TSTP Solution File: SEU129+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:27:07 EDT 2024

% Result   : Theorem 0.21s 0.49s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  258
% Syntax   : Number of formulae    :  871 (  46 unt;   0 def)
%            Number of atoms       : 3040 (  54 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 3688 (1519   ~;1872   |;  42   &)
%                                         ( 245 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :  244 ( 242 usr; 239 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   : 1592 (1575   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4064,plain,
    $false,
    inference(avatar_sat_refutation,[],[f73,f78,f83,f88,f93,f97,f101,f105,f109,f113,f119,f123,f128,f135,f139,f155,f159,f167,f173,f180,f184,f190,f195,f199,f203,f217,f232,f236,f249,f253,f257,f261,f276,f290,f294,f299,f303,f328,f332,f350,f366,f370,f374,f378,f410,f414,f422,f426,f430,f434,f446,f450,f454,f458,f462,f478,f482,f486,f490,f534,f542,f555,f559,f563,f567,f594,f598,f610,f614,f618,f629,f641,f645,f649,f653,f657,f661,f665,f703,f707,f711,f715,f719,f723,f727,f731,f735,f739,f743,f747,f953,f957,f961,f965,f969,f1033,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1167,f1383,f1456,f1485,f1489,f1493,f1497,f1502,f1506,f1510,f1514,f1554,f1558,f1562,f1566,f1570,f1574,f1578,f1582,f1586,f1590,f1591,f1599,f1603,f1607,f1611,f1615,f1619,f1623,f1683,f1723,f1727,f1731,f1735,f1765,f1782,f1786,f1805,f1809,f1813,f1817,f1821,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1877,f2322,f2326,f2330,f2335,f2361,f2365,f2439,f2444,f2448,f2461,f2465,f2469,f2473,f2477,f2481,f2485,f2489,f2493,f2497,f2501,f2505,f2509,f2661,f2760,f2768,f2772,f2776,f2780,f2784,f2788,f3049,f3053,f3057,f3061,f3065,f3069,f3073,f3078,f3082,f3236,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3428,f3432,f3436,f3875,f3941,f3945,f3949,f3953,f3995,f4013,f4017,f4021,f4025,f4029,f4033,f4037,f4041,f4045,f4060]) ).

fof(f4060,plain,
    ( spl8_2
    | ~ spl8_224 ),
    inference(avatar_contradiction_clause,[],[f4046]) ).

fof(f4046,plain,
    ( $false
    | spl8_2
    | ~ spl8_224 ),
    inference(resolution,[],[f3874,f77]) ).

fof(f77,plain,
    ( ~ subset(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3))
    | spl8_2 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f75,plain,
    ( spl8_2
  <=> subset(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f3874,plain,
    ( ! [X0] : subset(set_intersection2(sK1,X0),set_intersection2(sK2,X0))
    | ~ spl8_224 ),
    inference(avatar_component_clause,[],[f3873]) ).

fof(f3873,plain,
    ( spl8_224
  <=> ! [X0] : subset(set_intersection2(sK1,X0),set_intersection2(sK2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_224])]) ).

fof(f4045,plain,
    ( spl8_238
    | ~ spl8_35
    | ~ spl8_86 ),
    inference(avatar_split_clause,[],[f864,f725,f292,f4043]) ).

fof(f4043,plain,
    ( spl8_238
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(set_intersection2(X2,X3),X4))
        | in(sK5(X1,X0,set_intersection2(set_intersection2(X2,X3),X4)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_238])]) ).

fof(f292,plain,
    ( spl8_35
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,set_intersection2(X1,X2))
        | in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).

fof(f725,plain,
    ( spl8_86
  <=> ! [X0,X3,X2,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X1)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).

fof(f864,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(set_intersection2(X2,X3),X4))
        | in(sK5(X1,X0,set_intersection2(set_intersection2(X2,X3),X4)),X2) )
    | ~ spl8_35
    | ~ spl8_86 ),
    inference(resolution,[],[f726,f293]) ).

fof(f293,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,set_intersection2(X1,X2))
        | in(X0,X1) )
    | ~ spl8_35 ),
    inference(avatar_component_clause,[],[f292]) ).

fof(f726,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | ~ empty(X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_86 ),
    inference(avatar_component_clause,[],[f725]) ).

fof(f4041,plain,
    ( spl8_237
    | ~ spl8_37
    | ~ spl8_86 ),
    inference(avatar_split_clause,[],[f863,f725,f301,f4039]) ).

fof(f4039,plain,
    ( spl8_237
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(set_intersection2(X2,X3),X4))
        | in(sK5(X1,X0,set_intersection2(set_intersection2(X2,X3),X4)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_237])]) ).

fof(f301,plain,
    ( spl8_37
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,set_intersection2(X1,X2))
        | in(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).

fof(f863,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(set_intersection2(X2,X3),X4))
        | in(sK5(X1,X0,set_intersection2(set_intersection2(X2,X3),X4)),X3) )
    | ~ spl8_37
    | ~ spl8_86 ),
    inference(resolution,[],[f726,f302]) ).

fof(f302,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,set_intersection2(X1,X2))
        | in(X0,X2) )
    | ~ spl8_37 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f4037,plain,
    ( spl8_236
    | ~ spl8_35
    | ~ spl8_85 ),
    inference(avatar_split_clause,[],[f848,f721,f292,f4035]) ).

fof(f4035,plain,
    ( spl8_236
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,set_intersection2(X3,X4)))
        | in(sK5(X1,X0,set_intersection2(X2,set_intersection2(X3,X4))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_236])]) ).

fof(f721,plain,
    ( spl8_85
  <=> ! [X0,X3,X2,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X1)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).

fof(f848,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,set_intersection2(X3,X4)))
        | in(sK5(X1,X0,set_intersection2(X2,set_intersection2(X3,X4))),X3) )
    | ~ spl8_35
    | ~ spl8_85 ),
    inference(resolution,[],[f722,f293]) ).

fof(f722,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | ~ empty(X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_85 ),
    inference(avatar_component_clause,[],[f721]) ).

fof(f4033,plain,
    ( spl8_235
    | ~ spl8_37
    | ~ spl8_85 ),
    inference(avatar_split_clause,[],[f847,f721,f301,f4031]) ).

fof(f4031,plain,
    ( spl8_235
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,set_intersection2(X3,X4)))
        | in(sK5(X1,X0,set_intersection2(X2,set_intersection2(X3,X4))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_235])]) ).

fof(f847,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,set_intersection2(X3,X4)))
        | in(sK5(X1,X0,set_intersection2(X2,set_intersection2(X3,X4))),X4) )
    | ~ spl8_37
    | ~ spl8_85 ),
    inference(resolution,[],[f722,f302]) ).

fof(f4029,plain,
    ( spl8_234
    | ~ spl8_35
    | ~ spl8_84 ),
    inference(avatar_split_clause,[],[f830,f717,f292,f4027]) ).

fof(f4027,plain,
    ( spl8_234
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(set_intersection2(X2,X3),X4),X0)
        | in(sK5(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_234])]) ).

fof(f717,plain,
    ( spl8_84
  <=> ! [X0,X3,X2,X1] :
        ( sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X3)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).

fof(f830,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(set_intersection2(X2,X3),X4),X0)
        | in(sK5(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X2) )
    | ~ spl8_35
    | ~ spl8_84 ),
    inference(resolution,[],[f718,f293]) ).

fof(f718,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X1)
        | ~ empty(X3)
        | sP0(X0,set_intersection2(X1,X2),X3) )
    | ~ spl8_84 ),
    inference(avatar_component_clause,[],[f717]) ).

fof(f4025,plain,
    ( spl8_233
    | ~ spl8_37
    | ~ spl8_84 ),
    inference(avatar_split_clause,[],[f829,f717,f301,f4023]) ).

fof(f4023,plain,
    ( spl8_233
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(set_intersection2(X2,X3),X4),X0)
        | in(sK5(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_233])]) ).

fof(f829,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(set_intersection2(X2,X3),X4),X0)
        | in(sK5(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X3) )
    | ~ spl8_37
    | ~ spl8_84 ),
    inference(resolution,[],[f718,f302]) ).

fof(f4021,plain,
    ( spl8_232
    | ~ spl8_35
    | ~ spl8_83 ),
    inference(avatar_split_clause,[],[f814,f713,f292,f4019]) ).

fof(f4019,plain,
    ( spl8_232
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0)
        | in(sK5(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_232])]) ).

fof(f713,plain,
    ( spl8_83
  <=> ! [X0,X3,X2,X1] :
        ( sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X3)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).

fof(f814,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0)
        | in(sK5(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0),X3) )
    | ~ spl8_35
    | ~ spl8_83 ),
    inference(resolution,[],[f714,f293]) ).

fof(f714,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X2)
        | ~ empty(X3)
        | sP0(X0,set_intersection2(X1,X2),X3) )
    | ~ spl8_83 ),
    inference(avatar_component_clause,[],[f713]) ).

fof(f4017,plain,
    ( spl8_231
    | ~ spl8_37
    | ~ spl8_83 ),
    inference(avatar_split_clause,[],[f813,f713,f301,f4015]) ).

fof(f4015,plain,
    ( spl8_231
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0)
        | in(sK5(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_231])]) ).

fof(f813,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0)
        | in(sK5(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0),X4) )
    | ~ spl8_37
    | ~ spl8_83 ),
    inference(resolution,[],[f714,f302]) ).

fof(f4013,plain,
    ( spl8_230
    | ~ spl8_40
    | ~ spl8_72 ),
    inference(avatar_split_clause,[],[f630,f627,f348,f4011]) ).

fof(f4011,plain,
    ( spl8_230
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(set_intersection2(X0,X1),X2)
        | ~ in(set_intersection2(X0,X1),X3)
        | ~ in(set_intersection2(X3,X2),X0)
        | ~ in(set_intersection2(X3,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_230])]) ).

fof(f348,plain,
    ( spl8_40
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X0,X2)
        | in(X0,set_intersection2(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).

fof(f627,plain,
    ( spl8_72
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X0,X2)
        | ~ in(set_intersection2(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).

fof(f630,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(set_intersection2(X0,X1),X2)
        | ~ in(set_intersection2(X0,X1),X3)
        | ~ in(set_intersection2(X3,X2),X0)
        | ~ in(set_intersection2(X3,X2),X1) )
    | ~ spl8_40
    | ~ spl8_72 ),
    inference(resolution,[],[f628,f349]) ).

fof(f349,plain,
    ( ! [X2,X0,X1] :
        ( in(X0,set_intersection2(X2,X1))
        | ~ in(X0,X2)
        | ~ in(X0,X1) )
    | ~ spl8_40 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f628,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(set_intersection2(X1,X2),X0)
        | ~ in(X0,X2)
        | ~ in(X0,X1) )
    | ~ spl8_72 ),
    inference(avatar_component_clause,[],[f627]) ).

fof(f3995,plain,
    ( spl8_229
    | ~ spl8_117
    | ~ spl8_214 ),
    inference(avatar_split_clause,[],[f3743,f3398,f1508,f3993]) ).

fof(f3993,plain,
    ( spl8_229
  <=> ! [X0] : subset(set_intersection2(X0,sK1),set_intersection2(sK2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_229])]) ).

fof(f1508,plain,
    ( spl8_117
  <=> ! [X0,X1] :
        ( subset(set_intersection2(X0,sK1),X1)
        | in(sK4(set_intersection2(X0,sK1),X1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_117])]) ).

fof(f3398,plain,
    ( spl8_214
  <=> ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X0)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_214])]) ).

fof(f3743,plain,
    ( ! [X0] : subset(set_intersection2(X0,sK1),set_intersection2(sK2,X0))
    | ~ spl8_117
    | ~ spl8_214 ),
    inference(duplicate_literal_removal,[],[f3725]) ).

fof(f3725,plain,
    ( ! [X0] :
        ( subset(set_intersection2(X0,sK1),set_intersection2(sK2,X0))
        | subset(set_intersection2(X0,sK1),set_intersection2(sK2,X0)) )
    | ~ spl8_117
    | ~ spl8_214 ),
    inference(resolution,[],[f3399,f1509]) ).

fof(f1509,plain,
    ( ! [X0,X1] :
        ( in(sK4(set_intersection2(X0,sK1),X1),sK2)
        | subset(set_intersection2(X0,sK1),X1) )
    | ~ spl8_117 ),
    inference(avatar_component_clause,[],[f1508]) ).

fof(f3399,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X0)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X0)) )
    | ~ spl8_214 ),
    inference(avatar_component_clause,[],[f3398]) ).

fof(f3953,plain,
    ( spl8_228
    | ~ spl8_11
    | ~ spl8_96 ),
    inference(avatar_split_clause,[],[f1014,f967,f117,f3951]) ).

fof(f3951,plain,
    ( spl8_228
  <=> ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ in(X0,sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_228])]) ).

fof(f117,plain,
    ( spl8_11
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).

fof(f967,plain,
    ( spl8_96
  <=> ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | in(sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).

fof(f1014,plain,
    ( ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ in(X0,sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) )
    | ~ spl8_11
    | ~ spl8_96 ),
    inference(resolution,[],[f968,f118]) ).

fof(f118,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) )
    | ~ spl8_11 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f968,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
        | sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)) )
    | ~ spl8_96 ),
    inference(avatar_component_clause,[],[f967]) ).

fof(f3949,plain,
    ( spl8_227
    | ~ spl8_11
    | ~ spl8_95 ),
    inference(avatar_split_clause,[],[f999,f963,f117,f3947]) ).

fof(f3947,plain,
    ( spl8_227
  <=> ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ in(X1,sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_227])]) ).

fof(f963,plain,
    ( spl8_95
  <=> ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | in(sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).

fof(f999,plain,
    ( ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ in(X1,sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) )
    | ~ spl8_11
    | ~ spl8_95 ),
    inference(resolution,[],[f964,f118]) ).

fof(f964,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
        | sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)) )
    | ~ spl8_95 ),
    inference(avatar_component_clause,[],[f963]) ).

fof(f3945,plain,
    ( spl8_226
    | ~ spl8_11
    | ~ spl8_94 ),
    inference(avatar_split_clause,[],[f983,f959,f117,f3943]) ).

fof(f3943,plain,
    ( spl8_226
  <=> ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ in(X1,sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_226])]) ).

fof(f959,plain,
    ( spl8_94
  <=> ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | in(sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).

fof(f983,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ in(X1,sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) )
    | ~ spl8_11
    | ~ spl8_94 ),
    inference(resolution,[],[f960,f118]) ).

fof(f960,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1)
        | sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)) )
    | ~ spl8_94 ),
    inference(avatar_component_clause,[],[f959]) ).

fof(f3941,plain,
    ( spl8_225
    | ~ spl8_11
    | ~ spl8_93 ),
    inference(avatar_split_clause,[],[f970,f955,f117,f3939]) ).

fof(f3939,plain,
    ( spl8_225
  <=> ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ in(X2,sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_225])]) ).

fof(f955,plain,
    ( spl8_93
  <=> ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | in(sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).

fof(f970,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ in(X2,sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))) )
    | ~ spl8_11
    | ~ spl8_93 ),
    inference(resolution,[],[f956,f118]) ).

fof(f956,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2)
        | sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)) )
    | ~ spl8_93 ),
    inference(avatar_component_clause,[],[f955]) ).

fof(f3875,plain,
    ( spl8_224
    | ~ spl8_116
    | ~ spl8_213 ),
    inference(avatar_split_clause,[],[f3705,f3394,f1504,f3873]) ).

fof(f1504,plain,
    ( spl8_116
  <=> ! [X0,X1] :
        ( subset(set_intersection2(sK1,X0),X1)
        | in(sK4(set_intersection2(sK1,X0),X1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_116])]) ).

fof(f3394,plain,
    ( spl8_213
  <=> ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X1)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_213])]) ).

fof(f3705,plain,
    ( ! [X0] : subset(set_intersection2(sK1,X0),set_intersection2(sK2,X0))
    | ~ spl8_116
    | ~ spl8_213 ),
    inference(duplicate_literal_removal,[],[f3685]) ).

fof(f3685,plain,
    ( ! [X0] :
        ( subset(set_intersection2(sK1,X0),set_intersection2(sK2,X0))
        | subset(set_intersection2(sK1,X0),set_intersection2(sK2,X0)) )
    | ~ spl8_116
    | ~ spl8_213 ),
    inference(resolution,[],[f3395,f1505]) ).

fof(f1505,plain,
    ( ! [X0,X1] :
        ( in(sK4(set_intersection2(sK1,X0),X1),sK2)
        | subset(set_intersection2(sK1,X0),X1) )
    | ~ spl8_116 ),
    inference(avatar_component_clause,[],[f1504]) ).

fof(f3395,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X1)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X1)) )
    | ~ spl8_213 ),
    inference(avatar_component_clause,[],[f3394]) ).

fof(f3436,plain,
    ( spl8_223
    | ~ spl8_10
    | ~ spl8_106 ),
    inference(avatar_split_clause,[],[f1356,f1083,f111,f3434]) ).

fof(f3434,plain,
    ( spl8_223
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_223])]) ).

fof(f111,plain,
    ( spl8_10
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

fof(f1083,plain,
    ( spl8_106
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X1)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).

fof(f1356,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_106 ),
    inference(resolution,[],[f1084,f112]) ).

fof(f112,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | ~ empty(X1) )
    | ~ spl8_10 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f1084,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X1)
        | sP0(set_intersection2(X0,X1),X2,X3) )
    | ~ spl8_106 ),
    inference(avatar_component_clause,[],[f1083]) ).

fof(f3432,plain,
    ( spl8_222
    | ~ spl8_137
    | ~ spl8_170 ),
    inference(avatar_split_clause,[],[f2592,f2459,f1721,f3430]) ).

fof(f3430,plain,
    ( spl8_222
  <=> ! [X0] : sP0(sK2,set_intersection2(X0,sK1),set_intersection2(X0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_222])]) ).

fof(f1721,plain,
    ( spl8_137
  <=> ! [X0,X1] :
        ( sP0(X0,set_intersection2(X1,sK1),set_intersection2(X1,sK1))
        | in(sK5(X0,set_intersection2(X1,sK1),set_intersection2(X1,sK1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_137])]) ).

fof(f2459,plain,
    ( spl8_170
  <=> ! [X0,X1] :
        ( ~ in(sK5(X0,X1,X1),X0)
        | sP0(X0,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_170])]) ).

fof(f2592,plain,
    ( ! [X0] : sP0(sK2,set_intersection2(X0,sK1),set_intersection2(X0,sK1))
    | ~ spl8_137
    | ~ spl8_170 ),
    inference(duplicate_literal_removal,[],[f2558]) ).

fof(f2558,plain,
    ( ! [X0] :
        ( sP0(sK2,set_intersection2(X0,sK1),set_intersection2(X0,sK1))
        | sP0(sK2,set_intersection2(X0,sK1),set_intersection2(X0,sK1)) )
    | ~ spl8_137
    | ~ spl8_170 ),
    inference(resolution,[],[f2460,f1722]) ).

fof(f1722,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,sK1),set_intersection2(X1,sK1)),sK2)
        | sP0(X0,set_intersection2(X1,sK1),set_intersection2(X1,sK1)) )
    | ~ spl8_137 ),
    inference(avatar_component_clause,[],[f1721]) ).

fof(f2460,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,X1,X1),X0)
        | sP0(X0,X1,X1) )
    | ~ spl8_170 ),
    inference(avatar_component_clause,[],[f2459]) ).

fof(f3428,plain,
    ( spl8_221
    | ~ spl8_10
    | ~ spl8_105 ),
    inference(avatar_split_clause,[],[f1322,f1079,f111,f3426]) ).

fof(f3426,plain,
    ( spl8_221
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_221])]) ).

fof(f1079,plain,
    ( spl8_105
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X2)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).

fof(f1322,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_105 ),
    inference(resolution,[],[f1080,f112]) ).

fof(f1080,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X2)
        | sP0(X0,set_intersection2(X1,X2),X3) )
    | ~ spl8_105 ),
    inference(avatar_component_clause,[],[f1079]) ).

fof(f3424,plain,
    ( spl8_220
    | ~ spl8_10
    | ~ spl8_104 ),
    inference(avatar_split_clause,[],[f1282,f1075,f111,f3422]) ).

fof(f3422,plain,
    ( spl8_220
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_220])]) ).

fof(f1075,plain,
    ( spl8_104
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).

fof(f1282,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X3) )
    | ~ spl8_10
    | ~ spl8_104 ),
    inference(resolution,[],[f1076,f112]) ).

fof(f1076,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_104 ),
    inference(avatar_component_clause,[],[f1075]) ).

fof(f3420,plain,
    ( spl8_219
    | ~ spl8_10
    | ~ spl8_103 ),
    inference(avatar_split_clause,[],[f1249,f1071,f111,f3418]) ).

fof(f3418,plain,
    ( spl8_219
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_219])]) ).

fof(f1071,plain,
    ( spl8_103
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).

fof(f1249,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X3) )
    | ~ spl8_10
    | ~ spl8_103 ),
    inference(resolution,[],[f1072,f112]) ).

fof(f1072,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_103 ),
    inference(avatar_component_clause,[],[f1071]) ).

fof(f3416,plain,
    ( spl8_218
    | ~ spl8_10
    | ~ spl8_102 ),
    inference(avatar_split_clause,[],[f1217,f1067,f111,f3414]) ).

fof(f3414,plain,
    ( spl8_218
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_218])]) ).

fof(f1067,plain,
    ( spl8_102
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X0)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).

fof(f1217,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_102 ),
    inference(resolution,[],[f1068,f112]) ).

fof(f1068,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X0)
        | sP0(set_intersection2(X0,X1),X2,X3) )
    | ~ spl8_102 ),
    inference(avatar_component_clause,[],[f1067]) ).

fof(f3412,plain,
    ( spl8_217
    | ~ spl8_10
    | ~ spl8_101 ),
    inference(avatar_split_clause,[],[f1177,f1063,f111,f3410]) ).

fof(f3410,plain,
    ( spl8_217
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_217])]) ).

fof(f1063,plain,
    ( spl8_101
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X1)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).

fof(f1177,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_101 ),
    inference(resolution,[],[f1064,f112]) ).

fof(f1064,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X1)
        | sP0(X0,set_intersection2(X1,X2),X3) )
    | ~ spl8_101 ),
    inference(avatar_component_clause,[],[f1063]) ).

fof(f3408,plain,
    ( spl8_216
    | ~ spl8_10
    | ~ spl8_100 ),
    inference(avatar_split_clause,[],[f1127,f1059,f111,f3406]) ).

fof(f3406,plain,
    ( spl8_216
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_216])]) ).

fof(f1059,plain,
    ( spl8_100
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).

fof(f1127,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_100 ),
    inference(resolution,[],[f1060,f112]) ).

fof(f1060,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_100 ),
    inference(avatar_component_clause,[],[f1059]) ).

fof(f3404,plain,
    ( spl8_215
    | ~ spl8_10
    | ~ spl8_99 ),
    inference(avatar_split_clause,[],[f1088,f1055,f111,f3402]) ).

fof(f3402,plain,
    ( spl8_215
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_215])]) ).

fof(f1055,plain,
    ( spl8_99
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).

fof(f1088,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_99 ),
    inference(resolution,[],[f1056,f112]) ).

fof(f1056,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_99 ),
    inference(avatar_component_clause,[],[f1055]) ).

fof(f3400,plain,
    ( spl8_214
    | ~ spl8_73
    | ~ spl8_97 ),
    inference(avatar_split_clause,[],[f1048,f1031,f639,f3398]) ).

fof(f639,plain,
    ( spl8_73
  <=> ! [X2,X0,X1] :
        ( in(sK4(set_intersection2(X0,X1),X2),X0)
        | subset(set_intersection2(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).

fof(f1031,plain,
    ( spl8_97
  <=> ! [X2,X0,X1] :
        ( ~ in(sK4(X0,set_intersection2(X1,X2)),X1)
        | ~ in(sK4(X0,set_intersection2(X1,X2)),X2)
        | subset(X0,set_intersection2(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).

fof(f1048,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X0)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X0)) )
    | ~ spl8_73
    | ~ spl8_97 ),
    inference(duplicate_literal_removal,[],[f1035]) ).

fof(f1035,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X0)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X0))
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X0)) )
    | ~ spl8_73
    | ~ spl8_97 ),
    inference(resolution,[],[f1032,f640]) ).

fof(f640,plain,
    ( ! [X2,X0,X1] :
        ( in(sK4(set_intersection2(X0,X1),X2),X0)
        | subset(set_intersection2(X0,X1),X2) )
    | ~ spl8_73 ),
    inference(avatar_component_clause,[],[f639]) ).

fof(f1032,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(X0,set_intersection2(X1,X2)),X2)
        | ~ in(sK4(X0,set_intersection2(X1,X2)),X1)
        | subset(X0,set_intersection2(X1,X2)) )
    | ~ spl8_97 ),
    inference(avatar_component_clause,[],[f1031]) ).

fof(f3396,plain,
    ( spl8_213
    | ~ spl8_74
    | ~ spl8_97 ),
    inference(avatar_split_clause,[],[f1046,f1031,f643,f3394]) ).

fof(f643,plain,
    ( spl8_74
  <=> ! [X2,X0,X1] :
        ( in(sK4(set_intersection2(X0,X1),X2),X1)
        | subset(set_intersection2(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).

fof(f1046,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X1)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X1)) )
    | ~ spl8_74
    | ~ spl8_97 ),
    inference(duplicate_literal_removal,[],[f1037]) ).

fof(f1037,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(set_intersection2(X0,X1),set_intersection2(X2,X1)),X2)
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X1))
        | subset(set_intersection2(X0,X1),set_intersection2(X2,X1)) )
    | ~ spl8_74
    | ~ spl8_97 ),
    inference(resolution,[],[f1032,f644]) ).

fof(f644,plain,
    ( ! [X2,X0,X1] :
        ( in(sK4(set_intersection2(X0,X1),X2),X1)
        | subset(set_intersection2(X0,X1),X2) )
    | ~ spl8_74 ),
    inference(avatar_component_clause,[],[f643]) ).

fof(f3392,plain,
    ( spl8_212
    | ~ spl8_11
    | ~ spl8_90 ),
    inference(avatar_split_clause,[],[f933,f741,f117,f3390]) ).

fof(f3390,plain,
    ( spl8_212
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ in(X2,sK5(X0,X1,set_intersection2(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_212])]) ).

fof(f741,plain,
    ( spl8_90
  <=> ! [X0,X3,X2,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X0)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).

fof(f933,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ in(X2,sK5(X0,X1,set_intersection2(X2,X3))) )
    | ~ spl8_11
    | ~ spl8_90 ),
    inference(resolution,[],[f742,f118]) ).

fof(f742,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_90 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f3388,plain,
    ( spl8_211
    | ~ spl8_138
    | ~ spl8_170 ),
    inference(avatar_split_clause,[],[f2589,f2459,f1725,f3386]) ).

fof(f3386,plain,
    ( spl8_211
  <=> ! [X0] : sP0(sK2,set_intersection2(sK1,X0),set_intersection2(sK1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_211])]) ).

fof(f1725,plain,
    ( spl8_138
  <=> ! [X0,X1] :
        ( sP0(X0,set_intersection2(sK1,X1),set_intersection2(sK1,X1))
        | in(sK5(X0,set_intersection2(sK1,X1),set_intersection2(sK1,X1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_138])]) ).

fof(f2589,plain,
    ( ! [X0] : sP0(sK2,set_intersection2(sK1,X0),set_intersection2(sK1,X0))
    | ~ spl8_138
    | ~ spl8_170 ),
    inference(duplicate_literal_removal,[],[f2562]) ).

fof(f2562,plain,
    ( ! [X0] :
        ( sP0(sK2,set_intersection2(sK1,X0),set_intersection2(sK1,X0))
        | sP0(sK2,set_intersection2(sK1,X0),set_intersection2(sK1,X0)) )
    | ~ spl8_138
    | ~ spl8_170 ),
    inference(resolution,[],[f2460,f1726]) ).

fof(f1726,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,set_intersection2(sK1,X1),set_intersection2(sK1,X1)),sK2)
        | sP0(X0,set_intersection2(sK1,X1),set_intersection2(sK1,X1)) )
    | ~ spl8_138 ),
    inference(avatar_component_clause,[],[f1725]) ).

fof(f3384,plain,
    ( spl8_210
    | ~ spl8_11
    | ~ spl8_89 ),
    inference(avatar_split_clause,[],[f917,f737,f117,f3382]) ).

fof(f3382,plain,
    ( spl8_210
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ in(X3,sK5(X0,X1,set_intersection2(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_210])]) ).

fof(f737,plain,
    ( spl8_89
  <=> ! [X0,X3,X2,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X0)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).

fof(f917,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ in(X3,sK5(X0,X1,set_intersection2(X2,X3))) )
    | ~ spl8_11
    | ~ spl8_89 ),
    inference(resolution,[],[f738,f118]) ).

fof(f738,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_89 ),
    inference(avatar_component_clause,[],[f737]) ).

fof(f3380,plain,
    ( spl8_209
    | ~ spl8_11
    | ~ spl8_88 ),
    inference(avatar_split_clause,[],[f897,f733,f117,f3378]) ).

fof(f3378,plain,
    ( spl8_209
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ in(X1,sK5(set_intersection2(X1,X2),X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_209])]) ).

fof(f733,plain,
    ( spl8_88
  <=> ! [X0,X3,X2,X1] :
        ( sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X3)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).

fof(f897,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ in(X1,sK5(set_intersection2(X1,X2),X3,X0)) )
    | ~ spl8_11
    | ~ spl8_88 ),
    inference(resolution,[],[f734,f118]) ).

fof(f734,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X0)
        | ~ empty(X3)
        | sP0(set_intersection2(X0,X1),X2,X3) )
    | ~ spl8_88 ),
    inference(avatar_component_clause,[],[f733]) ).

fof(f3376,plain,
    ( spl8_208
    | ~ spl8_11
    | ~ spl8_87 ),
    inference(avatar_split_clause,[],[f879,f729,f117,f3374]) ).

fof(f3374,plain,
    ( spl8_208
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ in(X2,sK5(set_intersection2(X1,X2),X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_208])]) ).

fof(f729,plain,
    ( spl8_87
  <=> ! [X0,X3,X2,X1] :
        ( sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X3)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).

fof(f879,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ in(X2,sK5(set_intersection2(X1,X2),X3,X0)) )
    | ~ spl8_11
    | ~ spl8_87 ),
    inference(resolution,[],[f730,f118]) ).

fof(f730,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X1)
        | ~ empty(X3)
        | sP0(set_intersection2(X0,X1),X2,X3) )
    | ~ spl8_87 ),
    inference(avatar_component_clause,[],[f729]) ).

fof(f3372,plain,
    ( spl8_207
    | ~ spl8_11
    | ~ spl8_86 ),
    inference(avatar_split_clause,[],[f861,f725,f117,f3370]) ).

fof(f3370,plain,
    ( spl8_207
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ in(X2,sK5(X1,X0,set_intersection2(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_207])]) ).

fof(f861,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ in(X2,sK5(X1,X0,set_intersection2(X2,X3))) )
    | ~ spl8_11
    | ~ spl8_86 ),
    inference(resolution,[],[f726,f118]) ).

fof(f3368,plain,
    ( spl8_206
    | ~ spl8_11
    | ~ spl8_85 ),
    inference(avatar_split_clause,[],[f845,f721,f117,f3366]) ).

fof(f3366,plain,
    ( spl8_206
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ in(X3,sK5(X1,X0,set_intersection2(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_206])]) ).

fof(f845,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ in(X3,sK5(X1,X0,set_intersection2(X2,X3))) )
    | ~ spl8_11
    | ~ spl8_85 ),
    inference(resolution,[],[f722,f118]) ).

fof(f3364,plain,
    ( spl8_205
    | ~ spl8_11
    | ~ spl8_84 ),
    inference(avatar_split_clause,[],[f826,f717,f117,f3362]) ).

fof(f3362,plain,
    ( spl8_205
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ in(X2,sK5(X1,set_intersection2(X2,X3),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_205])]) ).

fof(f826,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ in(X2,sK5(X1,set_intersection2(X2,X3),X0)) )
    | ~ spl8_11
    | ~ spl8_84 ),
    inference(resolution,[],[f718,f118]) ).

fof(f3360,plain,
    ( spl8_204
    | ~ spl8_11
    | ~ spl8_83 ),
    inference(avatar_split_clause,[],[f810,f713,f117,f3358]) ).

fof(f3358,plain,
    ( spl8_204
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ in(X3,sK5(X1,set_intersection2(X2,X3),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_204])]) ).

fof(f810,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ in(X3,sK5(X1,set_intersection2(X2,X3),X0)) )
    | ~ spl8_11
    | ~ spl8_83 ),
    inference(resolution,[],[f714,f118]) ).

fof(f3356,plain,
    ( spl8_203
    | ~ spl8_35
    | ~ spl8_74 ),
    inference(avatar_split_clause,[],[f688,f643,f292,f3354]) ).

fof(f3354,plain,
    ( spl8_203
  <=> ! [X0,X3,X2,X1] :
        ( subset(set_intersection2(X0,set_intersection2(X1,X2)),X3)
        | in(sK4(set_intersection2(X0,set_intersection2(X1,X2)),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_203])]) ).

fof(f688,plain,
    ( ! [X2,X3,X0,X1] :
        ( subset(set_intersection2(X0,set_intersection2(X1,X2)),X3)
        | in(sK4(set_intersection2(X0,set_intersection2(X1,X2)),X3),X1) )
    | ~ spl8_35
    | ~ spl8_74 ),
    inference(resolution,[],[f644,f293]) ).

fof(f3352,plain,
    ( spl8_202
    | ~ spl8_37
    | ~ spl8_74 ),
    inference(avatar_split_clause,[],[f687,f643,f301,f3350]) ).

fof(f3350,plain,
    ( spl8_202
  <=> ! [X0,X3,X2,X1] :
        ( subset(set_intersection2(X0,set_intersection2(X1,X2)),X3)
        | in(sK4(set_intersection2(X0,set_intersection2(X1,X2)),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_202])]) ).

fof(f687,plain,
    ( ! [X2,X3,X0,X1] :
        ( subset(set_intersection2(X0,set_intersection2(X1,X2)),X3)
        | in(sK4(set_intersection2(X0,set_intersection2(X1,X2)),X3),X2) )
    | ~ spl8_37
    | ~ spl8_74 ),
    inference(resolution,[],[f644,f302]) ).

fof(f3348,plain,
    ( spl8_201
    | ~ spl8_35
    | ~ spl8_73 ),
    inference(avatar_split_clause,[],[f670,f639,f292,f3346]) ).

fof(f3346,plain,
    ( spl8_201
  <=> ! [X0,X3,X2,X1] :
        ( subset(set_intersection2(set_intersection2(X0,X1),X2),X3)
        | in(sK4(set_intersection2(set_intersection2(X0,X1),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_201])]) ).

fof(f670,plain,
    ( ! [X2,X3,X0,X1] :
        ( subset(set_intersection2(set_intersection2(X0,X1),X2),X3)
        | in(sK4(set_intersection2(set_intersection2(X0,X1),X2),X3),X0) )
    | ~ spl8_35
    | ~ spl8_73 ),
    inference(resolution,[],[f640,f293]) ).

fof(f3236,plain,
    ( spl8_200
    | ~ spl8_37
    | ~ spl8_73 ),
    inference(avatar_split_clause,[],[f669,f639,f301,f3234]) ).

fof(f3234,plain,
    ( spl8_200
  <=> ! [X0,X3,X2,X1] :
        ( subset(set_intersection2(set_intersection2(X0,X1),X2),X3)
        | in(sK4(set_intersection2(set_intersection2(X0,X1),X2),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_200])]) ).

fof(f669,plain,
    ( ! [X2,X3,X0,X1] :
        ( subset(set_intersection2(set_intersection2(X0,X1),X2),X3)
        | in(sK4(set_intersection2(set_intersection2(X0,X1),X2),X3),X1) )
    | ~ spl8_37
    | ~ spl8_73 ),
    inference(resolution,[],[f640,f302]) ).

fof(f3082,plain,
    ( spl8_199
    | ~ spl8_106 ),
    inference(avatar_split_clause,[],[f1362,f1083,f3080]) ).

fof(f3080,plain,
    ( spl8_199
  <=> ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X1),X1)
        | sP0(set_intersection2(X0,X1),X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_199])]) ).

fof(f1362,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X1),X1)
        | sP0(set_intersection2(X0,X1),X2,X1) )
    | ~ spl8_106 ),
    inference(factoring,[],[f1084]) ).

fof(f3078,plain,
    ( spl8_198
    | ~ spl8_19
    | ~ spl8_183 ),
    inference(avatar_split_clause,[],[f2764,f2658,f171,f3075]) ).

fof(f3075,plain,
    ( spl8_198
  <=> sK1 = set_intersection2(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_198])]) ).

fof(f171,plain,
    ( spl8_19
  <=> ! [X2,X0,X1] :
        ( set_intersection2(X0,X1) = X2
        | ~ sP0(X1,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).

fof(f2658,plain,
    ( spl8_183
  <=> sP0(sK2,sK1,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_183])]) ).

fof(f2764,plain,
    ( sK1 = set_intersection2(sK1,sK2)
    | ~ spl8_19
    | ~ spl8_183 ),
    inference(resolution,[],[f2660,f172]) ).

fof(f172,plain,
    ( ! [X2,X0,X1] :
        ( ~ sP0(X1,X0,X2)
        | set_intersection2(X0,X1) = X2 )
    | ~ spl8_19 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f2660,plain,
    ( sP0(sK2,sK1,sK1)
    | ~ spl8_183 ),
    inference(avatar_component_clause,[],[f2658]) ).

fof(f3073,plain,
    ( spl8_197
    | ~ spl8_105 ),
    inference(avatar_split_clause,[],[f1328,f1079,f3071]) ).

fof(f3071,plain,
    ( spl8_197
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X2),X2)
        | sP0(X0,set_intersection2(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_197])]) ).

fof(f1328,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X2),X2)
        | sP0(X0,set_intersection2(X1,X2),X2) )
    | ~ spl8_105 ),
    inference(factoring,[],[f1080]) ).

fof(f3069,plain,
    ( spl8_196
    | ~ spl8_104 ),
    inference(avatar_split_clause,[],[f1295,f1075,f3067]) ).

fof(f3067,plain,
    ( spl8_196
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X1)),X1)
        | sP0(X0,X1,set_intersection2(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_196])]) ).

fof(f1295,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X1)),X1)
        | sP0(X0,X1,set_intersection2(X2,X1)) )
    | ~ spl8_104 ),
    inference(factoring,[],[f1076]) ).

fof(f3065,plain,
    ( spl8_195
    | ~ spl8_103 ),
    inference(avatar_split_clause,[],[f1262,f1071,f3063]) ).

fof(f3063,plain,
    ( spl8_195
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X0)),X0)
        | sP0(X0,X1,set_intersection2(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_195])]) ).

fof(f1262,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X0)),X0)
        | sP0(X0,X1,set_intersection2(X2,X0)) )
    | ~ spl8_103 ),
    inference(factoring,[],[f1072]) ).

fof(f3061,plain,
    ( spl8_194
    | ~ spl8_102 ),
    inference(avatar_split_clause,[],[f1223,f1067,f3059]) ).

fof(f3059,plain,
    ( spl8_194
  <=> ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X0),X0)
        | sP0(set_intersection2(X0,X1),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_194])]) ).

fof(f1223,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X0),X0)
        | sP0(set_intersection2(X0,X1),X2,X0) )
    | ~ spl8_102 ),
    inference(factoring,[],[f1068]) ).

fof(f3057,plain,
    ( spl8_193
    | ~ spl8_101 ),
    inference(avatar_split_clause,[],[f1183,f1063,f3055]) ).

fof(f3055,plain,
    ( spl8_193
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X1),X1)
        | sP0(X0,set_intersection2(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_193])]) ).

fof(f1183,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X1),X1)
        | sP0(X0,set_intersection2(X1,X2),X1) )
    | ~ spl8_101 ),
    inference(factoring,[],[f1064]) ).

fof(f3053,plain,
    ( spl8_192
    | ~ spl8_100 ),
    inference(avatar_split_clause,[],[f1140,f1059,f3051]) ).

fof(f3051,plain,
    ( spl8_192
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X1,X2)),X1)
        | sP0(X0,X1,set_intersection2(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_192])]) ).

fof(f1140,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X1,X2)),X1)
        | sP0(X0,X1,set_intersection2(X1,X2)) )
    | ~ spl8_100 ),
    inference(factoring,[],[f1060]) ).

fof(f3049,plain,
    ( spl8_191
    | ~ spl8_99 ),
    inference(avatar_split_clause,[],[f1101,f1055,f3047]) ).

fof(f3047,plain,
    ( spl8_191
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X0,X2)),X0)
        | sP0(X0,X1,set_intersection2(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_191])]) ).

fof(f1101,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X0,X2)),X0)
        | sP0(X0,X1,set_intersection2(X0,X2)) )
    | ~ spl8_99 ),
    inference(factoring,[],[f1056]) ).

fof(f2788,plain,
    ( spl8_190
    | ~ spl8_16
    | ~ spl8_97 ),
    inference(avatar_split_clause,[],[f1049,f1031,f153,f2786]) ).

fof(f2786,plain,
    ( spl8_190
  <=> ! [X0,X1] :
        ( ~ in(sK4(X0,set_intersection2(X1,X0)),X1)
        | subset(X0,set_intersection2(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_190])]) ).

fof(f153,plain,
    ( spl8_16
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | in(sK4(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).

fof(f1049,plain,
    ( ! [X0,X1] :
        ( ~ in(sK4(X0,set_intersection2(X1,X0)),X1)
        | subset(X0,set_intersection2(X1,X0)) )
    | ~ spl8_16
    | ~ spl8_97 ),
    inference(duplicate_literal_removal,[],[f1034]) ).

fof(f1034,plain,
    ( ! [X0,X1] :
        ( ~ in(sK4(X0,set_intersection2(X1,X0)),X1)
        | subset(X0,set_intersection2(X1,X0))
        | subset(X0,set_intersection2(X1,X0)) )
    | ~ spl8_16
    | ~ spl8_97 ),
    inference(resolution,[],[f1032,f154]) ).

fof(f154,plain,
    ( ! [X0,X1] :
        ( in(sK4(X0,X1),X0)
        | subset(X0,X1) )
    | ~ spl8_16 ),
    inference(avatar_component_clause,[],[f153]) ).

fof(f2784,plain,
    ( spl8_189
    | ~ spl8_11
    | ~ spl8_74 ),
    inference(avatar_split_clause,[],[f685,f643,f117,f2782]) ).

fof(f2782,plain,
    ( spl8_189
  <=> ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ in(X1,sK4(set_intersection2(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_189])]) ).

fof(f685,plain,
    ( ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ in(X1,sK4(set_intersection2(X0,X1),X2)) )
    | ~ spl8_11
    | ~ spl8_74 ),
    inference(resolution,[],[f644,f118]) ).

fof(f2780,plain,
    ( spl8_188
    | ~ spl8_11
    | ~ spl8_73 ),
    inference(avatar_split_clause,[],[f667,f639,f117,f2778]) ).

fof(f2778,plain,
    ( spl8_188
  <=> ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ in(X0,sK4(set_intersection2(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_188])]) ).

fof(f667,plain,
    ( ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ in(X0,sK4(set_intersection2(X0,X1),X2)) )
    | ~ spl8_11
    | ~ spl8_73 ),
    inference(resolution,[],[f640,f118]) ).

fof(f2776,plain,
    ( spl8_187
    | ~ spl8_43
    | ~ spl8_64 ),
    inference(avatar_split_clause,[],[f577,f557,f372,f2774]) ).

fof(f2774,plain,
    ( spl8_187
  <=> ! [X2,X0,X1] :
        ( in(sK5(sK7,X0,X1),X2)
        | sP0(sK7,X0,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_187])]) ).

fof(f372,plain,
    ( spl8_43
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).

fof(f557,plain,
    ( spl8_64
  <=> ! [X0,X1] :
        ( ~ in(X0,sK7)
        | in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).

fof(f577,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(sK7,X0,X1),X2)
        | sP0(sK7,X0,X1)
        | ~ empty(X1) )
    | ~ spl8_43
    | ~ spl8_64 ),
    inference(resolution,[],[f558,f373]) ).

fof(f373,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ empty(X2) )
    | ~ spl8_43 ),
    inference(avatar_component_clause,[],[f372]) ).

fof(f558,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK7)
        | in(X0,X1) )
    | ~ spl8_64 ),
    inference(avatar_component_clause,[],[f557]) ).

fof(f2772,plain,
    ( spl8_186
    | ~ spl8_41
    | ~ spl8_64 ),
    inference(avatar_split_clause,[],[f575,f557,f364,f2770]) ).

fof(f2770,plain,
    ( spl8_186
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,sK7,X1),X2)
        | sP0(X0,sK7,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_186])]) ).

fof(f364,plain,
    ( spl8_41
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).

fof(f575,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,sK7,X1),X2)
        | sP0(X0,sK7,X1)
        | ~ empty(X1) )
    | ~ spl8_41
    | ~ spl8_64 ),
    inference(resolution,[],[f558,f365]) ).

fof(f365,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ empty(X2) )
    | ~ spl8_41 ),
    inference(avatar_component_clause,[],[f364]) ).

fof(f2768,plain,
    ( spl8_185
    | ~ spl8_42
    | ~ spl8_64 ),
    inference(avatar_split_clause,[],[f572,f557,f368,f2766]) ).

fof(f2766,plain,
    ( spl8_185
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,sK7),X2)
        | sP0(X0,X1,sK7)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_185])]) ).

fof(f368,plain,
    ( spl8_42
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).

fof(f572,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,sK7),X2)
        | sP0(X0,X1,sK7)
        | ~ empty(X1) )
    | ~ spl8_42
    | ~ spl8_64 ),
    inference(resolution,[],[f558,f369]) ).

fof(f369,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ empty(X1) )
    | ~ spl8_42 ),
    inference(avatar_component_clause,[],[f368]) ).

fof(f2760,plain,
    ( spl8_184
    | ~ spl8_44
    | ~ spl8_64 ),
    inference(avatar_split_clause,[],[f571,f557,f376,f2758]) ).

fof(f2758,plain,
    ( spl8_184
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,sK7),X2)
        | sP0(X0,X1,sK7)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_184])]) ).

fof(f376,plain,
    ( spl8_44
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).

fof(f571,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,sK7),X2)
        | sP0(X0,X1,sK7)
        | ~ empty(X0) )
    | ~ spl8_44
    | ~ spl8_64 ),
    inference(resolution,[],[f558,f377]) ).

fof(f377,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ empty(X0) )
    | ~ spl8_44 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f2661,plain,
    ( spl8_183
    | ~ spl8_49
    | ~ spl8_170 ),
    inference(avatar_split_clause,[],[f2586,f2459,f428,f2658]) ).

fof(f428,plain,
    ( spl8_49
  <=> ! [X0] :
        ( sP0(X0,sK1,sK1)
        | in(sK5(X0,sK1,sK1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).

fof(f2586,plain,
    ( sP0(sK2,sK1,sK1)
    | ~ spl8_49
    | ~ spl8_170 ),
    inference(duplicate_literal_removal,[],[f2566]) ).

fof(f2566,plain,
    ( sP0(sK2,sK1,sK1)
    | sP0(sK2,sK1,sK1)
    | ~ spl8_49
    | ~ spl8_170 ),
    inference(resolution,[],[f2460,f429]) ).

fof(f429,plain,
    ( ! [X0] :
        ( in(sK5(X0,sK1,sK1),sK2)
        | sP0(X0,sK1,sK1) )
    | ~ spl8_49 ),
    inference(avatar_component_clause,[],[f428]) ).

fof(f2509,plain,
    ( spl8_182
    | ~ spl8_10
    | ~ spl8_96 ),
    inference(avatar_split_clause,[],[f1015,f967,f111,f2507]) ).

fof(f2507,plain,
    ( spl8_182
  <=> ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_182])]) ).

fof(f1015,plain,
    ( ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_96 ),
    inference(resolution,[],[f968,f112]) ).

fof(f2505,plain,
    ( spl8_181
    | ~ spl8_10
    | ~ spl8_95 ),
    inference(avatar_split_clause,[],[f1000,f963,f111,f2503]) ).

fof(f2503,plain,
    ( spl8_181
  <=> ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_181])]) ).

fof(f1000,plain,
    ( ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_95 ),
    inference(resolution,[],[f964,f112]) ).

fof(f2501,plain,
    ( spl8_180
    | ~ spl8_10
    | ~ spl8_94 ),
    inference(avatar_split_clause,[],[f984,f959,f111,f2499]) ).

fof(f2499,plain,
    ( spl8_180
  <=> ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_180])]) ).

fof(f984,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_94 ),
    inference(resolution,[],[f960,f112]) ).

fof(f2497,plain,
    ( spl8_179
    | ~ spl8_10
    | ~ spl8_93 ),
    inference(avatar_split_clause,[],[f971,f955,f111,f2495]) ).

fof(f2495,plain,
    ( spl8_179
  <=> ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_179])]) ).

fof(f971,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_93 ),
    inference(resolution,[],[f956,f112]) ).

fof(f2493,plain,
    ( spl8_178
    | ~ spl8_10
    | ~ spl8_90 ),
    inference(avatar_split_clause,[],[f934,f741,f111,f2491]) ).

fof(f2491,plain,
    ( spl8_178
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_178])]) ).

fof(f934,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_90 ),
    inference(resolution,[],[f742,f112]) ).

fof(f2489,plain,
    ( spl8_177
    | ~ spl8_10
    | ~ spl8_89 ),
    inference(avatar_split_clause,[],[f918,f737,f111,f2487]) ).

fof(f2487,plain,
    ( spl8_177
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_177])]) ).

fof(f918,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X3) )
    | ~ spl8_10
    | ~ spl8_89 ),
    inference(resolution,[],[f738,f112]) ).

fof(f2485,plain,
    ( spl8_176
    | ~ spl8_10
    | ~ spl8_88 ),
    inference(avatar_split_clause,[],[f898,f733,f111,f2483]) ).

fof(f2483,plain,
    ( spl8_176
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_176])]) ).

fof(f898,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_88 ),
    inference(resolution,[],[f734,f112]) ).

fof(f2481,plain,
    ( spl8_175
    | ~ spl8_10
    | ~ spl8_87 ),
    inference(avatar_split_clause,[],[f880,f729,f111,f2479]) ).

fof(f2479,plain,
    ( spl8_175
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_175])]) ).

fof(f880,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,X2),X3,X0)
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_87 ),
    inference(resolution,[],[f730,f112]) ).

fof(f2477,plain,
    ( spl8_174
    | ~ spl8_10
    | ~ spl8_86 ),
    inference(avatar_split_clause,[],[f862,f725,f111,f2475]) ).

fof(f2475,plain,
    ( spl8_174
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_174])]) ).

fof(f862,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_86 ),
    inference(resolution,[],[f726,f112]) ).

fof(f2473,plain,
    ( spl8_173
    | ~ spl8_10
    | ~ spl8_85 ),
    inference(avatar_split_clause,[],[f846,f721,f111,f2471]) ).

fof(f2471,plain,
    ( spl8_173
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ empty(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_173])]) ).

fof(f846,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,X3))
        | ~ empty(X3) )
    | ~ spl8_10
    | ~ spl8_85 ),
    inference(resolution,[],[f722,f112]) ).

fof(f2469,plain,
    ( spl8_172
    | ~ spl8_10
    | ~ spl8_84 ),
    inference(avatar_split_clause,[],[f827,f717,f111,f2467]) ).

fof(f2467,plain,
    ( spl8_172
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ empty(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_172])]) ).

fof(f827,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_84 ),
    inference(resolution,[],[f718,f112]) ).

fof(f2465,plain,
    ( spl8_171
    | ~ spl8_10
    | ~ spl8_83 ),
    inference(avatar_split_clause,[],[f811,f713,f111,f2463]) ).

fof(f2463,plain,
    ( spl8_171
  <=> ! [X0,X3,X2,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ empty(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_171])]) ).

fof(f811,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,X3),X0)
        | ~ empty(X3) )
    | ~ spl8_10
    | ~ spl8_83 ),
    inference(resolution,[],[f714,f112]) ).

fof(f2461,plain,
    ( spl8_170
    | ~ spl8_38
    | ~ spl8_81 ),
    inference(avatar_split_clause,[],[f772,f705,f326,f2459]) ).

fof(f326,plain,
    ( spl8_38
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,X1),X1)
        | sP0(X0,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).

fof(f705,plain,
    ( spl8_81
  <=> ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ in(sK5(X0,X1,X1),X0)
        | ~ in(sK5(X0,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).

fof(f772,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,X1,X1),X0)
        | sP0(X0,X1,X1) )
    | ~ spl8_38
    | ~ spl8_81 ),
    inference(duplicate_literal_removal,[],[f749]) ).

fof(f749,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,X1,X1),X0)
        | sP0(X0,X1,X1)
        | sP0(X0,X1,X1) )
    | ~ spl8_38
    | ~ spl8_81 ),
    inference(resolution,[],[f706,f327]) ).

fof(f327,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,X1),X1)
        | sP0(X0,X1,X1) )
    | ~ spl8_38 ),
    inference(avatar_component_clause,[],[f326]) ).

fof(f706,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,X1,X1),X1)
        | ~ in(sK5(X0,X1,X1),X0)
        | sP0(X0,X1,X1) )
    | ~ spl8_81 ),
    inference(avatar_component_clause,[],[f705]) ).

fof(f2448,plain,
    ( spl8_169
    | ~ spl8_19
    | ~ spl8_68 ),
    inference(avatar_split_clause,[],[f606,f596,f171,f2446]) ).

fof(f2446,plain,
    ( spl8_169
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ empty(X1)
        | set_intersection2(X2,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_169])]) ).

fof(f596,plain,
    ( spl8_68
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).

fof(f606,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ empty(X1)
        | set_intersection2(X2,X1) = X0 )
    | ~ spl8_19
    | ~ spl8_68 ),
    inference(resolution,[],[f597,f172]) ).

fof(f597,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ empty(X0) )
    | ~ spl8_68 ),
    inference(avatar_component_clause,[],[f596]) ).

fof(f2444,plain,
    ( ~ spl8_168
    | spl8_2
    | ~ spl8_164 ),
    inference(avatar_split_clause,[],[f2350,f2333,f75,f2441]) ).

fof(f2441,plain,
    ( spl8_168
  <=> empty(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_168])]) ).

fof(f2333,plain,
    ( spl8_164
  <=> ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_164])]) ).

fof(f2350,plain,
    ( ~ empty(sK3)
    | spl8_2
    | ~ spl8_164 ),
    inference(resolution,[],[f2334,f77]) ).

fof(f2334,plain,
    ( ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ empty(X1) )
    | ~ spl8_164 ),
    inference(avatar_component_clause,[],[f2333]) ).

fof(f2439,plain,
    ( spl8_167
    | ~ spl8_19
    | ~ spl8_67 ),
    inference(avatar_split_clause,[],[f602,f592,f171,f2437]) ).

fof(f2437,plain,
    ( spl8_167
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ empty(X1)
        | set_intersection2(X1,X2) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_167])]) ).

fof(f592,plain,
    ( spl8_67
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).

fof(f602,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ empty(X1)
        | set_intersection2(X1,X2) = X0 )
    | ~ spl8_19
    | ~ spl8_67 ),
    inference(resolution,[],[f593,f172]) ).

fof(f593,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ empty(X1) )
    | ~ spl8_67 ),
    inference(avatar_component_clause,[],[f592]) ).

fof(f2365,plain,
    ( spl8_166
    | ~ spl8_53
    | ~ spl8_108 ),
    inference(avatar_split_clause,[],[f1433,f1381,f448,f2363]) ).

fof(f2363,plain,
    ( spl8_166
  <=> ! [X0,X1] :
        ( ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),X1)
        | ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),X0)
        | ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),sK1)
        | sP0(X0,sK1,set_intersection2(X1,sK2))
        | ~ empty(set_intersection2(X1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_166])]) ).

fof(f448,plain,
    ( spl8_53
  <=> ! [X0,X1] :
        ( sP0(X0,sK1,X1)
        | ~ empty(X1)
        | in(sK5(X0,sK1,X1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).

fof(f1381,plain,
    ( spl8_108
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_108])]) ).

fof(f1433,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),X1)
        | ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),X0)
        | ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),sK1)
        | sP0(X0,sK1,set_intersection2(X1,sK2))
        | ~ empty(set_intersection2(X1,sK2)) )
    | ~ spl8_53
    | ~ spl8_108 ),
    inference(duplicate_literal_removal,[],[f1401]) ).

fof(f1401,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),X1)
        | ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),X0)
        | ~ in(sK5(X0,sK1,set_intersection2(X1,sK2)),sK1)
        | sP0(X0,sK1,set_intersection2(X1,sK2))
        | ~ empty(set_intersection2(X1,sK2))
        | sP0(X0,sK1,set_intersection2(X1,sK2)) )
    | ~ spl8_53
    | ~ spl8_108 ),
    inference(resolution,[],[f1382,f449]) ).

fof(f449,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),sK2)
        | ~ empty(X1)
        | sP0(X0,sK1,X1) )
    | ~ spl8_53 ),
    inference(avatar_component_clause,[],[f448]) ).

fof(f1382,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_108 ),
    inference(avatar_component_clause,[],[f1381]) ).

fof(f2361,plain,
    ( spl8_165
    | ~ spl8_55
    | ~ spl8_108 ),
    inference(avatar_split_clause,[],[f1428,f1381,f456,f2359]) ).

fof(f2359,plain,
    ( spl8_165
  <=> ! [X0,X1] :
        ( ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),X1)
        | ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),sK1)
        | ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),X0)
        | sP0(sK1,X0,set_intersection2(X1,sK2))
        | ~ empty(set_intersection2(X1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_165])]) ).

fof(f456,plain,
    ( spl8_55
  <=> ! [X0,X1] :
        ( sP0(sK1,X0,X1)
        | ~ empty(X1)
        | in(sK5(sK1,X0,X1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).

fof(f1428,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),X1)
        | ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),sK1)
        | ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),X0)
        | sP0(sK1,X0,set_intersection2(X1,sK2))
        | ~ empty(set_intersection2(X1,sK2)) )
    | ~ spl8_55
    | ~ spl8_108 ),
    inference(duplicate_literal_removal,[],[f1409]) ).

fof(f1409,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),X1)
        | ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),sK1)
        | ~ in(sK5(sK1,X0,set_intersection2(X1,sK2)),X0)
        | sP0(sK1,X0,set_intersection2(X1,sK2))
        | ~ empty(set_intersection2(X1,sK2))
        | sP0(sK1,X0,set_intersection2(X1,sK2)) )
    | ~ spl8_55
    | ~ spl8_108 ),
    inference(resolution,[],[f1382,f457]) ).

fof(f457,plain,
    ( ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),sK2)
        | ~ empty(X1)
        | sP0(sK1,X0,X1) )
    | ~ spl8_55 ),
    inference(avatar_component_clause,[],[f456]) ).

fof(f2335,plain,
    ( spl8_164
    | ~ spl8_10
    | ~ spl8_74 ),
    inference(avatar_split_clause,[],[f686,f643,f111,f2333]) ).

fof(f686,plain,
    ( ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_74 ),
    inference(resolution,[],[f644,f112]) ).

fof(f2330,plain,
    ( spl8_163
    | ~ spl8_10
    | ~ spl8_73 ),
    inference(avatar_split_clause,[],[f668,f639,f111,f2328]) ).

fof(f2328,plain,
    ( spl8_163
  <=> ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_163])]) ).

fof(f668,plain,
    ( ! [X2,X0,X1] :
        ( subset(set_intersection2(X0,X1),X2)
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_73 ),
    inference(resolution,[],[f640,f112]) ).

fof(f2326,plain,
    ( spl8_162
    | ~ spl8_19
    | ~ spl8_66 ),
    inference(avatar_split_clause,[],[f590,f565,f171,f2324]) ).

fof(f2324,plain,
    ( spl8_162
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | set_intersection2(X1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_162])]) ).

fof(f565,plain,
    ( spl8_66
  <=> ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).

fof(f590,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | set_intersection2(X1,X0) = X0 )
    | ~ spl8_19
    | ~ spl8_66 ),
    inference(resolution,[],[f566,f172]) ).

fof(f566,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ empty(X0) )
    | ~ spl8_66 ),
    inference(avatar_component_clause,[],[f565]) ).

fof(f2322,plain,
    ( spl8_161
    | ~ spl8_19
    | ~ spl8_65 ),
    inference(avatar_split_clause,[],[f586,f561,f171,f2320]) ).

fof(f2320,plain,
    ( spl8_161
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | set_intersection2(X0,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_161])]) ).

fof(f561,plain,
    ( spl8_65
  <=> ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).

fof(f586,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | set_intersection2(X0,X1) = X0 )
    | ~ spl8_19
    | ~ spl8_65 ),
    inference(resolution,[],[f562,f172]) ).

fof(f562,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ empty(X1) )
    | ~ spl8_65 ),
    inference(avatar_component_clause,[],[f561]) ).

fof(f1877,plain,
    ( spl8_160
    | ~ spl8_24
    | ~ spl8_106 ),
    inference(avatar_split_clause,[],[f1360,f1083,f197,f1875]) ).

fof(f1875,plain,
    ( spl8_160
  <=> ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,sK1),X1,X2),X2)
        | sP0(set_intersection2(X0,sK1),X1,X2)
        | in(sK5(set_intersection2(X0,sK1),X1,X2),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_160])]) ).

fof(f197,plain,
    ( spl8_24
  <=> ! [X0] :
        ( ~ in(X0,sK1)
        | in(X0,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).

fof(f1360,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,sK1),X1,X2),X2)
        | sP0(set_intersection2(X0,sK1),X1,X2)
        | in(sK5(set_intersection2(X0,sK1),X1,X2),sK2) )
    | ~ spl8_24
    | ~ spl8_106 ),
    inference(resolution,[],[f1084,f198]) ).

fof(f198,plain,
    ( ! [X0] :
        ( ~ in(X0,sK1)
        | in(X0,sK2) )
    | ~ spl8_24 ),
    inference(avatar_component_clause,[],[f197]) ).

fof(f1866,plain,
    ( spl8_159
    | ~ spl8_24
    | ~ spl8_105 ),
    inference(avatar_split_clause,[],[f1326,f1079,f197,f1864]) ).

fof(f1864,plain,
    ( spl8_159
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,sK1),X2),X2)
        | sP0(X0,set_intersection2(X1,sK1),X2)
        | in(sK5(X0,set_intersection2(X1,sK1),X2),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_159])]) ).

fof(f1326,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,sK1),X2),X2)
        | sP0(X0,set_intersection2(X1,sK1),X2)
        | in(sK5(X0,set_intersection2(X1,sK1),X2),sK2) )
    | ~ spl8_24
    | ~ spl8_105 ),
    inference(resolution,[],[f1080,f198]) ).

fof(f1862,plain,
    ( spl8_158
    | ~ spl8_24
    | ~ spl8_104 ),
    inference(avatar_split_clause,[],[f1285,f1075,f197,f1860]) ).

fof(f1860,plain,
    ( spl8_158
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,sK1)),X1)
        | sP0(X0,X1,set_intersection2(X2,sK1))
        | in(sK5(X0,X1,set_intersection2(X2,sK1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_158])]) ).

fof(f1285,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,sK1)),X1)
        | sP0(X0,X1,set_intersection2(X2,sK1))
        | in(sK5(X0,X1,set_intersection2(X2,sK1)),sK2) )
    | ~ spl8_24
    | ~ spl8_104 ),
    inference(resolution,[],[f1076,f198]) ).

fof(f1858,plain,
    ( spl8_157
    | ~ spl8_24
    | ~ spl8_103 ),
    inference(avatar_split_clause,[],[f1252,f1071,f197,f1856]) ).

fof(f1856,plain,
    ( spl8_157
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,sK1)),X0)
        | sP0(X0,X1,set_intersection2(X2,sK1))
        | in(sK5(X0,X1,set_intersection2(X2,sK1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_157])]) ).

fof(f1252,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,sK1)),X0)
        | sP0(X0,X1,set_intersection2(X2,sK1))
        | in(sK5(X0,X1,set_intersection2(X2,sK1)),sK2) )
    | ~ spl8_24
    | ~ spl8_103 ),
    inference(resolution,[],[f1072,f198]) ).

fof(f1854,plain,
    ( spl8_156
    | ~ spl8_24
    | ~ spl8_102 ),
    inference(avatar_split_clause,[],[f1221,f1067,f197,f1852]) ).

fof(f1852,plain,
    ( spl8_156
  <=> ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(sK1,X0),X1,X2),X2)
        | sP0(set_intersection2(sK1,X0),X1,X2)
        | in(sK5(set_intersection2(sK1,X0),X1,X2),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_156])]) ).

fof(f1221,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(sK1,X0),X1,X2),X2)
        | sP0(set_intersection2(sK1,X0),X1,X2)
        | in(sK5(set_intersection2(sK1,X0),X1,X2),sK2) )
    | ~ spl8_24
    | ~ spl8_102 ),
    inference(resolution,[],[f1068,f198]) ).

fof(f1850,plain,
    ( spl8_155
    | ~ spl8_24
    | ~ spl8_101 ),
    inference(avatar_split_clause,[],[f1181,f1063,f197,f1848]) ).

fof(f1848,plain,
    ( spl8_155
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(sK1,X1),X2),X2)
        | sP0(X0,set_intersection2(sK1,X1),X2)
        | in(sK5(X0,set_intersection2(sK1,X1),X2),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_155])]) ).

fof(f1181,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(sK1,X1),X2),X2)
        | sP0(X0,set_intersection2(sK1,X1),X2)
        | in(sK5(X0,set_intersection2(sK1,X1),X2),sK2) )
    | ~ spl8_24
    | ~ spl8_101 ),
    inference(resolution,[],[f1064,f198]) ).

fof(f1846,plain,
    ( spl8_154
    | ~ spl8_24
    | ~ spl8_100 ),
    inference(avatar_split_clause,[],[f1130,f1059,f197,f1844]) ).

fof(f1844,plain,
    ( spl8_154
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(sK1,X2)),X1)
        | sP0(X0,X1,set_intersection2(sK1,X2))
        | in(sK5(X0,X1,set_intersection2(sK1,X2)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_154])]) ).

fof(f1130,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(sK1,X2)),X1)
        | sP0(X0,X1,set_intersection2(sK1,X2))
        | in(sK5(X0,X1,set_intersection2(sK1,X2)),sK2) )
    | ~ spl8_24
    | ~ spl8_100 ),
    inference(resolution,[],[f1060,f198]) ).

fof(f1842,plain,
    ( spl8_153
    | ~ spl8_24
    | ~ spl8_99 ),
    inference(avatar_split_clause,[],[f1091,f1055,f197,f1840]) ).

fof(f1840,plain,
    ( spl8_153
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(sK1,X2)),X0)
        | sP0(X0,X1,set_intersection2(sK1,X2))
        | in(sK5(X0,X1,set_intersection2(sK1,X2)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_153])]) ).

fof(f1091,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(sK1,X2)),X0)
        | sP0(X0,X1,set_intersection2(sK1,X2))
        | in(sK5(X0,X1,set_intersection2(sK1,X2)),sK2) )
    | ~ spl8_24
    | ~ spl8_99 ),
    inference(resolution,[],[f1056,f198]) ).

fof(f1838,plain,
    ( spl8_152
    | ~ spl8_35
    | ~ spl8_60 ),
    inference(avatar_split_clause,[],[f527,f488,f292,f1836]) ).

fof(f1836,plain,
    ( spl8_152
  <=> ! [X2,X0,X1] :
        ( in(sK5(sK1,X0,set_intersection2(X1,X2)),sK2)
        | sP0(sK1,X0,set_intersection2(X1,X2))
        | in(sK5(sK1,X0,set_intersection2(X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_152])]) ).

fof(f488,plain,
    ( spl8_60
  <=> ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),sK2)
        | in(sK5(sK1,X0,X1),X1)
        | sP0(sK1,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).

fof(f527,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(sK1,X0,set_intersection2(X1,X2)),sK2)
        | sP0(sK1,X0,set_intersection2(X1,X2))
        | in(sK5(sK1,X0,set_intersection2(X1,X2)),X1) )
    | ~ spl8_35
    | ~ spl8_60 ),
    inference(resolution,[],[f489,f293]) ).

fof(f489,plain,
    ( ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),sK2)
        | in(sK5(sK1,X0,X1),X1)
        | sP0(sK1,X0,X1) )
    | ~ spl8_60 ),
    inference(avatar_component_clause,[],[f488]) ).

fof(f1834,plain,
    ( spl8_151
    | ~ spl8_37
    | ~ spl8_60 ),
    inference(avatar_split_clause,[],[f526,f488,f301,f1832]) ).

fof(f1832,plain,
    ( spl8_151
  <=> ! [X2,X0,X1] :
        ( in(sK5(sK1,X0,set_intersection2(X1,X2)),sK2)
        | sP0(sK1,X0,set_intersection2(X1,X2))
        | in(sK5(sK1,X0,set_intersection2(X1,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_151])]) ).

fof(f526,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(sK1,X0,set_intersection2(X1,X2)),sK2)
        | sP0(sK1,X0,set_intersection2(X1,X2))
        | in(sK5(sK1,X0,set_intersection2(X1,X2)),X2) )
    | ~ spl8_37
    | ~ spl8_60 ),
    inference(resolution,[],[f489,f302]) ).

fof(f1830,plain,
    ( spl8_150
    | ~ spl8_35
    | ~ spl8_59 ),
    inference(avatar_split_clause,[],[f516,f484,f292,f1828]) ).

fof(f1828,plain,
    ( spl8_150
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,sK1,set_intersection2(X1,X2)),sK2)
        | sP0(X0,sK1,set_intersection2(X1,X2))
        | in(sK5(X0,sK1,set_intersection2(X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_150])]) ).

fof(f484,plain,
    ( spl8_59
  <=> ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),sK2)
        | in(sK5(X0,sK1,X1),X1)
        | sP0(X0,sK1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).

fof(f516,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,sK1,set_intersection2(X1,X2)),sK2)
        | sP0(X0,sK1,set_intersection2(X1,X2))
        | in(sK5(X0,sK1,set_intersection2(X1,X2)),X1) )
    | ~ spl8_35
    | ~ spl8_59 ),
    inference(resolution,[],[f485,f293]) ).

fof(f485,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),sK2)
        | in(sK5(X0,sK1,X1),X1)
        | sP0(X0,sK1,X1) )
    | ~ spl8_59 ),
    inference(avatar_component_clause,[],[f484]) ).

fof(f1826,plain,
    ( spl8_149
    | ~ spl8_19
    | ~ spl8_109 ),
    inference(avatar_split_clause,[],[f1595,f1449,f171,f1823]) ).

fof(f1823,plain,
    ( spl8_149
  <=> sK1 = set_intersection2(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_149])]) ).

fof(f1449,plain,
    ( spl8_109
  <=> sP0(sK1,sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_109])]) ).

fof(f1595,plain,
    ( sK1 = set_intersection2(sK2,sK1)
    | ~ spl8_19
    | ~ spl8_109 ),
    inference(resolution,[],[f1451,f172]) ).

fof(f1451,plain,
    ( sP0(sK1,sK2,sK1)
    | ~ spl8_109 ),
    inference(avatar_component_clause,[],[f1449]) ).

fof(f1821,plain,
    ( spl8_148
    | ~ spl8_37
    | ~ spl8_59 ),
    inference(avatar_split_clause,[],[f515,f484,f301,f1819]) ).

fof(f1819,plain,
    ( spl8_148
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,sK1,set_intersection2(X1,X2)),sK2)
        | sP0(X0,sK1,set_intersection2(X1,X2))
        | in(sK5(X0,sK1,set_intersection2(X1,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_148])]) ).

fof(f515,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,sK1,set_intersection2(X1,X2)),sK2)
        | sP0(X0,sK1,set_intersection2(X1,X2))
        | in(sK5(X0,sK1,set_intersection2(X1,X2)),X2) )
    | ~ spl8_37
    | ~ spl8_59 ),
    inference(resolution,[],[f485,f302]) ).

fof(f1817,plain,
    ( spl8_147
    | ~ spl8_35
    | ~ spl8_58 ),
    inference(avatar_split_clause,[],[f506,f480,f292,f1815]) ).

fof(f1815,plain,
    ( spl8_147
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),sK1),sK2)
        | sP0(X0,set_intersection2(X1,X2),sK1)
        | in(sK5(X0,set_intersection2(X1,X2),sK1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_147])]) ).

fof(f480,plain,
    ( spl8_58
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | in(sK5(X0,X1,sK1),X1)
        | sP0(X0,X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).

fof(f506,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),sK1),sK2)
        | sP0(X0,set_intersection2(X1,X2),sK1)
        | in(sK5(X0,set_intersection2(X1,X2),sK1),X1) )
    | ~ spl8_35
    | ~ spl8_58 ),
    inference(resolution,[],[f481,f293]) ).

fof(f481,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | in(sK5(X0,X1,sK1),X1)
        | sP0(X0,X1,sK1) )
    | ~ spl8_58 ),
    inference(avatar_component_clause,[],[f480]) ).

fof(f1813,plain,
    ( spl8_146
    | ~ spl8_37
    | ~ spl8_58 ),
    inference(avatar_split_clause,[],[f505,f480,f301,f1811]) ).

fof(f1811,plain,
    ( spl8_146
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),sK1),sK2)
        | sP0(X0,set_intersection2(X1,X2),sK1)
        | in(sK5(X0,set_intersection2(X1,X2),sK1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_146])]) ).

fof(f505,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),sK1),sK2)
        | sP0(X0,set_intersection2(X1,X2),sK1)
        | in(sK5(X0,set_intersection2(X1,X2),sK1),X2) )
    | ~ spl8_37
    | ~ spl8_58 ),
    inference(resolution,[],[f481,f302]) ).

fof(f1809,plain,
    ( spl8_145
    | ~ spl8_35
    | ~ spl8_57 ),
    inference(avatar_split_clause,[],[f497,f476,f292,f1807]) ).

fof(f1807,plain,
    ( spl8_145
  <=> ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,sK1),sK2)
        | sP0(set_intersection2(X0,X1),X2,sK1)
        | in(sK5(set_intersection2(X0,X1),X2,sK1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_145])]) ).

fof(f476,plain,
    ( spl8_57
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | in(sK5(X0,X1,sK1),X0)
        | sP0(X0,X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).

fof(f497,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,sK1),sK2)
        | sP0(set_intersection2(X0,X1),X2,sK1)
        | in(sK5(set_intersection2(X0,X1),X2,sK1),X0) )
    | ~ spl8_35
    | ~ spl8_57 ),
    inference(resolution,[],[f477,f293]) ).

fof(f477,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | in(sK5(X0,X1,sK1),X0)
        | sP0(X0,X1,sK1) )
    | ~ spl8_57 ),
    inference(avatar_component_clause,[],[f476]) ).

fof(f1805,plain,
    ( spl8_144
    | ~ spl8_37
    | ~ spl8_57 ),
    inference(avatar_split_clause,[],[f496,f476,f301,f1803]) ).

fof(f1803,plain,
    ( spl8_144
  <=> ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,sK1),sK2)
        | sP0(set_intersection2(X0,X1),X2,sK1)
        | in(sK5(set_intersection2(X0,X1),X2,sK1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_144])]) ).

fof(f496,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,sK1),sK2)
        | sP0(set_intersection2(X0,X1),X2,sK1)
        | in(sK5(set_intersection2(X0,X1),X2,sK1),X1) )
    | ~ spl8_37
    | ~ spl8_57 ),
    inference(resolution,[],[f477,f302]) ).

fof(f1786,plain,
    ( spl8_143
    | ~ spl8_17
    | ~ spl8_74 ),
    inference(avatar_split_clause,[],[f697,f643,f157,f1784]) ).

fof(f1784,plain,
    ( spl8_143
  <=> ! [X0,X1] : subset(set_intersection2(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_143])]) ).

fof(f157,plain,
    ( spl8_17
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ in(sK4(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).

fof(f697,plain,
    ( ! [X0,X1] : subset(set_intersection2(X0,X1),X1)
    | ~ spl8_17
    | ~ spl8_74 ),
    inference(duplicate_literal_removal,[],[f684]) ).

fof(f684,plain,
    ( ! [X0,X1] :
        ( subset(set_intersection2(X0,X1),X1)
        | subset(set_intersection2(X0,X1),X1) )
    | ~ spl8_17
    | ~ spl8_74 ),
    inference(resolution,[],[f644,f158]) ).

fof(f158,plain,
    ( ! [X0,X1] :
        ( ~ in(sK4(X0,X1),X1)
        | subset(X0,X1) )
    | ~ spl8_17 ),
    inference(avatar_component_clause,[],[f157]) ).

fof(f1782,plain,
    ( spl8_142
    | ~ spl8_17
    | ~ spl8_73 ),
    inference(avatar_split_clause,[],[f679,f639,f157,f1780]) ).

fof(f1780,plain,
    ( spl8_142
  <=> ! [X0,X1] : subset(set_intersection2(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_142])]) ).

fof(f679,plain,
    ( ! [X0,X1] : subset(set_intersection2(X0,X1),X0)
    | ~ spl8_17
    | ~ spl8_73 ),
    inference(duplicate_literal_removal,[],[f666]) ).

fof(f666,plain,
    ( ! [X0,X1] :
        ( subset(set_intersection2(X0,X1),X0)
        | subset(set_intersection2(X0,X1),X0) )
    | ~ spl8_17
    | ~ spl8_73 ),
    inference(resolution,[],[f640,f158]) ).

fof(f1765,plain,
    ( spl8_141
    | ~ spl8_16
    | ~ spl8_118 ),
    inference(avatar_split_clause,[],[f1546,f1512,f153,f1762]) ).

fof(f1762,plain,
    ( spl8_141
  <=> subset(sK1,set_intersection2(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_141])]) ).

fof(f1512,plain,
    ( spl8_118
  <=> ! [X0] :
        ( ~ in(sK4(sK1,set_intersection2(X0,sK2)),X0)
        | subset(sK1,set_intersection2(X0,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_118])]) ).

fof(f1546,plain,
    ( subset(sK1,set_intersection2(sK1,sK2))
    | ~ spl8_16
    | ~ spl8_118 ),
    inference(duplicate_literal_removal,[],[f1538]) ).

fof(f1538,plain,
    ( subset(sK1,set_intersection2(sK1,sK2))
    | subset(sK1,set_intersection2(sK1,sK2))
    | ~ spl8_16
    | ~ spl8_118 ),
    inference(resolution,[],[f1513,f154]) ).

fof(f1513,plain,
    ( ! [X0] :
        ( ~ in(sK4(sK1,set_intersection2(X0,sK2)),X0)
        | subset(sK1,set_intersection2(X0,sK2)) )
    | ~ spl8_118 ),
    inference(avatar_component_clause,[],[f1512]) ).

fof(f1735,plain,
    ( spl8_140
    | ~ spl8_24
    | ~ spl8_96 ),
    inference(avatar_split_clause,[],[f1018,f967,f197,f1733]) ).

fof(f1733,plain,
    ( spl8_140
  <=> ! [X0,X1] :
        ( sP0(set_intersection2(sK1,X0),X1,set_intersection2(sK1,X0))
        | in(sK5(set_intersection2(sK1,X0),X1,set_intersection2(sK1,X0)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_140])]) ).

fof(f1018,plain,
    ( ! [X0,X1] :
        ( sP0(set_intersection2(sK1,X0),X1,set_intersection2(sK1,X0))
        | in(sK5(set_intersection2(sK1,X0),X1,set_intersection2(sK1,X0)),sK2) )
    | ~ spl8_24
    | ~ spl8_96 ),
    inference(resolution,[],[f968,f198]) ).

fof(f1731,plain,
    ( spl8_139
    | ~ spl8_24
    | ~ spl8_95 ),
    inference(avatar_split_clause,[],[f1003,f963,f197,f1729]) ).

fof(f1729,plain,
    ( spl8_139
  <=> ! [X0,X1] :
        ( sP0(set_intersection2(X0,sK1),X1,set_intersection2(X0,sK1))
        | in(sK5(set_intersection2(X0,sK1),X1,set_intersection2(X0,sK1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_139])]) ).

fof(f1003,plain,
    ( ! [X0,X1] :
        ( sP0(set_intersection2(X0,sK1),X1,set_intersection2(X0,sK1))
        | in(sK5(set_intersection2(X0,sK1),X1,set_intersection2(X0,sK1)),sK2) )
    | ~ spl8_24
    | ~ spl8_95 ),
    inference(resolution,[],[f964,f198]) ).

fof(f1727,plain,
    ( spl8_138
    | ~ spl8_24
    | ~ spl8_94 ),
    inference(avatar_split_clause,[],[f987,f959,f197,f1725]) ).

fof(f987,plain,
    ( ! [X0,X1] :
        ( sP0(X0,set_intersection2(sK1,X1),set_intersection2(sK1,X1))
        | in(sK5(X0,set_intersection2(sK1,X1),set_intersection2(sK1,X1)),sK2) )
    | ~ spl8_24
    | ~ spl8_94 ),
    inference(resolution,[],[f960,f198]) ).

fof(f1723,plain,
    ( spl8_137
    | ~ spl8_24
    | ~ spl8_93 ),
    inference(avatar_split_clause,[],[f974,f955,f197,f1721]) ).

fof(f974,plain,
    ( ! [X0,X1] :
        ( sP0(X0,set_intersection2(X1,sK1),set_intersection2(X1,sK1))
        | in(sK5(X0,set_intersection2(X1,sK1),set_intersection2(X1,sK1)),sK2) )
    | ~ spl8_24
    | ~ spl8_93 ),
    inference(resolution,[],[f956,f198]) ).

fof(f1683,plain,
    ( spl8_136
    | ~ spl8_17
    | ~ spl8_117 ),
    inference(avatar_split_clause,[],[f1537,f1508,f157,f1681]) ).

fof(f1681,plain,
    ( spl8_136
  <=> ! [X0] : subset(set_intersection2(X0,sK1),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_136])]) ).

fof(f1537,plain,
    ( ! [X0] : subset(set_intersection2(X0,sK1),sK2)
    | ~ spl8_17
    | ~ spl8_117 ),
    inference(duplicate_literal_removal,[],[f1528]) ).

fof(f1528,plain,
    ( ! [X0] :
        ( subset(set_intersection2(X0,sK1),sK2)
        | subset(set_intersection2(X0,sK1),sK2) )
    | ~ spl8_17
    | ~ spl8_117 ),
    inference(resolution,[],[f1509,f158]) ).

fof(f1623,plain,
    ( spl8_135
    | ~ spl8_17
    | ~ spl8_116 ),
    inference(avatar_split_clause,[],[f1525,f1504,f157,f1621]) ).

fof(f1621,plain,
    ( spl8_135
  <=> ! [X0] : subset(set_intersection2(sK1,X0),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_135])]) ).

fof(f1525,plain,
    ( ! [X0] : subset(set_intersection2(sK1,X0),sK2)
    | ~ spl8_17
    | ~ spl8_116 ),
    inference(duplicate_literal_removal,[],[f1515]) ).

fof(f1515,plain,
    ( ! [X0] :
        ( subset(set_intersection2(sK1,X0),sK2)
        | subset(set_intersection2(sK1,X0),sK2) )
    | ~ spl8_17
    | ~ spl8_116 ),
    inference(resolution,[],[f1505,f158]) ).

fof(f1619,plain,
    ( spl8_134
    | ~ spl8_24
    | ~ spl8_90 ),
    inference(avatar_split_clause,[],[f937,f741,f197,f1617]) ).

fof(f1617,plain,
    ( spl8_134
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(sK1,X2))
        | in(sK5(X0,X1,set_intersection2(sK1,X2)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_134])]) ).

fof(f937,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(sK1,X2))
        | in(sK5(X0,X1,set_intersection2(sK1,X2)),sK2) )
    | ~ spl8_24
    | ~ spl8_90 ),
    inference(resolution,[],[f742,f198]) ).

fof(f1615,plain,
    ( spl8_133
    | ~ spl8_24
    | ~ spl8_89 ),
    inference(avatar_split_clause,[],[f921,f737,f197,f1613]) ).

fof(f1613,plain,
    ( spl8_133
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,sK1))
        | in(sK5(X0,X1,set_intersection2(X2,sK1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_133])]) ).

fof(f921,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,set_intersection2(X2,sK1))
        | in(sK5(X0,X1,set_intersection2(X2,sK1)),sK2) )
    | ~ spl8_24
    | ~ spl8_89 ),
    inference(resolution,[],[f738,f198]) ).

fof(f1611,plain,
    ( spl8_132
    | ~ spl8_24
    | ~ spl8_88 ),
    inference(avatar_split_clause,[],[f902,f733,f197,f1609]) ).

fof(f1609,plain,
    ( spl8_132
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(sK1,X1),X2,X0)
        | in(sK5(set_intersection2(sK1,X1),X2,X0),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_132])]) ).

fof(f902,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(sK1,X1),X2,X0)
        | in(sK5(set_intersection2(sK1,X1),X2,X0),sK2) )
    | ~ spl8_24
    | ~ spl8_88 ),
    inference(resolution,[],[f734,f198]) ).

fof(f1607,plain,
    ( spl8_131
    | ~ spl8_24
    | ~ spl8_87 ),
    inference(avatar_split_clause,[],[f884,f729,f197,f1605]) ).

fof(f1605,plain,
    ( spl8_131
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,sK1),X2,X0)
        | in(sK5(set_intersection2(X1,sK1),X2,X0),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_131])]) ).

fof(f884,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(set_intersection2(X1,sK1),X2,X0)
        | in(sK5(set_intersection2(X1,sK1),X2,X0),sK2) )
    | ~ spl8_24
    | ~ spl8_87 ),
    inference(resolution,[],[f730,f198]) ).

fof(f1603,plain,
    ( spl8_130
    | ~ spl8_24
    | ~ spl8_86 ),
    inference(avatar_split_clause,[],[f865,f725,f197,f1601]) ).

fof(f1601,plain,
    ( spl8_130
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(sK1,X2))
        | in(sK5(X1,X0,set_intersection2(sK1,X2)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_130])]) ).

fof(f865,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(sK1,X2))
        | in(sK5(X1,X0,set_intersection2(sK1,X2)),sK2) )
    | ~ spl8_24
    | ~ spl8_86 ),
    inference(resolution,[],[f726,f198]) ).

fof(f1599,plain,
    ( spl8_129
    | ~ spl8_24
    | ~ spl8_85 ),
    inference(avatar_split_clause,[],[f849,f721,f197,f1597]) ).

fof(f1597,plain,
    ( spl8_129
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,sK1))
        | in(sK5(X1,X0,set_intersection2(X2,sK1)),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_129])]) ).

fof(f849,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,set_intersection2(X2,sK1))
        | in(sK5(X1,X0,set_intersection2(X2,sK1)),sK2) )
    | ~ spl8_24
    | ~ spl8_85 ),
    inference(resolution,[],[f722,f198]) ).

fof(f1591,plain,
    ( spl8_109
    | ~ spl8_39
    | spl8_110 ),
    inference(avatar_split_clause,[],[f1463,f1453,f330,f1449]) ).

fof(f330,plain,
    ( spl8_39
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,X0),X0)
        | sP0(X0,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).

fof(f1453,plain,
    ( spl8_110
  <=> in(sK5(sK1,sK2,sK1),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_110])]) ).

fof(f1463,plain,
    ( sP0(sK1,sK2,sK1)
    | ~ spl8_39
    | spl8_110 ),
    inference(resolution,[],[f1455,f331]) ).

fof(f331,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,X0),X0)
        | sP0(X0,X1,X0) )
    | ~ spl8_39 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f1455,plain,
    ( ~ in(sK5(sK1,sK2,sK1),sK1)
    | spl8_110 ),
    inference(avatar_component_clause,[],[f1453]) ).

fof(f1590,plain,
    ( spl8_128
    | ~ spl8_24
    | ~ spl8_84 ),
    inference(avatar_split_clause,[],[f831,f717,f197,f1588]) ).

fof(f1588,plain,
    ( spl8_128
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(sK1,X2),X0)
        | in(sK5(X1,set_intersection2(sK1,X2),X0),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_128])]) ).

fof(f831,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(sK1,X2),X0)
        | in(sK5(X1,set_intersection2(sK1,X2),X0),sK2) )
    | ~ spl8_24
    | ~ spl8_84 ),
    inference(resolution,[],[f718,f198]) ).

fof(f1586,plain,
    ( spl8_127
    | ~ spl8_24
    | ~ spl8_83 ),
    inference(avatar_split_clause,[],[f815,f713,f197,f1584]) ).

fof(f1584,plain,
    ( spl8_127
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,sK1),X0)
        | in(sK5(X1,set_intersection2(X2,sK1),X0),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_127])]) ).

fof(f815,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,set_intersection2(X2,sK1),X0)
        | in(sK5(X1,set_intersection2(X2,sK1),X0),sK2) )
    | ~ spl8_24
    | ~ spl8_83 ),
    inference(resolution,[],[f714,f198]) ).

fof(f1582,plain,
    ( spl8_126
    | ~ spl8_11
    | ~ spl8_60 ),
    inference(avatar_split_clause,[],[f523,f488,f117,f1580]) ).

fof(f1580,plain,
    ( spl8_126
  <=> ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),sK2)
        | sP0(sK1,X0,X1)
        | ~ in(X1,sK5(sK1,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_126])]) ).

fof(f523,plain,
    ( ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),sK2)
        | sP0(sK1,X0,X1)
        | ~ in(X1,sK5(sK1,X0,X1)) )
    | ~ spl8_11
    | ~ spl8_60 ),
    inference(resolution,[],[f489,f118]) ).

fof(f1578,plain,
    ( spl8_125
    | ~ spl8_11
    | ~ spl8_60 ),
    inference(avatar_split_clause,[],[f520,f488,f117,f1576]) ).

fof(f1576,plain,
    ( spl8_125
  <=> ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),X1)
        | sP0(sK1,X0,X1)
        | ~ in(sK2,sK5(sK1,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_125])]) ).

fof(f520,plain,
    ( ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),X1)
        | sP0(sK1,X0,X1)
        | ~ in(sK2,sK5(sK1,X0,X1)) )
    | ~ spl8_11
    | ~ spl8_60 ),
    inference(resolution,[],[f489,f118]) ).

fof(f1574,plain,
    ( spl8_124
    | ~ spl8_11
    | ~ spl8_59 ),
    inference(avatar_split_clause,[],[f512,f484,f117,f1572]) ).

fof(f1572,plain,
    ( spl8_124
  <=> ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),sK2)
        | sP0(X0,sK1,X1)
        | ~ in(X1,sK5(X0,sK1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_124])]) ).

fof(f512,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),sK2)
        | sP0(X0,sK1,X1)
        | ~ in(X1,sK5(X0,sK1,X1)) )
    | ~ spl8_11
    | ~ spl8_59 ),
    inference(resolution,[],[f485,f118]) ).

fof(f1570,plain,
    ( spl8_123
    | ~ spl8_11
    | ~ spl8_59 ),
    inference(avatar_split_clause,[],[f509,f484,f117,f1568]) ).

fof(f1568,plain,
    ( spl8_123
  <=> ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),X1)
        | sP0(X0,sK1,X1)
        | ~ in(sK2,sK5(X0,sK1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_123])]) ).

fof(f509,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),X1)
        | sP0(X0,sK1,X1)
        | ~ in(sK2,sK5(X0,sK1,X1)) )
    | ~ spl8_11
    | ~ spl8_59 ),
    inference(resolution,[],[f485,f118]) ).

fof(f1566,plain,
    ( spl8_122
    | ~ spl8_11
    | ~ spl8_58 ),
    inference(avatar_split_clause,[],[f502,f480,f117,f1564]) ).

fof(f1564,plain,
    ( spl8_122
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | sP0(X0,X1,sK1)
        | ~ in(X1,sK5(X0,X1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_122])]) ).

fof(f502,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | sP0(X0,X1,sK1)
        | ~ in(X1,sK5(X0,X1,sK1)) )
    | ~ spl8_11
    | ~ spl8_58 ),
    inference(resolution,[],[f481,f118]) ).

fof(f1562,plain,
    ( spl8_121
    | ~ spl8_11
    | ~ spl8_58 ),
    inference(avatar_split_clause,[],[f500,f480,f117,f1560]) ).

fof(f1560,plain,
    ( spl8_121
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),X1)
        | sP0(X0,X1,sK1)
        | ~ in(sK2,sK5(X0,X1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_121])]) ).

fof(f500,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),X1)
        | sP0(X0,X1,sK1)
        | ~ in(sK2,sK5(X0,X1,sK1)) )
    | ~ spl8_11
    | ~ spl8_58 ),
    inference(resolution,[],[f481,f118]) ).

fof(f1558,plain,
    ( spl8_120
    | ~ spl8_11
    | ~ spl8_57 ),
    inference(avatar_split_clause,[],[f493,f476,f117,f1556]) ).

fof(f1556,plain,
    ( spl8_120
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | sP0(X0,X1,sK1)
        | ~ in(X0,sK5(X0,X1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_120])]) ).

fof(f493,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | sP0(X0,X1,sK1)
        | ~ in(X0,sK5(X0,X1,sK1)) )
    | ~ spl8_11
    | ~ spl8_57 ),
    inference(resolution,[],[f477,f118]) ).

fof(f1554,plain,
    ( spl8_119
    | ~ spl8_11
    | ~ spl8_57 ),
    inference(avatar_split_clause,[],[f491,f476,f117,f1552]) ).

fof(f1552,plain,
    ( spl8_119
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),X0)
        | sP0(X0,X1,sK1)
        | ~ in(sK2,sK5(X0,X1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_119])]) ).

fof(f491,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),X0)
        | sP0(X0,X1,sK1)
        | ~ in(sK2,sK5(X0,X1,sK1)) )
    | ~ spl8_11
    | ~ spl8_57 ),
    inference(resolution,[],[f477,f118]) ).

fof(f1514,plain,
    ( spl8_118
    | ~ spl8_29
    | ~ spl8_97 ),
    inference(avatar_split_clause,[],[f1047,f1031,f247,f1512]) ).

fof(f247,plain,
    ( spl8_29
  <=> ! [X0] :
        ( in(sK4(sK1,X0),sK2)
        | subset(sK1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).

fof(f1047,plain,
    ( ! [X0] :
        ( ~ in(sK4(sK1,set_intersection2(X0,sK2)),X0)
        | subset(sK1,set_intersection2(X0,sK2)) )
    | ~ spl8_29
    | ~ spl8_97 ),
    inference(duplicate_literal_removal,[],[f1036]) ).

fof(f1036,plain,
    ( ! [X0] :
        ( ~ in(sK4(sK1,set_intersection2(X0,sK2)),X0)
        | subset(sK1,set_intersection2(X0,sK2))
        | subset(sK1,set_intersection2(X0,sK2)) )
    | ~ spl8_29
    | ~ spl8_97 ),
    inference(resolution,[],[f1032,f248]) ).

fof(f248,plain,
    ( ! [X0] :
        ( in(sK4(sK1,X0),sK2)
        | subset(sK1,X0) )
    | ~ spl8_29 ),
    inference(avatar_component_clause,[],[f247]) ).

fof(f1510,plain,
    ( spl8_117
    | ~ spl8_24
    | ~ spl8_74 ),
    inference(avatar_split_clause,[],[f689,f643,f197,f1508]) ).

fof(f689,plain,
    ( ! [X0,X1] :
        ( subset(set_intersection2(X0,sK1),X1)
        | in(sK4(set_intersection2(X0,sK1),X1),sK2) )
    | ~ spl8_24
    | ~ spl8_74 ),
    inference(resolution,[],[f644,f198]) ).

fof(f1506,plain,
    ( spl8_116
    | ~ spl8_24
    | ~ spl8_73 ),
    inference(avatar_split_clause,[],[f671,f639,f197,f1504]) ).

fof(f671,plain,
    ( ! [X0,X1] :
        ( subset(set_intersection2(sK1,X0),X1)
        | in(sK4(set_intersection2(sK1,X0),X1),sK2) )
    | ~ spl8_24
    | ~ spl8_73 ),
    inference(resolution,[],[f640,f198]) ).

fof(f1502,plain,
    ( ~ spl8_115
    | ~ spl8_66
    | spl8_109 ),
    inference(avatar_split_clause,[],[f1457,f1449,f565,f1499]) ).

fof(f1499,plain,
    ( spl8_115
  <=> empty(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_115])]) ).

fof(f1457,plain,
    ( ~ empty(sK1)
    | ~ spl8_66
    | spl8_109 ),
    inference(resolution,[],[f1450,f566]) ).

fof(f1450,plain,
    ( ~ sP0(sK1,sK2,sK1)
    | spl8_109 ),
    inference(avatar_component_clause,[],[f1449]) ).

fof(f1497,plain,
    ( spl8_114
    | ~ spl8_11
    | ~ spl8_56 ),
    inference(avatar_split_clause,[],[f473,f460,f117,f1495]) ).

fof(f1495,plain,
    ( spl8_114
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,sK1)
        | ~ in(sK2,sK5(X0,X1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_114])]) ).

fof(f460,plain,
    ( spl8_56
  <=> ! [X0,X1] :
        ( sP0(X0,X1,sK1)
        | ~ empty(X0)
        | in(sK5(X0,X1,sK1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).

fof(f473,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(X0,X1,sK1)
        | ~ in(sK2,sK5(X0,X1,sK1)) )
    | ~ spl8_11
    | ~ spl8_56 ),
    inference(resolution,[],[f461,f118]) ).

fof(f461,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | ~ empty(X0)
        | sP0(X0,X1,sK1) )
    | ~ spl8_56 ),
    inference(avatar_component_clause,[],[f460]) ).

fof(f1493,plain,
    ( spl8_113
    | ~ spl8_11
    | ~ spl8_55 ),
    inference(avatar_split_clause,[],[f469,f456,f117,f1491]) ).

fof(f1491,plain,
    ( spl8_113
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(sK1,X1,X0)
        | ~ in(sK2,sK5(sK1,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_113])]) ).

fof(f469,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(sK1,X1,X0)
        | ~ in(sK2,sK5(sK1,X1,X0)) )
    | ~ spl8_11
    | ~ spl8_55 ),
    inference(resolution,[],[f457,f118]) ).

fof(f1489,plain,
    ( spl8_112
    | ~ spl8_11
    | ~ spl8_54 ),
    inference(avatar_split_clause,[],[f467,f452,f117,f1487]) ).

fof(f1487,plain,
    ( spl8_112
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,sK1)
        | ~ in(sK2,sK5(X1,X0,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_112])]) ).

fof(f452,plain,
    ( spl8_54
  <=> ! [X0,X1] :
        ( sP0(X0,X1,sK1)
        | ~ empty(X1)
        | in(sK5(X0,X1,sK1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).

fof(f467,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,X0,sK1)
        | ~ in(sK2,sK5(X1,X0,sK1)) )
    | ~ spl8_11
    | ~ spl8_54 ),
    inference(resolution,[],[f453,f118]) ).

fof(f453,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | ~ empty(X1)
        | sP0(X0,X1,sK1) )
    | ~ spl8_54 ),
    inference(avatar_component_clause,[],[f452]) ).

fof(f1485,plain,
    ( spl8_111
    | ~ spl8_11
    | ~ spl8_53 ),
    inference(avatar_split_clause,[],[f463,f448,f117,f1483]) ).

fof(f1483,plain,
    ( spl8_111
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,sK1,X0)
        | ~ in(sK2,sK5(X1,sK1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_111])]) ).

fof(f463,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | sP0(X1,sK1,X0)
        | ~ in(sK2,sK5(X1,sK1,X0)) )
    | ~ spl8_11
    | ~ spl8_53 ),
    inference(resolution,[],[f449,f118]) ).

fof(f1456,plain,
    ( spl8_109
    | ~ spl8_110
    | ~ spl8_50
    | ~ spl8_82 ),
    inference(avatar_split_clause,[],[f798,f709,f432,f1453,f1449]) ).

fof(f432,plain,
    ( spl8_50
  <=> ! [X0] :
        ( sP0(sK1,X0,sK1)
        | in(sK5(sK1,X0,sK1),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).

fof(f709,plain,
    ( spl8_82
  <=> ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ in(sK5(X0,X1,X0),X0)
        | ~ in(sK5(X0,X1,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).

fof(f798,plain,
    ( ~ in(sK5(sK1,sK2,sK1),sK1)
    | sP0(sK1,sK2,sK1)
    | ~ spl8_50
    | ~ spl8_82 ),
    inference(duplicate_literal_removal,[],[f791]) ).

fof(f791,plain,
    ( ~ in(sK5(sK1,sK2,sK1),sK1)
    | sP0(sK1,sK2,sK1)
    | sP0(sK1,sK2,sK1)
    | ~ spl8_50
    | ~ spl8_82 ),
    inference(resolution,[],[f710,f433]) ).

fof(f433,plain,
    ( ! [X0] :
        ( in(sK5(sK1,X0,sK1),sK2)
        | sP0(sK1,X0,sK1) )
    | ~ spl8_50 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f710,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,X1,X0),X1)
        | ~ in(sK5(X0,X1,X0),X0)
        | sP0(X0,X1,X0) )
    | ~ spl8_82 ),
    inference(avatar_component_clause,[],[f709]) ).

fof(f1383,plain,
    ( spl8_108
    | ~ spl8_26
    | ~ spl8_40 ),
    inference(avatar_split_clause,[],[f356,f348,f215,f1381]) ).

fof(f215,plain,
    ( spl8_26
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ in(sK5(X0,X1,X2),X0)
        | ~ in(sK5(X0,X1,X2),X1)
        | ~ in(sK5(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).

fof(f356,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | ~ in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_26
    | ~ spl8_40 ),
    inference(resolution,[],[f349,f216]) ).

fof(f216,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK5(X0,X1,X2),X2)
        | ~ in(sK5(X0,X1,X2),X0)
        | ~ in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2) )
    | ~ spl8_26 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f1167,plain,
    ( spl8_107
    | ~ spl8_60 ),
    inference(avatar_split_clause,[],[f529,f488,f1165]) ).

fof(f1165,plain,
    ( spl8_107
  <=> ! [X0] :
        ( in(sK5(sK1,X0,sK2),sK2)
        | sP0(sK1,X0,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).

fof(f529,plain,
    ( ! [X0] :
        ( in(sK5(sK1,X0,sK2),sK2)
        | sP0(sK1,X0,sK2) )
    | ~ spl8_60 ),
    inference(factoring,[],[f489]) ).

fof(f1085,plain,
    ( spl8_106
    | ~ spl8_25
    | ~ spl8_37 ),
    inference(avatar_split_clause,[],[f319,f301,f201,f1083]) ).

fof(f201,plain,
    ( spl8_25
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | in(sK5(X0,X1,X2),X0)
        | in(sK5(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).

fof(f319,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X1)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3) )
    | ~ spl8_25
    | ~ spl8_37 ),
    inference(resolution,[],[f302,f202]) ).

fof(f202,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | in(sK5(X0,X1,X2),X0)
        | sP0(X0,X1,X2) )
    | ~ spl8_25 ),
    inference(avatar_component_clause,[],[f201]) ).

fof(f1081,plain,
    ( spl8_105
    | ~ spl8_23
    | ~ spl8_37 ),
    inference(avatar_split_clause,[],[f318,f301,f193,f1079]) ).

fof(f193,plain,
    ( spl8_23
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | in(sK5(X0,X1,X2),X1)
        | in(sK5(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).

fof(f318,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X2)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3) )
    | ~ spl8_23
    | ~ spl8_37 ),
    inference(resolution,[],[f302,f194]) ).

fof(f194,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2) )
    | ~ spl8_23 ),
    inference(avatar_component_clause,[],[f193]) ).

fof(f1077,plain,
    ( spl8_104
    | ~ spl8_23
    | ~ spl8_37 ),
    inference(avatar_split_clause,[],[f317,f301,f193,f1075]) ).

fof(f317,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_23
    | ~ spl8_37 ),
    inference(resolution,[],[f302,f194]) ).

fof(f1073,plain,
    ( spl8_103
    | ~ spl8_25
    | ~ spl8_37 ),
    inference(avatar_split_clause,[],[f316,f301,f201,f1071]) ).

fof(f316,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X3)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_25
    | ~ spl8_37 ),
    inference(resolution,[],[f302,f202]) ).

fof(f1069,plain,
    ( spl8_102
    | ~ spl8_25
    | ~ spl8_35 ),
    inference(avatar_split_clause,[],[f308,f292,f201,f1067]) ).

fof(f308,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(set_intersection2(X0,X1),X2,X3),X0)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X3)
        | sP0(set_intersection2(X0,X1),X2,X3) )
    | ~ spl8_25
    | ~ spl8_35 ),
    inference(resolution,[],[f293,f202]) ).

fof(f1065,plain,
    ( spl8_101
    | ~ spl8_23
    | ~ spl8_35 ),
    inference(avatar_split_clause,[],[f307,f292,f193,f1063]) ).

fof(f307,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,set_intersection2(X1,X2),X3),X1)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X3)
        | sP0(X0,set_intersection2(X1,X2),X3) )
    | ~ spl8_23
    | ~ spl8_35 ),
    inference(resolution,[],[f293,f194]) ).

fof(f1061,plain,
    ( spl8_100
    | ~ spl8_23
    | ~ spl8_35 ),
    inference(avatar_split_clause,[],[f306,f292,f193,f1059]) ).

fof(f306,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X1)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_23
    | ~ spl8_35 ),
    inference(resolution,[],[f293,f194]) ).

fof(f1057,plain,
    ( spl8_99
    | ~ spl8_25
    | ~ spl8_35 ),
    inference(avatar_split_clause,[],[f305,f292,f201,f1055]) ).

fof(f305,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(X0,X1,set_intersection2(X2,X3)),X2)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X0)
        | sP0(X0,X1,set_intersection2(X2,X3)) )
    | ~ spl8_25
    | ~ spl8_35 ),
    inference(resolution,[],[f293,f202]) ).

fof(f1053,plain,
    ( spl8_98
    | ~ spl8_59 ),
    inference(avatar_split_clause,[],[f518,f484,f1051]) ).

fof(f1051,plain,
    ( spl8_98
  <=> ! [X0] :
        ( in(sK5(X0,sK1,sK2),sK2)
        | sP0(X0,sK1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).

fof(f518,plain,
    ( ! [X0] :
        ( in(sK5(X0,sK1,sK2),sK2)
        | sP0(X0,sK1,sK2) )
    | ~ spl8_59 ),
    inference(factoring,[],[f485]) ).

fof(f1033,plain,
    ( spl8_97
    | ~ spl8_17
    | ~ spl8_40 ),
    inference(avatar_split_clause,[],[f355,f348,f157,f1031]) ).

fof(f355,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(sK4(X0,set_intersection2(X1,X2)),X1)
        | ~ in(sK4(X0,set_intersection2(X1,X2)),X2)
        | subset(X0,set_intersection2(X1,X2)) )
    | ~ spl8_17
    | ~ spl8_40 ),
    inference(resolution,[],[f349,f158]) ).

fof(f969,plain,
    ( spl8_96
    | ~ spl8_35
    | ~ spl8_39 ),
    inference(avatar_split_clause,[],[f344,f330,f292,f967]) ).

fof(f344,plain,
    ( ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | in(sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) )
    | ~ spl8_35
    | ~ spl8_39 ),
    inference(resolution,[],[f331,f293]) ).

fof(f965,plain,
    ( spl8_95
    | ~ spl8_37
    | ~ spl8_39 ),
    inference(avatar_split_clause,[],[f343,f330,f301,f963]) ).

fof(f343,plain,
    ( ! [X2,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
        | in(sK5(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) )
    | ~ spl8_37
    | ~ spl8_39 ),
    inference(resolution,[],[f331,f302]) ).

fof(f961,plain,
    ( spl8_94
    | ~ spl8_35
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f337,f326,f292,f959]) ).

fof(f337,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | in(sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) )
    | ~ spl8_35
    | ~ spl8_38 ),
    inference(resolution,[],[f327,f293]) ).

fof(f957,plain,
    ( spl8_93
    | ~ spl8_37
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f336,f326,f301,f955]) ).

fof(f336,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
        | in(sK5(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) )
    | ~ spl8_37
    | ~ spl8_38 ),
    inference(resolution,[],[f327,f302]) ).

fof(f953,plain,
    ( spl8_92
    | ~ spl8_58 ),
    inference(avatar_split_clause,[],[f508,f480,f951]) ).

fof(f951,plain,
    ( spl8_92
  <=> ! [X0] :
        ( in(sK5(X0,sK2,sK1),sK2)
        | sP0(X0,sK2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).

fof(f508,plain,
    ( ! [X0] :
        ( in(sK5(X0,sK2,sK1),sK2)
        | sP0(X0,sK2,sK1) )
    | ~ spl8_58 ),
    inference(factoring,[],[f481]) ).

fof(f747,plain,
    ( spl8_91
    | ~ spl8_57 ),
    inference(avatar_split_clause,[],[f499,f476,f745]) ).

fof(f745,plain,
    ( spl8_91
  <=> ! [X0] :
        ( in(sK5(sK2,X0,sK1),sK2)
        | sP0(sK2,X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).

fof(f499,plain,
    ( ! [X0] :
        ( in(sK5(sK2,X0,sK1),sK2)
        | sP0(sK2,X0,sK1) )
    | ~ spl8_57 ),
    inference(factoring,[],[f477]) ).

fof(f743,plain,
    ( spl8_90
    | ~ spl8_35
    | ~ spl8_44 ),
    inference(avatar_split_clause,[],[f404,f376,f292,f741]) ).

fof(f404,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X0)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X2) )
    | ~ spl8_35
    | ~ spl8_44 ),
    inference(resolution,[],[f377,f293]) ).

fof(f739,plain,
    ( spl8_89
    | ~ spl8_37
    | ~ spl8_44 ),
    inference(avatar_split_clause,[],[f403,f376,f301,f737]) ).

fof(f403,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X0)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X3) )
    | ~ spl8_37
    | ~ spl8_44 ),
    inference(resolution,[],[f377,f302]) ).

fof(f735,plain,
    ( spl8_88
    | ~ spl8_35
    | ~ spl8_43 ),
    inference(avatar_split_clause,[],[f397,f372,f292,f733]) ).

fof(f397,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X3)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X0) )
    | ~ spl8_35
    | ~ spl8_43 ),
    inference(resolution,[],[f373,f293]) ).

fof(f731,plain,
    ( spl8_87
    | ~ spl8_37
    | ~ spl8_43 ),
    inference(avatar_split_clause,[],[f396,f372,f301,f729]) ).

fof(f396,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(set_intersection2(X0,X1),X2,X3)
        | ~ empty(X3)
        | in(sK5(set_intersection2(X0,X1),X2,X3),X1) )
    | ~ spl8_37
    | ~ spl8_43 ),
    inference(resolution,[],[f373,f302]) ).

fof(f727,plain,
    ( spl8_86
    | ~ spl8_35
    | ~ spl8_42 ),
    inference(avatar_split_clause,[],[f390,f368,f292,f725]) ).

fof(f390,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X1)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X2) )
    | ~ spl8_35
    | ~ spl8_42 ),
    inference(resolution,[],[f369,f293]) ).

fof(f723,plain,
    ( spl8_85
    | ~ spl8_37
    | ~ spl8_42 ),
    inference(avatar_split_clause,[],[f389,f368,f301,f721]) ).

fof(f389,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X0,X1,set_intersection2(X2,X3))
        | ~ empty(X1)
        | in(sK5(X0,X1,set_intersection2(X2,X3)),X3) )
    | ~ spl8_37
    | ~ spl8_42 ),
    inference(resolution,[],[f369,f302]) ).

fof(f719,plain,
    ( spl8_84
    | ~ spl8_35
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f383,f364,f292,f717]) ).

fof(f383,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X3)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X1) )
    | ~ spl8_35
    | ~ spl8_41 ),
    inference(resolution,[],[f365,f293]) ).

fof(f715,plain,
    ( spl8_83
    | ~ spl8_37
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f382,f364,f301,f713]) ).

fof(f382,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X0,set_intersection2(X1,X2),X3)
        | ~ empty(X3)
        | in(sK5(X0,set_intersection2(X1,X2),X3),X2) )
    | ~ spl8_37
    | ~ spl8_41 ),
    inference(resolution,[],[f365,f302]) ).

fof(f711,plain,
    ( spl8_82
    | ~ spl8_26
    | ~ spl8_39 ),
    inference(avatar_split_clause,[],[f346,f330,f215,f709]) ).

fof(f346,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ in(sK5(X0,X1,X0),X0)
        | ~ in(sK5(X0,X1,X0),X1) )
    | ~ spl8_26
    | ~ spl8_39 ),
    inference(duplicate_literal_removal,[],[f342]) ).

fof(f342,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ in(sK5(X0,X1,X0),X0)
        | ~ in(sK5(X0,X1,X0),X1)
        | sP0(X0,X1,X0) )
    | ~ spl8_26
    | ~ spl8_39 ),
    inference(resolution,[],[f331,f216]) ).

fof(f707,plain,
    ( spl8_81
    | ~ spl8_26
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f339,f326,f215,f705]) ).

fof(f339,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ in(sK5(X0,X1,X1),X0)
        | ~ in(sK5(X0,X1,X1),X1) )
    | ~ spl8_26
    | ~ spl8_38 ),
    inference(duplicate_literal_removal,[],[f335]) ).

fof(f335,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ in(sK5(X0,X1,X1),X0)
        | ~ in(sK5(X0,X1,X1),X1)
        | sP0(X0,X1,X1) )
    | ~ spl8_26
    | ~ spl8_38 ),
    inference(resolution,[],[f327,f216]) ).

fof(f703,plain,
    ( spl8_80
    | ~ spl8_11
    | ~ spl8_50 ),
    inference(avatar_split_clause,[],[f437,f432,f117,f701]) ).

fof(f701,plain,
    ( spl8_80
  <=> ! [X0] :
        ( sP0(sK1,X0,sK1)
        | ~ in(sK2,sK5(sK1,X0,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).

fof(f437,plain,
    ( ! [X0] :
        ( sP0(sK1,X0,sK1)
        | ~ in(sK2,sK5(sK1,X0,sK1)) )
    | ~ spl8_11
    | ~ spl8_50 ),
    inference(resolution,[],[f433,f118]) ).

fof(f665,plain,
    ( spl8_79
    | ~ spl8_11
    | ~ spl8_44 ),
    inference(avatar_split_clause,[],[f400,f376,f117,f663]) ).

fof(f663,plain,
    ( spl8_79
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X0)
        | ~ in(X2,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).

fof(f400,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X0)
        | ~ in(X2,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_44 ),
    inference(resolution,[],[f377,f118]) ).

fof(f661,plain,
    ( spl8_78
    | ~ spl8_11
    | ~ spl8_43 ),
    inference(avatar_split_clause,[],[f393,f372,f117,f659]) ).

fof(f659,plain,
    ( spl8_78
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ in(X0,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).

fof(f393,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ in(X0,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_43 ),
    inference(resolution,[],[f373,f118]) ).

fof(f657,plain,
    ( spl8_77
    | ~ spl8_11
    | ~ spl8_42 ),
    inference(avatar_split_clause,[],[f386,f368,f117,f655]) ).

fof(f655,plain,
    ( spl8_77
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X1)
        | ~ in(X2,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).

fof(f386,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X1)
        | ~ in(X2,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_42 ),
    inference(resolution,[],[f369,f118]) ).

fof(f653,plain,
    ( spl8_76
    | ~ spl8_11
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f379,f364,f117,f651]) ).

fof(f651,plain,
    ( spl8_76
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ in(X1,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).

fof(f379,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ in(X1,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_41 ),
    inference(resolution,[],[f365,f118]) ).

fof(f649,plain,
    ( spl8_75
    | ~ spl8_11
    | ~ spl8_49 ),
    inference(avatar_split_clause,[],[f435,f428,f117,f647]) ).

fof(f647,plain,
    ( spl8_75
  <=> ! [X0] :
        ( sP0(X0,sK1,sK1)
        | ~ in(sK2,sK5(X0,sK1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).

fof(f435,plain,
    ( ! [X0] :
        ( sP0(X0,sK1,sK1)
        | ~ in(sK2,sK5(X0,sK1,sK1)) )
    | ~ spl8_11
    | ~ spl8_49 ),
    inference(resolution,[],[f429,f118]) ).

fof(f645,plain,
    ( spl8_74
    | ~ spl8_16
    | ~ spl8_37 ),
    inference(avatar_split_clause,[],[f315,f301,f153,f643]) ).

fof(f315,plain,
    ( ! [X2,X0,X1] :
        ( in(sK4(set_intersection2(X0,X1),X2),X1)
        | subset(set_intersection2(X0,X1),X2) )
    | ~ spl8_16
    | ~ spl8_37 ),
    inference(resolution,[],[f302,f154]) ).

fof(f641,plain,
    ( spl8_73
    | ~ spl8_16
    | ~ spl8_35 ),
    inference(avatar_split_clause,[],[f304,f292,f153,f639]) ).

fof(f304,plain,
    ( ! [X2,X0,X1] :
        ( in(sK4(set_intersection2(X0,X1),X2),X0)
        | subset(set_intersection2(X0,X1),X2) )
    | ~ spl8_16
    | ~ spl8_35 ),
    inference(resolution,[],[f293,f154]) ).

fof(f629,plain,
    ( spl8_72
    | ~ spl8_11
    | ~ spl8_40 ),
    inference(avatar_split_clause,[],[f353,f348,f117,f627]) ).

fof(f353,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X0,X2)
        | ~ in(set_intersection2(X1,X2),X0) )
    | ~ spl8_11
    | ~ spl8_40 ),
    inference(resolution,[],[f349,f118]) ).

fof(f618,plain,
    ( spl8_71
    | ~ spl8_10
    | ~ spl8_40 ),
    inference(avatar_split_clause,[],[f354,f348,f111,f616]) ).

fof(f616,plain,
    ( spl8_71
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X0,X2)
        | ~ empty(set_intersection2(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).

fof(f354,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X0,X2)
        | ~ empty(set_intersection2(X1,X2)) )
    | ~ spl8_10
    | ~ spl8_40 ),
    inference(resolution,[],[f349,f112]) ).

fof(f614,plain,
    ( spl8_70
    | ~ spl8_11
    | ~ spl8_39 ),
    inference(avatar_split_clause,[],[f340,f330,f117,f612]) ).

fof(f612,plain,
    ( spl8_70
  <=> ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ in(X0,sK5(X0,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).

fof(f340,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ in(X0,sK5(X0,X1,X0)) )
    | ~ spl8_11
    | ~ spl8_39 ),
    inference(resolution,[],[f331,f118]) ).

fof(f610,plain,
    ( spl8_69
    | ~ spl8_11
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f333,f326,f117,f608]) ).

fof(f608,plain,
    ( spl8_69
  <=> ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ in(X1,sK5(X0,X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).

fof(f333,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ in(X1,sK5(X0,X1,X1)) )
    | ~ spl8_11
    | ~ spl8_38 ),
    inference(resolution,[],[f327,f118]) ).

fof(f598,plain,
    ( spl8_68
    | ~ spl8_10
    | ~ spl8_43 ),
    inference(avatar_split_clause,[],[f394,f372,f111,f596]) ).

fof(f394,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_43 ),
    inference(resolution,[],[f373,f112]) ).

fof(f594,plain,
    ( spl8_67
    | ~ spl8_10
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f380,f364,f111,f592]) ).

fof(f380,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ empty(X2)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_41 ),
    inference(resolution,[],[f365,f112]) ).

fof(f567,plain,
    ( spl8_66
    | ~ spl8_10
    | ~ spl8_39 ),
    inference(avatar_split_clause,[],[f341,f330,f111,f565]) ).

fof(f341,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X0)
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_39 ),
    inference(resolution,[],[f331,f112]) ).

fof(f563,plain,
    ( spl8_65
    | ~ spl8_10
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f334,f326,f111,f561]) ).

fof(f334,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,X1)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_38 ),
    inference(resolution,[],[f327,f112]) ).

fof(f559,plain,
    ( spl8_64
    | ~ spl8_20
    | ~ spl8_28 ),
    inference(avatar_split_clause,[],[f244,f234,f178,f557]) ).

fof(f178,plain,
    ( spl8_20
  <=> ! [X4,X0,X1,X2] :
        ( in(X4,X1)
        | ~ in(X4,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).

fof(f234,plain,
    ( spl8_28
  <=> ! [X0] : sP0(sK7,X0,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).

fof(f244,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK7)
        | in(X0,X1) )
    | ~ spl8_20
    | ~ spl8_28 ),
    inference(resolution,[],[f235,f179]) ).

fof(f179,plain,
    ( ! [X2,X0,X1,X4] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X4,X2)
        | in(X4,X1) )
    | ~ spl8_20 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f235,plain,
    ( ! [X0] : sP0(sK7,X0,sK7)
    | ~ spl8_28 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f555,plain,
    ( spl8_63
    | ~ spl8_11
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f416,f247,f117,f553]) ).

fof(f553,plain,
    ( spl8_63
  <=> ! [X0] :
        ( subset(sK1,X0)
        | ~ in(sK2,sK4(sK1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).

fof(f416,plain,
    ( ! [X0] :
        ( subset(sK1,X0)
        | ~ in(sK2,sK4(sK1,X0)) )
    | ~ spl8_11
    | ~ spl8_29 ),
    inference(resolution,[],[f248,f118]) ).

fof(f542,plain,
    ( spl8_62
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(avatar_split_clause,[],[f168,f125,f99,f540]) ).

fof(f540,plain,
    ( spl8_62
  <=> ! [X0] : sK7 = set_intersection2(X0,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).

fof(f99,plain,
    ( spl8_7
  <=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

fof(f125,plain,
    ( spl8_13
  <=> empty_set = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).

fof(f168,plain,
    ( ! [X0] : sK7 = set_intersection2(X0,sK7)
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(superposition,[],[f100,f127]) ).

fof(f127,plain,
    ( empty_set = sK7
    | ~ spl8_13 ),
    inference(avatar_component_clause,[],[f125]) ).

fof(f100,plain,
    ( ! [X0] : empty_set = set_intersection2(X0,empty_set)
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f99]) ).

fof(f534,plain,
    ( spl8_61
    | ~ spl8_12
    | ~ spl8_30 ),
    inference(avatar_split_clause,[],[f267,f251,f121,f532]) ).

fof(f532,plain,
    ( spl8_61
  <=> ! [X0] : sP0(X0,sK7,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).

fof(f121,plain,
    ( spl8_12
  <=> ! [X0,X1] : sP0(X1,X0,set_intersection2(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

fof(f251,plain,
    ( spl8_30
  <=> ! [X0] : sK7 = set_intersection2(sK7,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).

fof(f267,plain,
    ( ! [X0] : sP0(X0,sK7,sK7)
    | ~ spl8_12
    | ~ spl8_30 ),
    inference(superposition,[],[f122,f252]) ).

fof(f252,plain,
    ( ! [X0] : sK7 = set_intersection2(sK7,X0)
    | ~ spl8_30 ),
    inference(avatar_component_clause,[],[f251]) ).

fof(f122,plain,
    ( ! [X0,X1] : sP0(X1,X0,set_intersection2(X0,X1))
    | ~ spl8_12 ),
    inference(avatar_component_clause,[],[f121]) ).

fof(f490,plain,
    ( spl8_60
    | ~ spl8_24
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f228,f201,f197,f488]) ).

fof(f228,plain,
    ( ! [X0,X1] :
        ( in(sK5(sK1,X0,X1),sK2)
        | in(sK5(sK1,X0,X1),X1)
        | sP0(sK1,X0,X1) )
    | ~ spl8_24
    | ~ spl8_25 ),
    inference(resolution,[],[f198,f202]) ).

fof(f486,plain,
    ( spl8_59
    | ~ spl8_23
    | ~ spl8_24 ),
    inference(avatar_split_clause,[],[f227,f197,f193,f484]) ).

fof(f227,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,sK1,X1),sK2)
        | in(sK5(X0,sK1,X1),X1)
        | sP0(X0,sK1,X1) )
    | ~ spl8_23
    | ~ spl8_24 ),
    inference(resolution,[],[f198,f194]) ).

fof(f482,plain,
    ( spl8_58
    | ~ spl8_23
    | ~ spl8_24 ),
    inference(avatar_split_clause,[],[f226,f197,f193,f480]) ).

fof(f226,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | in(sK5(X0,X1,sK1),X1)
        | sP0(X0,X1,sK1) )
    | ~ spl8_23
    | ~ spl8_24 ),
    inference(resolution,[],[f198,f194]) ).

fof(f478,plain,
    ( spl8_57
    | ~ spl8_24
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f225,f201,f197,f476]) ).

fof(f225,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,sK1),sK2)
        | in(sK5(X0,X1,sK1),X0)
        | sP0(X0,X1,sK1) )
    | ~ spl8_24
    | ~ spl8_25 ),
    inference(resolution,[],[f198,f202]) ).

fof(f462,plain,
    ( spl8_56
    | ~ spl8_24
    | ~ spl8_44 ),
    inference(avatar_split_clause,[],[f405,f376,f197,f460]) ).

fof(f405,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,sK1)
        | ~ empty(X0)
        | in(sK5(X0,X1,sK1),sK2) )
    | ~ spl8_24
    | ~ spl8_44 ),
    inference(resolution,[],[f377,f198]) ).

fof(f458,plain,
    ( spl8_55
    | ~ spl8_24
    | ~ spl8_43 ),
    inference(avatar_split_clause,[],[f398,f372,f197,f456]) ).

fof(f398,plain,
    ( ! [X0,X1] :
        ( sP0(sK1,X0,X1)
        | ~ empty(X1)
        | in(sK5(sK1,X0,X1),sK2) )
    | ~ spl8_24
    | ~ spl8_43 ),
    inference(resolution,[],[f373,f198]) ).

fof(f454,plain,
    ( spl8_54
    | ~ spl8_24
    | ~ spl8_42 ),
    inference(avatar_split_clause,[],[f391,f368,f197,f452]) ).

fof(f391,plain,
    ( ! [X0,X1] :
        ( sP0(X0,X1,sK1)
        | ~ empty(X1)
        | in(sK5(X0,X1,sK1),sK2) )
    | ~ spl8_24
    | ~ spl8_42 ),
    inference(resolution,[],[f369,f198]) ).

fof(f450,plain,
    ( spl8_53
    | ~ spl8_24
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f384,f364,f197,f448]) ).

fof(f384,plain,
    ( ! [X0,X1] :
        ( sP0(X0,sK1,X1)
        | ~ empty(X1)
        | in(sK5(X0,sK1,X1),sK2) )
    | ~ spl8_24
    | ~ spl8_41 ),
    inference(resolution,[],[f365,f198]) ).

fof(f446,plain,
    ( ~ spl8_51
    | spl8_52
    | ~ spl8_10
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f417,f247,f111,f444,f440]) ).

fof(f440,plain,
    ( spl8_51
  <=> empty(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).

fof(f444,plain,
    ( spl8_52
  <=> ! [X0] : subset(sK1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).

fof(f417,plain,
    ( ! [X0] :
        ( subset(sK1,X0)
        | ~ empty(sK2) )
    | ~ spl8_10
    | ~ spl8_29 ),
    inference(resolution,[],[f248,f112]) ).

fof(f434,plain,
    ( spl8_50
    | ~ spl8_24
    | ~ spl8_39 ),
    inference(avatar_split_clause,[],[f345,f330,f197,f432]) ).

fof(f345,plain,
    ( ! [X0] :
        ( sP0(sK1,X0,sK1)
        | in(sK5(sK1,X0,sK1),sK2) )
    | ~ spl8_24
    | ~ spl8_39 ),
    inference(resolution,[],[f331,f198]) ).

fof(f430,plain,
    ( spl8_49
    | ~ spl8_24
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f338,f326,f197,f428]) ).

fof(f338,plain,
    ( ! [X0] :
        ( sP0(X0,sK1,sK1)
        | in(sK5(X0,sK1,sK1),sK2) )
    | ~ spl8_24
    | ~ spl8_38 ),
    inference(resolution,[],[f327,f198]) ).

fof(f426,plain,
    ( spl8_48
    | ~ spl8_11
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f211,f201,f117,f424]) ).

fof(f424,plain,
    ( spl8_48
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X0,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).

fof(f211,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X0,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_25 ),
    inference(resolution,[],[f202,f118]) ).

fof(f422,plain,
    ( spl8_47
    | ~ spl8_11
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f209,f201,f117,f420]) ).

fof(f420,plain,
    ( spl8_47
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).

fof(f209,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_25 ),
    inference(resolution,[],[f202,f118]) ).

fof(f414,plain,
    ( spl8_46
    | ~ spl8_11
    | ~ spl8_23 ),
    inference(avatar_split_clause,[],[f206,f193,f117,f412]) ).

fof(f412,plain,
    ( spl8_46
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X1,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).

fof(f206,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X1,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_23 ),
    inference(resolution,[],[f194,f118]) ).

fof(f410,plain,
    ( spl8_45
    | ~ spl8_11
    | ~ spl8_23 ),
    inference(avatar_split_clause,[],[f204,f193,f117,f408]) ).

fof(f408,plain,
    ( spl8_45
  <=> ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK5(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).

fof(f204,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK5(X0,X1,X2)) )
    | ~ spl8_11
    | ~ spl8_23 ),
    inference(resolution,[],[f194,f118]) ).

fof(f378,plain,
    ( spl8_44
    | ~ spl8_10
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f212,f201,f111,f376]) ).

fof(f212,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_25 ),
    inference(resolution,[],[f202,f112]) ).

fof(f374,plain,
    ( spl8_43
    | ~ spl8_10
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f210,f201,f111,f372]) ).

fof(f210,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_25 ),
    inference(resolution,[],[f202,f112]) ).

fof(f370,plain,
    ( spl8_42
    | ~ spl8_10
    | ~ spl8_23 ),
    inference(avatar_split_clause,[],[f207,f193,f111,f368]) ).

fof(f207,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ empty(X1) )
    | ~ spl8_10
    | ~ spl8_23 ),
    inference(resolution,[],[f194,f112]) ).

fof(f366,plain,
    ( spl8_41
    | ~ spl8_10
    | ~ spl8_23 ),
    inference(avatar_split_clause,[],[f205,f193,f111,f364]) ).

fof(f205,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ empty(X2) )
    | ~ spl8_10
    | ~ spl8_23 ),
    inference(resolution,[],[f194,f112]) ).

fof(f350,plain,
    ( spl8_40
    | ~ spl8_12
    | ~ spl8_22 ),
    inference(avatar_split_clause,[],[f191,f188,f121,f348]) ).

fof(f188,plain,
    ( spl8_22
  <=> ! [X4,X0,X2,X1] :
        ( in(X4,X2)
        | ~ in(X4,X0)
        | ~ in(X4,X1)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).

fof(f191,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X0,X2)
        | in(X0,set_intersection2(X2,X1)) )
    | ~ spl8_12
    | ~ spl8_22 ),
    inference(resolution,[],[f189,f122]) ).

fof(f189,plain,
    ( ! [X2,X0,X1,X4] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X4,X0)
        | ~ in(X4,X1)
        | in(X4,X2) )
    | ~ spl8_22 ),
    inference(avatar_component_clause,[],[f188]) ).

fof(f332,plain,
    ( spl8_39
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f213,f201,f330]) ).

fof(f213,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,X0),X0)
        | sP0(X0,X1,X0) )
    | ~ spl8_25 ),
    inference(factoring,[],[f202]) ).

fof(f328,plain,
    ( spl8_38
    | ~ spl8_23 ),
    inference(avatar_split_clause,[],[f208,f193,f326]) ).

fof(f208,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1,X1),X1)
        | sP0(X0,X1,X1) )
    | ~ spl8_23 ),
    inference(factoring,[],[f194]) ).

fof(f303,plain,
    ( spl8_37
    | ~ spl8_12
    | ~ spl8_21 ),
    inference(avatar_split_clause,[],[f186,f182,f121,f301]) ).

fof(f182,plain,
    ( spl8_21
  <=> ! [X4,X0,X2,X1] :
        ( in(X4,X0)
        | ~ in(X4,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).

fof(f186,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,set_intersection2(X1,X2))
        | in(X0,X2) )
    | ~ spl8_12
    | ~ spl8_21 ),
    inference(resolution,[],[f183,f122]) ).

fof(f183,plain,
    ( ! [X2,X0,X1,X4] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X4,X2)
        | in(X4,X0) )
    | ~ spl8_21 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f299,plain,
    ( ~ spl8_36
    | spl8_2
    | ~ spl8_32 ),
    inference(avatar_split_clause,[],[f271,f259,f75,f296]) ).

fof(f296,plain,
    ( spl8_36
  <=> empty(set_intersection2(sK1,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).

fof(f259,plain,
    ( spl8_32
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).

fof(f271,plain,
    ( ~ empty(set_intersection2(sK1,sK3))
    | spl8_2
    | ~ spl8_32 ),
    inference(resolution,[],[f260,f77]) ).

fof(f260,plain,
    ( ! [X0,X1] :
        ( subset(X0,X1)
        | ~ empty(X0) )
    | ~ spl8_32 ),
    inference(avatar_component_clause,[],[f259]) ).

fof(f294,plain,
    ( spl8_35
    | ~ spl8_12
    | ~ spl8_20 ),
    inference(avatar_split_clause,[],[f185,f178,f121,f292]) ).

fof(f185,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,set_intersection2(X1,X2))
        | in(X0,X1) )
    | ~ spl8_12
    | ~ spl8_20 ),
    inference(resolution,[],[f179,f122]) ).

fof(f290,plain,
    ( spl8_34
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(avatar_split_clause,[],[f160,f153,f117,f288]) ).

fof(f288,plain,
    ( spl8_34
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ in(X0,sK4(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).

fof(f160,plain,
    ( ! [X0,X1] :
        ( subset(X0,X1)
        | ~ in(X0,sK4(X0,X1)) )
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(resolution,[],[f154,f118]) ).

fof(f276,plain,
    ( spl8_33
    | ~ spl8_12
    | ~ spl8_14 ),
    inference(avatar_split_clause,[],[f142,f133,f121,f274]) ).

fof(f274,plain,
    ( spl8_33
  <=> ! [X0,X1] : sP0(X1,X0,set_intersection2(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).

fof(f133,plain,
    ( spl8_14
  <=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).

fof(f142,plain,
    ( ! [X0,X1] : sP0(X1,X0,set_intersection2(X1,X0))
    | ~ spl8_12
    | ~ spl8_14 ),
    inference(superposition,[],[f122,f134]) ).

fof(f134,plain,
    ( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
    | ~ spl8_14 ),
    inference(avatar_component_clause,[],[f133]) ).

fof(f261,plain,
    ( spl8_32
    | ~ spl8_10
    | ~ spl8_16 ),
    inference(avatar_split_clause,[],[f161,f153,f111,f259]) ).

fof(f161,plain,
    ( ! [X0,X1] :
        ( subset(X0,X1)
        | ~ empty(X0) )
    | ~ spl8_10
    | ~ spl8_16 ),
    inference(resolution,[],[f154,f112]) ).

fof(f257,plain,
    ( spl8_31
    | ~ spl8_5
    | ~ spl8_15 ),
    inference(avatar_split_clause,[],[f151,f137,f90,f255]) ).

fof(f255,plain,
    ( spl8_31
  <=> ! [X0] :
        ( sK7 = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).

fof(f90,plain,
    ( spl8_5
  <=> empty(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

fof(f137,plain,
    ( spl8_15
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).

fof(f151,plain,
    ( ! [X0] :
        ( sK7 = X0
        | ~ empty(X0) )
    | ~ spl8_5
    | ~ spl8_15 ),
    inference(resolution,[],[f138,f92]) ).

fof(f92,plain,
    ( empty(sK7)
    | ~ spl8_5 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f138,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) )
    | ~ spl8_15 ),
    inference(avatar_component_clause,[],[f137]) ).

fof(f253,plain,
    ( spl8_30
    | ~ spl8_7
    | ~ spl8_13
    | ~ spl8_14 ),
    inference(avatar_split_clause,[],[f146,f133,f125,f99,f251]) ).

fof(f146,plain,
    ( ! [X0] : sK7 = set_intersection2(sK7,X0)
    | ~ spl8_7
    | ~ spl8_13
    | ~ spl8_14 ),
    inference(forward_demodulation,[],[f140,f127]) ).

fof(f140,plain,
    ( ! [X0] : empty_set = set_intersection2(empty_set,X0)
    | ~ spl8_7
    | ~ spl8_14 ),
    inference(superposition,[],[f134,f100]) ).

fof(f249,plain,
    ( spl8_29
    | ~ spl8_16
    | ~ spl8_24 ),
    inference(avatar_split_clause,[],[f224,f197,f153,f247]) ).

fof(f224,plain,
    ( ! [X0] :
        ( in(sK4(sK1,X0),sK2)
        | subset(sK1,X0) )
    | ~ spl8_16
    | ~ spl8_24 ),
    inference(resolution,[],[f198,f154]) ).

fof(f236,plain,
    ( spl8_28
    | ~ spl8_7
    | ~ spl8_12
    | ~ spl8_13 ),
    inference(avatar_split_clause,[],[f131,f125,f121,f99,f234]) ).

fof(f131,plain,
    ( ! [X0] : sP0(sK7,X0,sK7)
    | ~ spl8_7
    | ~ spl8_12
    | ~ spl8_13 ),
    inference(forward_demodulation,[],[f129,f127]) ).

fof(f129,plain,
    ( ! [X0] : sP0(empty_set,X0,empty_set)
    | ~ spl8_7
    | ~ spl8_12 ),
    inference(superposition,[],[f122,f100]) ).

fof(f232,plain,
    ( spl8_27
    | ~ spl8_9
    | ~ spl8_12 ),
    inference(avatar_split_clause,[],[f130,f121,f107,f230]) ).

fof(f230,plain,
    ( spl8_27
  <=> ! [X0] : sP0(X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).

fof(f107,plain,
    ( spl8_9
  <=> ! [X0] : set_intersection2(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

fof(f130,plain,
    ( ! [X0] : sP0(X0,X0,X0)
    | ~ spl8_9
    | ~ spl8_12 ),
    inference(superposition,[],[f122,f108]) ).

fof(f108,plain,
    ( ! [X0] : set_intersection2(X0,X0) = X0
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f107]) ).

fof(f217,plain,
    spl8_26,
    inference(avatar_split_clause,[],[f63,f215]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | ~ in(sK5(X0,X1,X2),X0)
      | ~ in(sK5(X0,X1,X2),X1)
      | ~ in(sK5(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ~ in(sK5(X0,X1,X2),X0)
            | ~ in(sK5(X0,X1,X2),X1)
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( ( in(sK5(X0,X1,X2),X0)
              & in(sK5(X0,X1,X2),X1) )
            | in(sK5(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X0)
              | ~ in(X4,X1) )
            & ( ( in(X4,X0)
                & in(X4,X1) )
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f36,f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ~ in(X3,X1)
            | ~ in(X3,X2) )
          & ( ( in(X3,X0)
              & in(X3,X1) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK5(X0,X1,X2),X0)
          | ~ in(sK5(X0,X1,X2),X1)
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( ( in(sK5(X0,X1,X2),X0)
            & in(sK5(X0,X1,X2),X1) )
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X0)
              | ~ in(X4,X1) )
            & ( ( in(X4,X0)
                & in(X4,X1) )
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f203,plain,
    spl8_25,
    inference(avatar_split_clause,[],[f62,f201]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | in(sK5(X0,X1,X2),X0)
      | in(sK5(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f199,plain,
    ( spl8_24
    | ~ spl8_1
    | ~ spl8_18 ),
    inference(avatar_split_clause,[],[f174,f165,f70,f197]) ).

fof(f70,plain,
    ( spl8_1
  <=> subset(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f165,plain,
    ( spl8_18
  <=> ! [X0,X1,X3] :
        ( in(X3,X1)
        | ~ in(X3,X0)
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).

fof(f174,plain,
    ( ! [X0] :
        ( ~ in(X0,sK1)
        | in(X0,sK2) )
    | ~ spl8_1
    | ~ spl8_18 ),
    inference(resolution,[],[f166,f72]) ).

fof(f72,plain,
    ( subset(sK1,sK2)
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f70]) ).

fof(f166,plain,
    ( ! [X3,X0,X1] :
        ( ~ subset(X0,X1)
        | ~ in(X3,X0)
        | in(X3,X1) )
    | ~ spl8_18 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f195,plain,
    spl8_23,
    inference(avatar_split_clause,[],[f61,f193]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | in(sK5(X0,X1,X2),X1)
      | in(sK5(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f190,plain,
    spl8_22,
    inference(avatar_split_clause,[],[f60,f188]) ).

fof(f60,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | ~ in(X4,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f184,plain,
    spl8_21,
    inference(avatar_split_clause,[],[f59,f182]) ).

fof(f59,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f180,plain,
    spl8_20,
    inference(avatar_split_clause,[],[f58,f178]) ).

fof(f58,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f173,plain,
    spl8_19,
    inference(avatar_split_clause,[],[f65,f171]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | ~ sP0(X1,X0,X2) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP0(X1,X0,X2) )
      & ( sP0(X1,X0,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP0(X1,X0,X2) ),
    inference(definition_folding,[],[f4,f26]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f167,plain,
    spl8_18,
    inference(avatar_split_clause,[],[f53,f165]) ).

fof(f53,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f159,plain,
    spl8_17,
    inference(avatar_split_clause,[],[f55,f157]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f155,plain,
    spl8_16,
    inference(avatar_split_clause,[],[f54,f153]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f139,plain,
    spl8_15,
    inference(avatar_split_clause,[],[f56,f137]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f135,plain,
    spl8_14,
    inference(avatar_split_clause,[],[f51,f133]) ).

fof(f51,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f128,plain,
    ( spl8_13
    | ~ spl8_5
    | ~ spl8_8 ),
    inference(avatar_split_clause,[],[f115,f103,f90,f125]) ).

fof(f103,plain,
    ( spl8_8
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

fof(f115,plain,
    ( empty_set = sK7
    | ~ spl8_5
    | ~ spl8_8 ),
    inference(resolution,[],[f104,f92]) ).

fof(f104,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = X0 )
    | ~ spl8_8 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f123,plain,
    spl8_12,
    inference(avatar_split_clause,[],[f68,f121]) ).

fof(f68,plain,
    ! [X0,X1] : sP0(X1,X0,set_intersection2(X0,X1)),
    inference(equality_resolution,[],[f64]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f119,plain,
    spl8_11,
    inference(avatar_split_clause,[],[f52,f117]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f113,plain,
    spl8_10,
    inference(avatar_split_clause,[],[f57,f111]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f109,plain,
    spl8_9,
    inference(avatar_split_clause,[],[f50,f107]) ).

fof(f50,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] : set_intersection2(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

fof(f105,plain,
    spl8_8,
    inference(avatar_split_clause,[],[f48,f103]) ).

fof(f48,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f101,plain,
    spl8_7,
    inference(avatar_split_clause,[],[f47,f99]) ).

fof(f47,plain,
    ! [X0] : empty_set = set_intersection2(X0,empty_set),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] : empty_set = set_intersection2(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).

fof(f97,plain,
    spl8_6,
    inference(avatar_split_clause,[],[f49,f95]) ).

fof(f95,plain,
    ( spl8_6
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

fof(f49,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f93,plain,
    spl8_5,
    inference(avatar_split_clause,[],[f67,f90]) ).

fof(f67,plain,
    empty(sK7),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    empty(sK7),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f9,f42]) ).

fof(f42,plain,
    ( ? [X0] : empty(X0)
   => empty(sK7) ),
    introduced(choice_axiom,[]) ).

fof(f9,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f88,plain,
    ~ spl8_4,
    inference(avatar_split_clause,[],[f66,f85]) ).

fof(f85,plain,
    ( spl8_4
  <=> empty(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f66,plain,
    ~ empty(sK6),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ~ empty(sK6),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f10,f40]) ).

fof(f40,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK6) ),
    introduced(choice_axiom,[]) ).

fof(f10,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f83,plain,
    spl8_3,
    inference(avatar_split_clause,[],[f46,f80]) ).

fof(f80,plain,
    ( spl8_3
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

fof(f46,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f78,plain,
    ~ spl8_2,
    inference(avatar_split_clause,[],[f45,f75]) ).

fof(f45,plain,
    ~ subset(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ( ~ subset(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3))
    & subset(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f20,f28]) ).

fof(f28,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
        & subset(X0,X1) )
   => ( ~ subset(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3))
      & subset(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( subset(X0,X1)
       => subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
     => subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).

fof(f73,plain,
    spl8_1,
    inference(avatar_split_clause,[],[f44,f70]) ).

fof(f44,plain,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 11:37:33 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (4292)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (4295)WARNING: value z3 for option sas not known
% 0.14/0.37  % (4293)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (4296)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (4295)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (4297)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37  % (4294)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (4298)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37  % (4299)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [5]
% 0.14/0.39  TRYING [3]
% 0.21/0.42  TRYING [6]
% 0.21/0.42  TRYING [4]
% 0.21/0.44  TRYING [1]
% 0.21/0.44  TRYING [2]
% 0.21/0.44  TRYING [3]
% 0.21/0.44  TRYING [4]
% 0.21/0.46  TRYING [5]
% 0.21/0.46  TRYING [7]
% 0.21/0.48  % (4297)First to succeed.
% 0.21/0.48  TRYING [6]
% 0.21/0.49  % (4297)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4292"
% 0.21/0.49  % (4297)Refutation found. Thanks to Tanya!
% 0.21/0.49  % SZS status Theorem for theBenchmark
% 0.21/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49  % (4297)------------------------------
% 0.21/0.49  % (4297)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.49  % (4297)Termination reason: Refutation
% 0.21/0.49  
% 0.21/0.49  % (4297)Memory used [KB]: 2320
% 0.21/0.49  % (4297)Time elapsed: 0.114 s
% 0.21/0.49  % (4297)Instructions burned: 189 (million)
% 0.21/0.49  % (4292)Success in time 0.133 s
%------------------------------------------------------------------------------