TSTP Solution File: SWC351-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC351-1 : 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 : n005.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 10:25:09 EDT 2024

% Result   : Unsatisfiable 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  331
% Syntax   : Number of formulae    :  531 ( 225 unt;   0 def)
%            Number of atoms       : 1342 ( 136 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 1442 ( 631   ~; 642   |;   0   &)
%                                         ( 169 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  190 ( 188 usr; 170 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;   8 con; 0-2 aty)
%            Number of variables   :  486 ( 486   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1438,plain,
    $false,
    inference(avatar_sat_refutation,[],[f238,f243,f248,f253,f258,f263,f268,f277,f282,f287,f292,f297,f302,f307,f312,f317,f322,f327,f332,f336,f340,f344,f348,f352,f356,f360,f364,f368,f372,f376,f380,f384,f388,f392,f396,f400,f404,f408,f412,f416,f420,f424,f428,f432,f436,f440,f444,f448,f452,f456,f460,f464,f468,f472,f476,f481,f485,f489,f493,f497,f501,f505,f509,f513,f517,f521,f525,f529,f533,f537,f541,f545,f549,f553,f557,f561,f565,f569,f573,f577,f581,f588,f592,f596,f600,f666,f670,f674,f678,f682,f686,f691,f714,f718,f722,f726,f731,f735,f739,f743,f747,f751,f755,f759,f763,f768,f773,f777,f781,f785,f789,f793,f797,f801,f805,f809,f813,f818,f822,f826,f830,f845,f857,f861,f865,f869,f948,f952,f956,f960,f964,f968,f975,f979,f983,f987,f991,f1043,f1047,f1051,f1055,f1066,f1070,f1074,f1078,f1169,f1173,f1177,f1181,f1185,f1189,f1193,f1197,f1212,f1216,f1247,f1255,f1259,f1263,f1267,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1437]) ).

fof(f1437,plain,
    ( ~ spl0_2
    | ~ spl0_4
    | ~ spl0_1
    | spl0_5
    | ~ spl0_7
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1032,f989,f265,f255,f235,f250,f240]) ).

fof(f240,plain,
    ( spl0_2
  <=> ssList(sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f250,plain,
    ( spl0_4
  <=> ssList(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f235,plain,
    ( spl0_1
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f255,plain,
    ( spl0_5
  <=> frontsegP(sk4,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f265,plain,
    ( spl0_7
  <=> sk4 = app(sk3,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f989,plain,
    ( spl0_139
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | frontsegP(app(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f1032,plain,
    ( frontsegP(sk4,sk3)
    | ~ ssList(sk4)
    | ~ ssList(sk3)
    | ~ ssList(sk5)
    | ~ spl0_7
    | ~ spl0_139 ),
    inference(superposition,[],[f990,f267]) ).

fof(f267,plain,
    ( sk4 = app(sk3,sk5)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f990,plain,
    ( ! [X0,X1] :
        ( frontsegP(app(X0,X1),X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | ~ ssList(X1) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f989]) ).

fof(f1367,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f161,f1365]) ).

fof(f1365,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

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(f1363,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f160,f1361]) ).

fof(f1361,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

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(f1359,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f159,f1357]) ).

fof(f1357,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

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(f1355,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f158,f1353]) ).

fof(f1353,plain,
    ( spl0_166
  <=> ! [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_166])]) ).

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(f1351,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f157,f1349]) ).

fof(f1349,plain,
    ( spl0_165
  <=> ! [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_165])]) ).

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(f1347,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f149,f1345]) ).

fof(f1345,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

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(f1343,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f142,f1341]) ).

fof(f1341,plain,
    ( spl0_163
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

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(f1267,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f227,f1265]) ).

fof(f1265,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

fof(f227,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(duplicate_literal_removal,[],[f220]) ).

fof(f220,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(f1263,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f151,f1261]) ).

fof(f1261,plain,
    ( spl0_161
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | X0 = X2
        | app(X0,X1) != app(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

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(f1259,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f150,f1257]) ).

fof(f1257,plain,
    ( spl0_160
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | X1 = X2
        | app(X0,X1) != app(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

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(f1255,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f133,f1253]) ).

fof(f1253,plain,
    ( spl0_159
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

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(f1247,plain,
    ( ~ spl0_4
    | ~ spl0_2
    | ~ spl0_1
    | spl0_158
    | ~ spl0_7
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1023,f985,f265,f1244,f235,f240,f250]) ).

fof(f1244,plain,
    ( spl0_158
  <=> rearsegP(sk4,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f985,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | rearsegP(app(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1023,plain,
    ( rearsegP(sk4,sk5)
    | ~ ssList(sk4)
    | ~ ssList(sk5)
    | ~ ssList(sk3)
    | ~ spl0_7
    | ~ spl0_138 ),
    inference(superposition,[],[f986,f267]) ).

fof(f986,plain,
    ( ! [X0,X1] :
        ( rearsegP(app(X0,X1),X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f985]) ).

fof(f1216,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f156,f1214]) ).

fof(f1214,plain,
    ( spl0_157
  <=> ! [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_157])]) ).

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(f1212,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f155,f1210]) ).

fof(f1210,plain,
    ( spl0_156
  <=> ! [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_156])]) ).

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(f1197,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f154,f1195]) ).

fof(f1195,plain,
    ( spl0_155
  <=> ! [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_155])]) ).

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(f1193,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f153,f1191]) ).

fof(f1191,plain,
    ( spl0_154
  <=> ! [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_154])]) ).

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(f1189,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f152,f1187]) ).

fof(f1187,plain,
    ( spl0_153
  <=> ! [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_153])]) ).

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(f1185,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f148,f1183]) ).

fof(f1183,plain,
    ( spl0_152
  <=> ! [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_152])]) ).

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(f1181,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f147,f1179]) ).

fof(f1179,plain,
    ( spl0_151
  <=> ! [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_151])]) ).

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(f1177,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f146,f1175]) ).

fof(f1175,plain,
    ( spl0_150
  <=> ! [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_150])]) ).

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(f1173,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f135,f1171]) ).

fof(f1171,plain,
    ( spl0_149
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

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(f1169,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f134,f1167]) ).

fof(f1167,plain,
    ( spl0_148
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

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(f1078,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f141,f1076]) ).

fof(f1076,plain,
    ( spl0_147
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ memberP(X0,X1)
        | memberP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

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(f1074,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f140,f1072]) ).

fof(f1072,plain,
    ( spl0_146
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

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(f1070,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f139,f1068]) ).

fof(f1068,plain,
    ( spl0_145
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(cons(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

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(f1066,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f137,f1064]) ).

fof(f1064,plain,
    ( spl0_144
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ frontsegP(X0,X1)
        | frontsegP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

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(f1055,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f136,f1053]) ).

fof(f1053,plain,
    ( spl0_143
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ rearsegP(X0,X1)
        | rearsegP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

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(f1051,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f132,f1049]) ).

fof(f1049,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | app(X1,skaf45(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

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(f1047,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f131,f1045]) ).

fof(f1045,plain,
    ( spl0_141
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X0,X1)
        | app(skaf46(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

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(f1043,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f123,f1041]) ).

fof(f1041,plain,
    ( spl0_140
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

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(f991,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f214,f989]) ).

fof(f214,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(f987,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f213,f985]) ).

fof(f213,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(f983,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f130,f981]) ).

fof(f981,plain,
    ( spl0_137
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X1,X0)
        | ~ leq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

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(f979,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f129,f977]) ).

fof(f977,plain,
    ( spl0_136
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X1,X0)
        | ~ frontsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

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(f975,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f128,f973]) ).

fof(f973,plain,
    ( spl0_135
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

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(f968,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f127,f966]) ).

fof(f966,plain,
    ( spl0_134
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

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(f964,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f126,f962]) ).

fof(f962,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

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(f960,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f125,f958]) ).

fof(f958,plain,
    ( spl0_132
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

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(f956,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f124,f954]) ).

fof(f954,plain,
    ( spl0_131
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

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(f952,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f122,f950]) ).

fof(f950,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

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(f948,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f120,f946]) ).

fof(f946,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

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(f869,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f119,f867]) ).

fof(f867,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

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

fof(f865,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f118,f863]) ).

fof(f863,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

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

fof(f861,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f109,f859]) ).

fof(f859,plain,
    ( spl0_126
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

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

fof(f857,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f104,f855]) ).

fof(f855,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

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

fof(f845,plain,
    ( spl0_124
    | ~ spl0_2
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f662,f598,f240,f842]) ).

fof(f842,plain,
    ( spl0_124
  <=> sk5 = app(nil,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f598,plain,
    ( spl0_87
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f662,plain,
    ( sk5 = app(nil,sk5)
    | ~ spl0_2
    | ~ spl0_87 ),
    inference(resolution,[],[f599,f242]) ).

fof(f242,plain,
    ( ssList(sk5)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f599,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f598]) ).

fof(f830,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f208,f828]) ).

fof(f828,plain,
    ( spl0_123
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f208,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(f826,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f114,f824]) ).

fof(f824,plain,
    ( spl0_122
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

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

fof(f822,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f110,f820]) ).

fof(f820,plain,
    ( spl0_121
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

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

fof(f818,plain,
    ( spl0_120
    | ~ spl0_1
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f661,f598,f235,f815]) ).

fof(f815,plain,
    ( spl0_120
  <=> sk4 = app(nil,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f661,plain,
    ( sk4 = app(nil,sk4)
    | ~ spl0_1
    | ~ spl0_87 ),
    inference(resolution,[],[f599,f237]) ).

fof(f237,plain,
    ( ssList(sk4)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f813,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f108,f811]) ).

fof(f811,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

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

fof(f809,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f107,f807]) ).

fof(f807,plain,
    ( spl0_118
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

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

fof(f805,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f106,f803]) ).

fof(f803,plain,
    ( spl0_117
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

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

fof(f801,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f105,f799]) ).

fof(f799,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

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

fof(f797,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f103,f795]) ).

fof(f795,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

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

fof(f793,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f102,f791]) ).

fof(f791,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

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

fof(f789,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f101,f787]) ).

fof(f787,plain,
    ( spl0_113
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

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

fof(f785,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f100,f783]) ).

fof(f783,plain,
    ( spl0_112
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

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

fof(f781,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f97,f779]) ).

fof(f779,plain,
    ( spl0_111
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

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

fof(f777,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f96,f775]) ).

fof(f775,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

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

fof(f773,plain,
    ( spl0_109
    | ~ spl0_4
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f660,f598,f250,f770]) ).

fof(f770,plain,
    ( spl0_109
  <=> sk3 = app(nil,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f660,plain,
    ( sk3 = app(nil,sk3)
    | ~ spl0_4
    | ~ spl0_87 ),
    inference(resolution,[],[f599,f252]) ).

fof(f252,plain,
    ( ssList(sk3)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f768,plain,
    ( spl0_108
    | ~ spl0_2
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f631,f594,f240,f765]) ).

fof(f765,plain,
    ( spl0_108
  <=> sk5 = app(sk5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f594,plain,
    ( spl0_86
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f631,plain,
    ( sk5 = app(sk5,nil)
    | ~ spl0_2
    | ~ spl0_86 ),
    inference(resolution,[],[f595,f242]) ).

fof(f595,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f594]) ).

fof(f763,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f229,f761]) ).

fof(f761,plain,
    ( spl0_107
  <=> ! [X2,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f229,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f212]) ).

fof(f212,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(f759,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f99,f757]) ).

fof(f757,plain,
    ( spl0_106
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

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

fof(f755,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f98,f753]) ).

fof(f753,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

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

fof(f751,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f95,f749]) ).

fof(f749,plain,
    ( spl0_104
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

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

fof(f747,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f94,f745]) ).

fof(f745,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

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

fof(f743,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f93,f741]) ).

fof(f741,plain,
    ( spl0_102
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

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

fof(f739,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f92,f737]) ).

fof(f737,plain,
    ( spl0_101
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

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

fof(f735,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f91,f733]) ).

fof(f733,plain,
    ( spl0_100
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

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

fof(f731,plain,
    ( spl0_99
    | ~ spl0_1
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f630,f594,f235,f728]) ).

fof(f728,plain,
    ( spl0_99
  <=> sk4 = app(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f630,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_1
    | ~ spl0_86 ),
    inference(resolution,[],[f595,f237]) ).

fof(f726,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f90,f724]) ).

fof(f724,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

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

fof(f722,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f89,f720]) ).

fof(f720,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

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

fof(f718,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f88,f716]) ).

fof(f716,plain,
    ( spl0_96
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

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

fof(f714,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f87,f712]) ).

fof(f712,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

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

fof(f691,plain,
    ( spl0_94
    | ~ spl0_4
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f629,f594,f250,f688]) ).

fof(f688,plain,
    ( spl0_94
  <=> sk3 = app(sk3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f629,plain,
    ( sk3 = app(sk3,nil)
    | ~ spl0_4
    | ~ spl0_86 ),
    inference(resolution,[],[f595,f252]) ).

fof(f686,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f86,f684]) ).

fof(f684,plain,
    ( spl0_93
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

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

fof(f682,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f85,f680]) ).

fof(f680,plain,
    ( spl0_92
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

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

fof(f678,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f84,f676]) ).

fof(f676,plain,
    ( spl0_91
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

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

fof(f674,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f82,f672]) ).

fof(f672,plain,
    ( spl0_90
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

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

fof(f670,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f80,f668]) ).

fof(f668,plain,
    ( spl0_89
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

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

fof(f666,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f75,f664]) ).

fof(f664,plain,
    ( spl0_88
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f75,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssList(tl(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).

fof(f600,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f74,f598]) ).

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

fof(f596,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f73,f594]) ).

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

fof(f592,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f196,f590]) ).

fof(f590,plain,
    ( spl0_85
  <=> ! [X9,X7,X6,X8] :
        ( ~ ssItem(X6)
        | ~ ssItem(X8)
        | ~ ssList(X9)
        | ~ ssList(X7)
        | ~ lt(X8,X6)
        | sk5 != app(cons(X6,nil),X7)
        | sk3 != app(X9,cons(X8,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f196,axiom,
    ! [X8,X6,X9,X7] :
      ( ~ ssItem(X6)
      | ~ ssItem(X8)
      | ~ ssList(X9)
      | ~ ssList(X7)
      | ~ lt(X8,X6)
      | sk5 != app(cons(X6,nil),X7)
      | sk3 != app(X9,cons(X8,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).

fof(f588,plain,
    ( spl0_83
    | spl0_84 ),
    inference(avatar_split_clause,[],[f72,f586,f583]) ).

fof(f583,plain,
    ( spl0_83
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f586,plain,
    ( spl0_84
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

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

fof(f581,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f70,f579]) ).

fof(f579,plain,
    ( spl0_82
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

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

fof(f577,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f69,f575]) ).

fof(f575,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

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

fof(f573,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f68,f571]) ).

fof(f571,plain,
    ( spl0_80
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

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

fof(f569,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f67,f567]) ).

fof(f567,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

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

fof(f565,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f66,f563]) ).

fof(f563,plain,
    ( spl0_78
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

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

fof(f561,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f65,f559]) ).

fof(f559,plain,
    ( spl0_77
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | duplicatefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

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

fof(f557,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f64,f555]) ).

fof(f555,plain,
    ( spl0_76
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

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

fof(f553,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f232,f551]) ).

fof(f551,plain,
    ( spl0_75
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f232,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f206]) ).

fof(f206,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(f549,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f230,f547]) ).

fof(f547,plain,
    ( spl0_74
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f230,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f211]) ).

fof(f211,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(f545,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f71,f543]) ).

fof(f543,plain,
    ( spl0_73
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

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

fof(f541,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f63,f539]) ).

fof(f539,plain,
    ( spl0_72
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

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

fof(f537,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f62,f535]) ).

fof(f535,plain,
    ( spl0_71
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

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

fof(f533,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f61,f531]) ).

fof(f531,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

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

fof(f529,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f60,f527]) ).

fof(f527,plain,
    ( spl0_69
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

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

fof(f525,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f59,f523]) ).

fof(f523,plain,
    ( spl0_68
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

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

fof(f521,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f58,f519]) ).

fof(f519,plain,
    ( spl0_67
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

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

fof(f517,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f57,f515]) ).

fof(f515,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

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

fof(f513,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f56,f511]) ).

fof(f511,plain,
    ( spl0_65
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

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

fof(f509,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f55,f507]) ).

fof(f507,plain,
    ( spl0_64
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

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

fof(f505,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f53,f503]) ).

fof(f503,plain,
    ( spl0_63
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

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

fof(f501,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f52,f499]) ).

fof(f499,plain,
    ( spl0_62
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

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

fof(f497,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f51,f495]) ).

fof(f495,plain,
    ( spl0_61
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

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

fof(f493,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f50,f491]) ).

fof(f491,plain,
    ( spl0_60
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

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

fof(f489,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f49,f487]) ).

fof(f487,plain,
    ( spl0_59
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

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

fof(f485,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f48,f483]) ).

fof(f483,plain,
    ( spl0_58
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

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

fof(f481,plain,
    ~ spl0_57,
    inference(avatar_split_clause,[],[f54,f478]) ).

fof(f478,plain,
    ( spl0_57
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

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

fof(f476,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f47,f474]) ).

fof(f474,plain,
    ( spl0_56
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

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

fof(f472,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f46,f470]) ).

fof(f470,plain,
    ( spl0_55
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

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

fof(f468,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f45,f466]) ).

fof(f466,plain,
    ( spl0_54
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

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

fof(f464,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f44,f462]) ).

fof(f462,plain,
    ( spl0_53
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

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

fof(f460,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f43,f458]) ).

fof(f458,plain,
    ( spl0_52
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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

fof(f456,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f42,f454]) ).

fof(f454,plain,
    ( spl0_51
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

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

fof(f452,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f41,f450]) ).

fof(f450,plain,
    ( spl0_50
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

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

fof(f448,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f40,f446]) ).

fof(f446,plain,
    ( spl0_49
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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

fof(f444,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f39,f442]) ).

fof(f442,plain,
    ( spl0_48
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

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

fof(f440,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f38,f438]) ).

fof(f438,plain,
    ( spl0_47
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

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

fof(f436,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f37,f434]) ).

fof(f434,plain,
    ( spl0_46
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

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

fof(f432,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f36,f430]) ).

fof(f430,plain,
    ( spl0_45
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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

fof(f428,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f35,f426]) ).

fof(f426,plain,
    ( spl0_44
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

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

fof(f424,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f34,f422]) ).

fof(f422,plain,
    ( spl0_43
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f420,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f33,f418]) ).

fof(f418,plain,
    ( spl0_42
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

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

fof(f416,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f32,f414]) ).

fof(f414,plain,
    ( spl0_41
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

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

fof(f412,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f31,f410]) ).

fof(f410,plain,
    ( spl0_40
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

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

fof(f408,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f30,f406]) ).

fof(f406,plain,
    ( spl0_39
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f404,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f29,f402]) ).

fof(f402,plain,
    ( spl0_38
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

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

fof(f400,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f28,f398]) ).

fof(f398,plain,
    ( spl0_37
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

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

fof(f396,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f27,f394]) ).

fof(f394,plain,
    ( spl0_36
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

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

fof(f392,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f26,f390]) ).

fof(f390,plain,
    ( spl0_35
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

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

fof(f388,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f25,f386]) ).

fof(f386,plain,
    ( spl0_34
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

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

fof(f384,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f24,f382]) ).

fof(f382,plain,
    ( spl0_33
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

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

fof(f380,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f23,f378]) ).

fof(f378,plain,
    ( spl0_32
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

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

fof(f376,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f22,f374]) ).

fof(f374,plain,
    ( spl0_31
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

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

fof(f372,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f21,f370]) ).

fof(f370,plain,
    ( spl0_30
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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

fof(f368,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f20,f366]) ).

fof(f366,plain,
    ( spl0_29
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

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

fof(f364,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f19,f362]) ).

fof(f362,plain,
    ( spl0_28
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f360,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f18,f358]) ).

fof(f358,plain,
    ( spl0_27
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

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

fof(f356,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f17,f354]) ).

fof(f354,plain,
    ( spl0_26
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

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

fof(f352,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f16,f350]) ).

fof(f350,plain,
    ( spl0_25
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

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

fof(f348,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f15,f346]) ).

fof(f346,plain,
    ( spl0_24
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

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

fof(f344,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f14,f342]) ).

fof(f342,plain,
    ( spl0_23
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

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

fof(f340,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f13,f338]) ).

fof(f338,plain,
    ( spl0_22
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

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

fof(f336,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f12,f334]) ).

fof(f334,plain,
    ( spl0_21
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

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

fof(f332,plain,
    ~ spl0_20,
    inference(avatar_split_clause,[],[f11,f329]) ).

fof(f329,plain,
    ( spl0_20
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

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

fof(f327,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f10,f324]) ).

fof(f324,plain,
    ( spl0_19
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

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

fof(f322,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f9,f319]) ).

fof(f319,plain,
    ( spl0_18
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

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

fof(f317,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f8,f314]) ).

fof(f314,plain,
    ( spl0_17
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

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

fof(f312,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f7,f309]) ).

fof(f309,plain,
    ( spl0_16
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

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

fof(f307,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f6,f304]) ).

fof(f304,plain,
    ( spl0_15
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

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

fof(f302,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f5,f299]) ).

fof(f299,plain,
    ( spl0_14
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

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

fof(f297,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f4,f294]) ).

fof(f294,plain,
    ( spl0_13
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

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

fof(f292,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f3,f289]) ).

fof(f289,plain,
    ( spl0_12
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

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

fof(f287,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f2,f284]) ).

fof(f284,plain,
    ( spl0_11
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

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

fof(f282,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f1,f279]) ).

fof(f279,plain,
    ( spl0_10
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

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

fof(f277,plain,
    ( spl0_8
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f233,f274,f270]) ).

fof(f270,plain,
    ( spl0_8
  <=> sk3 = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f274,plain,
    ( spl0_9
  <=> nil = sk3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f233,plain,
    ( nil != sk3
    | sk3 = sk4 ),
    inference(inner_rewriting,[],[f198]) ).

fof(f198,axiom,
    ( nil != sk3
    | nil = sk4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).

fof(f268,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f194,f265]) ).

fof(f194,axiom,
    sk4 = app(sk3,sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

fof(f263,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f202,f260]) ).

fof(f260,plain,
    ( spl0_6
  <=> neq(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f202,plain,
    neq(sk4,nil),
    inference(definition_unfolding,[],[f192,f190]) ).

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

fof(f192,axiom,
    neq(sk2,nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

fof(f258,plain,
    ~ spl0_5,
    inference(avatar_split_clause,[],[f201,f255]) ).

fof(f201,plain,
    ~ frontsegP(sk4,sk3),
    inference(definition_unfolding,[],[f197,f190,f191]) ).

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

fof(f197,axiom,
    ~ frontsegP(sk2,sk1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).

fof(f253,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f199,f250]) ).

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(f248,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f195,f245]) ).

fof(f245,plain,
    ( spl0_3
  <=> strictorderedP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f195,axiom,
    strictorderedP(sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).

fof(f243,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f193,f240]) ).

fof(f193,axiom,
    ssList(sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).

fof(f238,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f189,f235]) ).

fof(f189,axiom,
    ssList(sk4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC351-1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 20:25:38 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (15370)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (15373)WARNING: value z3 for option sas not known
% 0.21/0.37  % (15373)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)
% 0.21/0.38  % (15372)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (15374)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (15375)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)
% 0.21/0.38  % (15371)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (15376)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)
% 0.21/0.39  % (15377)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)
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [2]
% 0.21/0.41  TRYING [3]
% 0.21/0.41  % (15375)First to succeed.
% 0.21/0.41  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.41  % (15375)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15370"
% 0.21/0.42  % (15375)Refutation found. Thanks to Tanya!
% 0.21/0.42  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42  % (15375)------------------------------
% 0.21/0.42  % (15375)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.42  % (15375)Termination reason: Refutation
% 0.21/0.42  
% 0.21/0.42  % (15375)Memory used [KB]: 1671
% 0.21/0.42  % (15375)Time elapsed: 0.038 s
% 0.21/0.42  % (15375)Instructions burned: 61 (million)
% 0.21/0.42  % (15370)Success in time 0.04 s
%------------------------------------------------------------------------------