TSTP Solution File: SWC353-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC353-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 10:25:10 EDT 2024

% Result   : Unsatisfiable 0.22s 0.42s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  329
% Syntax   : Number of formulae    :  528 ( 223 unt;   0 def)
%            Number of atoms       : 1338 ( 136 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 1441 ( 631   ~; 642   |;   0   &)
%                                         ( 168 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  189 ( 187 usr; 169 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;   8 con; 0-2 aty)
%            Number of variables   :  486 ( 486   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1444,plain,
    $false,
    inference(avatar_sat_refutation,[],[f236,f241,f246,f251,f256,f261,f270,f275,f280,f285,f290,f295,f300,f305,f310,f315,f320,f325,f329,f333,f337,f341,f345,f349,f353,f357,f361,f365,f369,f373,f377,f381,f385,f389,f393,f397,f401,f405,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f449,f453,f457,f461,f465,f469,f474,f478,f482,f486,f490,f494,f498,f502,f506,f510,f514,f518,f522,f526,f530,f534,f538,f542,f546,f550,f554,f558,f562,f566,f570,f574,f581,f585,f589,f593,f659,f663,f667,f671,f675,f679,f690,f707,f711,f715,f719,f723,f727,f732,f736,f740,f744,f748,f752,f756,f761,f765,f769,f774,f778,f782,f786,f790,f794,f798,f802,f806,f810,f814,f819,f823,f840,f850,f854,f858,f862,f941,f945,f949,f953,f957,f961,f965,f969,f976,f980,f984,f1036,f1040,f1044,f1048,f1052,f1056,f1067,f1071,f1162,f1166,f1170,f1174,f1178,f1182,f1186,f1190,f1194,f1198,f1244,f1248,f1252,f1256,f1260,f1333,f1337,f1344,f1348,f1352,f1356,f1360,f1443]) ).

fof(f1443,plain,
    ( ~ spl0_1
    | ~ spl0_4
    | ~ spl0_3
    | spl0_5
    | ~ spl0_6
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1025,f982,f258,f253,f243,f248,f233]) ).

fof(f233,plain,
    ( spl0_1
  <=> ssList(sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f248,plain,
    ( spl0_4
  <=> ssList(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f243,plain,
    ( spl0_3
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f253,plain,
    ( spl0_5
  <=> frontsegP(sk4,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f258,plain,
    ( spl0_6
  <=> sk4 = app(sk3,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f982,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | frontsegP(app(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1025,plain,
    ( frontsegP(sk4,sk3)
    | ~ ssList(sk4)
    | ~ ssList(sk3)
    | ~ ssList(sk5)
    | ~ spl0_6
    | ~ spl0_138 ),
    inference(superposition,[],[f983,f260]) ).

fof(f260,plain,
    ( sk4 = app(sk3,sk5)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f983,plain,
    ( ! [X0,X1] :
        ( frontsegP(app(X0,X1),X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | ~ ssList(X1) )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f982]) ).

fof(f1360,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f161,f1358]) ).

fof(f1358,plain,
    ( spl0_168
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | X0 = X2
        | memberP(X1,X2)
        | ~ memberP(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f161,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | X0 = X2
      | memberP(X1,X2)
      | ~ memberP(cons(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).

fof(f1356,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f160,f1354]) ).

fof(f1354,plain,
    ( spl0_167
  <=> ! [X0,X1] :
        ( ~ strictorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ lt(X0,hd(X1))
        | strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f160,axiom,
    ! [X0,X1] :
      ( ~ strictorderedP(X1)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | nil = X1
      | ~ lt(X0,hd(X1))
      | strictorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).

fof(f1352,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f159,f1350]) ).

fof(f1350,plain,
    ( spl0_166
  <=> ! [X0,X1] :
        ( ~ totalorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ leq(X0,hd(X1))
        | totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f159,axiom,
    ! [X0,X1] :
      ( ~ totalorderedP(X1)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | nil = X1
      | ~ leq(X0,hd(X1))
      | totalorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).

fof(f1348,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f158,f1346]) ).

fof(f1346,plain,
    ( spl0_165
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | memberP(X1,X2)
        | memberP(X0,X2)
        | ~ memberP(app(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f158,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | memberP(X1,X2)
      | memberP(X0,X2)
      | ~ memberP(app(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).

fof(f1344,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f157,f1342]) ).

fof(f1342,plain,
    ( spl0_164
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f157,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).

fof(f1337,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f149,f1335]) ).

fof(f1335,plain,
    ( spl0_163
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | app(app(X2,X1),X0) = app(X2,app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f149,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | app(app(X2,X1),X0) = app(X2,app(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).

fof(f1333,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f142,f1331]) ).

fof(f1331,plain,
    ( spl0_162
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f142,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | equalelemsP(X0)
      | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).

fof(f1260,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f225,f1258]) ).

fof(f1258,plain,
    ( spl0_161
  <=> ! [X0,X1,X3] :
        ( ~ ssItem(X3)
        | ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | frontsegP(cons(X3,X0),cons(X3,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f225,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(duplicate_literal_removal,[],[f218]) ).

fof(f218,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(equality_resolution,[],[f178]) ).

fof(f178,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | X2 != X3
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X2,X0),cons(X3,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).

fof(f1256,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f151,f1254]) ).

fof(f1254,plain,
    ( spl0_160
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | X0 = X2
        | app(X0,X1) != app(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f151,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | X0 = X2
      | app(X0,X1) != app(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).

fof(f1252,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f150,f1250]) ).

fof(f1250,plain,
    ( spl0_159
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | X1 = X2
        | app(X0,X1) != app(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f150,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | X1 = X2
      | app(X0,X1) != app(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).

fof(f1248,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f133,f1246]) ).

fof(f1246,plain,
    ( spl0_158
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f133,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | nil = X1
      | tl(app(X1,X0)) = app(tl(X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).

fof(f1244,plain,
    ( ~ spl0_4
    | ~ spl0_1
    | ~ spl0_3
    | spl0_157
    | ~ spl0_6
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1016,f978,f258,f1241,f243,f233,f248]) ).

fof(f1241,plain,
    ( spl0_157
  <=> rearsegP(sk4,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f978,plain,
    ( spl0_137
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | rearsegP(app(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1016,plain,
    ( rearsegP(sk4,sk5)
    | ~ ssList(sk4)
    | ~ ssList(sk5)
    | ~ ssList(sk3)
    | ~ spl0_6
    | ~ spl0_137 ),
    inference(superposition,[],[f979,f260]) ).

fof(f979,plain,
    ( ! [X0,X1] :
        ( rearsegP(app(X0,X1),X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f978]) ).

fof(f1198,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f156,f1196]) ).

fof(f1196,plain,
    ( spl0_156
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X1,X2)
        | ~ leq(X0,X1)
        | leq(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f156,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ leq(X1,X2)
      | ~ leq(X0,X1)
      | leq(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).

fof(f1194,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f155,f1192]) ).

fof(f1192,plain,
    ( spl0_155
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X1,X2)
        | ~ lt(X0,X1)
        | lt(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f155,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X1,X2)
      | ~ lt(X0,X1)
      | lt(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).

fof(f1190,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f154,f1188]) ).

fof(f1188,plain,
    ( spl0_154
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ frontsegP(X1,X2)
        | ~ frontsegP(X0,X1)
        | frontsegP(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f154,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ frontsegP(X1,X2)
      | ~ frontsegP(X0,X1)
      | frontsegP(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).

fof(f1186,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f153,f1184]) ).

fof(f1184,plain,
    ( spl0_153
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ rearsegP(X1,X2)
        | ~ rearsegP(X0,X1)
        | rearsegP(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f153,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ rearsegP(X1,X2)
      | ~ rearsegP(X0,X1)
      | rearsegP(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).

fof(f1182,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f152,f1180]) ).

fof(f1180,plain,
    ( spl0_152
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ segmentP(X1,X2)
        | ~ segmentP(X0,X1)
        | segmentP(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f152,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ segmentP(X1,X2)
      | ~ segmentP(X0,X1)
      | segmentP(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).

fof(f1178,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f148,f1176]) ).

fof(f1176,plain,
    ( spl0_151
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ geq(X1,X2)
        | ~ geq(X0,X1)
        | geq(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f148,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ geq(X1,X2)
      | ~ geq(X0,X1)
      | geq(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).

fof(f1174,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f147,f1172]) ).

fof(f1172,plain,
    ( spl0_150
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X1,X2)
        | ~ leq(X0,X1)
        | lt(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f147,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X1,X2)
      | ~ leq(X0,X1)
      | lt(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).

fof(f1170,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f146,f1168]) ).

fof(f1168,plain,
    ( spl0_149
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ gt(X1,X2)
        | ~ gt(X0,X1)
        | gt(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f146,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ gt(X1,X2)
      | ~ gt(X0,X1)
      | gt(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause146) ).

fof(f1166,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f135,f1164]) ).

fof(f1164,plain,
    ( spl0_148
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f135,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | nil = X1
      | ~ totalorderedP(cons(X0,X1))
      | leq(X0,hd(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).

fof(f1162,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f134,f1160]) ).

fof(f1160,plain,
    ( spl0_147
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f134,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | nil = X1
      | ~ strictorderedP(cons(X0,X1))
      | lt(X0,hd(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).

fof(f1071,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f141,f1069]) ).

fof(f1069,plain,
    ( spl0_146
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ memberP(X0,X1)
        | memberP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f141,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ memberP(X0,X1)
      | memberP(app(X2,X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).

fof(f1067,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f140,f1065]) ).

fof(f1065,plain,
    ( spl0_145
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f140,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ memberP(X0,X1)
      | memberP(app(X0,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).

fof(f1056,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f139,f1054]) ).

fof(f1054,plain,
    ( spl0_144
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(cons(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f139,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ ssList(X0)
      | ~ memberP(X0,X1)
      | memberP(cons(X2,X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).

fof(f1052,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f137,f1050]) ).

fof(f1050,plain,
    ( spl0_143
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ frontsegP(X0,X1)
        | frontsegP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f137,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ frontsegP(X0,X1)
      | frontsegP(app(X0,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).

fof(f1048,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f136,f1046]) ).

fof(f1046,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ rearsegP(X0,X1)
        | rearsegP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f136,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ rearsegP(X0,X1)
      | rearsegP(app(X2,X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).

fof(f1044,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f132,f1042]) ).

fof(f1042,plain,
    ( spl0_141
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | app(X1,skaf45(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f132,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | app(X1,skaf45(X0,X1)) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).

fof(f1040,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f131,f1038]) ).

fof(f1038,plain,
    ( spl0_140
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X0,X1)
        | app(skaf46(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f131,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ rearsegP(X0,X1)
      | app(skaf46(X0,X1),X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).

fof(f1036,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f123,f1034]) ).

fof(f1034,plain,
    ( spl0_139
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f123,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | nil = X1
      | hd(app(X1,X0)) = hd(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).

fof(f984,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f212,f982]) ).

fof(f212,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(app(X0,X1))
      | ~ ssList(X0)
      | frontsegP(app(X0,X1),X0) ),
    inference(equality_resolution,[],[f144]) ).

fof(f144,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | frontsegP(X2,X0)
      | app(X0,X1) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).

fof(f980,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f211,f978]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | rearsegP(app(X0,X1),X1) ),
    inference(equality_resolution,[],[f143]) ).

fof(f143,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | rearsegP(X2,X1)
      | app(X0,X1) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).

fof(f976,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f130,f974]) ).

fof(f974,plain,
    ( spl0_136
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X1,X0)
        | ~ leq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f130,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X0)
      | ~ leq(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).

fof(f969,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f129,f967]) ).

fof(f967,plain,
    ( spl0_135
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X1,X0)
        | ~ frontsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f129,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X1,X0)
      | ~ frontsegP(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).

fof(f965,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f128,f963]) ).

fof(f963,plain,
    ( spl0_134
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f128,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ rearsegP(X1,X0)
      | ~ rearsegP(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).

fof(f961,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f127,f959]) ).

fof(f959,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f127,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ segmentP(X1,X0)
      | ~ segmentP(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).

fof(f957,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f126,f955]) ).

fof(f955,plain,
    ( spl0_132
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f126,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ geq(X1,X0)
      | ~ geq(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).

fof(f953,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f125,f951]) ).

fof(f951,plain,
    ( spl0_131
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | totalorderedP(X1)
      | nil = X1
      | ~ totalorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).

fof(f949,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f124,f947]) ).

fof(f947,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f124,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | strictorderedP(X1)
      | nil = X1
      | ~ strictorderedP(cons(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).

fof(f945,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f122,f943]) ).

fof(f943,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f122,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X0,X1)
      | X0 = X1
      | lt(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).

fof(f941,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f120,f939]) ).

fof(f939,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f120,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | cons(X0,X1) = app(cons(X0,nil),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).

fof(f862,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f119,f860]) ).

fof(f860,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f119,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | nil = X1
      | nil != app(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).

fof(f858,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f118,f856]) ).

fof(f856,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f118,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | nil = X0
      | nil != app(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).

fof(f854,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f109,f852]) ).

fof(f852,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f109,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(skaf83(X0),skaf82(X0)) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).

fof(f850,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f104,f848]) ).

fof(f848,plain,
    ( spl0_124
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f104,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(hd(X0),tl(X0)) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).

fof(f840,plain,
    ( spl0_123
    | ~ spl0_1
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f655,f591,f233,f837]) ).

fof(f837,plain,
    ( spl0_123
  <=> sk5 = app(nil,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f591,plain,
    ( spl0_86
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f655,plain,
    ( sk5 = app(nil,sk5)
    | ~ spl0_1
    | ~ spl0_86 ),
    inference(resolution,[],[f592,f235]) ).

fof(f235,plain,
    ( ssList(sk5)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f592,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f591]) ).

fof(f823,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f206,f821]) ).

fof(f821,plain,
    ( spl0_122
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f206,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | singletonP(cons(X0,nil)) ),
    inference(equality_resolution,[],[f116]) ).

fof(f116,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | singletonP(X1)
      | cons(X0,nil) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).

fof(f819,plain,
    ( spl0_121
    | ~ spl0_3
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f654,f591,f243,f816]) ).

fof(f816,plain,
    ( spl0_121
  <=> sk4 = app(nil,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f654,plain,
    ( sk4 = app(nil,sk4)
    | ~ spl0_3
    | ~ spl0_86 ),
    inference(resolution,[],[f592,f245]) ).

fof(f245,plain,
    ( ssList(sk4)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f243]) ).

fof(f814,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f114,f812]) ).

fof(f812,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f114,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X1,X0)
      | ~ lt(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).

fof(f810,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f110,f808]) ).

fof(f808,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f110,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ gt(X1,X0)
      | ~ gt(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).

fof(f806,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f108,f804]) ).

fof(f804,plain,
    ( spl0_118
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f108,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ leq(X0,X1)
      | geq(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).

fof(f802,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f107,f800]) ).

fof(f800,plain,
    ( spl0_117
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f107,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ geq(X0,X1)
      | leq(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).

fof(f798,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f106,f796]) ).

fof(f796,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f106,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X0,X1)
      | gt(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).

fof(f794,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f105,f792]) ).

fof(f792,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f105,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ gt(X0,X1)
      | lt(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).

fof(f790,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f103,f788]) ).

fof(f788,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f103,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X0,X1)
      | leq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).

fof(f786,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f102,f784]) ).

fof(f784,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f102,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | X0 = X1
      | neq(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).

fof(f782,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f101,f780]) ).

fof(f780,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f101,axiom,
    ! [X0] :
      ( ~ singletonP(X0)
      | ~ ssList(X0)
      | cons(skaf44(X0),nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).

fof(f778,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f100,f776]) ).

fof(f776,plain,
    ( spl0_111
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f100,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | X0 = X1
      | neq(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).

fof(f774,plain,
    ( spl0_110
    | ~ spl0_4
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f653,f591,f248,f771]) ).

fof(f771,plain,
    ( spl0_110
  <=> sk3 = app(nil,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f653,plain,
    ( sk3 = app(nil,sk3)
    | ~ spl0_4
    | ~ spl0_86 ),
    inference(resolution,[],[f592,f250]) ).

fof(f250,plain,
    ( ssList(sk3)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f248]) ).

fof(f769,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f97,f767]) ).

fof(f767,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | hd(cons(X0,X1)) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).

fof(f765,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f96,f763]) ).

fof(f763,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f96,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | tl(cons(X0,X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).

fof(f761,plain,
    ( spl0_107
    | ~ spl0_1
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f624,f587,f233,f758]) ).

fof(f758,plain,
    ( spl0_107
  <=> sk5 = app(sk5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f587,plain,
    ( spl0_85
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f624,plain,
    ( sk5 = app(sk5,nil)
    | ~ spl0_1
    | ~ spl0_85 ),
    inference(resolution,[],[f588,f235]) ).

fof(f588,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f587]) ).

fof(f756,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f227,f754]) ).

fof(f754,plain,
    ( spl0_106
  <=> ! [X2,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f227,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f210]) ).

fof(f210,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | X0 != X1
      | memberP(cons(X1,X2),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).

fof(f752,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f99,f750]) ).

fof(f750,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | cons(X0,X1) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).

fof(f748,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f98,f746]) ).

fof(f746,plain,
    ( spl0_104
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f98,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | nil != cons(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).

fof(f744,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f95,f742]) ).

fof(f742,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f95,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderP(X0)
      | ~ leq(skaf54(X0),skaf55(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).

fof(f740,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f94,f738]) ).

fof(f738,plain,
    ( spl0_102
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f94,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderP(X0)
      | ~ leq(skaf55(X0),skaf54(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).

fof(f736,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f93,f734]) ).

fof(f734,plain,
    ( spl0_101
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f93,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | strictorderP(X0)
      | ~ lt(skaf59(X0),skaf60(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).

fof(f732,plain,
    ( spl0_100
    | ~ spl0_3
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f623,f587,f243,f729]) ).

fof(f729,plain,
    ( spl0_100
  <=> sk4 = app(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f623,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_3
    | ~ spl0_85 ),
    inference(resolution,[],[f588,f245]) ).

fof(f727,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f92,f725]) ).

fof(f725,plain,
    ( spl0_99
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f92,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | strictorderP(X0)
      | ~ lt(skaf60(X0),skaf59(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).

fof(f723,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f91,f721]) ).

fof(f721,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f91,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | ~ leq(skaf64(X0),skaf65(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).

fof(f719,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f90,f717]) ).

fof(f717,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f90,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | strictorderedP(X0)
      | ~ lt(skaf69(X0),skaf70(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).

fof(f715,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f89,f713]) ).

fof(f713,plain,
    ( spl0_96
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f89,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | equalelemsP(X0)
      | skaf79(X0) != skaf78(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).

fof(f711,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f88,f709]) ).

fof(f709,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f88,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | cyclefreeP(X0)
      | leq(skaf49(X0),skaf50(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).

fof(f707,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f87,f705]) ).

fof(f705,plain,
    ( spl0_94
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f87,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | cyclefreeP(X0)
      | leq(skaf50(X0),skaf49(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).

fof(f690,plain,
    ( spl0_93
    | ~ spl0_4
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f622,f587,f248,f687]) ).

fof(f687,plain,
    ( spl0_93
  <=> sk3 = app(sk3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f622,plain,
    ( sk3 = app(sk3,nil)
    | ~ spl0_4
    | ~ spl0_85 ),
    inference(resolution,[],[f588,f250]) ).

fof(f679,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f86,f677]) ).

fof(f677,plain,
    ( spl0_92
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f86,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ssList(cons(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).

fof(f675,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f85,f673]) ).

fof(f673,plain,
    ( spl0_91
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f85,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ssList(app(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).

fof(f671,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f84,f669]) ).

fof(f669,plain,
    ( spl0_90
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f84,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ frontsegP(nil,X0)
      | nil = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).

fof(f667,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f82,f665]) ).

fof(f665,plain,
    ( spl0_89
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f82,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ rearsegP(nil,X0)
      | nil = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).

fof(f663,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f80,f661]) ).

fof(f661,plain,
    ( spl0_88
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f80,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ segmentP(nil,X0)
      | nil = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).

fof(f659,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f77,f657]) ).

fof(f657,plain,
    ( spl0_87
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f77,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssList(tl(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).

fof(f593,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f74,f591]) ).

fof(f74,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).

fof(f589,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f73,f587]) ).

fof(f73,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).

fof(f585,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f195,f583]) ).

fof(f583,plain,
    ( spl0_84
  <=> ! [X9,X7,X6,X8] :
        ( ~ ssItem(X6)
        | ~ ssItem(X8)
        | ~ ssList(X9)
        | ~ ssList(X7)
        | ~ leq(X8,X6)
        | sk5 != app(cons(X6,nil),X7)
        | sk3 != app(X9,cons(X8,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f195,axiom,
    ! [X8,X6,X9,X7] :
      ( ~ ssItem(X6)
      | ~ ssItem(X8)
      | ~ ssList(X9)
      | ~ ssList(X7)
      | ~ leq(X8,X6)
      | sk5 != app(cons(X6,nil),X7)
      | sk3 != app(X9,cons(X8,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).

fof(f581,plain,
    ( spl0_82
    | spl0_83 ),
    inference(avatar_split_clause,[],[f72,f579,f576]) ).

fof(f576,plain,
    ( spl0_82
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f579,plain,
    ( spl0_83
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f72,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssItem(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).

fof(f574,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f70,f572]) ).

fof(f572,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f70,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | cyclefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).

fof(f570,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f69,f568]) ).

fof(f568,plain,
    ( spl0_80
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f69,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | totalorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).

fof(f566,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f68,f564]) ).

fof(f564,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f68,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | strictorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).

fof(f562,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f67,f560]) ).

fof(f560,plain,
    ( spl0_78
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f67,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).

fof(f558,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f66,f556]) ).

fof(f556,plain,
    ( spl0_77
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f66,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).

fof(f554,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f65,f552]) ).

fof(f552,plain,
    ( spl0_76
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | duplicatefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f65,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).

fof(f550,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f64,f548]) ).

fof(f548,plain,
    ( spl0_75
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f64,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | equalelemsP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).

fof(f546,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f230,f544]) ).

fof(f544,plain,
    ( spl0_74
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f230,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f204]) ).

fof(f204,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f117]) ).

fof(f117,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | X0 != X1
      | ~ neq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).

fof(f542,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f228,f540]) ).

fof(f540,plain,
    ( spl0_73
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f228,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f209]) ).

fof(f209,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f115]) ).

fof(f115,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 != X1
      | ~ neq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).

fof(f538,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f71,f536]) ).

fof(f536,plain,
    ( spl0_72
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f71,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).

fof(f534,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f63,f532]) ).

fof(f532,plain,
    ( spl0_71
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f63,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ lt(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).

fof(f530,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f62,f528]) ).

fof(f528,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f62,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | leq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).

fof(f526,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f61,f524]) ).

fof(f524,plain,
    ( spl0_69
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f61,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).

fof(f522,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f60,f520]) ).

fof(f520,plain,
    ( spl0_68
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).

fof(f518,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f59,f516]) ).

fof(f516,plain,
    ( spl0_67
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f59,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | rearsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).

fof(f514,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f58,f512]) ).

fof(f512,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f58,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | rearsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).

fof(f510,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f57,f508]) ).

fof(f508,plain,
    ( spl0_65
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f57,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).

fof(f506,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f56,f504]) ).

fof(f504,plain,
    ( spl0_64
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f56,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).

fof(f502,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f55,f500]) ).

fof(f500,plain,
    ( spl0_63
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f55,axiom,
    ! [X0] :
      ( ~ ssItem(X0)
      | geq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).

fof(f498,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f53,f496]) ).

fof(f496,plain,
    ( spl0_62
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f53,axiom,
    ! [X0,X1] : ssList(skaf42(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).

fof(f494,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f52,f492]) ).

fof(f492,plain,
    ( spl0_61
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f52,axiom,
    ! [X0,X1] : ssList(skaf43(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).

fof(f490,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f51,f488]) ).

fof(f488,plain,
    ( spl0_60
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f51,axiom,
    ! [X0,X1] : ssList(skaf45(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).

fof(f486,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f50,f484]) ).

fof(f484,plain,
    ( spl0_59
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f50,axiom,
    ! [X0,X1] : ssList(skaf46(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).

fof(f482,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f49,f480]) ).

fof(f480,plain,
    ( spl0_58
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f49,axiom,
    ! [X0,X1] : ssList(skaf47(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).

fof(f478,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f48,f476]) ).

fof(f476,plain,
    ( spl0_57
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f48,axiom,
    ! [X0,X1] : ssList(skaf48(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).

fof(f474,plain,
    ~ spl0_56,
    inference(avatar_split_clause,[],[f54,f471]) ).

fof(f471,plain,
    ( spl0_56
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f54,axiom,
    skac3 != skac2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).

fof(f469,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f47,f467]) ).

fof(f467,plain,
    ( spl0_55
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f47,axiom,
    ! [X0] : ssItem(skaf44(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).

fof(f465,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f46,f463]) ).

fof(f463,plain,
    ( spl0_54
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f46,axiom,
    ! [X0] : ssItem(skaf49(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).

fof(f461,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f45,f459]) ).

fof(f459,plain,
    ( spl0_53
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f45,axiom,
    ! [X0] : ssItem(skaf50(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).

fof(f457,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f44,f455]) ).

fof(f455,plain,
    ( spl0_52
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f44,axiom,
    ! [X0] : ssList(skaf51(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).

fof(f453,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f43,f451]) ).

fof(f451,plain,
    ( spl0_51
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f43,axiom,
    ! [X0] : ssList(skaf52(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).

fof(f449,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f42,f447]) ).

fof(f447,plain,
    ( spl0_50
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f42,axiom,
    ! [X0] : ssList(skaf53(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).

fof(f445,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f41,f443]) ).

fof(f443,plain,
    ( spl0_49
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f41,axiom,
    ! [X0] : ssItem(skaf54(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).

fof(f441,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f40,f439]) ).

fof(f439,plain,
    ( spl0_48
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f40,axiom,
    ! [X0] : ssItem(skaf55(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).

fof(f437,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f39,f435]) ).

fof(f435,plain,
    ( spl0_47
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f39,axiom,
    ! [X0] : ssList(skaf56(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).

fof(f433,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f38,f431]) ).

fof(f431,plain,
    ( spl0_46
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f38,axiom,
    ! [X0] : ssList(skaf57(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).

fof(f429,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f37,f427]) ).

fof(f427,plain,
    ( spl0_45
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f37,axiom,
    ! [X0] : ssList(skaf58(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).

fof(f425,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f36,f423]) ).

fof(f423,plain,
    ( spl0_44
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f36,axiom,
    ! [X0] : ssItem(skaf59(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).

fof(f421,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f35,f419]) ).

fof(f419,plain,
    ( spl0_43
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f35,axiom,
    ! [X0] : ssItem(skaf60(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).

fof(f417,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f34,f415]) ).

fof(f415,plain,
    ( spl0_42
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f34,axiom,
    ! [X0] : ssList(skaf61(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).

fof(f413,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f33,f411]) ).

fof(f411,plain,
    ( spl0_41
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f33,axiom,
    ! [X0] : ssList(skaf62(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).

fof(f409,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f32,f407]) ).

fof(f407,plain,
    ( spl0_40
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f32,axiom,
    ! [X0] : ssList(skaf63(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).

fof(f405,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f31,f403]) ).

fof(f403,plain,
    ( spl0_39
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f31,axiom,
    ! [X0] : ssItem(skaf64(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).

fof(f401,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f30,f399]) ).

fof(f399,plain,
    ( spl0_38
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f30,axiom,
    ! [X0] : ssItem(skaf65(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).

fof(f397,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f29,f395]) ).

fof(f395,plain,
    ( spl0_37
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f29,axiom,
    ! [X0] : ssList(skaf66(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).

fof(f393,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f28,f391]) ).

fof(f391,plain,
    ( spl0_36
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f28,axiom,
    ! [X0] : ssList(skaf67(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).

fof(f389,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f27,f387]) ).

fof(f387,plain,
    ( spl0_35
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f27,axiom,
    ! [X0] : ssList(skaf68(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).

fof(f385,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f26,f383]) ).

fof(f383,plain,
    ( spl0_34
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f26,axiom,
    ! [X0] : ssItem(skaf69(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).

fof(f381,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f25,f379]) ).

fof(f379,plain,
    ( spl0_33
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f25,axiom,
    ! [X0] : ssItem(skaf70(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).

fof(f377,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f24,f375]) ).

fof(f375,plain,
    ( spl0_32
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f24,axiom,
    ! [X0] : ssList(skaf71(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).

fof(f373,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f23,f371]) ).

fof(f371,plain,
    ( spl0_31
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f23,axiom,
    ! [X0] : ssList(skaf72(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).

fof(f369,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f22,f367]) ).

fof(f367,plain,
    ( spl0_30
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f22,axiom,
    ! [X0] : ssList(skaf73(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).

fof(f365,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f21,f363]) ).

fof(f363,plain,
    ( spl0_29
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f21,axiom,
    ! [X0] : ssItem(skaf74(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).

fof(f361,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f20,f359]) ).

fof(f359,plain,
    ( spl0_28
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f20,axiom,
    ! [X0] : ssList(skaf75(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).

fof(f357,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f19,f355]) ).

fof(f355,plain,
    ( spl0_27
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f19,axiom,
    ! [X0] : ssList(skaf76(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).

fof(f353,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f18,f351]) ).

fof(f351,plain,
    ( spl0_26
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f18,axiom,
    ! [X0] : ssList(skaf77(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).

fof(f349,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f17,f347]) ).

fof(f347,plain,
    ( spl0_25
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f17,axiom,
    ! [X0] : ssItem(skaf78(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).

fof(f345,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f16,f343]) ).

fof(f343,plain,
    ( spl0_24
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f16,axiom,
    ! [X0] : ssItem(skaf79(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).

fof(f341,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f15,f339]) ).

fof(f339,plain,
    ( spl0_23
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f15,axiom,
    ! [X0] : ssList(skaf80(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).

fof(f337,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f14,f335]) ).

fof(f335,plain,
    ( spl0_22
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f14,axiom,
    ! [X0] : ssList(skaf81(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).

fof(f333,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f13,f331]) ).

fof(f331,plain,
    ( spl0_21
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f13,axiom,
    ! [X0] : ssList(skaf82(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).

fof(f329,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f12,f327]) ).

fof(f327,plain,
    ( spl0_20
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f12,axiom,
    ! [X0] : ssItem(skaf83(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).

fof(f325,plain,
    ~ spl0_19,
    inference(avatar_split_clause,[],[f11,f322]) ).

fof(f322,plain,
    ( spl0_19
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f11,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).

fof(f320,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f10,f317]) ).

fof(f317,plain,
    ( spl0_18
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f10,axiom,
    ssItem(skac2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).

fof(f315,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f9,f312]) ).

fof(f312,plain,
    ( spl0_17
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f9,axiom,
    ssItem(skac3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).

fof(f310,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f8,f307]) ).

fof(f307,plain,
    ( spl0_16
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).

fof(f305,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f7,f302]) ).

fof(f302,plain,
    ( spl0_15
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f7,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).

fof(f300,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f6,f297]) ).

fof(f297,plain,
    ( spl0_14
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f6,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).

fof(f295,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f5,f292]) ).

fof(f292,plain,
    ( spl0_13
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f5,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).

fof(f290,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f4,f287]) ).

fof(f287,plain,
    ( spl0_12
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f4,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).

fof(f285,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f3,f282]) ).

fof(f282,plain,
    ( spl0_11
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f3,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).

fof(f280,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f2,f277]) ).

fof(f277,plain,
    ( spl0_10
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f2,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).

fof(f275,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f1,f272]) ).

fof(f272,plain,
    ( spl0_9
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f1,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).

fof(f270,plain,
    ( spl0_7
    | ~ spl0_8 ),
    inference(avatar_split_clause,[],[f231,f267,f263]) ).

fof(f263,plain,
    ( spl0_7
  <=> sk3 = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f267,plain,
    ( spl0_8
  <=> nil = sk3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f231,plain,
    ( nil != sk3
    | sk3 = sk4 ),
    inference(inner_rewriting,[],[f197]) ).

fof(f197,axiom,
    ( nil != sk3
    | nil = sk4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).

fof(f261,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f193,f258]) ).

fof(f193,axiom,
    sk4 = app(sk3,sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).

fof(f256,plain,
    ~ spl0_5,
    inference(avatar_split_clause,[],[f200,f253]) ).

fof(f200,plain,
    ~ frontsegP(sk4,sk3),
    inference(definition_unfolding,[],[f196,f190,f191]) ).

fof(f191,axiom,
    sk1 = sk3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).

fof(f190,axiom,
    sk2 = sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).

fof(f196,axiom,
    ~ frontsegP(sk2,sk1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).

fof(f251,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f199,f248]) ).

fof(f199,plain,
    ssList(sk3),
    inference(definition_unfolding,[],[f186,f191]) ).

fof(f186,axiom,
    ssList(sk1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).

fof(f246,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f198,f243]) ).

fof(f198,plain,
    ssList(sk4),
    inference(definition_unfolding,[],[f187,f190]) ).

fof(f187,axiom,
    ssList(sk2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).

fof(f241,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f194,f238]) ).

fof(f238,plain,
    ( spl0_2
  <=> totalorderedP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f194,axiom,
    totalorderedP(sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

fof(f236,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f192,f233]) ).

fof(f192,axiom,
    ssList(sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC353-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 20:27:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (4006)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (4009)WARNING: value z3 for option sas not known
% 0.15/0.38  % (4008)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (4007)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (4011)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)
% 0.15/0.38  % (4009)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)
% 0.15/0.38  % (4010)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (4012)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)
% 0.15/0.39  % (4013)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)
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [2]
% 0.15/0.41  TRYING [3]
% 0.15/0.42  % (4011)First to succeed.
% 0.15/0.42  TRYING [1]
% 0.15/0.42  TRYING [2]
% 0.22/0.42  % (4011)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4006"
% 0.22/0.42  % (4011)Refutation found. Thanks to Tanya!
% 0.22/0.42  % SZS status Unsatisfiable for theBenchmark
% 0.22/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43  % (4011)------------------------------
% 0.22/0.43  % (4011)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43  % (4011)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (4011)Memory used [KB]: 1672
% 0.22/0.43  % (4011)Time elapsed: 0.038 s
% 0.22/0.43  % (4011)Instructions burned: 62 (million)
% 0.22/0.43  % (4006)Success in time 0.049 s
%------------------------------------------------------------------------------