_total(X2,X0,X1)
      & function(X2)
      & relation(X2)
      & relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_funct_2) ).

fof(f544,plain,
    spl27_60,
    inference(avatar_split_clause,[],[f197,f542]) ).

fof(f197,plain,
    ! [X0,X1] : relation_of2(sK16(X0,X1),X0,X1),
    inference(cnf_transformation,[],[f119]) ).

fof(f540,plain,
    spl27_59,
    inference(avatar_split_clause,[],[f194,f538]) ).

fof(f194,plain,
    ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( function(sK15(X0,X1))
      & relation(sK15(X0,X1))
      & relation_of2(sK15(X0,X1),X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f37,f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( function(X2)
          & relation(X2)
          & relation_of2(X2,X0,X1) )
     => ( function(sK15(X0,X1))
        & relation(sK15(X0,X1))
        & relation_of2(sK15(X0,X1),X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,axiom,
    ! [X0,X1] :
    ? [X2] :
      ( function(X2)
      & relation(X2)
      & relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_partfun1) ).

fof(f536,plain,
    spl27_58,
    inference(avatar_split_clause,[],[f193,f534]) ).

fof(f193,plain,
    ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f18,f114]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ? [X2] : relation_of2(X2,X0,X1)
     => relation_of2(sK14(X0,X1),X0,X1) ),
    introduced(choice_axiom,[]) ).

fof(f18,axiom,
    ! [X0,X1] :
    ? [X2] : relation_of2(X2,X0,X1),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',existence_m1_relset_1) ).

fof(f532,plain,
    spl27_57,
    inference(avatar_split_clause,[],[f192,f530]) ).

fof(f192,plain,
    ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f20,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ? [X2] : relation_of2_as_subset(X2,X0,X1)
     => relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
    introduced(choice_axiom,[]) ).

fof(f20,axiom,
    ! [X0,X1] :
    ? [X2] : relation_of2_as_subset(X2,X0,X1),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',existence_m2_relset_1) ).

fof(f528,plain,
    spl27_56,
    inference(avatar_split_clause,[],[f185,f526]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t1_subset) ).

fof(f524,plain,
    spl27_55,
    inference(avatar_split_clause,[],[f184,f522]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,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/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',antisymmetry_r2_hidden) ).

fof(f520,plain,
    spl27_54,
    inference(avatar_split_clause,[],[f176,f518]) ).

fof(f176,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_folding,[],[f71,f92,f91]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',d5_funct_1) ).

fof(f514,plain,
    ( spl27_53
    | ~ spl27_14
    | ~ spl27_36 ),
    inference(avatar_split_clause,[],[f442,f412,f305,f511]) ).

fof(f511,plain,
    ( spl27_53
  <=> function(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_53])]) ).

fof(f442,plain,
    ( function(sK20)
    | ~ spl27_14
    | ~ spl27_36 ),
    inference(resolution,[],[f413,f307]) ).

fof(f492,plain,
    spl27_52,
    inference(avatar_split_clause,[],[f191,f490]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t7_boole) ).

fof(f488,plain,
    spl27_51,
    inference(avatar_split_clause,[],[f181,f486]) ).

fof(f181,plain,
    ! [X0] : element(sK12(X0),powerset(X0)),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( empty(sK12(X0))
      & element(sK12(X0),powerset(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f39,f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ? [X1] :
          ( empty(X1)
          & element(X1,powerset(X0)) )
     => ( empty(sK12(X0))
        & element(sK12(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,axiom,
    ! [X0] :
    ? [X1] :
      ( empty(X1)
      & element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_subset_1) ).

fof(f484,plain,
    spl27_50,
    inference(avatar_split_clause,[],[f165,f482]) ).

fof(f165,plain,
    ! [X0] :
      ( relation(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc7_relat_1) ).

fof(f480,plain,
    spl27_49,
    inference(avatar_split_clause,[],[f164,f478]) ).

fof(f164,plain,
    ! [X0] :
      ( empty(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f476,plain,
    ( spl27_48
    | ~ spl27_11
    | ~ spl27_36 ),
    inference(avatar_split_clause,[],[f441,f412,f290,f473]) ).

fof(f441,plain,
    ( function(sK18)
    | ~ spl27_11
    | ~ spl27_36 ),
    inference(resolution,[],[f413,f292]) ).

fof(f471,plain,
    spl27_47,
    inference(avatar_split_clause,[],[f163,f469]) ).

fof(f163,plain,
    ! [X0] :
      ( relation(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc8_relat_1) ).

fof(f467,plain,
    spl27_46,
    inference(avatar_split_clause,[],[f162,f465]) ).

fof(f162,plain,
    ! [X0] :
      ( empty(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f463,plain,
    spl27_45,
    inference(avatar_split_clause,[],[f161,f461]) ).

fof(f161,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t6_boole) ).

fof(f459,plain,
    spl27_44,
    inference(avatar_split_clause,[],[f158,f457]) ).

fof(f457,plain,
    ( spl27_44
  <=> ! [X0] :
        ( ~ empty(sK7(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_44])]) ).

fof(f158,plain,
    ! [X0] :
      ( ~ empty(sK7(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f449,plain,
    ( spl27_43
    | ~ spl27_7
    | ~ spl27_36 ),
    inference(avatar_split_clause,[],[f439,f412,f270,f446]) ).

fof(f446,plain,
    ( spl27_43
  <=> function(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_43])]) ).

fof(f439,plain,
    ( function(empty_set)
    | ~ spl27_7
    | ~ spl27_36 ),
    inference(resolution,[],[f413,f272]) ).

fof(f438,plain,
    spl27_42,
    inference(avatar_split_clause,[],[f199,f436]) ).

fof(f199,plain,
    ! [X0,X1] : function(sK16(X0,X1)),
    inference(cnf_transformation,[],[f119]) ).

fof(f434,plain,
    spl27_41,
    inference(avatar_split_clause,[],[f198,f432]) ).

fof(f198,plain,
    ! [X0,X1] : relation(sK16(X0,X1)),
    inference(cnf_transformation,[],[f119]) ).

fof(f430,plain,
    spl27_40,
    inference(avatar_split_clause,[],[f196,f428]) ).

fof(f196,plain,
    ! [X0,X1] : function(sK15(X0,X1)),
    inference(cnf_transformation,[],[f117]) ).

fof(f426,plain,
    spl27_39,
    inference(avatar_split_clause,[],[f195,f424]) ).

fof(f195,plain,
    ! [X0,X1] : relation(sK15(X0,X1)),
    inference(cnf_transformation,[],[f117]) ).

fof(f422,plain,
    spl27_38,
    inference(avatar_split_clause,[],[f180,f420]) ).

fof(f180,plain,
    ! [X0] : element(sK11(X0),X0),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] : element(sK11(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f19,f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK11(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f19,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',existence_m1_subset_1) ).

fof(f418,plain,
    spl27_37,
    inference(avatar_split_clause,[],[f160,f416]) ).

fof(f160,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc1_relat_1) ).

fof(f414,plain,
    spl27_36,
    inference(avatar_split_clause,[],[f159,f412]) ).

fof(f159,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( empty(X0)
     => function(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc1_funct_1) ).

fof(f410,plain,
    spl27_35,
    inference(avatar_split_clause,[],[f183,f408]) ).

fof(f183,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',reflexivity_r1_tarski) ).

fof(f406,plain,
    spl27_34,
    inference(avatar_split_clause,[],[f182,f404]) ).

fof(f182,plain,
    ! [X0] : empty(sK12(X0)),
    inference(cnf_transformation,[],[f110]) ).

fof(f402,plain,
    spl27_33,
    inference(avatar_split_clause,[],[f156,f400]) ).

fof(f400,plain,
    ( spl27_33
  <=> ! [X0] : ~ empty(powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_33])]) ).

fof(f156,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc1_subset_1) ).

fof(f398,plain,
    spl27_32,
    inference(avatar_split_clause,[],[f238,f395]) ).

fof(f395,plain,
    ( spl27_32
  <=> function(sK26) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_32])]) ).

fof(f238,plain,
    function(sK26),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ( function(sK26)
    & empty(sK26)
    & relation(sK26) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f36,f142]) ).

fof(f142,plain,
    ( ? [X0] :
        ( function(X0)
        & empty(X0)
        & relation(X0) )
   => ( function(sK26)
      & empty(sK26)
      & relation(sK26) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,axiom,
    ? [X0] :
      ( function(X0)
      & empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_funct_1) ).

fof(f393,plain,
    spl27_31,
    inference(avatar_split_clause,[],[f237,f390]) ).

fof(f237,plain,
    empty(sK26),
    inference(cnf_transformation,[],[f143]) ).

fof(f388,plain,
    spl27_30,
    inference(avatar_split_clause,[],[f236,f385]) ).

fof(f385,plain,
    ( spl27_30
  <=> relation(sK26) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).

fof(f236,plain,
    relation(sK26),
    inference(cnf_transformation,[],[f143]) ).

fof(f383,plain,
    spl27_29,
    inference(avatar_split_clause,[],[f235,f380]) ).

fof(f235,plain,
    empty(sK25),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ( empty(sK25)
    & one_to_one(sK25)
    & function(sK25)
    & relation(sK25) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f32,f140]) ).

fof(f140,plain,
    ( ? [X0] :
        ( empty(X0)
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( empty(sK25)
      & one_to_one(sK25)
      & function(sK25)
      & relation(sK25) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,axiom,
    ? [X0] :
      ( empty(X0)
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_partfun1) ).

fof(f378,plain,
    spl27_28,
    inference(avatar_split_clause,[],[f234,f375]) ).

fof(f234,plain,
    one_to_one(sK25),
    inference(cnf_transformation,[],[f141]) ).

fof(f373,plain,
    spl27_27,
    inference(avatar_split_clause,[],[f233,f370]) ).

fof(f370,plain,
    ( spl27_27
  <=> function(sK25) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_27])]) ).

fof(f233,plain,
    function(sK25),
    inference(cnf_transformation,[],[f141]) ).

fof(f368,plain,
    spl27_26,
    inference(avatar_split_clause,[],[f232,f365]) ).

fof(f365,plain,
    ( spl27_26
  <=> relation(sK25) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_26])]) ).

fof(f232,plain,
    relation(sK25),
    inference(cnf_transformation,[],[f141]) ).

fof(f363,plain,
    spl27_25,
    inference(avatar_split_clause,[],[f231,f360]) ).

fof(f360,plain,
    ( spl27_25
  <=> one_to_one(sK24) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_25])]) ).

fof(f231,plain,
    one_to_one(sK24),
    inference(cnf_transformation,[],[f139]) ).

fof(f139,plain,
    ( one_to_one(sK24)
    & function(sK24)
    & relation(sK24) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f41,f138]) ).

fof(f138,plain,
    ( ? [X0] :
        ( one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( one_to_one(sK24)
      & function(sK24)
      & relation(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,axiom,
    ? [X0] :
      ( one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc3_funct_1) ).

fof(f358,plain,
    spl27_24,
    inference(avatar_split_clause,[],[f230,f355]) ).

fof(f230,plain,
    function(sK24),
    inference(cnf_transformation,[],[f139]) ).

fof(f353,plain,
    spl27_23,
    inference(avatar_split_clause,[],[f229,f350]) ).

fof(f229,plain,
    relation(sK24),
    inference(cnf_transformation,[],[f139]) ).

fof(f348,plain,
    spl27_22,
    inference(avatar_split_clause,[],[f228,f345]) ).

fof(f228,plain,
    function(sK23),
    inference(cnf_transformation,[],[f137]) ).

fof(f137,plain,
    ( function(sK23)
    & relation(sK23) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f30,f136]) ).

fof(f136,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK23)
      & relation(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,axiom,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_funct_1) ).

fof(f343,plain,
    spl27_21,
    inference(avatar_split_clause,[],[f227,f340]) ).

fof(f227,plain,
    relation(sK23),
    inference(cnf_transformation,[],[f137]) ).

fof(f338,plain,
    spl27_20,
    inference(avatar_split_clause,[],[f226,f335]) ).

fof(f226,plain,
    function(sK22),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ( function(sK22)
    & relation_empty_yielding(sK22)
    & relation(sK22) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f43,f134]) ).

fof(f134,plain,
    ( ? [X0] :
        ( function(X0)
        & relation_empty_yielding(X0)
        & relation(X0) )
   => ( function(sK22)
      & relation_empty_yielding(sK22)
      & relation(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,axiom,
    ? [X0] :
      ( function(X0)
      & relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc4_funct_1) ).

fof(f333,plain,
    spl27_19,
    inference(avatar_split_clause,[],[f225,f330]) ).

fof(f330,plain,
    ( spl27_19
  <=> relation_empty_yielding(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_19])]) ).

fof(f225,plain,
    relation_empty_yielding(sK22),
    inference(cnf_transformation,[],[f135]) ).

fof(f328,plain,
    spl27_18,
    inference(avatar_split_clause,[],[f224,f325]) ).

fof(f224,plain,
    relation(sK22),
    inference(cnf_transformation,[],[f135]) ).

fof(f323,plain,
    spl27_17,
    inference(avatar_split_clause,[],[f223,f320]) ).

fof(f320,plain,
    ( spl27_17
  <=> relation_empty_yielding(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).

fof(f223,plain,
    relation_empty_yielding(sK21),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ( relation_empty_yielding(sK21)
    & relation(sK21) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f42,f132]) ).

fof(f132,plain,
    ( ? [X0] :
        ( relation_empty_yielding(X0)
        & relation(X0) )
   => ( relation_empty_yielding(sK21)
      & relation(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,axiom,
    ? [X0] :
      ( relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc3_relat_1) ).

fof(f318,plain,
    spl27_16,
    inference(avatar_split_clause,[],[f222,f315]) ).

fof(f222,plain,
    relation(sK21),
    inference(cnf_transformation,[],[f133]) ).

fof(f313,plain,
    spl27_15,
    inference(avatar_split_clause,[],[f221,f310]) ).

fof(f310,plain,
    ( spl27_15
  <=> relation(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).

fof(f221,plain,
    relation(sK20),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,plain,
    ( relation(sK20)
    & empty(sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f33,f130]) ).

fof(f130,plain,
    ( ? [X0] :
        ( relation(X0)
        & empty(X0) )
   => ( relation(sK20)
      & empty(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,axiom,
    ? [X0] :
      ( relation(X0)
      & empty(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_relat_1) ).

fof(f308,plain,
    spl27_14,
    inference(avatar_split_clause,[],[f220,f305]) ).

fof(f220,plain,
    empty(sK20),
    inference(cnf_transformation,[],[f131]) ).

fof(f303,plain,
    spl27_13,
    inference(avatar_split_clause,[],[f219,f300]) ).

fof(f219,plain,
    relation(sK19),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ( relation(sK19)
    & ~ empty(sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f38,f128]) ).

fof(f128,plain,
    ( ? [X0] :
        ( relation(X0)
        & ~ empty(X0) )
   => ( relation(sK19)
      & ~ empty(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,axiom,
    ? [X0] :
      ( relation(X0)
      & ~ empty(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_relat_1) ).

fof(f298,plain,
    ~ spl27_12,
    inference(avatar_split_clause,[],[f218,f295]) ).

fof(f295,plain,
    ( spl27_12
  <=> empty(sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).

fof(f218,plain,
    ~ empty(sK19),
    inference(cnf_transformation,[],[f129]) ).

fof(f293,plain,
    spl27_11,
    inference(avatar_split_clause,[],[f217,f290]) ).

fof(f217,plain,
    empty(sK18),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    empty(sK18),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f35,f126]) ).

fof(f126,plain,
    ( ? [X0] : empty(X0)
   => empty(sK18) ),
    introduced(choice_axiom,[]) ).

fof(f35,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_xboole_0) ).

fof(f288,plain,
    ~ spl27_10,
    inference(avatar_split_clause,[],[f216,f285]) ).

fof(f285,plain,
    ( spl27_10
  <=> empty(sK17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).

fof(f216,plain,
    ~ empty(sK17),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ~ empty(sK17),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f40,f124]) ).

fof(f124,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK17) ),
    introduced(choice_axiom,[]) ).

fof(f40,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_xboole_0) ).

fof(f283,plain,
    spl27_9,
    inference(avatar_split_clause,[],[f155,f280]) ).

fof(f155,plain,
    relation_empty_yielding(empty_set),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ( relation_empty_yielding(empty_set)
    & relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc12_relat_1) ).

fof(f278,plain,
    spl27_8,
    inference(avatar_split_clause,[],[f152,f275]) ).

fof(f152,plain,
    relation(empty_set),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc4_relat_1) ).

fof(f273,plain,
    spl27_7,
    inference(avatar_split_clause,[],[f150,f270]) ).

fof(f150,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc1_xboole_0) ).

fof(f268,plain,
    ~ spl27_6,
    inference(avatar_split_clause,[],[f149,f265]) ).

fof(f149,plain,
    ~ in(apply(sK6,sK5),relation_rng(sK6)),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ( ~ in(apply(sK6,sK5),relation_rng(sK6))
    & empty_set != sK4
    & in(sK5,sK3)
    & relation_of2_as_subset(sK6,sK3,sK4)
    & quasi_total(sK6,sK3,sK4)
    & function(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f59,f96]) ).

fof(f96,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ in(apply(X3,X2),relation_rng(X3))
        & empty_set != X1
        & in(X2,X0)
        & relation_of2_as_subset(X3,X0,X1)
        & quasi_total(X3,X0,X1)
        & function(X3) )
   => ( ~ in(apply(sK6,sK5),relation_rng(sK6))
      & empty_set != sK4
      & in(sK5,sK3)
      & relation_of2_as_subset(sK6,sK3,sK4)
      & quasi_total(sK6,sK3,sK4)
      & function(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ? [X0,X1,X2,X3] :
      ( ~ in(apply(X3,X2),relation_rng(X3))
      & empty_set != X1
      & in(X2,X0)
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ? [X0,X1,X2,X3] :
      ( ~ in(apply(X3,X2),relation_rng(X3))
      & empty_set != X1
      & in(X2,X0)
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( relation_of2_as_subset(X3,X0,X1)
          & quasi_total(X3,X0,X1)
          & function(X3) )
       => ( in(X2,X0)
         => ( in(apply(X3,X2),relation_rng(X3))
            | empty_set = X1 ) ) ),
    inference(negated_conjecture,[],[f53]) ).

fof(f53,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( relation_of2_as_subset(X3,X0,X1)
        & quasi_total(X3,X0,X1)
        & function(X3) )
     => ( in(X2,X0)
       => ( in(apply(X3,X2),relation_rng(X3))
          | empty_set = X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t6_funct_2) ).

fof(f263,plain,
    spl27_5,
    inference(avatar_split_clause,[],[f146,f260]) ).

fof(f146,plain,
    relation_of2_as_subset(sK6,sK3,sK4),
    inference(cnf_transformation,[],[f97]) ).

fof(f258,plain,
    spl27_4,
    inference(avatar_split_clause,[],[f145,f255]) ).

fof(f145,plain,
    quasi_total(sK6,sK3,sK4),
    inference(cnf_transformation,[],[f97]) ).

fof(f253,plain,
    ~ spl27_3,
    inference(avatar_split_clause,[],[f148,f250]) ).

fof(f148,plain,
    empty_set != sK4,
    inference(cnf_transformation,[],[f97]) ).

fof(f248,plain,
    spl27_2,
    inference(avatar_split_clause,[],[f147,f245]) ).

fof(f147,plain,
    in(sK5,sK3),
    inference(cnf_transformation,[],[f97]) ).

fof(f243,plain,
    spl27_1,
    inference(avatar_split_clause,[],[f144,f240]) ).

fof(f144,plain,
    function(sK6),
    inference(cnf_transformation,[],[f97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.09/0.29  % Computer : n017.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Wed Aug 30 13:23:44 EDT 2023
% 0.09/0.30  % CPUTime    : 
% 0.15/0.33  % (7858)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33  % (7967)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.15/0.33  % (7965)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.15/0.33  % (7964)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.15/0.33  % (7966)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.15/0.33  % (7969)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.15/0.33  % (7968)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.15/0.33  % (7970)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [3]
% 0.15/0.34  TRYING [4]
% 0.15/0.34  TRYING [1]
% 0.15/0.34  TRYING [2]
% 0.15/0.35  TRYING [5]
% 0.15/0.36  % (7968)First to succeed.
% 0.15/0.37  TRYING [3]
% 0.15/0.37  % (7968)Refutation found. Thanks to Tanya!
% 0.15/0.37  % SZS status Theorem for Vampire---4
% 0.15/0.37  % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.37  % (7968)------------------------------
% 0.15/0.37  % (7968)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.15/0.37  % (7968)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.15/0.37  % (7968)Termination reason: Refutation
% 0.15/0.37  
% 0.15/0.37  % (7968)Memory used [KB]: 6524
% 0.15/0.37  % (7968)Time elapsed: 0.036 s
% 0.15/0.37  % (7968)------------------------------
% 0.15/0.37  % (7968)------------------------------
% 0.15/0.37  % (7858)Success in time 0.075 s
% 0.15/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------