TSTP Solution File: SWC330-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC330-1 : 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 : n002.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 10:25:03 EDT 2024

% Result   : Unsatisfiable 0.21s 0.50s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  497
% Syntax   : Number of formulae    : 1057 ( 236 unt;   0 def)
%            Number of atoms       : 3191 ( 362 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 3853 (1719   ~;1827   |;   0   &)
%                                         ( 307 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  328 ( 326 usr; 308 prp; 0-2 aty)
%            Number of functors    :   56 (  56 usr;  10 con; 0-2 aty)
%            Number of variables   :  921 ( 921   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3957,plain,
    $false,
    inference(avatar_sat_refutation,[],[f244,f249,f258,f263,f268,f274,f279,f281,f291,f298,f303,f308,f315,f320,f322,f328,f334,f339,f345,f348,f351,f357,f364,f370,f376,f383,f390,f395,f400,f405,f410,f415,f420,f425,f430,f434,f438,f442,f446,f450,f454,f458,f462,f466,f470,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,f578,f582,f587,f591,f595,f599,f603,f607,f611,f615,f619,f623,f627,f631,f635,f639,f643,f647,f651,f655,f659,f661,f665,f669,f673,f677,f681,f685,f689,f696,f739,f744,f748,f816,f820,f824,f828,f832,f837,f841,f845,f872,f877,f881,f885,f889,f893,f897,f901,f905,f909,f913,f917,f921,f928,f932,f936,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f1023,f1040,f1044,f1048,f1052,f1128,f1132,f1136,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1233,f1238,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1332,f1336,f1340,f1344,f1348,f1353,f1357,f1361,f1365,f1369,f1373,f1411,f1415,f1419,f1423,f1463,f1480,f1484,f1488,f1492,f1496,f1500,f1504,f1609,f1613,f1617,f1622,f1626,f1630,f1634,f1638,f1680,f1690,f1694,f1711,f1715,f1719,f1723,f1727,f1732,f1911,f1917,f1924,f1929,f1936,f1940,f1950,f1954,f1958,f1969,f1977,f1982,f1987,f2136,f2142,f2147,f2151,f2227,f2232,f2273,f2280,f2324,f2368,f2408,f2413,f2453,f2493,f2533,f2577,f2582,f2587,f2627,f2666,f2706,f2746,f2751,f2755,f2759,f2763,f2767,f2771,f2775,f2779,f2783,f2787,f2791,f2796,f2800,f2804,f2808,f2812,f2816,f2820,f2824,f2828,f2832,f2836,f2841,f2846,f2851,f2855,f2861,f2909,f2952,f2995,f3000,f3055,f3060,f3064,f3140,f3185,f3213,f3217,f3221,f3225,f3229,f3233,f3238,f3459,f3472,f3485,f3499,f3513,f3527,f3531,f3535,f3539,f3543,f3547,f3557,f3592,f3631,f3670,f3716,f3725,f3764,f3765,f3803,f3807,f3848,f3896,f3943,f3955,f3956]) ).

fof(f3956,plain,
    ( spl0_4
    | spl0_7
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f3945,f251,f271,f255]) ).

fof(f255,plain,
    ( spl0_4
  <=> ssItem(sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f271,plain,
    ( spl0_7
  <=> sk3 = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f251,plain,
    ( spl0_3
  <=> nil = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f3945,plain,
    ( sk3 = sk4
    | ssItem(sk5)
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f193,f253]) ).

fof(f253,plain,
    ( nil = sk4
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f251]) ).

fof(f193,axiom,
    ( ssItem(sk5)
    | nil = sk3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

fof(f3955,plain,
    ( spl0_300
    | ~ spl0_3
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f3861,f392,f251,f3667]) ).

fof(f3667,plain,
    ( spl0_300
  <=> strictorderP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f392,plain,
    ( spl0_24
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f3861,plain,
    ( strictorderP(sk4)
    | ~ spl0_3
    | ~ spl0_24 ),
    inference(superposition,[],[f394,f253]) ).

fof(f394,plain,
    ( strictorderP(nil)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f392]) ).

fof(f3943,plain,
    ( spl0_31
    | spl0_6 ),
    inference(avatar_split_clause,[],[f203,f265,f427]) ).

fof(f427,plain,
    ( spl0_31
  <=> sk4 = app(app(sk6,sk3),sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f265,plain,
    ( spl0_6
  <=> nil = sk3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f203,axiom,
    ( nil = sk3
    | sk4 = app(app(sk6,sk3),sk7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).

fof(f3896,plain,
    ( spl0_307
    | ~ spl0_3
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f388,f305,f251,f3893]) ).

fof(f3893,plain,
    ( spl0_307
  <=> sk3 = cons(sk5,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f305,plain,
    ( spl0_13
  <=> sk3 = cons(sk5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f388,plain,
    ( sk3 = cons(sk5,sk4)
    | ~ spl0_3
    | ~ spl0_13 ),
    inference(forward_demodulation,[],[f307,f253]) ).

fof(f307,plain,
    ( sk3 = cons(sk5,nil)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f3848,plain,
    ( spl0_10
    | ~ spl0_6
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f3813,f317,f265,f288]) ).

fof(f288,plain,
    ( spl0_10
  <=> equalelemsP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f317,plain,
    ( spl0_15
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f3813,plain,
    ( equalelemsP(sk3)
    | ~ spl0_6
    | ~ spl0_15 ),
    inference(superposition,[],[f319,f267]) ).

fof(f267,plain,
    ( nil = sk3
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f319,plain,
    ( equalelemsP(nil)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f317]) ).

fof(f3807,plain,
    ( ~ spl0_4
    | spl0_10
    | ~ spl0_13
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f729,f663,f305,f288,f255]) ).

fof(f663,plain,
    ( spl0_89
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f729,plain,
    ( equalelemsP(sk3)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_89 ),
    inference(superposition,[],[f664,f307]) ).

fof(f664,plain,
    ( ! [X0] :
        ( equalelemsP(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f663]) ).

fof(f3803,plain,
    ( ~ spl0_8
    | ~ spl0_5
    | ~ spl0_2
    | ~ spl0_1
    | spl0_9
    | ~ spl0_31
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1704,f1692,f427,f284,f241,f246,f260,f276]) ).

fof(f276,plain,
    ( spl0_8
  <=> ssList(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f260,plain,
    ( spl0_5
  <=> ssList(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f246,plain,
    ( spl0_2
  <=> ssList(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f241,plain,
    ( spl0_1
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f284,plain,
    ( spl0_9
  <=> segmentP(sk4,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f1692,plain,
    ( spl0_194
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(app(app(X0,X1),X2))
        | ~ ssList(X1)
        | ~ ssList(X0)
        | segmentP(app(app(X0,X1),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f1704,plain,
    ( segmentP(sk4,sk3)
    | ~ ssList(sk4)
    | ~ ssList(sk3)
    | ~ ssList(sk6)
    | ~ ssList(sk7)
    | ~ spl0_31
    | ~ spl0_194 ),
    inference(superposition,[],[f1693,f429]) ).

fof(f429,plain,
    ( sk4 = app(app(sk6,sk3),sk7)
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f427]) ).

fof(f1693,plain,
    ( ! [X2,X0,X1] :
        ( segmentP(app(app(X0,X1),X2),X1)
        | ~ ssList(app(app(X0,X1),X2))
        | ~ ssList(X1)
        | ~ ssList(X0)
        | ~ ssList(X2) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f1692]) ).

fof(f3765,plain,
    ( ~ spl0_2
    | ~ spl0_5
    | ~ spl0_107
    | spl0_231 ),
    inference(avatar_split_clause,[],[f2578,f2570,f839,f260,f246]) ).

fof(f839,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f2570,plain,
    ( spl0_231
  <=> ssList(app(sk6,sk3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2578,plain,
    ( ~ ssList(sk6)
    | ~ ssList(sk3)
    | ~ spl0_107
    | spl0_231 ),
    inference(resolution,[],[f2572,f840]) ).

fof(f840,plain,
    ( ! [X0,X1] :
        ( ssList(app(X1,X0))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f839]) ).

fof(f2572,plain,
    ( ~ ssList(app(sk6,sk3))
    | spl0_231 ),
    inference(avatar_component_clause,[],[f2570]) ).

fof(f3764,plain,
    ( spl0_305
    | spl0_306
    | ~ spl0_8
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1872,f1721,f276,f3761,f3757]) ).

fof(f3757,plain,
    ( spl0_305
  <=> sk7 = app(app(skaf56(sk7),cons(skaf54(sk7),skaf57(sk7))),cons(skaf55(sk7),skaf58(sk7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f3761,plain,
    ( spl0_306
  <=> totalorderP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f1721,plain,
    ( spl0_198
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f1872,plain,
    ( totalorderP(sk7)
    | sk7 = app(app(skaf56(sk7),cons(skaf54(sk7),skaf57(sk7))),cons(skaf55(sk7),skaf58(sk7)))
    | ~ spl0_8
    | ~ spl0_198 ),
    inference(resolution,[],[f1722,f278]) ).

fof(f278,plain,
    ( ssList(sk7)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f276]) ).

fof(f1722,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 )
    | ~ spl0_198 ),
    inference(avatar_component_clause,[],[f1721]) ).

fof(f3725,plain,
    ( spl0_303
    | spl0_304
    | ~ spl0_1
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1870,f1721,f241,f3722,f3718]) ).

fof(f3718,plain,
    ( spl0_303
  <=> sk4 = app(app(skaf56(sk4),cons(skaf54(sk4),skaf57(sk4))),cons(skaf55(sk4),skaf58(sk4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f3722,plain,
    ( spl0_304
  <=> totalorderP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f1870,plain,
    ( totalorderP(sk4)
    | sk4 = app(app(skaf56(sk4),cons(skaf54(sk4),skaf57(sk4))),cons(skaf55(sk4),skaf58(sk4)))
    | ~ spl0_1
    | ~ spl0_198 ),
    inference(resolution,[],[f1722,f243]) ).

fof(f243,plain,
    ( ssList(sk4)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f241]) ).

fof(f3716,plain,
    ( spl0_301
    | spl0_302
    | ~ spl0_8
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1837,f1717,f276,f3713,f3709]) ).

fof(f3709,plain,
    ( spl0_301
  <=> sk7 = app(app(skaf61(sk7),cons(skaf59(sk7),skaf62(sk7))),cons(skaf60(sk7),skaf63(sk7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f3713,plain,
    ( spl0_302
  <=> strictorderP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f1717,plain,
    ( spl0_197
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f1837,plain,
    ( strictorderP(sk7)
    | sk7 = app(app(skaf61(sk7),cons(skaf59(sk7),skaf62(sk7))),cons(skaf60(sk7),skaf63(sk7)))
    | ~ spl0_8
    | ~ spl0_197 ),
    inference(resolution,[],[f1718,f278]) ).

fof(f1718,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f1717]) ).

fof(f3670,plain,
    ( spl0_299
    | spl0_300
    | ~ spl0_1
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1835,f1717,f241,f3667,f3663]) ).

fof(f3663,plain,
    ( spl0_299
  <=> sk4 = app(app(skaf61(sk4),cons(skaf59(sk4),skaf62(sk4))),cons(skaf60(sk4),skaf63(sk4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f1835,plain,
    ( strictorderP(sk4)
    | sk4 = app(app(skaf61(sk4),cons(skaf59(sk4),skaf62(sk4))),cons(skaf60(sk4),skaf63(sk4)))
    | ~ spl0_1
    | ~ spl0_197 ),
    inference(resolution,[],[f1718,f243]) ).

fof(f3631,plain,
    ( spl0_297
    | spl0_298
    | ~ spl0_8
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1802,f1713,f276,f3628,f3624]) ).

fof(f3624,plain,
    ( spl0_297
  <=> sk7 = app(app(skaf66(sk7),cons(skaf64(sk7),skaf67(sk7))),cons(skaf65(sk7),skaf68(sk7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f3628,plain,
    ( spl0_298
  <=> totalorderedP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f1713,plain,
    ( spl0_196
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f1802,plain,
    ( totalorderedP(sk7)
    | sk7 = app(app(skaf66(sk7),cons(skaf64(sk7),skaf67(sk7))),cons(skaf65(sk7),skaf68(sk7)))
    | ~ spl0_8
    | ~ spl0_196 ),
    inference(resolution,[],[f1714,f278]) ).

fof(f1714,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 )
    | ~ spl0_196 ),
    inference(avatar_component_clause,[],[f1713]) ).

fof(f3592,plain,
    ( spl0_296
    | spl0_23
    | ~ spl0_1
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1800,f1713,f241,f380,f3589]) ).

fof(f3589,plain,
    ( spl0_296
  <=> sk4 = app(app(skaf66(sk4),cons(skaf64(sk4),skaf67(sk4))),cons(skaf65(sk4),skaf68(sk4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f380,plain,
    ( spl0_23
  <=> totalorderedP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f1800,plain,
    ( totalorderedP(sk4)
    | sk4 = app(app(skaf66(sk4),cons(skaf64(sk4),skaf67(sk4))),cons(skaf65(sk4),skaf68(sk4)))
    | ~ spl0_1
    | ~ spl0_196 ),
    inference(resolution,[],[f1714,f243]) ).

fof(f3557,plain,
    ( spl0_294
    | spl0_295
    | ~ spl0_8
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1767,f1709,f276,f3554,f3550]) ).

fof(f3550,plain,
    ( spl0_294
  <=> sk7 = app(app(skaf71(sk7),cons(skaf69(sk7),skaf72(sk7))),cons(skaf70(sk7),skaf73(sk7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f3554,plain,
    ( spl0_295
  <=> strictorderedP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f1709,plain,
    ( spl0_195
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f1767,plain,
    ( strictorderedP(sk7)
    | sk7 = app(app(skaf71(sk7),cons(skaf69(sk7),skaf72(sk7))),cons(skaf70(sk7),skaf73(sk7)))
    | ~ spl0_8
    | ~ spl0_195 ),
    inference(resolution,[],[f1710,f278]) ).

fof(f1710,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f1709]) ).

fof(f3547,plain,
    ( spl0_293
    | ~ spl0_76
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f724,f694,f609,f3545]) ).

fof(f3545,plain,
    ( spl0_293
  <=> ! [X0,X1] : duplicatefreeP(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f609,plain,
    ( spl0_76
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f694,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f724,plain,
    ( ! [X0,X1] : duplicatefreeP(skaf42(X0,X1))
    | ~ spl0_76
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f610]) ).

fof(f610,plain,
    ( ! [X0,X1] : ssList(skaf42(X0,X1))
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f695,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f694]) ).

fof(f3543,plain,
    ( spl0_292
    | ~ spl0_75
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f723,f694,f605,f3541]) ).

fof(f3541,plain,
    ( spl0_292
  <=> ! [X0,X1] : duplicatefreeP(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f605,plain,
    ( spl0_75
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f723,plain,
    ( ! [X0,X1] : duplicatefreeP(skaf43(X0,X1))
    | ~ spl0_75
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f606]) ).

fof(f606,plain,
    ( ! [X0,X1] : ssList(skaf43(X0,X1))
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f605]) ).

fof(f3539,plain,
    ( spl0_291
    | ~ spl0_74
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f722,f694,f601,f3537]) ).

fof(f3537,plain,
    ( spl0_291
  <=> ! [X0,X1] : duplicatefreeP(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f601,plain,
    ( spl0_74
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f722,plain,
    ( ! [X0,X1] : duplicatefreeP(skaf45(X0,X1))
    | ~ spl0_74
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f602]) ).

fof(f602,plain,
    ( ! [X0,X1] : ssList(skaf45(X0,X1))
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f601]) ).

fof(f3535,plain,
    ( spl0_290
    | ~ spl0_73
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f721,f694,f597,f3533]) ).

fof(f3533,plain,
    ( spl0_290
  <=> ! [X0,X1] : duplicatefreeP(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f597,plain,
    ( spl0_73
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f721,plain,
    ( ! [X0,X1] : duplicatefreeP(skaf46(X0,X1))
    | ~ spl0_73
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f598]) ).

fof(f598,plain,
    ( ! [X0,X1] : ssList(skaf46(X0,X1))
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f3531,plain,
    ( spl0_289
    | ~ spl0_72
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f720,f694,f593,f3529]) ).

fof(f3529,plain,
    ( spl0_289
  <=> ! [X0,X1] : duplicatefreeP(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f593,plain,
    ( spl0_72
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f720,plain,
    ( ! [X0,X1] : duplicatefreeP(skaf47(X0,X1))
    | ~ spl0_72
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f594]) ).

fof(f594,plain,
    ( ! [X0,X1] : ssList(skaf47(X0,X1))
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f593]) ).

fof(f3527,plain,
    ( spl0_288
    | ~ spl0_71
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f719,f694,f589,f3525]) ).

fof(f3525,plain,
    ( spl0_288
  <=> ! [X0,X1] : duplicatefreeP(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f589,plain,
    ( spl0_71
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f719,plain,
    ( ! [X0,X1] : duplicatefreeP(skaf48(X0,X1))
    | ~ spl0_71
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f590]) ).

fof(f590,plain,
    ( ! [X0,X1] : ssList(skaf48(X0,X1))
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f589]) ).

fof(f3513,plain,
    ( ~ spl0_27
    | ~ spl0_4
    | spl0_287
    | ~ spl0_13
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1684,f1636,f305,f3511,f255,f407]) ).

fof(f407,plain,
    ( spl0_27
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f3511,plain,
    ( spl0_287
  <=> ! [X0,X1] :
        ( ~ frontsegP(cons(X0,X1),sk3)
        | ~ ssItem(X0)
        | sk5 = X0
        | ~ ssList(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f1636,plain,
    ( spl0_191
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | X0 = X2
        | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1684,plain,
    ( ! [X0,X1] :
        ( ~ frontsegP(cons(X0,X1),sk3)
        | ~ ssItem(sk5)
        | ~ ssList(X1)
        | ~ ssList(nil)
        | sk5 = X0
        | ~ ssItem(X0) )
    | ~ spl0_13
    | ~ spl0_191 ),
    inference(superposition,[],[f1637,f307]) ).

fof(f1637,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ frontsegP(cons(X0,X1),cons(X2,X3))
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | X0 = X2
        | ~ ssItem(X0) )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f1636]) ).

fof(f3499,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_286
    | ~ spl0_13
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1683,f1636,f305,f3497,f407,f255]) ).

fof(f3497,plain,
    ( spl0_286
  <=> ! [X0,X1] :
        ( ~ frontsegP(sk3,cons(X0,X1))
        | sk5 = X0
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f1683,plain,
    ( ! [X0,X1] :
        ( ~ frontsegP(sk3,cons(X0,X1))
        | ~ ssItem(X0)
        | ~ ssList(nil)
        | ~ ssList(X1)
        | sk5 = X0
        | ~ ssItem(sk5) )
    | ~ spl0_13
    | ~ spl0_191 ),
    inference(superposition,[],[f1637,f307]) ).

fof(f3485,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_285
    | ~ spl0_13
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1672,f1632,f305,f3483,f407,f255]) ).

fof(f3483,plain,
    ( spl0_285
  <=> ! [X0,X1] :
        ( ~ frontsegP(sk3,cons(X0,X1))
        | frontsegP(nil,X1)
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f1632,plain,
    ( spl0_190
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | frontsegP(X1,X3)
        | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1672,plain,
    ( ! [X0,X1] :
        ( ~ frontsegP(sk3,cons(X0,X1))
        | ~ ssItem(X0)
        | ~ ssList(nil)
        | ~ ssList(X1)
        | frontsegP(nil,X1)
        | ~ ssItem(sk5) )
    | ~ spl0_13
    | ~ spl0_190 ),
    inference(superposition,[],[f1633,f307]) ).

fof(f1633,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ frontsegP(cons(X0,X1),cons(X2,X3))
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | frontsegP(X1,X3)
        | ~ ssItem(X0) )
    | ~ spl0_190 ),
    inference(avatar_component_clause,[],[f1632]) ).

fof(f3472,plain,
    ( ~ spl0_27
    | ~ spl0_4
    | spl0_284
    | ~ spl0_13
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1658,f1624,f305,f3470,f255,f407]) ).

fof(f3470,plain,
    ( spl0_284
  <=> ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssItem(X0)
        | nil = X1
        | ~ ssList(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f1624,plain,
    ( spl0_188
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | X1 = X3
        | cons(X0,X1) != cons(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f1658,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssItem(sk5)
        | ~ ssList(nil)
        | ~ ssList(X1)
        | nil = X1
        | ~ ssItem(X0) )
    | ~ spl0_13
    | ~ spl0_188 ),
    inference(superposition,[],[f1625,f307]) ).

fof(f1625,plain,
    ( ! [X2,X3,X0,X1] :
        ( cons(X0,X1) != cons(X2,X3)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | X1 = X3
        | ~ ssItem(X2) )
    | ~ spl0_188 ),
    inference(avatar_component_clause,[],[f1624]) ).

fof(f3459,plain,
    ( ~ spl0_27
    | ~ spl0_4
    | spl0_283
    | ~ spl0_13
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1654,f1615,f305,f3457,f255,f407]) ).

fof(f3457,plain,
    ( spl0_283
  <=> ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssItem(X0)
        | sk5 = X0
        | ~ ssList(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f1615,plain,
    ( spl0_186
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssItem(X2)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | X0 = X2
        | cons(X0,X1) != cons(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f1654,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssItem(sk5)
        | ~ ssList(nil)
        | ~ ssList(X1)
        | sk5 = X0
        | ~ ssItem(X0) )
    | ~ spl0_13
    | ~ spl0_186 ),
    inference(superposition,[],[f1616,f307]) ).

fof(f1616,plain,
    ( ! [X2,X3,X0,X1] :
        ( cons(X0,X1) != cons(X2,X3)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | X0 = X2
        | ~ ssItem(X2) )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1615]) ).

fof(f3238,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_282
    | ~ spl0_13
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1697,f1688,f305,f3236,f407,f255]) ).

fof(f3236,plain,
    ( spl0_282
  <=> ! [X0] :
        ( memberP(app(X0,sk3),sk5)
        | ~ ssList(X0)
        | ~ ssList(app(X0,sk3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f1688,plain,
    ( spl0_193
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(X0)
        | ~ ssList(X2)
        | memberP(app(X0,cons(X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f1697,plain,
    ( ! [X0] :
        ( memberP(app(X0,sk3),sk5)
        | ~ ssList(app(X0,sk3))
        | ~ ssList(X0)
        | ~ ssList(nil)
        | ~ ssItem(sk5) )
    | ~ spl0_13
    | ~ spl0_193 ),
    inference(superposition,[],[f1689,f307]) ).

fof(f1689,plain,
    ( ! [X2,X0,X1] :
        ( memberP(app(X0,cons(X1,X2)),X1)
        | ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssItem(X1) )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f1688]) ).

fof(f3233,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_281
    | ~ spl0_13
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f1603,f1502,f305,f3231,f407,f255]) ).

fof(f3231,plain,
    ( spl0_281
  <=> ! [X0] :
        ( ~ memberP(sk3,X0)
        | memberP(nil,X0)
        | sk5 = X0
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f1502,plain,
    ( spl0_183
  <=> ! [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_183])]) ).

fof(f1603,plain,
    ( ! [X0] :
        ( ~ memberP(sk3,X0)
        | ~ ssItem(X0)
        | ~ ssList(nil)
        | sk5 = X0
        | memberP(nil,X0)
        | ~ ssItem(sk5) )
    | ~ spl0_13
    | ~ spl0_183 ),
    inference(superposition,[],[f1503,f307]) ).

fof(f1503,plain,
    ( ! [X2,X0,X1] :
        ( ~ memberP(cons(X0,X1),X2)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | X0 = X2
        | memberP(X1,X2)
        | ~ ssItem(X0) )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1502]) ).

fof(f3229,plain,
    ( spl0_280
    | ~ spl0_4
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1593,f1486,f255,f3227]) ).

fof(f3227,plain,
    ( spl0_280
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | cons(sk5,app(X1,X0)) = app(cons(sk5,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1486,plain,
    ( spl0_179
  <=> ! [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_179])]) ).

fof(f1593,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | cons(sk5,app(X1,X0)) = app(cons(sk5,X1),X0) )
    | ~ spl0_4
    | ~ spl0_179 ),
    inference(resolution,[],[f1487,f257]) ).

fof(f257,plain,
    ( ssItem(sk5)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f1487,plain,
    ( ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) )
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f1486]) ).

fof(f3225,plain,
    ( spl0_279
    | ~ spl0_8
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1574,f1482,f276,f3223]) ).

fof(f3223,plain,
    ( spl0_279
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk7,X1),X0) = app(sk7,app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f1482,plain,
    ( spl0_178
  <=> ! [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_178])]) ).

fof(f1574,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk7,X1),X0) = app(sk7,app(X1,X0)) )
    | ~ spl0_8
    | ~ spl0_178 ),
    inference(resolution,[],[f1483,f278]) ).

fof(f1483,plain,
    ( ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(X2,X1),X0) = app(X2,app(X1,X0)) )
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f1482]) ).

fof(f3221,plain,
    ( spl0_278
    | ~ spl0_5
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1573,f1482,f260,f3219]) ).

fof(f3219,plain,
    ( spl0_278
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk6,X1),X0) = app(sk6,app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f1573,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk6,X1),X0) = app(sk6,app(X1,X0)) )
    | ~ spl0_5
    | ~ spl0_178 ),
    inference(resolution,[],[f1483,f262]) ).

fof(f262,plain,
    ( ssList(sk6)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f260]) ).

fof(f3217,plain,
    ( spl0_277
    | ~ spl0_1
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1572,f1482,f241,f3215]) ).

fof(f3215,plain,
    ( spl0_277
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f1572,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) )
    | ~ spl0_1
    | ~ spl0_178 ),
    inference(resolution,[],[f1483,f243]) ).

fof(f3213,plain,
    ( spl0_276
    | ~ spl0_2
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1571,f1482,f246,f3211]) ).

fof(f3211,plain,
    ( spl0_276
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f1571,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) )
    | ~ spl0_2
    | ~ spl0_178 ),
    inference(resolution,[],[f1483,f248]) ).

fof(f248,plain,
    ( ssList(sk3)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f3185,plain,
    ( spl0_274
    | spl0_275
    | ~ spl0_8
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1539,f1478,f276,f3182,f3178]) ).

fof(f3178,plain,
    ( spl0_274
  <=> sk7 = app(skaf80(sk7),cons(skaf78(sk7),cons(skaf79(sk7),skaf81(sk7)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f3182,plain,
    ( spl0_275
  <=> equalelemsP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f1478,plain,
    ( spl0_177
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f1539,plain,
    ( equalelemsP(sk7)
    | sk7 = app(skaf80(sk7),cons(skaf78(sk7),cons(skaf79(sk7),skaf81(sk7))))
    | ~ spl0_8
    | ~ spl0_177 ),
    inference(resolution,[],[f1479,f278]) ).

fof(f1479,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f1478]) ).

fof(f3140,plain,
    ( spl0_223
    | spl0_273
    | ~ spl0_5
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1457,f1409,f260,f3138,f2321]) ).

fof(f2321,plain,
    ( spl0_223
  <=> nil = sk6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f3138,plain,
    ( spl0_273
  <=> ! [X0] :
        ( ~ ssList(X0)
        | tl(app(sk6,X0)) = app(tl(sk6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f1409,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1457,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk6
        | tl(app(sk6,X0)) = app(tl(sk6),X0) )
    | ~ spl0_5
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f262]) ).

fof(f1410,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) )
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1409]) ).

fof(f3064,plain,
    ( spl0_272
    | ~ spl0_219
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2856,f2853,f2229,f3062]) ).

fof(f3062,plain,
    ( spl0_272
  <=> ! [X0] :
        ( app(nil,X0) = tl(app(sk3,X0))
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f2229,plain,
    ( spl0_219
  <=> nil = tl(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f2853,plain,
    ( spl0_264
  <=> ! [X0] :
        ( ~ ssList(X0)
        | tl(app(sk3,X0)) = app(tl(sk3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2856,plain,
    ( ! [X0] :
        ( app(nil,X0) = tl(app(sk3,X0))
        | ~ ssList(X0) )
    | ~ spl0_219
    | ~ spl0_264 ),
    inference(forward_demodulation,[],[f2854,f2231]) ).

fof(f2231,plain,
    ( nil = tl(sk3)
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2229]) ).

fof(f2854,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | tl(app(sk3,X0)) = app(tl(sk3),X0) )
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f2853]) ).

fof(f3060,plain,
    ( spl0_271
    | ~ spl0_27
    | ~ spl0_187
    | ~ spl0_200
    | ~ spl0_219
    | ~ spl0_265
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f3056,f3053,f2859,f2229,f1729,f1619,f407,f3058]) ).

fof(f3058,plain,
    ( spl0_271
  <=> ! [X0] :
        ( ~ frontsegP(X0,sk6)
        | frontsegP(cons(sk5,X0),sk3)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f1619,plain,
    ( spl0_187
  <=> sk3 = app(sk3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f1729,plain,
    ( spl0_200
  <=> sk6 = app(sk6,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f2859,plain,
    ( spl0_265
  <=> ! [X0] :
        ( app(sk6,X0) = tl(app(sk3,X0))
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f3053,plain,
    ( spl0_270
  <=> ! [X0] :
        ( frontsegP(cons(sk5,X0),sk3)
        | ~ frontsegP(X0,nil)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f3056,plain,
    ( ! [X0] :
        ( ~ frontsegP(X0,sk6)
        | frontsegP(cons(sk5,X0),sk3)
        | ~ ssList(X0) )
    | ~ spl0_27
    | ~ spl0_187
    | ~ spl0_200
    | ~ spl0_219
    | ~ spl0_265
    | ~ spl0_270 ),
    inference(forward_demodulation,[],[f3054,f2899]) ).

fof(f2899,plain,
    ( nil = sk6
    | ~ spl0_27
    | ~ spl0_187
    | ~ spl0_200
    | ~ spl0_219
    | ~ spl0_265 ),
    inference(forward_demodulation,[],[f2898,f1731]) ).

fof(f1731,plain,
    ( sk6 = app(sk6,nil)
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f1729]) ).

fof(f2898,plain,
    ( nil = app(sk6,nil)
    | ~ spl0_27
    | ~ spl0_187
    | ~ spl0_219
    | ~ spl0_265 ),
    inference(forward_demodulation,[],[f2897,f2231]) ).

fof(f2897,plain,
    ( app(sk6,nil) = tl(sk3)
    | ~ spl0_27
    | ~ spl0_187
    | ~ spl0_265 ),
    inference(forward_demodulation,[],[f2862,f1621]) ).

fof(f1621,plain,
    ( sk3 = app(sk3,nil)
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1619]) ).

fof(f2862,plain,
    ( app(sk6,nil) = tl(app(sk3,nil))
    | ~ spl0_27
    | ~ spl0_265 ),
    inference(resolution,[],[f2860,f409]) ).

fof(f409,plain,
    ( ssList(nil)
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f407]) ).

fof(f2860,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(sk6,X0) = tl(app(sk3,X0)) )
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f2859]) ).

fof(f3054,plain,
    ( ! [X0] :
        ( frontsegP(cons(sk5,X0),sk3)
        | ~ frontsegP(X0,nil)
        | ~ ssList(X0) )
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f3053]) ).

fof(f3055,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_270
    | ~ spl0_13
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1476,f1421,f305,f3053,f407,f255]) ).

fof(f1421,plain,
    ( spl0_175
  <=> ! [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_175])]) ).

fof(f1476,plain,
    ( ! [X0] :
        ( frontsegP(cons(sk5,X0),sk3)
        | ~ ssList(nil)
        | ~ ssList(X0)
        | ~ frontsegP(X0,nil)
        | ~ ssItem(sk5) )
    | ~ spl0_13
    | ~ spl0_175 ),
    inference(superposition,[],[f1422,f307]) ).

fof(f1422,plain,
    ( ! [X3,X0,X1] :
        ( frontsegP(cons(X3,X0),cons(X3,X1))
        | ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | ~ ssItem(X3) )
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f1421]) ).

fof(f3000,plain,
    ( spl0_269
    | ~ spl0_223
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2996,f2993,f2321,f2998]) ).

fof(f2998,plain,
    ( spl0_269
  <=> ! [X0] :
        ( ~ frontsegP(sk6,X0)
        | frontsegP(sk3,cons(sk5,X0))
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f2993,plain,
    ( spl0_268
  <=> ! [X0] :
        ( frontsegP(sk3,cons(sk5,X0))
        | ~ frontsegP(nil,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f2996,plain,
    ( ! [X0] :
        ( ~ frontsegP(sk6,X0)
        | frontsegP(sk3,cons(sk5,X0))
        | ~ ssList(X0) )
    | ~ spl0_223
    | ~ spl0_268 ),
    inference(forward_demodulation,[],[f2994,f2323]) ).

fof(f2323,plain,
    ( nil = sk6
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2321]) ).

fof(f2994,plain,
    ( ! [X0] :
        ( frontsegP(sk3,cons(sk5,X0))
        | ~ frontsegP(nil,X0)
        | ~ ssList(X0) )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f2993]) ).

fof(f2995,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_268
    | ~ spl0_13
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1475,f1421,f305,f2993,f407,f255]) ).

fof(f1475,plain,
    ( ! [X0] :
        ( frontsegP(sk3,cons(sk5,X0))
        | ~ ssList(X0)
        | ~ ssList(nil)
        | ~ frontsegP(nil,X0)
        | ~ ssItem(sk5) )
    | ~ spl0_13
    | ~ spl0_175 ),
    inference(superposition,[],[f1422,f307]) ).

fof(f2952,plain,
    ( spl0_225
    | spl0_267
    | ~ spl0_8
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1458,f1409,f276,f2950,f2365]) ).

fof(f2365,plain,
    ( spl0_225
  <=> nil = sk7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2950,plain,
    ( spl0_267
  <=> ! [X0] :
        ( ~ ssList(X0)
        | tl(app(sk7,X0)) = app(tl(sk7),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f1458,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk7
        | tl(app(sk7,X0)) = app(tl(sk7),X0) )
    | ~ spl0_8
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f278]) ).

fof(f2909,plain,
    ( spl0_3
    | spl0_266
    | ~ spl0_1
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1456,f1409,f241,f2907,f251]) ).

fof(f2907,plain,
    ( spl0_266
  <=> ! [X0] :
        ( ~ ssList(X0)
        | tl(app(sk4,X0)) = app(tl(sk4),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f1456,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk4
        | tl(app(sk4,X0)) = app(tl(sk4),X0) )
    | ~ spl0_1
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f243]) ).

fof(f2861,plain,
    ( spl0_265
    | ~ spl0_219
    | ~ spl0_223
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2857,f2853,f2321,f2229,f2859]) ).

fof(f2857,plain,
    ( ! [X0] :
        ( app(sk6,X0) = tl(app(sk3,X0))
        | ~ ssList(X0) )
    | ~ spl0_219
    | ~ spl0_223
    | ~ spl0_264 ),
    inference(forward_demodulation,[],[f2856,f2323]) ).

fof(f2855,plain,
    ( spl0_6
    | spl0_264
    | ~ spl0_2
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1455,f1409,f246,f2853,f265]) ).

fof(f1455,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk3
        | tl(app(sk3,X0)) = app(tl(sk3),X0) )
    | ~ spl0_2
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f248]) ).

fof(f2851,plain,
    ( spl0_263
    | ~ spl0_25
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2675,f2321,f397,f2848]) ).

fof(f2848,plain,
    ( spl0_263
  <=> totalorderP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f397,plain,
    ( spl0_25
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f2675,plain,
    ( totalorderP(sk6)
    | ~ spl0_25
    | ~ spl0_223 ),
    inference(superposition,[],[f399,f2323]) ).

fof(f399,plain,
    ( totalorderP(nil)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f397]) ).

fof(f2846,plain,
    ( spl0_262
    | ~ spl0_24
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2674,f2321,f392,f2843]) ).

fof(f2843,plain,
    ( spl0_262
  <=> strictorderP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f2674,plain,
    ( strictorderP(sk6)
    | ~ spl0_24
    | ~ spl0_223 ),
    inference(superposition,[],[f394,f2323]) ).

fof(f2841,plain,
    ( spl0_261
    | ~ spl0_22
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2673,f2321,f373,f2838]) ).

fof(f2838,plain,
    ( spl0_261
  <=> totalorderedP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f373,plain,
    ( spl0_22
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f2673,plain,
    ( totalorderedP(sk6)
    | ~ spl0_22
    | ~ spl0_223 ),
    inference(superposition,[],[f375,f2323]) ).

fof(f375,plain,
    ( totalorderedP(nil)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f373]) ).

fof(f2836,plain,
    ( spl0_260
    | ~ spl0_66
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f718,f694,f568,f2834]) ).

fof(f2834,plain,
    ( spl0_260
  <=> ! [X0] : duplicatefreeP(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f568,plain,
    ( spl0_66
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f718,plain,
    ( ! [X0] : duplicatefreeP(skaf51(X0))
    | ~ spl0_66
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f569]) ).

fof(f569,plain,
    ( ! [X0] : ssList(skaf51(X0))
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f568]) ).

fof(f2832,plain,
    ( spl0_259
    | ~ spl0_65
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f717,f694,f564,f2830]) ).

fof(f2830,plain,
    ( spl0_259
  <=> ! [X0] : duplicatefreeP(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f564,plain,
    ( spl0_65
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f717,plain,
    ( ! [X0] : duplicatefreeP(skaf52(X0))
    | ~ spl0_65
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f565]) ).

fof(f565,plain,
    ( ! [X0] : ssList(skaf52(X0))
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f564]) ).

fof(f2828,plain,
    ( spl0_258
    | ~ spl0_64
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f716,f694,f560,f2826]) ).

fof(f2826,plain,
    ( spl0_258
  <=> ! [X0] : duplicatefreeP(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f560,plain,
    ( spl0_64
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f716,plain,
    ( ! [X0] : duplicatefreeP(skaf53(X0))
    | ~ spl0_64
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f561]) ).

fof(f561,plain,
    ( ! [X0] : ssList(skaf53(X0))
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f560]) ).

fof(f2824,plain,
    ( spl0_257
    | ~ spl0_61
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f715,f694,f548,f2822]) ).

fof(f2822,plain,
    ( spl0_257
  <=> ! [X0] : duplicatefreeP(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f548,plain,
    ( spl0_61
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f715,plain,
    ( ! [X0] : duplicatefreeP(skaf56(X0))
    | ~ spl0_61
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f549]) ).

fof(f549,plain,
    ( ! [X0] : ssList(skaf56(X0))
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f548]) ).

fof(f2820,plain,
    ( spl0_256
    | ~ spl0_60
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f714,f694,f544,f2818]) ).

fof(f2818,plain,
    ( spl0_256
  <=> ! [X0] : duplicatefreeP(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f544,plain,
    ( spl0_60
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f714,plain,
    ( ! [X0] : duplicatefreeP(skaf57(X0))
    | ~ spl0_60
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f545]) ).

fof(f545,plain,
    ( ! [X0] : ssList(skaf57(X0))
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f544]) ).

fof(f2816,plain,
    ( spl0_255
    | ~ spl0_59
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f713,f694,f540,f2814]) ).

fof(f2814,plain,
    ( spl0_255
  <=> ! [X0] : duplicatefreeP(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f540,plain,
    ( spl0_59
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f713,plain,
    ( ! [X0] : duplicatefreeP(skaf58(X0))
    | ~ spl0_59
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f541]) ).

fof(f541,plain,
    ( ! [X0] : ssList(skaf58(X0))
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f540]) ).

fof(f2812,plain,
    ( spl0_254
    | ~ spl0_56
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f712,f694,f528,f2810]) ).

fof(f2810,plain,
    ( spl0_254
  <=> ! [X0] : duplicatefreeP(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f528,plain,
    ( spl0_56
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f712,plain,
    ( ! [X0] : duplicatefreeP(skaf61(X0))
    | ~ spl0_56
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f529]) ).

fof(f529,plain,
    ( ! [X0] : ssList(skaf61(X0))
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f528]) ).

fof(f2808,plain,
    ( spl0_253
    | ~ spl0_55
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f711,f694,f524,f2806]) ).

fof(f2806,plain,
    ( spl0_253
  <=> ! [X0] : duplicatefreeP(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f524,plain,
    ( spl0_55
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f711,plain,
    ( ! [X0] : duplicatefreeP(skaf62(X0))
    | ~ spl0_55
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f525]) ).

fof(f525,plain,
    ( ! [X0] : ssList(skaf62(X0))
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f2804,plain,
    ( spl0_252
    | ~ spl0_54
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f710,f694,f520,f2802]) ).

fof(f2802,plain,
    ( spl0_252
  <=> ! [X0] : duplicatefreeP(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f520,plain,
    ( spl0_54
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f710,plain,
    ( ! [X0] : duplicatefreeP(skaf63(X0))
    | ~ spl0_54
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f521]) ).

fof(f521,plain,
    ( ! [X0] : ssList(skaf63(X0))
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f520]) ).

fof(f2800,plain,
    ( spl0_251
    | ~ spl0_51
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f709,f694,f508,f2798]) ).

fof(f2798,plain,
    ( spl0_251
  <=> ! [X0] : duplicatefreeP(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f508,plain,
    ( spl0_51
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f709,plain,
    ( ! [X0] : duplicatefreeP(skaf66(X0))
    | ~ spl0_51
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f509]) ).

fof(f509,plain,
    ( ! [X0] : ssList(skaf66(X0))
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f508]) ).

fof(f2796,plain,
    ( spl0_250
    | ~ spl0_18
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2672,f2321,f336,f2793]) ).

fof(f2793,plain,
    ( spl0_250
  <=> strictorderedP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f336,plain,
    ( spl0_18
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f2672,plain,
    ( strictorderedP(sk6)
    | ~ spl0_18
    | ~ spl0_223 ),
    inference(superposition,[],[f338,f2323]) ).

fof(f338,plain,
    ( strictorderedP(nil)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f336]) ).

fof(f2791,plain,
    ( spl0_249
    | ~ spl0_50
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f708,f694,f504,f2789]) ).

fof(f2789,plain,
    ( spl0_249
  <=> ! [X0] : duplicatefreeP(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f504,plain,
    ( spl0_50
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f708,plain,
    ( ! [X0] : duplicatefreeP(skaf67(X0))
    | ~ spl0_50
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f505]) ).

fof(f505,plain,
    ( ! [X0] : ssList(skaf67(X0))
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f504]) ).

fof(f2787,plain,
    ( spl0_248
    | ~ spl0_49
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f707,f694,f500,f2785]) ).

fof(f2785,plain,
    ( spl0_248
  <=> ! [X0] : duplicatefreeP(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f500,plain,
    ( spl0_49
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f707,plain,
    ( ! [X0] : duplicatefreeP(skaf68(X0))
    | ~ spl0_49
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f501]) ).

fof(f501,plain,
    ( ! [X0] : ssList(skaf68(X0))
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f500]) ).

fof(f2783,plain,
    ( spl0_247
    | ~ spl0_46
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f706,f694,f488,f2781]) ).

fof(f2781,plain,
    ( spl0_247
  <=> ! [X0] : duplicatefreeP(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f488,plain,
    ( spl0_46
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f706,plain,
    ( ! [X0] : duplicatefreeP(skaf71(X0))
    | ~ spl0_46
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f489]) ).

fof(f489,plain,
    ( ! [X0] : ssList(skaf71(X0))
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f488]) ).

fof(f2779,plain,
    ( spl0_246
    | ~ spl0_45
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f705,f694,f484,f2777]) ).

fof(f2777,plain,
    ( spl0_246
  <=> ! [X0] : duplicatefreeP(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f484,plain,
    ( spl0_45
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f705,plain,
    ( ! [X0] : duplicatefreeP(skaf72(X0))
    | ~ spl0_45
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f485]) ).

fof(f485,plain,
    ( ! [X0] : ssList(skaf72(X0))
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f484]) ).

fof(f2775,plain,
    ( spl0_245
    | ~ spl0_44
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f704,f694,f480,f2773]) ).

fof(f2773,plain,
    ( spl0_245
  <=> ! [X0] : duplicatefreeP(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f480,plain,
    ( spl0_44
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f704,plain,
    ( ! [X0] : duplicatefreeP(skaf73(X0))
    | ~ spl0_44
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f481]) ).

fof(f481,plain,
    ( ! [X0] : ssList(skaf73(X0))
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f480]) ).

fof(f2771,plain,
    ( spl0_244
    | ~ spl0_42
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f703,f694,f472,f2769]) ).

fof(f2769,plain,
    ( spl0_244
  <=> ! [X0] : duplicatefreeP(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f472,plain,
    ( spl0_42
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f703,plain,
    ( ! [X0] : duplicatefreeP(skaf75(X0))
    | ~ spl0_42
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f473]) ).

fof(f473,plain,
    ( ! [X0] : ssList(skaf75(X0))
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f472]) ).

fof(f2767,plain,
    ( spl0_243
    | ~ spl0_41
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f702,f694,f468,f2765]) ).

fof(f2765,plain,
    ( spl0_243
  <=> ! [X0] : duplicatefreeP(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f468,plain,
    ( spl0_41
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f702,plain,
    ( ! [X0] : duplicatefreeP(skaf76(X0))
    | ~ spl0_41
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f469]) ).

fof(f469,plain,
    ( ! [X0] : ssList(skaf76(X0))
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f468]) ).

fof(f2763,plain,
    ( spl0_242
    | ~ spl0_40
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f701,f694,f464,f2761]) ).

fof(f2761,plain,
    ( spl0_242
  <=> ! [X0] : duplicatefreeP(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f464,plain,
    ( spl0_40
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f701,plain,
    ( ! [X0] : duplicatefreeP(skaf77(X0))
    | ~ spl0_40
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f465]) ).

fof(f465,plain,
    ( ! [X0] : ssList(skaf77(X0))
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f464]) ).

fof(f2759,plain,
    ( spl0_241
    | ~ spl0_37
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f700,f694,f452,f2757]) ).

fof(f2757,plain,
    ( spl0_241
  <=> ! [X0] : duplicatefreeP(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f452,plain,
    ( spl0_37
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f700,plain,
    ( ! [X0] : duplicatefreeP(skaf80(X0))
    | ~ spl0_37
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f453]) ).

fof(f453,plain,
    ( ! [X0] : ssList(skaf80(X0))
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f452]) ).

fof(f2755,plain,
    ( spl0_240
    | ~ spl0_36
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f699,f694,f448,f2753]) ).

fof(f2753,plain,
    ( spl0_240
  <=> ! [X0] : duplicatefreeP(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f448,plain,
    ( spl0_36
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f699,plain,
    ( ! [X0] : duplicatefreeP(skaf81(X0))
    | ~ spl0_36
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f449]) ).

fof(f449,plain,
    ( ! [X0] : ssList(skaf81(X0))
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f448]) ).

fof(f2751,plain,
    ( spl0_239
    | ~ spl0_15
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2670,f2321,f317,f2748]) ).

fof(f2748,plain,
    ( spl0_239
  <=> equalelemsP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f2670,plain,
    ( equalelemsP(sk6)
    | ~ spl0_15
    | ~ spl0_223 ),
    inference(superposition,[],[f319,f2323]) ).

fof(f2746,plain,
    ( spl0_238
    | ~ spl0_35
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f698,f694,f444,f2744]) ).

fof(f2744,plain,
    ( spl0_238
  <=> ! [X0] : duplicatefreeP(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f444,plain,
    ( spl0_35
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f698,plain,
    ( ! [X0] : duplicatefreeP(skaf82(X0))
    | ~ spl0_35
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f445]) ).

fof(f445,plain,
    ( ! [X0] : ssList(skaf82(X0))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f2706,plain,
    ( spl0_225
    | spl0_237
    | ~ spl0_8
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1301,f1231,f276,f2704,f2365]) ).

fof(f2704,plain,
    ( spl0_237
  <=> ! [X0] :
        ( ~ ssList(X0)
        | hd(sk7) = hd(app(sk7,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f1231,plain,
    ( spl0_152
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1301,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk7
        | hd(sk7) = hd(app(sk7,X0)) )
    | ~ spl0_8
    | ~ spl0_152 ),
    inference(resolution,[],[f1232,f278]) ).

fof(f1232,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1231]) ).

fof(f2666,plain,
    ( spl0_223
    | spl0_236
    | ~ spl0_5
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1300,f1231,f260,f2664,f2321]) ).

fof(f2664,plain,
    ( spl0_236
  <=> ! [X0] :
        ( ~ ssList(X0)
        | hd(sk6) = hd(app(sk6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f1300,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk6
        | hd(sk6) = hd(app(sk6,X0)) )
    | ~ spl0_5
    | ~ spl0_152 ),
    inference(resolution,[],[f1232,f262]) ).

fof(f2627,plain,
    ( spl0_3
    | spl0_235
    | ~ spl0_1
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1299,f1231,f241,f2625,f251]) ).

fof(f2625,plain,
    ( spl0_235
  <=> ! [X0] :
        ( ~ ssList(X0)
        | hd(sk4) = hd(app(sk4,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f1299,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk4
        | hd(sk4) = hd(app(sk4,X0)) )
    | ~ spl0_1
    | ~ spl0_152 ),
    inference(resolution,[],[f1232,f243]) ).

fof(f2587,plain,
    ( spl0_234
    | ~ spl0_226
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2583,f2580,f2405,f2585]) ).

fof(f2585,plain,
    ( spl0_234
  <=> ! [X0] :
        ( sk5 = hd(app(sk3,X0))
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f2405,plain,
    ( spl0_226
  <=> sk5 = hd(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f2580,plain,
    ( spl0_233
  <=> ! [X0] :
        ( ~ ssList(X0)
        | hd(sk3) = hd(app(sk3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f2583,plain,
    ( ! [X0] :
        ( sk5 = hd(app(sk3,X0))
        | ~ ssList(X0) )
    | ~ spl0_226
    | ~ spl0_233 ),
    inference(forward_demodulation,[],[f2581,f2407]) ).

fof(f2407,plain,
    ( sk5 = hd(sk3)
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f2405]) ).

fof(f2581,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | hd(sk3) = hd(app(sk3,X0)) )
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2580]) ).

fof(f2582,plain,
    ( spl0_6
    | spl0_233
    | ~ spl0_2
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1298,f1231,f246,f2580,f265]) ).

fof(f1298,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = sk3
        | hd(sk3) = hd(app(sk3,X0)) )
    | ~ spl0_2
    | ~ spl0_152 ),
    inference(resolution,[],[f1232,f248]) ).

fof(f2577,plain,
    ( ~ spl0_231
    | ~ spl0_8
    | ~ spl0_1
    | spl0_232
    | ~ spl0_31
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1225,f1167,f427,f2574,f241,f276,f2570]) ).

fof(f2574,plain,
    ( spl0_232
  <=> rearsegP(sk4,sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f1167,plain,
    ( spl0_150
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | rearsegP(app(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1225,plain,
    ( rearsegP(sk4,sk7)
    | ~ ssList(sk4)
    | ~ ssList(sk7)
    | ~ ssList(app(sk6,sk3))
    | ~ spl0_31
    | ~ spl0_150 ),
    inference(superposition,[],[f1168,f429]) ).

fof(f1168,plain,
    ( ! [X0,X1] :
        ( rearsegP(app(X0,X1),X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1167]) ).

fof(f2533,plain,
    ( spl0_230
    | spl0_225
    | ~ spl0_8
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1122,f1042,f276,f2365,f2530]) ).

fof(f2530,plain,
    ( spl0_230
  <=> sk7 = cons(skaf83(sk7),skaf82(sk7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f1042,plain,
    ( spl0_137
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1122,plain,
    ( nil = sk7
    | sk7 = cons(skaf83(sk7),skaf82(sk7))
    | ~ spl0_8
    | ~ spl0_137 ),
    inference(resolution,[],[f1043,f278]) ).

fof(f1043,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1042]) ).

fof(f2493,plain,
    ( spl0_229
    | spl0_223
    | ~ spl0_5
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1121,f1042,f260,f2321,f2490]) ).

fof(f2490,plain,
    ( spl0_229
  <=> sk6 = cons(skaf83(sk6),skaf82(sk6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f1121,plain,
    ( nil = sk6
    | sk6 = cons(skaf83(sk6),skaf82(sk6))
    | ~ spl0_5
    | ~ spl0_137 ),
    inference(resolution,[],[f1043,f262]) ).

fof(f2453,plain,
    ( spl0_228
    | spl0_3
    | ~ spl0_1
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1120,f1042,f241,f251,f2450]) ).

fof(f2450,plain,
    ( spl0_228
  <=> sk4 = cons(skaf83(sk4),skaf82(sk4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f1120,plain,
    ( nil = sk4
    | sk4 = cons(skaf83(sk4),skaf82(sk4))
    | ~ spl0_1
    | ~ spl0_137 ),
    inference(resolution,[],[f1043,f243]) ).

fof(f2413,plain,
    ( spl0_227
    | spl0_6
    | ~ spl0_2
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1119,f1042,f246,f265,f2410]) ).

fof(f2410,plain,
    ( spl0_227
  <=> sk3 = cons(skaf83(sk3),skaf82(sk3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f1119,plain,
    ( nil = sk3
    | sk3 = cons(skaf83(sk3),skaf82(sk3))
    | ~ spl0_2
    | ~ spl0_137 ),
    inference(resolution,[],[f1043,f248]) ).

fof(f2408,plain,
    ( spl0_226
    | ~ spl0_13
    | ~ spl0_27
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2223,f2149,f407,f305,f2405]) ).

fof(f2149,plain,
    ( spl0_217
  <=> ! [X0] :
        ( ~ ssList(X0)
        | sk5 = hd(cons(sk5,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f2223,plain,
    ( sk5 = hd(sk3)
    | ~ spl0_13
    | ~ spl0_27
    | ~ spl0_217 ),
    inference(forward_demodulation,[],[f2188,f307]) ).

fof(f2188,plain,
    ( sk5 = hd(cons(sk5,nil))
    | ~ spl0_27
    | ~ spl0_217 ),
    inference(resolution,[],[f2150,f409]) ).

fof(f2150,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sk5 = hd(cons(sk5,X0)) )
    | ~ spl0_217 ),
    inference(avatar_component_clause,[],[f2149]) ).

fof(f2368,plain,
    ( spl0_224
    | spl0_225
    | ~ spl0_8
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1087,f1038,f276,f2365,f2361]) ).

fof(f2361,plain,
    ( spl0_224
  <=> sk7 = cons(hd(sk7),tl(sk7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f1038,plain,
    ( spl0_136
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1087,plain,
    ( nil = sk7
    | sk7 = cons(hd(sk7),tl(sk7))
    | ~ spl0_8
    | ~ spl0_136 ),
    inference(resolution,[],[f1039,f278]) ).

fof(f1039,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1038]) ).

fof(f2324,plain,
    ( spl0_222
    | spl0_223
    | ~ spl0_5
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1086,f1038,f260,f2321,f2317]) ).

fof(f2317,plain,
    ( spl0_222
  <=> sk6 = cons(hd(sk6),tl(sk6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f1086,plain,
    ( nil = sk6
    | sk6 = cons(hd(sk6),tl(sk6))
    | ~ spl0_5
    | ~ spl0_136 ),
    inference(resolution,[],[f1039,f262]) ).

fof(f2280,plain,
    ( spl0_221
    | spl0_3
    | ~ spl0_1
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1085,f1038,f241,f251,f2277]) ).

fof(f2277,plain,
    ( spl0_221
  <=> sk4 = cons(hd(sk4),tl(sk4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f1085,plain,
    ( nil = sk4
    | sk4 = cons(hd(sk4),tl(sk4))
    | ~ spl0_1
    | ~ spl0_136 ),
    inference(resolution,[],[f1039,f243]) ).

fof(f2273,plain,
    ( spl0_220
    | spl0_6
    | ~ spl0_2
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1084,f1038,f246,f265,f2270]) ).

fof(f2270,plain,
    ( spl0_220
  <=> sk3 = cons(hd(sk3),tl(sk3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f1084,plain,
    ( nil = sk3
    | sk3 = cons(hd(sk3),tl(sk3))
    | ~ spl0_2
    | ~ spl0_136 ),
    inference(resolution,[],[f1039,f248]) ).

fof(f2232,plain,
    ( spl0_219
    | ~ spl0_13
    | ~ spl0_27
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2187,f2145,f407,f305,f2229]) ).

fof(f2145,plain,
    ( spl0_216
  <=> ! [X0] :
        ( ~ ssList(X0)
        | tl(cons(sk5,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2187,plain,
    ( nil = tl(sk3)
    | ~ spl0_13
    | ~ spl0_27
    | ~ spl0_216 ),
    inference(forward_demodulation,[],[f2152,f307]) ).

fof(f2152,plain,
    ( nil = tl(cons(sk5,nil))
    | ~ spl0_27
    | ~ spl0_216 ),
    inference(resolution,[],[f2146,f409]) ).

fof(f2146,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | tl(cons(sk5,X0)) = X0 )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2145]) ).

fof(f2227,plain,
    ( spl0_218
    | ~ spl0_4
    | ~ spl0_13
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1193,f1126,f305,f255,f2225]) ).

fof(f2225,plain,
    ( spl0_218
  <=> ! [X0] :
        ( cons(sk5,X0) = app(sk3,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f1126,plain,
    ( spl0_140
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1193,plain,
    ( ! [X0] :
        ( cons(sk5,X0) = app(sk3,X0)
        | ~ ssList(X0) )
    | ~ spl0_4
    | ~ spl0_13
    | ~ spl0_140 ),
    inference(forward_demodulation,[],[f1192,f307]) ).

fof(f1192,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | cons(sk5,X0) = app(cons(sk5,nil),X0) )
    | ~ spl0_4
    | ~ spl0_140 ),
    inference(resolution,[],[f1127,f257]) ).

fof(f1127,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1126]) ).

fof(f2151,plain,
    ( spl0_217
    | ~ spl0_4
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1014,f930,f255,f2149]) ).

fof(f930,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1014,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sk5 = hd(cons(sk5,X0)) )
    | ~ spl0_4
    | ~ spl0_123 ),
    inference(resolution,[],[f931,f257]) ).

fof(f931,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f930]) ).

fof(f2147,plain,
    ( spl0_216
    | ~ spl0_4
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f995,f926,f255,f2145]) ).

fof(f926,plain,
    ( spl0_122
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f995,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | tl(cons(sk5,X0)) = X0 )
    | ~ spl0_4
    | ~ spl0_122 ),
    inference(resolution,[],[f927,f257]) ).

fof(f927,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 )
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f926]) ).

fof(f2142,plain,
    ( ~ spl0_4
    | ~ spl0_27
    | spl0_215
    | ~ spl0_13
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f924,f919,f305,f2139,f407,f255]) ).

fof(f2139,plain,
    ( spl0_215
  <=> memberP(sk3,sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f919,plain,
    ( spl0_121
  <=> ! [X2,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f924,plain,
    ( memberP(sk3,sk5)
    | ~ ssList(nil)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_121 ),
    inference(superposition,[],[f920,f307]) ).

fof(f920,plain,
    ( ! [X2,X1] :
        ( memberP(cons(X1,X2),X1)
        | ~ ssList(X2)
        | ~ ssItem(X1) )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f919]) ).

fof(f2136,plain,
    ( spl0_214
    | ~ spl0_4
    | ~ spl0_2
    | ~ spl0_13
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1035,f974,f305,f246,f255,f2133]) ).

fof(f2133,plain,
    ( spl0_214
  <=> singletonP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f974,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1035,plain,
    ( ~ ssList(sk3)
    | ~ ssItem(sk5)
    | singletonP(sk3)
    | ~ spl0_13
    | ~ spl0_134 ),
    inference(superposition,[],[f975,f307]) ).

fof(f975,plain,
    ( ! [X0] :
        ( ~ ssList(cons(X0,nil))
        | ~ ssItem(X0)
        | singletonP(cons(X0,nil)) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f974]) ).

fof(f1987,plain,
    ( spl0_213
    | ~ spl0_8
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f812,f746,f276,f1984]) ).

fof(f1984,plain,
    ( spl0_213
  <=> sk7 = app(nil,sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f746,plain,
    ( spl0_100
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f812,plain,
    ( sk7 = app(nil,sk7)
    | ~ spl0_8
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f278]) ).

fof(f747,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f746]) ).

fof(f1982,plain,
    ( spl0_212
    | ~ spl0_5
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f811,f746,f260,f1979]) ).

fof(f1979,plain,
    ( spl0_212
  <=> sk6 = app(nil,sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f811,plain,
    ( sk6 = app(nil,sk6)
    | ~ spl0_5
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f262]) ).

fof(f1977,plain,
    ( spl0_211
    | ~ spl0_1
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f810,f746,f241,f1974]) ).

fof(f1974,plain,
    ( spl0_211
  <=> sk4 = app(nil,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f810,plain,
    ( sk4 = app(nil,sk4)
    | ~ spl0_1
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f243]) ).

fof(f1969,plain,
    ( spl0_210
    | ~ spl0_2
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f809,f746,f246,f1966]) ).

fof(f1966,plain,
    ( spl0_210
  <=> sk3 = app(nil,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f809,plain,
    ( sk3 = app(nil,sk3)
    | ~ spl0_2
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f248]) ).

fof(f1958,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f233,f1956]) ).

fof(f1956,plain,
    ( spl0_209
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssItem(X3)
        | ~ ssItem(X1)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X4)
        | ~ ssList(X0)
        | ~ ssList(X2)
        | leq(X1,X3)
        | leq(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f233,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | leq(X1,X3)
      | leq(X3,X1) ),
    inference(equality_resolution,[],[f184]) ).

fof(f184,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ totalorderP(X5)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X5)
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | leq(X1,X3)
      | leq(X3,X1)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).

fof(f1954,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f232,f1952]) ).

fof(f1952,plain,
    ( spl0_208
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssItem(X3)
        | ~ ssItem(X1)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X4)
        | ~ ssList(X0)
        | ~ ssList(X2)
        | lt(X1,X3)
        | lt(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f232,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | lt(X1,X3)
      | lt(X3,X1) ),
    inference(equality_resolution,[],[f183]) ).

fof(f183,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ strictorderP(X5)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X5)
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | lt(X1,X3)
      | lt(X3,X1)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).

fof(f1950,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f231,f1948]) ).

fof(f1948,plain,
    ( spl0_207
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
        | ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
        | ~ ssList(X2)
        | ~ ssList(X3)
        | ~ ssList(X4)
        | ~ leq(X0,X1)
        | ~ leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f231,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
      | ~ ssList(X2)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ leq(X0,X1)
      | ~ leq(X1,X0) ),
    inference(equality_resolution,[],[f185]) ).

fof(f185,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ cyclefreeP(X5)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssList(X5)
      | ~ ssList(X2)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ leq(X0,X1)
      | ~ leq(X1,X0)
      | app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).

fof(f1940,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f230,f1938]) ).

fof(f1938,plain,
    ( spl0_206
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssItem(X1)
        | ~ ssItem(X3)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X4)
        | leq(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f230,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | leq(X1,X3) ),
    inference(equality_resolution,[],[f182]) ).

fof(f182,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ totalorderedP(X5)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X5)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | leq(X1,X3)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).

fof(f1936,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f229,f1934]) ).

fof(f1934,plain,
    ( spl0_205
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssItem(X1)
        | ~ ssItem(X3)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X4)
        | lt(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f229,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | lt(X1,X3) ),
    inference(equality_resolution,[],[f181]) ).

fof(f181,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ strictorderedP(X5)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | ~ ssList(X5)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X4)
      | lt(X1,X3)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).

fof(f1929,plain,
    ( spl0_204
    | ~ spl0_8
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f780,f742,f276,f1926]) ).

fof(f1926,plain,
    ( spl0_204
  <=> sk7 = app(sk7,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f742,plain,
    ( spl0_99
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f780,plain,
    ( sk7 = app(sk7,nil)
    | ~ spl0_8
    | ~ spl0_99 ),
    inference(resolution,[],[f743,f278]) ).

fof(f743,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f742]) ).

fof(f1924,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f226,f1922]) ).

fof(f1922,plain,
    ( spl0_203
  <=> ! [X0,X3,X2,X1] :
        ( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
        | ~ ssItem(X1)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f226,plain,
    ! [X2,X3,X0,X1] :
      ( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssItem(X1)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X3) ),
    inference(equality_resolution,[],[f179]) ).

fof(f179,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ duplicatefreeP(X4)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X3)
      | app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).

fof(f1917,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f228,f1915]) ).

fof(f1915,plain,
    ( spl0_202
  <=> ! [X0,X3,X2,X1] :
        ( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
        | ~ ssItem(X2)
        | ~ ssItem(X1)
        | ~ ssList(app(X0,cons(X1,cons(X2,X3))))
        | ~ ssList(X0)
        | ~ ssList(X3)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f228,plain,
    ! [X2,X3,X0,X1] :
      ( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X0,cons(X1,cons(X2,X3))))
      | ~ ssList(X0)
      | ~ ssList(X3)
      | X1 = X2 ),
    inference(equality_resolution,[],[f180]) ).

fof(f180,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ equalelemsP(X4)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X3)
      | X1 = X2
      | app(X0,cons(X1,cons(X2,X3))) != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).

fof(f1911,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f177,f1909]) ).

fof(f1909,plain,
    ( spl0_201
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | X0 = X1
        | nil = X0
        | nil = X1
        | tl(X0) != tl(X1)
        | hd(X0) != hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f177,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1
      | nil = X0
      | nil = X1
      | tl(X0) != tl(X1)
      | hd(X0) != hd(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).

fof(f1732,plain,
    ( spl0_200
    | ~ spl0_5
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f779,f742,f260,f1729]) ).

fof(f779,plain,
    ( sk6 = app(sk6,nil)
    | ~ spl0_5
    | ~ spl0_99 ),
    inference(resolution,[],[f743,f262]) ).

fof(f1727,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f167,f1725]) ).

fof(f1725,plain,
    ( spl0_199
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f167,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | cyclefreeP(X0)
      | app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).

fof(f1723,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f166,f1721]) ).

fof(f166,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderP(X0)
      | app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).

fof(f1719,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f165,f1717]) ).

fof(f165,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | strictorderP(X0)
      | app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).

fof(f1715,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f164,f1713]) ).

fof(f164,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | totalorderedP(X0)
      | app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).

fof(f1711,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f163,f1709]) ).

fof(f163,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | strictorderedP(X0)
      | app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).

fof(f1694,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f225,f1692]) ).

fof(f225,plain,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(app(app(X0,X1),X2))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | segmentP(app(app(X0,X1),X2),X1) ),
    inference(equality_resolution,[],[f173]) ).

fof(f173,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | segmentP(X3,X1)
      | app(app(X0,X1),X2) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).

fof(f1690,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f224,f1688]) ).

fof(f224,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(app(X0,cons(X1,X2)))
      | ~ ssList(X0)
      | ~ ssList(X2)
      | memberP(app(X0,cons(X1,X2)),X1) ),
    inference(equality_resolution,[],[f175]) ).

fof(f175,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X3)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | memberP(X3,X1)
      | app(X0,cons(X1,X2)) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).

fof(f1680,plain,
    ( spl0_192
    | ~ spl0_1
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f778,f742,f241,f1677]) ).

fof(f1677,plain,
    ( spl0_192
  <=> sk4 = app(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f778,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_1
    | ~ spl0_99 ),
    inference(resolution,[],[f743,f243]) ).

fof(f1638,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f176,f1636]) ).

fof(f176,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X3)
      | X0 = X2
      | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).

fof(f1634,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f174,f1632]) ).

fof(f174,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X3)
      | frontsegP(X1,X3)
      | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).

fof(f1630,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f172,f1628]) ).

fof(f1628,plain,
    ( spl0_189
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ ssList(X3)
        | ~ segmentP(X0,X1)
        | segmentP(app(app(X3,X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f172,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(X3)
      | ~ segmentP(X0,X1)
      | segmentP(app(app(X3,X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).

fof(f1626,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f171,f1624]) ).

fof(f171,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X3)
      | X1 = X3
      | cons(X0,X1) != cons(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).

fof(f1622,plain,
    ( spl0_187
    | ~ spl0_2
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f777,f742,f246,f1619]) ).

fof(f777,plain,
    ( sk3 = app(sk3,nil)
    | ~ spl0_2
    | ~ spl0_99 ),
    inference(resolution,[],[f743,f248]) ).

fof(f1617,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f170,f1615]) ).

fof(f170,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X2)
      | ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X3)
      | X0 = X2
      | cons(X0,X1) != cons(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).

fof(f1613,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f169,f1611]) ).

fof(f1611,plain,
    ( spl0_185
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f169,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X0)
      | ~ memberP(X0,X1)
      | app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).

fof(f1609,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f168,f1607]) ).

fof(f1607,plain,
    ( spl0_184
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X0,X1)
        | app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f168,axiom,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ segmentP(X0,X1)
      | app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).

fof(f1504,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f161,f1502]) ).

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/sandbox/benchmark/theBenchmark.p',clause161) ).

fof(f1500,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f160,f1498]) ).

fof(f1498,plain,
    ( spl0_182
  <=> ! [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_182])]) ).

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

fof(f1496,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f159,f1494]) ).

fof(f1494,plain,
    ( spl0_181
  <=> ! [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_181])]) ).

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

fof(f1492,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f158,f1490]) ).

fof(f1490,plain,
    ( spl0_180
  <=> ! [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_180])]) ).

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/sandbox/benchmark/theBenchmark.p',clause158) ).

fof(f1488,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f157,f1486]) ).

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/sandbox/benchmark/theBenchmark.p',clause157) ).

fof(f1484,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f149,f1482]) ).

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/sandbox/benchmark/theBenchmark.p',clause149) ).

fof(f1480,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f142,f1478]) ).

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

fof(f1463,plain,
    ( ~ spl0_4
    | spl0_176
    | ~ spl0_13
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f740,f687,f305,f1460,f255]) ).

fof(f1460,plain,
    ( spl0_176
  <=> cyclefreeP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f687,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f740,plain,
    ( cyclefreeP(sk3)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_95 ),
    inference(superposition,[],[f688,f307]) ).

fof(f688,plain,
    ( ! [X0] :
        ( cyclefreeP(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f687]) ).

fof(f1423,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f234,f1421]) ).

fof(f234,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(duplicate_literal_removal,[],[f227]) ).

fof(f227,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/sandbox/benchmark/theBenchmark.p',clause178) ).

fof(f1419,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f151,f1417]) ).

fof(f1417,plain,
    ( spl0_174
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | X0 = X2
        | app(X0,X1) != app(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

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

fof(f1415,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f150,f1413]) ).

fof(f1413,plain,
    ( spl0_173
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | X1 = X2
        | app(X0,X1) != app(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

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

fof(f1411,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f133,f1409]) ).

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

fof(f1373,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f156,f1371]) ).

fof(f1371,plain,
    ( spl0_171
  <=> ! [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_171])]) ).

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

fof(f1369,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f155,f1367]) ).

fof(f1367,plain,
    ( spl0_170
  <=> ! [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_170])]) ).

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

fof(f1365,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f154,f1363]) ).

fof(f1363,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

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

fof(f1361,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f153,f1359]) ).

fof(f1359,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

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

fof(f1357,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f152,f1355]) ).

fof(f1355,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

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

fof(f1353,plain,
    ( ~ spl0_4
    | spl0_166
    | ~ spl0_13
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f734,f683,f305,f1350,f255]) ).

fof(f1350,plain,
    ( spl0_166
  <=> totalorderP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f683,plain,
    ( spl0_94
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f734,plain,
    ( totalorderP(sk3)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_94 ),
    inference(superposition,[],[f684,f307]) ).

fof(f684,plain,
    ( ! [X0] :
        ( totalorderP(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f683]) ).

fof(f1348,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f148,f1346]) ).

fof(f1346,plain,
    ( spl0_165
  <=> ! [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_165])]) ).

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

fof(f1344,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f147,f1342]) ).

fof(f1342,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

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

fof(f1340,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f146,f1338]) ).

fof(f1338,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

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

fof(f1336,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f135,f1334]) ).

fof(f1334,plain,
    ( spl0_162
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

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

fof(f1332,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f134,f1330]) ).

fof(f1330,plain,
    ( spl0_161
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

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

fof(f1266,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f141,f1264]) ).

fof(f1264,plain,
    ( spl0_160
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ memberP(X0,X1)
        | memberP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

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

fof(f1262,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f140,f1260]) ).

fof(f1260,plain,
    ( spl0_159
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

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

fof(f1258,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f139,f1256]) ).

fof(f1256,plain,
    ( spl0_158
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(cons(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

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

fof(f1254,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f137,f1252]) ).

fof(f1252,plain,
    ( spl0_157
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ frontsegP(X0,X1)
        | frontsegP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

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

fof(f1250,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f136,f1248]) ).

fof(f1248,plain,
    ( spl0_156
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ rearsegP(X0,X1)
        | rearsegP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

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

fof(f1246,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f132,f1244]) ).

fof(f1244,plain,
    ( spl0_155
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | app(X1,skaf45(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

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

fof(f1242,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f131,f1240]) ).

fof(f1240,plain,
    ( spl0_154
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X0,X1)
        | app(skaf46(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

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

fof(f1238,plain,
    ( ~ spl0_4
    | spl0_153
    | ~ spl0_13
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f733,f679,f305,f1235,f255]) ).

fof(f1235,plain,
    ( spl0_153
  <=> strictorderP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f679,plain,
    ( spl0_93
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f733,plain,
    ( strictorderP(sk3)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_93 ),
    inference(superposition,[],[f680,f307]) ).

fof(f680,plain,
    ( ! [X0] :
        ( strictorderP(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f679]) ).

fof(f1233,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f123,f1231]) ).

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

fof(f1173,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f221,f1171]) ).

fof(f1171,plain,
    ( spl0_151
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | frontsegP(app(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f221,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/sandbox/benchmark/theBenchmark.p',clause144) ).

fof(f1169,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f220,f1167]) ).

fof(f220,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/sandbox/benchmark/theBenchmark.p',clause143) ).

fof(f1165,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f130,f1163]) ).

fof(f1163,plain,
    ( spl0_149
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X1,X0)
        | ~ leq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

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

fof(f1161,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f129,f1159]) ).

fof(f1159,plain,
    ( spl0_148
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X1,X0)
        | ~ frontsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

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

fof(f1157,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f128,f1155]) ).

fof(f1155,plain,
    ( spl0_147
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

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

fof(f1153,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f127,f1151]) ).

fof(f1151,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

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

fof(f1149,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f126,f1147]) ).

fof(f1147,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

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

fof(f1145,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f125,f1143]) ).

fof(f1143,plain,
    ( spl0_144
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

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

fof(f1141,plain,
    ( ~ spl0_4
    | spl0_143
    | ~ spl0_13
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f732,f675,f305,f1138,f255]) ).

fof(f1138,plain,
    ( spl0_143
  <=> totalorderedP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f675,plain,
    ( spl0_92
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f732,plain,
    ( totalorderedP(sk3)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_92 ),
    inference(superposition,[],[f676,f307]) ).

fof(f676,plain,
    ( ! [X0] :
        ( totalorderedP(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f675]) ).

fof(f1136,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f124,f1134]) ).

fof(f1134,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

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

fof(f1132,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f122,f1130]) ).

fof(f1130,plain,
    ( spl0_141
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

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

fof(f1128,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f120,f1126]) ).

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

fof(f1052,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f119,f1050]) ).

fof(f1050,plain,
    ( spl0_139
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

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

fof(f1048,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f118,f1046]) ).

fof(f1046,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

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

fof(f1044,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f109,f1042]) ).

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

fof(f1040,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f104,f1038]) ).

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

fof(f1023,plain,
    ( ~ spl0_4
    | spl0_135
    | ~ spl0_13
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f731,f671,f305,f1020,f255]) ).

fof(f1020,plain,
    ( spl0_135
  <=> strictorderedP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f671,plain,
    ( spl0_91
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f731,plain,
    ( strictorderedP(sk3)
    | ~ ssItem(sk5)
    | ~ spl0_13
    | ~ spl0_91 ),
    inference(superposition,[],[f672,f307]) ).

fof(f672,plain,
    ( ! [X0] :
        ( strictorderedP(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f671]) ).

fof(f976,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f215,f974]) ).

fof(f215,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/sandbox/benchmark/theBenchmark.p',clause116) ).

fof(f972,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f114,f970]) ).

fof(f970,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

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

fof(f968,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f110,f966]) ).

fof(f966,plain,
    ( spl0_132
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

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

fof(f964,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f108,f962]) ).

fof(f962,plain,
    ( spl0_131
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

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

fof(f960,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f107,f958]) ).

fof(f958,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

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

fof(f956,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f106,f954]) ).

fof(f954,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

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

fof(f952,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f105,f950]) ).

fof(f950,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

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

fof(f948,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f103,f946]) ).

fof(f946,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

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

fof(f944,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f102,f942]) ).

fof(f942,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

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

fof(f940,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f101,f938]) ).

fof(f938,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

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

fof(f936,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f100,f934]) ).

fof(f934,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

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

fof(f932,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f97,f930]) ).

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

fof(f928,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f96,f926]) ).

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

fof(f921,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f236,f919]) ).

fof(f236,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f219]) ).

fof(f219,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/sandbox/benchmark/theBenchmark.p',clause138) ).

fof(f917,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f99,f915]) ).

fof(f915,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

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

fof(f913,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f98,f911]) ).

fof(f911,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

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

fof(f909,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f95,f907]) ).

fof(f907,plain,
    ( spl0_118
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

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

fof(f905,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f94,f903]) ).

fof(f903,plain,
    ( spl0_117
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

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

fof(f901,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f93,f899]) ).

fof(f899,plain,
    ( spl0_116
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

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

fof(f897,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f92,f895]) ).

fof(f895,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

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

fof(f893,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f91,f891]) ).

fof(f891,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

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

fof(f889,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f90,f887]) ).

fof(f887,plain,
    ( spl0_113
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

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

fof(f885,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f89,f883]) ).

fof(f883,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

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

fof(f881,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f88,f879]) ).

fof(f879,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

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

fof(f877,plain,
    ( spl0_110
    | ~ spl0_8
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f728,f694,f276,f874]) ).

fof(f874,plain,
    ( spl0_110
  <=> duplicatefreeP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f728,plain,
    ( duplicatefreeP(sk7)
    | ~ spl0_8
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f278]) ).

fof(f872,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f87,f870]) ).

fof(f870,plain,
    ( spl0_109
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

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

fof(f845,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f86,f843]) ).

fof(f843,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

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

fof(f841,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f85,f839]) ).

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

fof(f837,plain,
    ( spl0_106
    | ~ spl0_5
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f727,f694,f260,f834]) ).

fof(f834,plain,
    ( spl0_106
  <=> duplicatefreeP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f727,plain,
    ( duplicatefreeP(sk6)
    | ~ spl0_5
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f262]) ).

fof(f832,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f84,f830]) ).

fof(f830,plain,
    ( spl0_105
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

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

fof(f828,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f82,f826]) ).

fof(f826,plain,
    ( spl0_104
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

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

fof(f824,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f80,f822]) ).

fof(f822,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

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

fof(f820,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f76,f818]) ).

fof(f818,plain,
    ( spl0_102
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssItem(hd(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f76,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssItem(hd(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).

fof(f816,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f75,f814]) ).

fof(f814,plain,
    ( spl0_101
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

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

fof(f748,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f74,f746]) ).

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

fof(f744,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f73,f742]) ).

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

fof(f739,plain,
    ( spl0_98
    | ~ spl0_2
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f725,f694,f246,f736]) ).

fof(f736,plain,
    ( spl0_98
  <=> duplicatefreeP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f725,plain,
    ( duplicatefreeP(sk3)
    | ~ spl0_2
    | ~ spl0_97 ),
    inference(resolution,[],[f695,f248]) ).

fof(f696,plain,
    ( spl0_96
    | spl0_97 ),
    inference(avatar_split_clause,[],[f72,f694,f691]) ).

fof(f691,plain,
    ( spl0_96
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

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

fof(f689,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f70,f687]) ).

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

fof(f685,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f69,f683]) ).

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

fof(f681,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f68,f679]) ).

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

fof(f677,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f67,f675]) ).

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

fof(f673,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f66,f671]) ).

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

fof(f669,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f65,f667]) ).

fof(f667,plain,
    ( spl0_90
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | duplicatefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

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

fof(f665,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f64,f663]) ).

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

fof(f661,plain,
    ( ~ spl0_1
    | spl0_12
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f660,f621,f300,f241]) ).

fof(f300,plain,
    ( spl0_12
  <=> segmentP(sk4,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f621,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f660,plain,
    ( ~ ssList(sk4)
    | spl0_12
    | ~ spl0_79 ),
    inference(resolution,[],[f622,f302]) ).

fof(f302,plain,
    ( ~ segmentP(sk4,sk4)
    | spl0_12 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f622,plain,
    ( ! [X0] :
        ( segmentP(X0,X0)
        | ~ ssList(X0) )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f621]) ).

fof(f659,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f239,f657]) ).

fof(f657,plain,
    ( spl0_88
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f239,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f213]) ).

fof(f213,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/sandbox/benchmark/theBenchmark.p',clause117) ).

fof(f655,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f237,f653]) ).

fof(f653,plain,
    ( spl0_87
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f237,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f218]) ).

fof(f218,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/sandbox/benchmark/theBenchmark.p',clause115) ).

fof(f651,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f71,f649]) ).

fof(f649,plain,
    ( spl0_86
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

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

fof(f647,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f63,f645]) ).

fof(f645,plain,
    ( spl0_85
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

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

fof(f643,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f62,f641]) ).

fof(f641,plain,
    ( spl0_84
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

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

fof(f639,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f61,f637]) ).

fof(f637,plain,
    ( spl0_83
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

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

fof(f635,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f60,f633]) ).

fof(f633,plain,
    ( spl0_82
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

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

fof(f631,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f59,f629]) ).

fof(f629,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

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

fof(f627,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f58,f625]) ).

fof(f625,plain,
    ( spl0_80
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

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

fof(f623,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f57,f621]) ).

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

fof(f619,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f56,f617]) ).

fof(f617,plain,
    ( spl0_78
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

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

fof(f615,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f55,f613]) ).

fof(f613,plain,
    ( spl0_77
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

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

fof(f611,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f53,f609]) ).

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

fof(f607,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f52,f605]) ).

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

fof(f603,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f51,f601]) ).

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

fof(f599,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f50,f597]) ).

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

fof(f595,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f49,f593]) ).

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

fof(f591,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f48,f589]) ).

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

fof(f587,plain,
    ~ spl0_70,
    inference(avatar_split_clause,[],[f54,f584]) ).

fof(f584,plain,
    ( spl0_70
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

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

fof(f582,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f47,f580]) ).

fof(f580,plain,
    ( spl0_69
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

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

fof(f578,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f46,f576]) ).

fof(f576,plain,
    ( spl0_68
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

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

fof(f574,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f45,f572]) ).

fof(f572,plain,
    ( spl0_67
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

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

fof(f570,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f44,f568]) ).

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

fof(f566,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f43,f564]) ).

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

fof(f562,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f42,f560]) ).

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

fof(f558,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f41,f556]) ).

fof(f556,plain,
    ( spl0_63
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

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

fof(f554,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f40,f552]) ).

fof(f552,plain,
    ( spl0_62
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

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

fof(f550,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f39,f548]) ).

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

fof(f546,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f38,f544]) ).

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

fof(f542,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f37,f540]) ).

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

fof(f538,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f36,f536]) ).

fof(f536,plain,
    ( spl0_58
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

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

fof(f534,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f35,f532]) ).

fof(f532,plain,
    ( spl0_57
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

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

fof(f530,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f34,f528]) ).

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

fof(f526,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f33,f524]) ).

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

fof(f522,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f32,f520]) ).

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

fof(f518,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f31,f516]) ).

fof(f516,plain,
    ( spl0_53
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

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

fof(f514,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f30,f512]) ).

fof(f512,plain,
    ( spl0_52
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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

fof(f510,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f29,f508]) ).

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

fof(f506,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f28,f504]) ).

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

fof(f502,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f27,f500]) ).

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

fof(f498,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f26,f496]) ).

fof(f496,plain,
    ( spl0_48
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

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

fof(f494,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f25,f492]) ).

fof(f492,plain,
    ( spl0_47
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

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

fof(f490,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f24,f488]) ).

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

fof(f486,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f23,f484]) ).

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

fof(f482,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f22,f480]) ).

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

fof(f478,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f21,f476]) ).

fof(f476,plain,
    ( spl0_43
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f474,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f20,f472]) ).

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

fof(f470,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f19,f468]) ).

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

fof(f466,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f18,f464]) ).

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

fof(f462,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f17,f460]) ).

fof(f460,plain,
    ( spl0_39
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f458,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f16,f456]) ).

fof(f456,plain,
    ( spl0_38
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

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

fof(f454,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f15,f452]) ).

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

fof(f450,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f14,f448]) ).

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

fof(f446,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f13,f444]) ).

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

fof(f442,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f12,f440]) ).

fof(f440,plain,
    ( spl0_34
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

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

fof(f438,plain,
    ( spl0_3
    | spl0_33 ),
    inference(avatar_split_clause,[],[f199,f436,f251]) ).

fof(f436,plain,
    ( spl0_33
  <=> ! [X6] :
        ( ~ ssItem(X6)
        | ~ lt(X6,sk5)
        | ~ memberP(sk7,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f199,axiom,
    ! [X6] :
      ( ~ ssItem(X6)
      | ~ memberP(sk7,X6)
      | ~ lt(X6,sk5)
      | nil = sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).

fof(f434,plain,
    ( spl0_3
    | spl0_32 ),
    inference(avatar_split_clause,[],[f198,f432,f251]) ).

fof(f432,plain,
    ( spl0_32
  <=> ! [X6] :
        ( ~ ssItem(X6)
        | ~ lt(sk5,X6)
        | ~ memberP(sk6,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f198,axiom,
    ! [X6] :
      ( ~ ssItem(X6)
      | ~ memberP(sk6,X6)
      | ~ lt(sk5,X6)
      | nil = sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).

fof(f430,plain,
    ( spl0_31
    | spl0_3 ),
    inference(avatar_split_clause,[],[f197,f251,f427]) ).

fof(f197,axiom,
    ( nil = sk4
    | sk4 = app(app(sk6,sk3),sk7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

fof(f425,plain,
    ~ spl0_30,
    inference(avatar_split_clause,[],[f11,f422]) ).

fof(f422,plain,
    ( spl0_30
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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

fof(f420,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f10,f417]) ).

fof(f417,plain,
    ( spl0_29
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

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

fof(f415,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f9,f412]) ).

fof(f412,plain,
    ( spl0_28
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f410,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f8,f407]) ).

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

fof(f405,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f7,f402]) ).

fof(f402,plain,
    ( spl0_26
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

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

fof(f400,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f6,f397]) ).

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

fof(f395,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f5,f392]) ).

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

fof(f390,plain,
    ( spl0_23
    | ~ spl0_3
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f384,f373,f251,f380]) ).

fof(f384,plain,
    ( totalorderedP(sk4)
    | ~ spl0_3
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f375,f253]) ).

fof(f383,plain,
    ( spl0_23
    | ~ spl0_6
    | ~ spl0_7
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f378,f373,f271,f265,f380]) ).

fof(f378,plain,
    ( totalorderedP(sk4)
    | ~ spl0_6
    | ~ spl0_7
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f377,f272]) ).

fof(f272,plain,
    ( sk3 = sk4
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f377,plain,
    ( totalorderedP(sk3)
    | ~ spl0_6
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f375,f267]) ).

fof(f376,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f4,f373]) ).

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

fof(f370,plain,
    ( ~ spl0_21
    | ~ spl0_6
    | ~ spl0_7
    | spl0_13 ),
    inference(avatar_split_clause,[],[f352,f305,f271,f265,f367]) ).

fof(f367,plain,
    ( spl0_21
  <=> sk4 = cons(sk5,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f352,plain,
    ( sk4 != cons(sk5,sk3)
    | ~ spl0_6
    | ~ spl0_7
    | spl0_13 ),
    inference(forward_demodulation,[],[f346,f267]) ).

fof(f346,plain,
    ( sk4 != cons(sk5,nil)
    | ~ spl0_7
    | spl0_13 ),
    inference(forward_demodulation,[],[f306,f272]) ).

fof(f306,plain,
    ( sk3 != cons(sk5,nil)
    | spl0_13 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f364,plain,
    ( ~ spl0_20
    | ~ spl0_6
    | spl0_13 ),
    inference(avatar_split_clause,[],[f349,f305,f265,f361]) ).

fof(f361,plain,
    ( spl0_20
  <=> sk3 = cons(sk5,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f349,plain,
    ( sk3 != cons(sk5,sk3)
    | ~ spl0_6
    | spl0_13 ),
    inference(forward_demodulation,[],[f306,f267]) ).

fof(f357,plain,
    ( spl0_3
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f347,f271,f265,f251]) ).

fof(f347,plain,
    ( nil = sk4
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f267,f272]) ).

fof(f351,plain,
    ( spl0_3
    | spl0_8 ),
    inference(avatar_split_clause,[],[f195,f276,f251]) ).

fof(f195,axiom,
    ( ssList(sk7)
    | nil = sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

fof(f348,plain,
    ( spl0_3
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f347,f271,f265,f251]) ).

fof(f345,plain,
    ( spl0_19
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f340,f336,f251,f342]) ).

fof(f342,plain,
    ( spl0_19
  <=> strictorderedP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f340,plain,
    ( strictorderedP(sk4)
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f338,f253]) ).

fof(f339,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f3,f336]) ).

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

fof(f334,plain,
    ( spl0_17
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f329,f325,f251,f331]) ).

fof(f331,plain,
    ( spl0_17
  <=> duplicatefreeP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f325,plain,
    ( spl0_16
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f329,plain,
    ( duplicatefreeP(sk4)
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(forward_demodulation,[],[f327,f253]) ).

fof(f327,plain,
    ( duplicatefreeP(nil)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f325]) ).

fof(f328,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f2,f325]) ).

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

fof(f322,plain,
    ( spl0_11
    | ~ spl0_3
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f321,f317,f251,f295]) ).

fof(f295,plain,
    ( spl0_11
  <=> equalelemsP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f321,plain,
    ( equalelemsP(sk4)
    | ~ spl0_3
    | ~ spl0_15 ),
    inference(forward_demodulation,[],[f319,f253]) ).

fof(f320,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f1,f317]) ).

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

fof(f315,plain,
    ( ~ spl0_14
    | ~ spl0_3
    | ~ spl0_7
    | spl0_13 ),
    inference(avatar_split_clause,[],[f310,f305,f271,f251,f312]) ).

fof(f312,plain,
    ( spl0_14
  <=> sk4 = cons(sk5,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f310,plain,
    ( sk4 != cons(sk5,sk4)
    | ~ spl0_3
    | ~ spl0_7
    | spl0_13 ),
    inference(forward_demodulation,[],[f309,f272]) ).

fof(f309,plain,
    ( sk3 != cons(sk5,sk4)
    | ~ spl0_3
    | spl0_13 ),
    inference(forward_demodulation,[],[f306,f253]) ).

fof(f308,plain,
    ( spl0_13
    | spl0_6 ),
    inference(avatar_split_clause,[],[f202,f265,f305]) ).

fof(f202,axiom,
    ( nil = sk3
    | sk3 = cons(sk5,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).

fof(f303,plain,
    ( ~ spl0_12
    | ~ spl0_7
    | spl0_9 ),
    inference(avatar_split_clause,[],[f293,f284,f271,f300]) ).

fof(f293,plain,
    ( ~ segmentP(sk4,sk4)
    | ~ spl0_7
    | spl0_9 ),
    inference(forward_demodulation,[],[f286,f272]) ).

fof(f286,plain,
    ( ~ segmentP(sk4,sk3)
    | spl0_9 ),
    inference(avatar_component_clause,[],[f284]) ).

fof(f298,plain,
    ( ~ spl0_11
    | ~ spl0_7
    | spl0_10 ),
    inference(avatar_split_clause,[],[f292,f288,f271,f295]) ).

fof(f292,plain,
    ( ~ equalelemsP(sk4)
    | ~ spl0_7
    | spl0_10 ),
    inference(forward_demodulation,[],[f290,f272]) ).

fof(f290,plain,
    ( ~ equalelemsP(sk3)
    | spl0_10 ),
    inference(avatar_component_clause,[],[f288]) ).

fof(f291,plain,
    ( ~ spl0_9
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f209,f288,f284]) ).

fof(f209,plain,
    ( ~ equalelemsP(sk3)
    | ~ segmentP(sk4,sk3) ),
    inference(definition_unfolding,[],[f206,f191,f190,f191]) ).

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

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

fof(f206,axiom,
    ( ~ equalelemsP(sk1)
    | ~ segmentP(sk2,sk1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).

fof(f281,plain,
    ( spl0_7
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f280,f265,f251,f271]) ).

fof(f280,plain,
    ( sk3 = sk4
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f267,f253]) ).

fof(f279,plain,
    ( spl0_6
    | spl0_8 ),
    inference(avatar_split_clause,[],[f201,f276,f265]) ).

fof(f201,axiom,
    ( ssList(sk7)
    | nil = sk3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).

fof(f274,plain,
    ( ~ spl0_7
    | ~ spl0_3
    | spl0_6 ),
    inference(avatar_split_clause,[],[f269,f265,f251,f271]) ).

fof(f269,plain,
    ( sk3 != sk4
    | ~ spl0_3
    | spl0_6 ),
    inference(forward_demodulation,[],[f266,f253]) ).

fof(f266,plain,
    ( nil != sk3
    | spl0_6 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f268,plain,
    ( spl0_6
    | spl0_5 ),
    inference(avatar_split_clause,[],[f200,f260,f265]) ).

fof(f200,axiom,
    ( ssList(sk6)
    | nil = sk3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).

fof(f263,plain,
    ( spl0_3
    | spl0_5 ),
    inference(avatar_split_clause,[],[f194,f260,f251]) ).

fof(f194,axiom,
    ( ssList(sk6)
    | nil = sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

fof(f258,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f192,f255,f251]) ).

fof(f192,axiom,
    ( ssItem(sk5)
    | nil = sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

fof(f249,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f208,f246]) ).

fof(f208,plain,
    ssList(sk3),
    inference(definition_unfolding,[],[f186,f191]) ).

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

fof(f244,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f207,f241]) ).

fof(f207,plain,
    ssList(sk4),
    inference(definition_unfolding,[],[f187,f190]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWC330-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n002.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 20:25:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (7562)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (7565)WARNING: value z3 for option sas not known
% 0.15/0.38  % (7563)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (7564)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  % (7565)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  % (7566)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (7567)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  % (7568)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)
% 0.15/0.38  % (7569)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)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.40  TRYING [3]
% 0.21/0.43  TRYING [1]
% 0.21/0.44  TRYING [2]
% 0.21/0.45  TRYING [4]
% 0.21/0.46  TRYING [1]
% 0.21/0.46  TRYING [2]
% 0.21/0.47  TRYING [3]
% 0.21/0.49  % (7567)First to succeed.
% 0.21/0.49  % (7567)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7562"
% 0.21/0.50  % (7567)Refutation found. Thanks to Tanya!
% 0.21/0.50  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50  % (7567)------------------------------
% 0.21/0.50  % (7567)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.50  % (7567)Termination reason: Refutation
% 0.21/0.50  
% 0.21/0.50  % (7567)Memory used [KB]: 3518
% 0.21/0.50  % (7567)Time elapsed: 0.119 s
% 0.21/0.50  % (7567)Instructions burned: 240 (million)
% 0.21/0.50  % (7562)Success in time 0.144 s
%------------------------------------------------------------------------------