TSTP Solution File: SWC413-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC413-1 : 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 : n013.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 10:26:56 EDT 2024

% Result   : Unsatisfiable 0.21s 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  416
% Syntax   : Number of formulae    :  713 ( 235 unt;   0 def)
%            Number of atoms       : 2028 ( 234 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 2348 (1033   ~;1107   |;   0   &)
%                                         ( 208 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  229 ( 227 usr; 209 prp; 0-2 aty)
%            Number of functors    :   62 (  62 usr;  16 con; 0-2 aty)
%            Number of variables   :  715 ( 715   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2415,plain,
    $false,
    inference(avatar_sat_refutation,[],[f296,f301,f310,f315,f320,f325,f330,f335,f340,f345,f350,f355,f360,f365,f370,f375,f380,f385,f390,f394,f398,f402,f406,f410,f414,f418,f422,f426,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,f539,f548,f552,f556,f560,f564,f568,f572,f576,f581,f587,f591,f595,f599,f603,f607,f608,f609,f610,f611,f619,f626,f632,f638,f642,f646,f647,f648,f649,f653,f657,f661,f665,f669,f673,f677,f681,f685,f689,f696,f698,f736,f740,f744,f815,f819,f832,f836,f840,f844,f848,f852,f856,f864,f890,f894,f898,f902,f907,f911,f915,f919,f923,f927,f931,f935,f939,f944,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f992,f996,f1062,f1066,f1070,f1074,f1166,f1170,f1174,f1178,f1182,f1186,f1190,f1194,f1198,f1202,f1206,f1244,f1276,f1280,f1284,f1288,f1293,f1297,f1301,f1305,f1309,f1380,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1425,f1429,f1433,f1464,f1472,f1476,f1480,f1484,f1548,f1552,f1556,f1560,f1564,f1568,f1572,f1576,f1676,f1694,f1698,f1702,f1706,f1710,f1714,f1719,f1723,f1766,f1770,f1775,f1797,f1801,f1805,f1809,f1813,f1926,f2002,f2008,f2014,f2019,f2023,f2047,f2051,f2055,f2221,f2226,f2231,f2246,f2261,f2266,f2272,f2284,f2310,f2354,f2383,f2387,f2393,f2414]) ).

fof(f2414,plain,
    ( spl0_74
    | spl0_66 ),
    inference(avatar_split_clause,[],[f204,f574,f616]) ).

fof(f616,plain,
    ( spl0_74
  <=> sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f574,plain,
    ( spl0_66
  <=> ! [X6,X8,X7] :
        ( ~ ssList(X8)
        | ~ ssItem(X6)
        | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8)
        | ~ ssItem(X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f204,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8)
      | sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).

fof(f2393,plain,
    ( spl0_208
    | ~ spl0_3
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f1015,f946,f303,f2391]) ).

fof(f2391,plain,
    ( spl0_208
  <=> ! [X0] :
        ( ~ ssList(X0)
        | tl(cons(sk11,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f303,plain,
    ( spl0_3
  <=> ssItem(sk11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f946,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1015,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | tl(cons(sk11,X0)) = X0 )
    | ~ spl0_3
    | ~ spl0_119 ),
    inference(resolution,[],[f947,f305]) ).

fof(f305,plain,
    ( ssItem(sk11)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f303]) ).

fof(f947,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f946]) ).

fof(f2387,plain,
    ( spl0_75
    | spl0_66 ),
    inference(avatar_split_clause,[],[f205,f574,f623]) ).

fof(f623,plain,
    ( spl0_75
  <=> sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f205,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8)
      | sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).

fof(f2383,plain,
    ( spl0_66
    | spl0_96 ),
    inference(avatar_split_clause,[],[f261,f817,f574]) ).

fof(f817,plain,
    ( spl0_96
  <=> ! [X6,X8,X7] :
        ( ~ ssList(X8)
        | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8)
        | ~ ssItem(X6)
        | ~ ssItem(X7)
        | sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f261,plain,
    ! [X10,X11,X8,X6,X9,X7] :
      ( ~ ssList(X8)
      | ~ ssList(X11)
      | ~ ssItem(X6)
      | ~ ssItem(X10)
      | ~ ssItem(X7)
      | ~ ssItem(X9)
      | sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8)
      | sk4 != app(app(cons(X9,nil),cons(X10,nil)),X11)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    inference(definition_unfolding,[],[f192,f191,f190]) ).

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

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

fof(f192,axiom,
    ! [X10,X11,X8,X6,X9,X7] :
      ( ~ ssList(X8)
      | ~ ssList(X11)
      | ~ ssItem(X6)
      | ~ ssItem(X10)
      | ~ ssItem(X7)
      | ~ ssItem(X9)
      | sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8)
      | sk4 != app(app(cons(X9,nil),cons(X10,nil)),X11)
      | sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

fof(f2354,plain,
    ( spl0_58
    | spl0_9 ),
    inference(avatar_split_clause,[],[f249,f332,f541]) ).

fof(f541,plain,
    ( spl0_58
  <=> sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f332,plain,
    ( spl0_9
  <=> ssItem(sk8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f249,plain,
    ( ssItem(sk8)
    | sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    inference(definition_unfolding,[],[f229,f190]) ).

fof(f229,axiom,
    ( ssItem(sk8)
    | sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_44) ).

fof(f2310,plain,
    ( spl0_74
    | spl0_8 ),
    inference(avatar_split_clause,[],[f237,f327,f616]) ).

fof(f327,plain,
    ( spl0_8
  <=> ssList(sk13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f237,axiom,
    ( ssList(sk13)
    | sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_52) ).

fof(f2284,plain,
    ( spl0_58
    | spl0_74 ),
    inference(avatar_split_clause,[],[f254,f616,f541]) ).

fof(f254,plain,
    ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
    | sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    inference(definition_unfolding,[],[f240,f190]) ).

fof(f240,axiom,
    ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
    | sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_55) ).

fof(f2272,plain,
    ( spl0_3
    | spl0_67 ),
    inference(avatar_split_clause,[],[f223,f578,f303]) ).

fof(f578,plain,
    ( spl0_67
  <=> ssItem(sk9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f223,axiom,
    ( ssItem(sk9)
    | ssItem(sk11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_38) ).

fof(f2266,plain,
    ( spl0_74
    | spl0_3 ),
    inference(avatar_split_clause,[],[f225,f303,f616]) ).

fof(f225,axiom,
    ( ssItem(sk11)
    | sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_40) ).

fof(f2261,plain,
    ( spl0_3
    | spl0_9 ),
    inference(avatar_split_clause,[],[f222,f332,f303]) ).

fof(f222,axiom,
    ( ssItem(sk8)
    | ssItem(sk11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_37) ).

fof(f2246,plain,
    ( spl0_3
    | spl0_59 ),
    inference(avatar_split_clause,[],[f224,f545,f303]) ).

fof(f545,plain,
    ( spl0_59
  <=> ssList(sk10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f224,axiom,
    ( ssList(sk10)
    | ssItem(sk11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_39) ).

fof(f2231,plain,
    ( spl0_8
    | spl0_59 ),
    inference(avatar_split_clause,[],[f236,f545,f327]) ).

fof(f236,axiom,
    ( ssList(sk10)
    | ssList(sk13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_51) ).

fof(f2226,plain,
    ( spl0_59
    | spl0_66 ),
    inference(avatar_split_clause,[],[f203,f574,f545]) ).

fof(f203,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | ssList(sk10)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).

fof(f2221,plain,
    ( ~ spl0_67
    | ~ spl0_9
    | ~ spl0_59
    | ~ spl0_74
    | ~ spl0_75
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f828,f817,f623,f616,f545,f332,f578]) ).

fof(f828,plain,
    ( ~ ssList(sk10)
    | ~ ssItem(sk8)
    | ~ ssItem(sk9)
    | ~ spl0_74
    | ~ spl0_75
    | ~ spl0_96 ),
    inference(trivial_inequality_removal,[],[f827]) ).

fof(f827,plain,
    ( sk3 != sk3
    | ~ ssList(sk10)
    | ~ ssItem(sk8)
    | ~ ssItem(sk9)
    | ~ spl0_74
    | ~ spl0_75
    | ~ spl0_96 ),
    inference(forward_demodulation,[],[f824,f625]) ).

fof(f625,plain,
    ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f623]) ).

fof(f824,plain,
    ( ~ ssList(sk10)
    | ~ ssItem(sk8)
    | ~ ssItem(sk9)
    | sk3 != app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
    | ~ spl0_74
    | ~ spl0_96 ),
    inference(trivial_inequality_removal,[],[f822]) ).

fof(f822,plain,
    ( sk4 != sk4
    | ~ ssList(sk10)
    | ~ ssItem(sk8)
    | ~ ssItem(sk9)
    | sk3 != app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
    | ~ spl0_74
    | ~ spl0_96 ),
    inference(superposition,[],[f818,f618]) ).

fof(f618,plain,
    ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f616]) ).

fof(f818,plain,
    ( ! [X8,X6,X7] :
        ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8)
        | ~ ssList(X8)
        | ~ ssItem(X6)
        | ~ ssItem(X7)
        | sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f817]) ).

fof(f2055,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f285,f2053]) ).

fof(f2053,plain,
    ( spl0_207
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X4)
        | ~ ssList(X2)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssItem(X3)
        | leq(X1,X3)
        | leq(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f285,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | leq(X1,X3)
      | leq(X3,X1) ),
    inference(equality_resolution,[],[f184]) ).

fof(f184,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ totalorderP(X5)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X5)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | leq(X1,X3)
      | leq(X3,X1)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause184) ).

fof(f2051,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f284,f2049]) ).

fof(f2049,plain,
    ( spl0_206
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X4)
        | ~ ssList(X2)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssItem(X3)
        | lt(X1,X3)
        | lt(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f284,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | lt(X1,X3)
      | lt(X3,X1) ),
    inference(equality_resolution,[],[f183]) ).

fof(f183,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ strictorderP(X5)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X5)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | lt(X1,X3)
      | lt(X3,X1)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause183) ).

fof(f2047,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f283,f2045]) ).

fof(f2045,plain,
    ( spl0_205
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
        | ~ ssList(X4)
        | ~ ssList(X3)
        | ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X1,X0)
        | ~ leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f283,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
      | ~ ssList(X4)
      | ~ ssList(X3)
      | ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X0)
      | ~ leq(X0,X1) ),
    inference(equality_resolution,[],[f185]) ).

fof(f185,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ cyclefreeP(X5)
      | ~ ssList(X4)
      | ~ ssList(X3)
      | ~ ssList(X5)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X1,X0)
      | ~ leq(X0,X1)
      | app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).

fof(f2023,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f282,f2021]) ).

fof(f2021,plain,
    ( spl0_204
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X4)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssItem(X3)
        | leq(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f282,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | leq(X1,X3) ),
    inference(equality_resolution,[],[f182]) ).

fof(f182,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ totalorderedP(X5)
      | ~ ssList(X5)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | leq(X1,X3)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause182) ).

fof(f2019,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f281,f2017]) ).

fof(f2017,plain,
    ( spl0_203
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
        | ~ ssList(X4)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssItem(X3)
        | lt(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f281,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | lt(X1,X3) ),
    inference(equality_resolution,[],[f181]) ).

fof(f181,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ strictorderedP(X5)
      | ~ ssList(X5)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X3)
      | lt(X1,X3)
      | app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause181) ).

fof(f2014,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f278,f2012]) ).

fof(f2012,plain,
    ( spl0_202
  <=> ! [X0,X3,X2,X1] :
        ( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
        | ~ ssList(X3)
        | ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssItem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f278,plain,
    ! [X2,X3,X0,X1] :
      ( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X3)
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f179]) ).

fof(f179,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ duplicatefreeP(X4)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).

fof(f2008,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f280,f2006]) ).

fof(f2006,plain,
    ( spl0_201
  <=> ! [X0,X3,X2,X1] :
        ( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
        | ~ ssList(X3)
        | ~ ssList(app(X0,cons(X1,cons(X2,X3))))
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssItem(X2)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f280,plain,
    ! [X2,X3,X0,X1] :
      ( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
      | ~ ssList(X3)
      | ~ ssList(app(X0,cons(X1,cons(X2,X3))))
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | X1 = X2 ),
    inference(equality_resolution,[],[f180]) ).

fof(f180,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ equalelemsP(X4)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | X1 = X2
      | app(X0,cons(X1,cons(X2,X3))) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause180) ).

fof(f2002,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f177,f2000]) ).

fof(f2000,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause177) ).

fof(f1926,plain,
    ( spl0_199
    | ~ spl0_59
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f810,f742,f545,f1923]) ).

fof(f1923,plain,
    ( spl0_199
  <=> sk10 = app(nil,sk10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f742,plain,
    ( spl0_94
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f810,plain,
    ( sk10 = app(nil,sk10)
    | ~ spl0_59
    | ~ spl0_94 ),
    inference(resolution,[],[f743,f547]) ).

fof(f547,plain,
    ( ssList(sk10)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f545]) ).

fof(f743,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f742]) ).

fof(f1813,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f167,f1811]) ).

fof(f1811,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause167) ).

fof(f1809,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f166,f1807]) ).

fof(f1807,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause166) ).

fof(f1805,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f165,f1803]) ).

fof(f1803,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause165) ).

fof(f1801,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f164,f1799]) ).

fof(f1799,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause164) ).

fof(f1797,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f163,f1795]) ).

fof(f1795,plain,
    ( spl0_194
  <=> ! [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_194])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause163) ).

fof(f1775,plain,
    ( spl0_193
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f809,f742,f322,f1772]) ).

fof(f1772,plain,
    ( spl0_193
  <=> sk7 = app(nil,sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f322,plain,
    ( spl0_7
  <=> ssList(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f809,plain,
    ( sk7 = app(nil,sk7)
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(resolution,[],[f743,f324]) ).

fof(f324,plain,
    ( ssList(sk7)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f1770,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f277,f1768]) ).

fof(f1768,plain,
    ( spl0_192
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(app(X0,cons(X1,X2)))
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | memberP(app(X0,cons(X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f277,plain,
    ! [X2,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(app(X0,cons(X1,X2)))
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | memberP(app(X0,cons(X1,X2)),X1) ),
    inference(equality_resolution,[],[f175]) ).

fof(f175,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X3)
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | memberP(X3,X1)
      | app(X0,cons(X1,X2)) != X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).

fof(f1766,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f276,f1764]) ).

fof(f1764,plain,
    ( spl0_191
  <=> ! [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_191])]) ).

fof(f276,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/sandbox2/benchmark/theBenchmark.p',clause173) ).

fof(f1723,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f176,f1721]) ).

fof(f1721,plain,
    ( spl0_190
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssList(X3)
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ~ ssItem(X2)
        | X0 = X2
        | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f176,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X3)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | X0 = X2
      | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause176) ).

fof(f1719,plain,
    ( spl0_189
    | ~ spl0_8
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f808,f742,f327,f1716]) ).

fof(f1716,plain,
    ( spl0_189
  <=> sk13 = app(nil,sk13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f808,plain,
    ( sk13 = app(nil,sk13)
    | ~ spl0_8
    | ~ spl0_94 ),
    inference(resolution,[],[f743,f329]) ).

fof(f329,plain,
    ( ssList(sk13)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f1714,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f174,f1712]) ).

fof(f1712,plain,
    ( spl0_188
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssList(X3)
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ~ ssItem(X2)
        | frontsegP(X1,X3)
        | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f174,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X3)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | frontsegP(X1,X3)
      | ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).

fof(f1710,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f172,f1708]) ).

fof(f1708,plain,
    ( spl0_187
  <=> ! [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_187])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause172) ).

fof(f1706,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f171,f1704]) ).

fof(f1704,plain,
    ( spl0_186
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X3)
        | ~ ssItem(X0)
        | ~ ssItem(X2)
        | X1 = X3
        | cons(X0,X1) != cons(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f171,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | X1 = X3
      | cons(X0,X1) != cons(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).

fof(f1702,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f170,f1700]) ).

fof(f1700,plain,
    ( spl0_185
  <=> ! [X0,X3,X2,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X3)
        | ~ ssItem(X0)
        | ~ ssItem(X2)
        | X0 = X2
        | cons(X0,X1) != cons(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f170,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssItem(X0)
      | ~ ssItem(X2)
      | X0 = X2
      | cons(X0,X1) != cons(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).

fof(f1698,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f169,f1696]) ).

fof(f1696,plain,
    ( spl0_184
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ memberP(X0,X1)
        | app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f169,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ memberP(X0,X1)
      | app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause169) ).

fof(f1694,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f168,f1692]) ).

fof(f1692,plain,
    ( spl0_183
  <=> ! [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_183])]) ).

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/sandbox2/benchmark/theBenchmark.p',clause168) ).

fof(f1676,plain,
    ( spl0_182
    | ~ spl0_1
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f807,f742,f293,f1673]) ).

fof(f1673,plain,
    ( spl0_182
  <=> sk4 = app(nil,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f293,plain,
    ( spl0_1
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f807,plain,
    ( sk4 = app(nil,sk4)
    | ~ spl0_1
    | ~ spl0_94 ),
    inference(resolution,[],[f743,f295]) ).

fof(f295,plain,
    ( ssList(sk4)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f293]) ).

fof(f1576,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f161,f1574]) ).

fof(f1574,plain,
    ( spl0_181
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | ~ ssItem(X2)
        | X0 = X2
        | memberP(X1,X2)
        | ~ memberP(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

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

fof(f1572,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f160,f1570]) ).

fof(f1570,plain,
    ( spl0_180
  <=> ! [X0,X1] :
        ( ~ strictorderedP(X1)
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | nil = X1
        | ~ lt(X0,hd(X1))
        | strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

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

fof(f1568,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f159,f1566]) ).

fof(f1566,plain,
    ( spl0_179
  <=> ! [X0,X1] :
        ( ~ totalorderedP(X1)
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | nil = X1
        | ~ leq(X0,hd(X1))
        | totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

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

fof(f1564,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f158,f1562]) ).

fof(f1562,plain,
    ( spl0_178
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ ssItem(X2)
        | memberP(X1,X2)
        | memberP(X0,X2)
        | ~ memberP(app(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

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

fof(f1560,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f157,f1558]) ).

fof(f1558,plain,
    ( spl0_177
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssItem(X0)
        | cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

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

fof(f1556,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f149,f1554]) ).

fof(f1554,plain,
    ( spl0_176
  <=> ! [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_176])]) ).

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

fof(f1552,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f142,f1550]) ).

fof(f1550,plain,
    ( spl0_175
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

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

fof(f1548,plain,
    ( spl0_174
    | ~ spl0_2
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f806,f742,f298,f1545]) ).

fof(f1545,plain,
    ( spl0_174
  <=> sk3 = app(nil,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f298,plain,
    ( spl0_2
  <=> ssList(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f806,plain,
    ( sk3 = app(nil,sk3)
    | ~ spl0_2
    | ~ spl0_94 ),
    inference(resolution,[],[f743,f300]) ).

fof(f300,plain,
    ( ssList(sk3)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f298]) ).

fof(f1484,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f286,f1482]) ).

fof(f1482,plain,
    ( spl0_173
  <=> ! [X0,X1,X3] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ ssItem(X3)
        | ~ frontsegP(X0,X1)
        | frontsegP(cons(X3,X0),cons(X3,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f286,plain,
    ! [X3,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssItem(X3)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(duplicate_literal_removal,[],[f279]) ).

fof(f279,plain,
    ! [X3,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssItem(X3)
      | ~ ssItem(X3)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(equality_resolution,[],[f178]) ).

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

fof(f1480,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f151,f1478]) ).

fof(f1478,plain,
    ( spl0_172
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | X0 = X2
        | app(X0,X1) != app(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

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

fof(f1476,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f150,f1474]) ).

fof(f1474,plain,
    ( spl0_171
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | X1 = X2
        | app(X0,X1) != app(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

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

fof(f1472,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f133,f1470]) ).

fof(f1470,plain,
    ( spl0_170
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

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

fof(f1464,plain,
    ( spl0_169
    | ~ spl0_59
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f777,f738,f545,f1461]) ).

fof(f1461,plain,
    ( spl0_169
  <=> sk10 = app(sk10,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f738,plain,
    ( spl0_93
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f777,plain,
    ( sk10 = app(sk10,nil)
    | ~ spl0_59
    | ~ spl0_93 ),
    inference(resolution,[],[f739,f547]) ).

fof(f739,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f738]) ).

fof(f1433,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f156,f1431]) ).

fof(f1431,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

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

fof(f1429,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f155,f1427]) ).

fof(f1427,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

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

fof(f1425,plain,
    ( spl0_166
    | ~ spl0_7
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f776,f738,f322,f1422]) ).

fof(f1422,plain,
    ( spl0_166
  <=> sk7 = app(sk7,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f776,plain,
    ( sk7 = app(sk7,nil)
    | ~ spl0_7
    | ~ spl0_93 ),
    inference(resolution,[],[f739,f324]) ).

fof(f1420,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f154,f1418]) ).

fof(f1418,plain,
    ( spl0_165
  <=> ! [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_165])]) ).

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

fof(f1416,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f153,f1414]) ).

fof(f1414,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

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

fof(f1412,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f152,f1410]) ).

fof(f1410,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

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

fof(f1408,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f148,f1406]) ).

fof(f1406,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

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

fof(f1404,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f147,f1402]) ).

fof(f1402,plain,
    ( spl0_161
  <=> ! [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_161])]) ).

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

fof(f1400,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f146,f1398]) ).

fof(f1398,plain,
    ( spl0_160
  <=> ! [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_160])]) ).

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

fof(f1396,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f135,f1394]) ).

fof(f1394,plain,
    ( spl0_159
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

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

fof(f1392,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f134,f1390]) ).

fof(f1390,plain,
    ( spl0_158
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

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

fof(f1380,plain,
    ( spl0_157
    | ~ spl0_8
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f775,f738,f327,f1377]) ).

fof(f1377,plain,
    ( spl0_157
  <=> sk13 = app(sk13,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f775,plain,
    ( sk13 = app(sk13,nil)
    | ~ spl0_8
    | ~ spl0_93 ),
    inference(resolution,[],[f739,f329]) ).

fof(f1309,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f141,f1307]) ).

fof(f1307,plain,
    ( spl0_156
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ memberP(X0,X1)
        | memberP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

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

fof(f1305,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f140,f1303]) ).

fof(f1303,plain,
    ( spl0_155
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ memberP(X0,X1)
        | memberP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

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

fof(f1301,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f139,f1299]) ).

fof(f1299,plain,
    ( spl0_154
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | ~ ssItem(X2)
        | ~ memberP(X0,X1)
        | memberP(cons(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

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

fof(f1297,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f137,f1295]) ).

fof(f1295,plain,
    ( spl0_153
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ frontsegP(X0,X1)
        | frontsegP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

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

fof(f1293,plain,
    ( spl0_152
    | ~ spl0_1
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f774,f738,f293,f1290]) ).

fof(f1290,plain,
    ( spl0_152
  <=> sk4 = app(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f774,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_1
    | ~ spl0_93 ),
    inference(resolution,[],[f739,f295]) ).

fof(f1288,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f136,f1286]) ).

fof(f1286,plain,
    ( spl0_151
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ rearsegP(X0,X1)
        | rearsegP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

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

fof(f1284,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f132,f1282]) ).

fof(f1282,plain,
    ( spl0_150
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | app(X1,skaf45(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

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

fof(f1280,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f131,f1278]) ).

fof(f1278,plain,
    ( spl0_149
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X0,X1)
        | app(skaf46(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

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

fof(f1276,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f123,f1274]) ).

fof(f1274,plain,
    ( spl0_148
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

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

fof(f1244,plain,
    ( spl0_147
    | ~ spl0_2
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f773,f738,f298,f1241]) ).

fof(f1241,plain,
    ( spl0_147
  <=> sk3 = app(sk3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f773,plain,
    ( sk3 = app(sk3,nil)
    | ~ spl0_2
    | ~ spl0_93 ),
    inference(resolution,[],[f739,f300]) ).

fof(f1206,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f272,f1204]) ).

fof(f1204,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | frontsegP(app(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f272,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(app(X0,X1))
      | ~ ssList(X0)
      | frontsegP(app(X0,X1),X0) ),
    inference(equality_resolution,[],[f144]) ).

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

fof(f1202,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f271,f1200]) ).

fof(f1200,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | rearsegP(app(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | rearsegP(app(X0,X1),X1) ),
    inference(equality_resolution,[],[f143]) ).

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

fof(f1198,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f130,f1196]) ).

fof(f1196,plain,
    ( spl0_144
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X1,X0)
        | ~ leq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

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

fof(f1194,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f129,f1192]) ).

fof(f1192,plain,
    ( spl0_143
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X1,X0)
        | ~ frontsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

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

fof(f1190,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f128,f1188]) ).

fof(f1188,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

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

fof(f1186,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f127,f1184]) ).

fof(f1184,plain,
    ( spl0_141
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

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

fof(f1182,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f126,f1180]) ).

fof(f1180,plain,
    ( spl0_140
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

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

fof(f1178,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f125,f1176]) ).

fof(f1176,plain,
    ( spl0_139
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

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

fof(f1174,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f124,f1172]) ).

fof(f1172,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

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

fof(f1170,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f121,f1168]) ).

fof(f1168,plain,
    ( spl0_137
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f121,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ leq(X0,X1)
      | X0 = X1
      | lt(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).

fof(f1166,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f120,f1164]) ).

fof(f1164,plain,
    ( spl0_136
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

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

fof(f1074,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f119,f1072]) ).

fof(f1072,plain,
    ( spl0_135
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

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

fof(f1070,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f118,f1068]) ).

fof(f1068,plain,
    ( spl0_134
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

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

fof(f1066,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f109,f1064]) ).

fof(f1064,plain,
    ( spl0_133
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

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

fof(f1062,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f104,f1060]) ).

fof(f1060,plain,
    ( spl0_132
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

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

fof(f996,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f266,f994]) ).

fof(f994,plain,
    ( spl0_131
  <=> ! [X0] :
        ( ~ ssList(cons(X0,nil))
        | ~ ssItem(X0)
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f266,plain,
    ! [X0] :
      ( ~ ssList(cons(X0,nil))
      | ~ ssItem(X0)
      | singletonP(cons(X0,nil)) ),
    inference(equality_resolution,[],[f116]) ).

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

fof(f992,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f114,f990]) ).

fof(f990,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

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

fof(f988,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f110,f986]) ).

fof(f986,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

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

fof(f984,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f108,f982]) ).

fof(f982,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

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

fof(f980,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f107,f978]) ).

fof(f978,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

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

fof(f976,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f106,f974]) ).

fof(f974,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

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

fof(f972,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f105,f970]) ).

fof(f970,plain,
    ( spl0_125
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

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

fof(f968,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f103,f966]) ).

fof(f966,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

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

fof(f964,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f102,f962]) ).

fof(f962,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

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

fof(f960,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f101,f958]) ).

fof(f958,plain,
    ( spl0_122
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

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

fof(f956,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f100,f954]) ).

fof(f954,plain,
    ( spl0_121
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

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

fof(f952,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f97,f950]) ).

fof(f950,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

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

fof(f948,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f96,f946]) ).

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

fof(f944,plain,
    ( spl0_118
    | ~ spl0_59
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f731,f694,f545,f941]) ).

fof(f941,plain,
    ( spl0_118
  <=> duplicatefreeP(sk10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f694,plain,
    ( spl0_91
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f731,plain,
    ( duplicatefreeP(sk10)
    | ~ spl0_59
    | ~ spl0_91 ),
    inference(resolution,[],[f695,f547]) ).

fof(f695,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f694]) ).

fof(f939,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f287,f937]) ).

fof(f937,plain,
    ( spl0_117
  <=> ! [X2,X1] :
        ( ~ ssList(X2)
        | ~ ssItem(X1)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f287,plain,
    ! [X2,X1] :
      ( ~ ssList(X2)
      | ~ ssItem(X1)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f275]) ).

fof(f275,plain,
    ! [X2,X1] :
      ( ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1)
      | memberP(cons(X1,X2),X1) ),
    inference(equality_resolution,[],[f138]) ).

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

fof(f935,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f99,f933]) ).

fof(f933,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

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

fof(f931,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f98,f929]) ).

fof(f929,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

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

fof(f927,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f95,f925]) ).

fof(f925,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

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

fof(f923,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f94,f921]) ).

fof(f921,plain,
    ( spl0_113
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

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

fof(f919,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f93,f917]) ).

fof(f917,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

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

fof(f915,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f92,f913]) ).

fof(f913,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

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

fof(f911,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f91,f909]) ).

fof(f909,plain,
    ( spl0_110
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

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

fof(f907,plain,
    ( spl0_109
    | ~ spl0_7
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f730,f694,f322,f904]) ).

fof(f904,plain,
    ( spl0_109
  <=> duplicatefreeP(sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f730,plain,
    ( duplicatefreeP(sk7)
    | ~ spl0_7
    | ~ spl0_91 ),
    inference(resolution,[],[f695,f324]) ).

fof(f902,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f90,f900]) ).

fof(f900,plain,
    ( spl0_108
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

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

fof(f898,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f89,f896]) ).

fof(f896,plain,
    ( spl0_107
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

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

fof(f894,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f88,f892]) ).

fof(f892,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

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

fof(f890,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f87,f888]) ).

fof(f888,plain,
    ( spl0_105
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

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

fof(f864,plain,
    ( spl0_104
    | ~ spl0_8
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f729,f694,f327,f861]) ).

fof(f861,plain,
    ( spl0_104
  <=> duplicatefreeP(sk13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f729,plain,
    ( duplicatefreeP(sk13)
    | ~ spl0_8
    | ~ spl0_91 ),
    inference(resolution,[],[f695,f329]) ).

fof(f856,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f86,f854]) ).

fof(f854,plain,
    ( spl0_103
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssItem(X0)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

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

fof(f852,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f85,f850]) ).

fof(f850,plain,
    ( spl0_102
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

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

fof(f848,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f84,f846]) ).

fof(f846,plain,
    ( spl0_101
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

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

fof(f844,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f82,f842]) ).

fof(f842,plain,
    ( spl0_100
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

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

fof(f840,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f80,f838]) ).

fof(f838,plain,
    ( spl0_99
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

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

fof(f836,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f78,f834]) ).

fof(f834,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssItem(hd(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f78,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssItem(hd(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).

fof(f832,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f75,f830]) ).

fof(f830,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

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

fof(f819,plain,
    ( spl0_6
    | spl0_96 ),
    inference(avatar_split_clause,[],[f258,f817,f317]) ).

fof(f317,plain,
    ( spl0_6
  <=> ssItem(sk12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f258,plain,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssItem(sk12)
      | sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    inference(definition_unfolding,[],[f194,f191,f190]) ).

fof(f194,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssItem(sk12)
      | sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8)
      | sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

fof(f815,plain,
    ( spl0_95
    | ~ spl0_1
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f728,f694,f293,f812]) ).

fof(f812,plain,
    ( spl0_95
  <=> duplicatefreeP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f728,plain,
    ( duplicatefreeP(sk4)
    | ~ spl0_1
    | ~ spl0_91 ),
    inference(resolution,[],[f695,f295]) ).

fof(f744,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f74,f742]) ).

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

fof(f740,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f73,f738]) ).

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

fof(f736,plain,
    ( spl0_92
    | ~ spl0_2
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f727,f694,f298,f733]) ).

fof(f733,plain,
    ( spl0_92
  <=> duplicatefreeP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f727,plain,
    ( duplicatefreeP(sk3)
    | ~ spl0_2
    | ~ spl0_91 ),
    inference(resolution,[],[f695,f300]) ).

fof(f698,plain,
    ( spl0_6
    | ~ spl0_90 ),
    inference(avatar_contradiction_clause,[],[f697]) ).

fof(f697,plain,
    ( $false
    | spl0_6
    | ~ spl0_90 ),
    inference(resolution,[],[f692,f318]) ).

fof(f318,plain,
    ( ~ ssItem(sk12)
    | spl0_6 ),
    inference(avatar_component_clause,[],[f317]) ).

fof(f692,plain,
    ( ! [X1] : ssItem(X1)
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f691]) ).

fof(f691,plain,
    ( spl0_90
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f696,plain,
    ( spl0_90
    | spl0_91 ),
    inference(avatar_split_clause,[],[f72,f694,f691]) ).

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

fof(f689,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f70,f687]) ).

fof(f687,plain,
    ( spl0_89
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

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

fof(f685,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f69,f683]) ).

fof(f683,plain,
    ( spl0_88
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

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

fof(f681,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f68,f679]) ).

fof(f679,plain,
    ( spl0_87
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

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

fof(f677,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f67,f675]) ).

fof(f675,plain,
    ( spl0_86
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

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

fof(f673,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f66,f671]) ).

fof(f671,plain,
    ( spl0_85
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

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

fof(f669,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f65,f667]) ).

fof(f667,plain,
    ( spl0_84
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | duplicatefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

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

fof(f665,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f64,f663]) ).

fof(f663,plain,
    ( spl0_83
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

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

fof(f661,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f291,f659]) ).

fof(f659,plain,
    ( spl0_82
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f291,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f265]) ).

fof(f265,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f115]) ).

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

fof(f657,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f290,f655]) ).

fof(f655,plain,
    ( spl0_81
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f290,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f269]) ).

fof(f269,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f117]) ).

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

fof(f653,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f71,f651]) ).

fof(f651,plain,
    ( spl0_80
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

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

fof(f649,plain,
    ( spl0_6
    | spl0_59 ),
    inference(avatar_split_clause,[],[f231,f545,f317]) ).

fof(f231,axiom,
    ( ssList(sk10)
    | ssItem(sk12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_46) ).

fof(f648,plain,
    ( spl0_6
    | spl0_9 ),
    inference(avatar_split_clause,[],[f227,f332,f317]) ).

fof(f227,axiom,
    ( ssItem(sk8)
    | ssItem(sk12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_42) ).

fof(f647,plain,
    ( ~ spl0_67
    | ~ spl0_59
    | ~ spl0_9
    | ~ spl0_66
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f621,f616,f574,f332,f545,f578]) ).

fof(f621,plain,
    ( ~ ssItem(sk8)
    | ~ ssList(sk10)
    | ~ ssItem(sk9)
    | ~ spl0_66
    | ~ spl0_74 ),
    inference(trivial_inequality_removal,[],[f620]) ).

fof(f620,plain,
    ( sk4 != sk4
    | ~ ssItem(sk8)
    | ~ ssList(sk10)
    | ~ ssItem(sk9)
    | ~ spl0_66
    | ~ spl0_74 ),
    inference(superposition,[],[f575,f618]) ).

fof(f575,plain,
    ( ! [X8,X6,X7] :
        ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8)
        | ~ ssItem(X6)
        | ~ ssList(X8)
        | ~ ssItem(X7) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f574]) ).

fof(f646,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f63,f644]) ).

fof(f644,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

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

fof(f642,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f62,f640]) ).

fof(f640,plain,
    ( spl0_78
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

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

fof(f638,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f61,f636]) ).

fof(f636,plain,
    ( spl0_77
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

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

fof(f632,plain,
    ( spl0_76
    | spl0_6 ),
    inference(avatar_split_clause,[],[f251,f317,f629]) ).

fof(f629,plain,
    ( spl0_76
  <=> sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f251,plain,
    ( ssItem(sk12)
    | sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
    inference(definition_unfolding,[],[f215,f190]) ).

fof(f215,axiom,
    ( ssItem(sk12)
    | sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_30) ).

fof(f626,plain,
    ( spl0_75
    | spl0_6 ),
    inference(avatar_split_clause,[],[f233,f317,f623]) ).

fof(f233,axiom,
    ( ssItem(sk12)
    | sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_48) ).

fof(f619,plain,
    ( spl0_74
    | spl0_6 ),
    inference(avatar_split_clause,[],[f232,f317,f616]) ).

fof(f232,axiom,
    ( ssItem(sk12)
    | sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_47) ).

fof(f611,plain,
    ( spl0_58
    | spl0_67 ),
    inference(avatar_split_clause,[],[f250,f578,f541]) ).

fof(f250,plain,
    ( ssItem(sk9)
    | sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    inference(definition_unfolding,[],[f235,f190]) ).

fof(f235,axiom,
    ( ssItem(sk9)
    | sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_50) ).

fof(f610,plain,
    ( spl0_67
    | spl0_8 ),
    inference(avatar_split_clause,[],[f234,f327,f578]) ).

fof(f234,axiom,
    ( ssList(sk13)
    | ssItem(sk9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_49) ).

fof(f609,plain,
    ( spl0_6
    | spl0_67 ),
    inference(avatar_split_clause,[],[f230,f578,f317]) ).

fof(f230,axiom,
    ( ssItem(sk9)
    | ssItem(sk12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_45) ).

fof(f608,plain,
    ( ~ spl0_6
    | ~ spl0_8
    | ~ spl0_3
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f583,f574,f541,f303,f327,f317]) ).

fof(f583,plain,
    ( ~ ssItem(sk11)
    | ~ ssList(sk13)
    | ~ ssItem(sk12)
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(trivial_inequality_removal,[],[f582]) ).

fof(f582,plain,
    ( sk4 != sk4
    | ~ ssItem(sk11)
    | ~ ssList(sk13)
    | ~ ssItem(sk12)
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(superposition,[],[f575,f543]) ).

fof(f543,plain,
    ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f541]) ).

fof(f607,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f60,f605]) ).

fof(f605,plain,
    ( spl0_73
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

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

fof(f603,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f59,f601]) ).

fof(f601,plain,
    ( spl0_72
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

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

fof(f599,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f58,f597]) ).

fof(f597,plain,
    ( spl0_71
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

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

fof(f595,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f57,f593]) ).

fof(f593,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

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

fof(f591,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f56,f589]) ).

fof(f589,plain,
    ( spl0_69
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

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

fof(f587,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f55,f585]) ).

fof(f585,plain,
    ( spl0_68
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

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

fof(f581,plain,
    ( spl0_67
    | spl0_66 ),
    inference(avatar_split_clause,[],[f202,f574,f578]) ).

fof(f202,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | ssItem(sk9)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).

fof(f576,plain,
    ( spl0_9
    | spl0_66 ),
    inference(avatar_split_clause,[],[f201,f574,f332]) ).

fof(f201,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X8)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | ssItem(sk8)
      | sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).

fof(f572,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f53,f570]) ).

fof(f570,plain,
    ( spl0_65
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

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

fof(f568,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f52,f566]) ).

fof(f566,plain,
    ( spl0_64
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

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

fof(f564,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f51,f562]) ).

fof(f562,plain,
    ( spl0_63
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

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

fof(f560,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f50,f558]) ).

fof(f558,plain,
    ( spl0_62
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

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

fof(f556,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f49,f554]) ).

fof(f554,plain,
    ( spl0_61
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

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

fof(f552,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f48,f550]) ).

fof(f550,plain,
    ( spl0_60
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

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

fof(f548,plain,
    ( spl0_58
    | spl0_59 ),
    inference(avatar_split_clause,[],[f245,f545,f541]) ).

fof(f245,plain,
    ( ssList(sk10)
    | sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    inference(definition_unfolding,[],[f239,f190]) ).

fof(f239,axiom,
    ( ssList(sk10)
    | sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_54) ).

fof(f539,plain,
    ~ spl0_57,
    inference(avatar_split_clause,[],[f54,f536]) ).

fof(f536,plain,
    ( spl0_57
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

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

fof(f534,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f47,f532]) ).

fof(f532,plain,
    ( spl0_56
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

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

fof(f530,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f46,f528]) ).

fof(f528,plain,
    ( spl0_55
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

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

fof(f526,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f45,f524]) ).

fof(f524,plain,
    ( spl0_54
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

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

fof(f522,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f44,f520]) ).

fof(f520,plain,
    ( spl0_53
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

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

fof(f518,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f43,f516]) ).

fof(f516,plain,
    ( spl0_52
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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

fof(f514,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f42,f512]) ).

fof(f512,plain,
    ( spl0_51
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

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

fof(f510,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f41,f508]) ).

fof(f508,plain,
    ( spl0_50
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

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

fof(f506,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f40,f504]) ).

fof(f504,plain,
    ( spl0_49
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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

fof(f502,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f39,f500]) ).

fof(f500,plain,
    ( spl0_48
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

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

fof(f498,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f38,f496]) ).

fof(f496,plain,
    ( spl0_47
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

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

fof(f494,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f37,f492]) ).

fof(f492,plain,
    ( spl0_46
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

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

fof(f490,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f36,f488]) ).

fof(f488,plain,
    ( spl0_45
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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

fof(f486,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f35,f484]) ).

fof(f484,plain,
    ( spl0_44
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

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

fof(f482,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f34,f480]) ).

fof(f480,plain,
    ( spl0_43
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f478,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f33,f476]) ).

fof(f476,plain,
    ( spl0_42
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

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

fof(f474,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f32,f472]) ).

fof(f472,plain,
    ( spl0_41
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

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

fof(f470,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f31,f468]) ).

fof(f468,plain,
    ( spl0_40
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

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

fof(f466,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f30,f464]) ).

fof(f464,plain,
    ( spl0_39
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f462,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f29,f460]) ).

fof(f460,plain,
    ( spl0_38
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

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

fof(f458,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f28,f456]) ).

fof(f456,plain,
    ( spl0_37
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

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

fof(f454,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f27,f452]) ).

fof(f452,plain,
    ( spl0_36
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

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

fof(f450,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f26,f448]) ).

fof(f448,plain,
    ( spl0_35
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

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

fof(f446,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f25,f444]) ).

fof(f444,plain,
    ( spl0_34
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

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

fof(f442,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f24,f440]) ).

fof(f440,plain,
    ( spl0_33
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

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

fof(f438,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f23,f436]) ).

fof(f436,plain,
    ( spl0_32
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

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

fof(f434,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f22,f432]) ).

fof(f432,plain,
    ( spl0_31
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

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

fof(f430,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f21,f428]) ).

fof(f428,plain,
    ( spl0_30
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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

fof(f426,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f20,f424]) ).

fof(f424,plain,
    ( spl0_29
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

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

fof(f422,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f19,f420]) ).

fof(f420,plain,
    ( spl0_28
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f418,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f18,f416]) ).

fof(f416,plain,
    ( spl0_27
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

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

fof(f414,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f17,f412]) ).

fof(f412,plain,
    ( spl0_26
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

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

fof(f410,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f16,f408]) ).

fof(f408,plain,
    ( spl0_25
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

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

fof(f406,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f15,f404]) ).

fof(f404,plain,
    ( spl0_24
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

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

fof(f402,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f14,f400]) ).

fof(f400,plain,
    ( spl0_23
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

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

fof(f398,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f13,f396]) ).

fof(f396,plain,
    ( spl0_22
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

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

fof(f394,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f12,f392]) ).

fof(f392,plain,
    ( spl0_21
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

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

fof(f390,plain,
    ~ spl0_20,
    inference(avatar_split_clause,[],[f11,f387]) ).

fof(f387,plain,
    ( spl0_20
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

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

fof(f385,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f10,f382]) ).

fof(f382,plain,
    ( spl0_19
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

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

fof(f380,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f9,f377]) ).

fof(f377,plain,
    ( spl0_18
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

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

fof(f375,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f8,f372]) ).

fof(f372,plain,
    ( spl0_17
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

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

fof(f370,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f7,f367]) ).

fof(f367,plain,
    ( spl0_16
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

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

fof(f365,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f6,f362]) ).

fof(f362,plain,
    ( spl0_15
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

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

fof(f360,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f5,f357]) ).

fof(f357,plain,
    ( spl0_14
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

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

fof(f355,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f4,f352]) ).

fof(f352,plain,
    ( spl0_13
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

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

fof(f350,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f3,f347]) ).

fof(f347,plain,
    ( spl0_12
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

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

fof(f345,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f2,f342]) ).

fof(f342,plain,
    ( spl0_11
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

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

fof(f340,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f1,f337]) ).

fof(f337,plain,
    ( spl0_10
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

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

fof(f335,plain,
    ( spl0_9
    | spl0_8 ),
    inference(avatar_split_clause,[],[f228,f327,f332]) ).

fof(f228,axiom,
    ( ssList(sk13)
    | ssItem(sk8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_43) ).

fof(f330,plain,
    ( spl0_8
    | spl0_7 ),
    inference(avatar_split_clause,[],[f218,f322,f327]) ).

fof(f218,axiom,
    ( ssList(sk7)
    | ssList(sk13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_33) ).

fof(f325,plain,
    ( spl0_6
    | spl0_7 ),
    inference(avatar_split_clause,[],[f214,f322,f317]) ).

fof(f214,axiom,
    ( ssList(sk7)
    | ssItem(sk12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_29) ).

fof(f320,plain,
    ( spl0_6
    | spl0_5 ),
    inference(avatar_split_clause,[],[f213,f312,f317]) ).

fof(f312,plain,
    ( spl0_5
  <=> ssItem(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f213,axiom,
    ( ssItem(sk6)
    | ssItem(sk12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_28) ).

fof(f315,plain,
    ( spl0_3
    | spl0_5 ),
    inference(avatar_split_clause,[],[f207,f312,f303]) ).

fof(f207,axiom,
    ( ssItem(sk6)
    | ssItem(sk11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).

fof(f310,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f206,f307,f303]) ).

fof(f307,plain,
    ( spl0_4
  <=> ssItem(sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f206,axiom,
    ( ssItem(sk5)
    | ssItem(sk11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).

fof(f301,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f242,f298]) ).

fof(f242,plain,
    ssList(sk3),
    inference(definition_unfolding,[],[f186,f191]) ).

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

fof(f296,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f189,f293]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC413-1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n013.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 20:33:53 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (27330)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (27333)WARNING: value z3 for option sas not known
% 0.21/0.38  % (27333)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38  % (27334)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (27332)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (27331)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (27335)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38  % (27336)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38  % (27337)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.40  TRYING [1]
% 0.21/0.40  TRYING [2]
% 0.21/0.42  TRYING [3]
% 0.21/0.46  % (27335)First to succeed.
% 0.21/0.47  % (27335)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27330"
% 0.21/0.47  % (27335)Refutation found. Thanks to Tanya!
% 0.21/0.47  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47  % (27335)------------------------------
% 0.21/0.47  % (27335)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.47  % (27335)Termination reason: Refutation
% 0.21/0.47  
% 0.21/0.47  % (27335)Memory used [KB]: 2484
% 0.21/0.47  % (27335)Time elapsed: 0.087 s
% 0.21/0.47  % (27335)Instructions burned: 149 (million)
% 0.21/0.47  % (27330)Success in time 0.102 s
%------------------------------------------------------------------------------