TSTP Solution File: SWC322-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC322-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Tue May 21 05:13:00 EDT 2024

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  380
% Syntax   : Number of formulae    :  759 ( 213 unt;   0 def)
%            Number of atoms       : 2175 ( 297 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 2560 (1144   ~;1202   |;   0   &)
%                                         ( 214 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  235 ( 233 usr; 215 prp; 0-2 aty)
%            Number of functors    :   55 (  55 usr;   9 con; 0-2 aty)
%            Number of variables   :  635 ( 635   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1863,plain,
    $false,
    inference(avatar_sat_refutation,[],[f249,f254,f263,f268,f274,f280,f287,f292,f299,f304,f311,f316,f323,f324,f334,f339,f344,f349,f354,f359,f364,f369,f374,f379,f383,f387,f391,f395,f399,f403,f407,f411,f415,f419,f423,f427,f431,f435,f439,f443,f447,f451,f455,f459,f463,f467,f471,f475,f479,f483,f487,f491,f495,f499,f503,f507,f511,f515,f519,f523,f528,f532,f536,f540,f544,f548,f552,f556,f561,f567,f571,f575,f579,f583,f587,f588,f590,f591,f596,f601,f602,f609,f630,f636,f641,f645,f649,f653,f657,f662,f666,f670,f676,f682,f688,f692,f696,f701,f705,f710,f714,f719,f724,f728,f733,f737,f742,f746,f751,f758,f794,f799,f836,f841,f878,f883,f890,f895,f899,f905,f912,f918,f925,f931,f938,f942,f953,f957,f961,f965,f969,f973,f977,f981,f985,f989,f994,f998,f1003,f1007,f1011,f1015,f1019,f1023,f1028,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1074,f1099,f1136,f1140,f1145,f1183,f1188,f1226,f1232,f1238,f1245,f1249,f1255,f1260,f1283,f1287,f1292,f1298,f1304,f1308,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1347,f1384,f1389,f1431,f1435,f1439,f1443,f1447,f1451,f1455,f1496,f1501,f1507,f1512,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1600,f1605,f1643,f1663,f1667,f1694,f1698,f1702,f1706,f1710,f1730,f1736,f1741,f1745,f1845,f1857,f1858,f1862]) ).

fof(f1862,plain,
    ( spl0_15
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f1860,f256,f331]) ).

fof(f331,plain,
    ( spl0_15
  <=> ssList(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f256,plain,
    ( spl0_3
  <=> nil = sk3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1860,plain,
    ( ssList(sk6)
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f1859]) ).

fof(f1859,plain,
    ( sk3 != sk3
    | ssList(sk6)
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f206,f257]) ).

fof(f257,plain,
    ( nil = sk3
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f206,plain,
    ( ssList(sk6)
    | nil != sk3 ),
    inference(definition_unfolding,[],[f199,f191]) ).

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

fof(f199,axiom,
    ( ssList(sk6)
    | nil != sk1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).

fof(f1858,plain,
    ( spl0_214
    | ~ spl0_3
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f1849,f376,f256,f1854]) ).

fof(f1854,plain,
    ( spl0_214
  <=> sk3 = app(cons(sk5,sk3),sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f376,plain,
    ( spl0_24
  <=> sk3 = app(cons(sk5,nil),sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f1849,plain,
    ( sk3 = app(cons(sk5,sk3),sk6)
    | ~ spl0_3
    | ~ spl0_24 ),
    inference(forward_demodulation,[],[f377,f257]) ).

fof(f377,plain,
    ( sk3 = app(cons(sk5,nil),sk6)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f1857,plain,
    ( ~ spl0_214
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f1848,f256,f1854]) ).

fof(f1848,plain,
    ( sk3 != app(cons(sk5,sk3),sk6)
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f1847]) ).

fof(f1847,plain,
    ( sk3 != sk3
    | sk3 != app(cons(sk5,sk3),sk6)
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f243,f257]) ).

fof(f243,plain,
    ( nil != sk3
    | sk3 != app(cons(sk5,sk3),sk6) ),
    inference(inner_rewriting,[],[f208]) ).

fof(f208,plain,
    ( nil != sk3
    | sk3 != app(cons(sk5,nil),sk6) ),
    inference(definition_unfolding,[],[f201,f191,f191]) ).

fof(f201,axiom,
    ( nil != sk1
    | sk1 != app(cons(sk5,nil),sk6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).

fof(f1845,plain,
    ( ~ spl0_78
    | ~ spl0_3
    | spl0_23 ),
    inference(avatar_split_clause,[],[f619,f371,f256,f633]) ).

fof(f633,plain,
    ( spl0_78
  <=> sk3 = app(sk6,cons(sk5,sk3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f371,plain,
    ( spl0_23
  <=> sk3 = app(sk6,cons(sk5,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f619,plain,
    ( sk3 != app(sk6,cons(sk5,sk3))
    | ~ spl0_3
    | spl0_23 ),
    inference(superposition,[],[f372,f257]) ).

fof(f372,plain,
    ( sk3 != app(sk6,cons(sk5,nil))
    | spl0_23 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f1745,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f161,f1743]) ).

fof(f1743,plain,
    ( spl0_213
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | X0 = X2
        | memberP(X1,X2)
        | ~ memberP(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

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

fof(f1741,plain,
    ( spl0_212
    | ~ spl0_3
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1737,f1734,f256,f1739]) ).

fof(f1739,plain,
    ( spl0_212
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ strictorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ lt(X0,hd(X1))
        | strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f1734,plain,
    ( spl0_211
  <=> ! [X0,X1] :
        ( ~ strictorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ lt(X0,hd(X1))
        | strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f1737,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ strictorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ lt(X0,hd(X1))
        | strictorderedP(cons(X0,X1)) )
    | ~ spl0_3
    | ~ spl0_211 ),
    inference(forward_demodulation,[],[f1735,f257]) ).

fof(f1735,plain,
    ( ! [X0,X1] :
        ( ~ strictorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ lt(X0,hd(X1))
        | strictorderedP(cons(X0,X1)) )
    | ~ spl0_211 ),
    inference(avatar_component_clause,[],[f1734]) ).

fof(f1736,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f160,f1734]) ).

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

fof(f1730,plain,
    ( spl0_210
    | ~ spl0_3
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1711,f1708,f256,f1728]) ).

fof(f1728,plain,
    ( spl0_210
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ totalorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ leq(X0,hd(X1))
        | totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f1708,plain,
    ( spl0_209
  <=> ! [X0,X1] :
        ( ~ totalorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ leq(X0,hd(X1))
        | totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f1711,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ totalorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ leq(X0,hd(X1))
        | totalorderedP(cons(X0,X1)) )
    | ~ spl0_3
    | ~ spl0_209 ),
    inference(forward_demodulation,[],[f1709,f257]) ).

fof(f1709,plain,
    ( ! [X0,X1] :
        ( ~ totalorderedP(X1)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ leq(X0,hd(X1))
        | totalorderedP(cons(X0,X1)) )
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f1708]) ).

fof(f1710,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f159,f1708]) ).

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

fof(f1706,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f158,f1704]) ).

fof(f1704,plain,
    ( spl0_208
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | memberP(X1,X2)
        | memberP(X0,X2)
        | ~ memberP(app(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

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

fof(f1702,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f157,f1700]) ).

fof(f1700,plain,
    ( spl0_207
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

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

fof(f1698,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f149,f1696]) ).

fof(f1696,plain,
    ( spl0_206
  <=> ! [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_206])]) ).

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(f1694,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f142,f1692]) ).

fof(f1692,plain,
    ( spl0_205
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

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(f1667,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f236,f1665]) ).

fof(f1665,plain,
    ( spl0_204
  <=> ! [X0,X1,X3] :
        ( ~ ssItem(X3)
        | ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | frontsegP(cons(X3,X0),cons(X3,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f236,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(duplicate_literal_removal,[],[f229]) ).

fof(f229,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(equality_resolution,[],[f178]) ).

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

fof(f1663,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f151,f1661]) ).

fof(f1661,plain,
    ( spl0_203
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | X0 = X2
        | app(X0,X1) != app(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

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(f1643,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f150,f1641]) ).

fof(f1641,plain,
    ( spl0_202
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | X1 = X2
        | app(X0,X1) != app(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

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(f1605,plain,
    ( spl0_201
    | ~ spl0_3
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1601,f1598,f256,f1603]) ).

fof(f1603,plain,
    ( spl0_201
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ ssList(X0)
        | ~ ssList(X1)
        | tl(app(X1,X0)) = app(tl(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1598,plain,
    ( spl0_200
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f1601,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssList(X0)
        | ~ ssList(X1)
        | tl(app(X1,X0)) = app(tl(X1),X0) )
    | ~ spl0_3
    | ~ spl0_200 ),
    inference(forward_demodulation,[],[f1599,f257]) ).

fof(f1599,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | tl(app(X1,X0)) = app(tl(X1),X0) )
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f1598]) ).

fof(f1600,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f133,f1598]) ).

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(f1553,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f156,f1551]) ).

fof(f1551,plain,
    ( spl0_199
  <=> ! [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_199])]) ).

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(f1549,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f155,f1547]) ).

fof(f1547,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

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(f1545,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f154,f1543]) ).

fof(f1543,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

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(f1541,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f153,f1539]) ).

fof(f1539,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

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(f1537,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f152,f1535]) ).

fof(f1535,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

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(f1533,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f148,f1531]) ).

fof(f1531,plain,
    ( spl0_194
  <=> ! [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_194])]) ).

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(f1529,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f147,f1527]) ).

fof(f1527,plain,
    ( spl0_193
  <=> ! [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_193])]) ).

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(f1525,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f146,f1523]) ).

fof(f1523,plain,
    ( spl0_192
  <=> ! [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_192])]) ).

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(f1512,plain,
    ( spl0_191
    | ~ spl0_3
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1508,f1505,f256,f1510]) ).

fof(f1510,plain,
    ( spl0_191
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1505,plain,
    ( spl0_190
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1508,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) )
    | ~ spl0_3
    | ~ spl0_190 ),
    inference(forward_demodulation,[],[f1506,f257]) ).

fof(f1506,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1))
        | leq(X0,hd(X1)) )
    | ~ spl0_190 ),
    inference(avatar_component_clause,[],[f1505]) ).

fof(f1507,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f135,f1505]) ).

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

fof(f1501,plain,
    ( spl0_189
    | ~ spl0_3
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1497,f1494,f256,f1499]) ).

fof(f1499,plain,
    ( spl0_189
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1494,plain,
    ( spl0_188
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f1497,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) )
    | ~ spl0_3
    | ~ spl0_188 ),
    inference(forward_demodulation,[],[f1495,f257]) ).

fof(f1495,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1))
        | lt(X0,hd(X1)) )
    | ~ spl0_188 ),
    inference(avatar_component_clause,[],[f1494]) ).

fof(f1496,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f134,f1494]) ).

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

fof(f1455,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f141,f1453]) ).

fof(f1453,plain,
    ( spl0_187
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X0)
        | ~ ssList(X2)
        | ~ memberP(X0,X1)
        | memberP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

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

fof(f1451,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f140,f1449]) ).

fof(f1449,plain,
    ( spl0_186
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

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

fof(f1447,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f139,f1445]) ).

fof(f1445,plain,
    ( spl0_185
  <=> ! [X2,X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X2)
        | ~ ssList(X0)
        | ~ memberP(X0,X1)
        | memberP(cons(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

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

fof(f1443,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f137,f1441]) ).

fof(f1441,plain,
    ( spl0_184
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ frontsegP(X0,X1)
        | frontsegP(app(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

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(f1439,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f136,f1437]) ).

fof(f1437,plain,
    ( spl0_183
  <=> ! [X2,X0,X1] :
        ( ~ ssList(X2)
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ~ rearsegP(X0,X1)
        | rearsegP(app(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

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(f1435,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f132,f1433]) ).

fof(f1433,plain,
    ( spl0_182
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X0,X1)
        | app(X1,skaf45(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

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(f1431,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f131,f1429]) ).

fof(f1429,plain,
    ( spl0_181
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X0,X1)
        | app(skaf46(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

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(f1389,plain,
    ( spl0_180
    | ~ spl0_3
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1385,f1382,f256,f1387]) ).

fof(f1387,plain,
    ( spl0_180
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ ssList(X0)
        | ~ ssList(X1)
        | hd(app(X1,X0)) = hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f1382,plain,
    ( spl0_179
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1385,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssList(X0)
        | ~ ssList(X1)
        | hd(app(X1,X0)) = hd(X1) )
    | ~ spl0_3
    | ~ spl0_179 ),
    inference(forward_demodulation,[],[f1383,f257]) ).

fof(f1383,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | nil = X1
        | hd(app(X1,X0)) = hd(X1) )
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f1382]) ).

fof(f1384,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f123,f1382]) ).

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(f1347,plain,
    ( spl0_178
    | ~ spl0_15
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f872,f839,f331,f1344]) ).

fof(f1344,plain,
    ( spl0_178
  <=> sk6 = app(sk3,sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f839,plain,
    ( spl0_109
  <=> ! [X0] :
        ( app(sk3,X0) = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f872,plain,
    ( sk6 = app(sk3,sk6)
    | ~ spl0_15
    | ~ spl0_109 ),
    inference(resolution,[],[f840,f333]) ).

fof(f333,plain,
    ( ssList(sk6)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f331]) ).

fof(f840,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(sk3,X0) = X0 )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f839]) ).

fof(f1338,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f223,f1336]) ).

fof(f1336,plain,
    ( spl0_177
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X0)
        | frontsegP(app(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f223,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(f1334,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f222,f1332]) ).

fof(f1332,plain,
    ( spl0_176
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(app(X0,X1))
        | ~ ssList(X1)
        | rearsegP(app(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f222,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(f1330,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f130,f1328]) ).

fof(f1328,plain,
    ( spl0_175
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X1,X0)
        | ~ leq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

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(f1326,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f129,f1324]) ).

fof(f1324,plain,
    ( spl0_174
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ frontsegP(X1,X0)
        | ~ frontsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

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(f1322,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f128,f1320]) ).

fof(f1320,plain,
    ( spl0_173
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

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(f1318,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f127,f1316]) ).

fof(f1316,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

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(f1314,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f126,f1312]) ).

fof(f1312,plain,
    ( spl0_171
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

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(f1308,plain,
    ( spl0_170
    | ~ spl0_3
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1299,f1296,f256,f1306]) ).

fof(f1306,plain,
    ( spl0_170
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f1296,plain,
    ( spl0_168
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1299,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | ~ totalorderedP(cons(X0,X1)) )
    | ~ spl0_3
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1297,f257]) ).

fof(f1297,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) )
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1296]) ).

fof(f1304,plain,
    ( spl0_169
    | ~ spl0_3
    | ~ spl0_19
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f831,f797,f351,f256,f1301]) ).

fof(f1301,plain,
    ( spl0_169
  <=> sk3 = app(sk3,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f351,plain,
    ( spl0_19
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f797,plain,
    ( spl0_107
  <=> ! [X0] :
        ( app(X0,sk3) = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f831,plain,
    ( sk3 = app(sk3,sk3)
    | ~ spl0_3
    | ~ spl0_19
    | ~ spl0_107 ),
    inference(forward_demodulation,[],[f800,f257]) ).

fof(f800,plain,
    ( nil = app(nil,sk3)
    | ~ spl0_19
    | ~ spl0_107 ),
    inference(resolution,[],[f798,f353]) ).

fof(f353,plain,
    ( ssList(nil)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f798,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,sk3) = X0 )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f797]) ).

fof(f1298,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f125,f1296]) ).

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

fof(f1292,plain,
    ( spl0_167
    | ~ spl0_3
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1288,f1285,f256,f1290]) ).

fof(f1290,plain,
    ( spl0_167
  <=> ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1285,plain,
    ( spl0_166
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f1288,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | ~ strictorderedP(cons(X0,X1)) )
    | ~ spl0_3
    | ~ spl0_166 ),
    inference(forward_demodulation,[],[f1286,f257]) ).

fof(f1286,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1285]) ).

fof(f1287,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f124,f1285]) ).

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

fof(f1283,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f122,f1281]) ).

fof(f1281,plain,
    ( spl0_165
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

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

fof(f1260,plain,
    ( spl0_164
    | ~ spl0_3
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1256,f1253,f256,f1258]) ).

fof(f1258,plain,
    ( spl0_164
  <=> ! [X0,X1] :
        ( cons(X0,X1) = app(cons(X0,sk3),X1)
        | ~ ssItem(X0)
        | ~ ssList(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f1253,plain,
    ( spl0_163
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f1256,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) = app(cons(X0,sk3),X1)
        | ~ ssItem(X0)
        | ~ ssList(X1) )
    | ~ spl0_3
    | ~ spl0_163 ),
    inference(forward_demodulation,[],[f1254,f257]) ).

fof(f1254,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1253]) ).

fof(f1255,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f120,f1253]) ).

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

fof(f1249,plain,
    ( spl0_162
    | ~ spl0_3
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1240,f1236,f256,f1247]) ).

fof(f1247,plain,
    ( spl0_162
  <=> ! [X0,X1] :
        ( app(X0,X1) != sk3
        | sk3 = X1
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f1236,plain,
    ( spl0_160
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f1240,plain,
    ( ! [X0,X1] :
        ( app(X0,X1) != sk3
        | sk3 = X1
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_160 ),
    inference(forward_demodulation,[],[f1239,f257]) ).

fof(f1239,plain,
    ( ! [X0,X1] :
        ( sk3 = X1
        | ~ ssList(X1)
        | ~ ssList(X0)
        | nil != app(X0,X1) )
    | ~ spl0_3
    | ~ spl0_160 ),
    inference(forward_demodulation,[],[f1237,f257]) ).

fof(f1237,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1236]) ).

fof(f1245,plain,
    ( spl0_161
    | ~ spl0_15
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f830,f797,f331,f1242]) ).

fof(f1242,plain,
    ( spl0_161
  <=> sk6 = app(sk6,sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f830,plain,
    ( sk6 = app(sk6,sk3)
    | ~ spl0_15
    | ~ spl0_107 ),
    inference(resolution,[],[f798,f333]) ).

fof(f1238,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f119,f1236]) ).

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

fof(f1232,plain,
    ( spl0_159
    | ~ spl0_3
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1228,f1224,f256,f1230]) ).

fof(f1230,plain,
    ( spl0_159
  <=> ! [X0,X1] :
        ( app(X0,X1) != sk3
        | sk3 = X0
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f1224,plain,
    ( spl0_158
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1228,plain,
    ( ! [X0,X1] :
        ( app(X0,X1) != sk3
        | sk3 = X0
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_158 ),
    inference(forward_demodulation,[],[f1227,f257]) ).

fof(f1227,plain,
    ( ! [X0,X1] :
        ( sk3 = X0
        | ~ ssList(X1)
        | ~ ssList(X0)
        | nil != app(X0,X1) )
    | ~ spl0_3
    | ~ spl0_158 ),
    inference(forward_demodulation,[],[f1225,f257]) ).

fof(f1225,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1224]) ).

fof(f1226,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f118,f1224]) ).

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

fof(f1188,plain,
    ( spl0_157
    | ~ spl0_3
    | ~ spl0_156 ),
    inference(avatar_split_clause,[],[f1184,f1181,f256,f1186]) ).

fof(f1186,plain,
    ( spl0_157
  <=> ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f1181,plain,
    ( spl0_156
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f1184,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | cons(skaf83(X0),skaf82(X0)) = X0 )
    | ~ spl0_3
    | ~ spl0_156 ),
    inference(forward_demodulation,[],[f1182,f257]) ).

fof(f1182,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 )
    | ~ spl0_156 ),
    inference(avatar_component_clause,[],[f1181]) ).

fof(f1183,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f109,f1181]) ).

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

fof(f1145,plain,
    ( spl0_155
    | ~ spl0_3
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1141,f1138,f256,f1143]) ).

fof(f1143,plain,
    ( spl0_155
  <=> ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1138,plain,
    ( spl0_154
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1141,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | cons(hd(X0),tl(X0)) = X0 )
    | ~ spl0_3
    | ~ spl0_154 ),
    inference(forward_demodulation,[],[f1139,f257]) ).

fof(f1139,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1138]) ).

fof(f1140,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f104,f1138]) ).

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

fof(f1136,plain,
    ( spl0_153
    | ~ spl0_3
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f678,f585,f256,f1134]) ).

fof(f1134,plain,
    ( spl0_153
  <=> ! [X0] :
        ( frontsegP(X0,sk3)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f585,plain,
    ( spl0_75
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f678,plain,
    ( ! [X0] :
        ( frontsegP(X0,sk3)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_75 ),
    inference(superposition,[],[f586,f257]) ).

fof(f586,plain,
    ( ! [X0] :
        ( frontsegP(X0,nil)
        | ~ ssList(X0) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f585]) ).

fof(f1099,plain,
    ( spl0_152
    | ~ spl0_3
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f677,f577,f256,f1097]) ).

fof(f1097,plain,
    ( spl0_152
  <=> ! [X0] :
        ( rearsegP(X0,sk3)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f577,plain,
    ( spl0_73
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f677,plain,
    ( ! [X0] :
        ( rearsegP(X0,sk3)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_73 ),
    inference(superposition,[],[f578,f257]) ).

fof(f578,plain,
    ( ! [X0] :
        ( rearsegP(X0,nil)
        | ~ ssList(X0) )
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f577]) ).

fof(f1074,plain,
    ( spl0_151
    | ~ spl0_3
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1070,f1066,f256,f1072]) ).

fof(f1072,plain,
    ( spl0_151
  <=> ! [X0] :
        ( singletonP(cons(X0,sk3))
        | ~ ssList(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1066,plain,
    ( spl0_150
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1070,plain,
    ( ! [X0] :
        ( singletonP(cons(X0,sk3))
        | ~ ssList(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_150 ),
    inference(forward_demodulation,[],[f1069,f257]) ).

fof(f1069,plain,
    ( ! [X0] :
        ( ~ ssList(cons(X0,sk3))
        | ~ ssItem(X0)
        | singletonP(cons(X0,nil)) )
    | ~ spl0_3
    | ~ spl0_150 ),
    inference(forward_demodulation,[],[f1067,f257]) ).

fof(f1067,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) )
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1066]) ).

fof(f1068,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f217,f1066]) ).

fof(f217,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | singletonP(cons(X0,nil)) ),
    inference(equality_resolution,[],[f116]) ).

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

fof(f1064,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f114,f1062]) ).

fof(f1062,plain,
    ( spl0_149
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

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

fof(f1060,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f110,f1058]) ).

fof(f1058,plain,
    ( spl0_148
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

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

fof(f1056,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f108,f1054]) ).

fof(f1054,plain,
    ( spl0_147
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

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

fof(f1052,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f107,f1050]) ).

fof(f1050,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

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

fof(f1048,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f106,f1046]) ).

fof(f1046,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

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

fof(f1044,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f105,f1042]) ).

fof(f1042,plain,
    ( spl0_144
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

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

fof(f1040,plain,
    ( spl0_143
    | ~ spl0_3
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f671,f569,f256,f1038]) ).

fof(f1038,plain,
    ( spl0_143
  <=> ! [X0] :
        ( segmentP(X0,sk3)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f569,plain,
    ( spl0_71
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f671,plain,
    ( ! [X0] :
        ( segmentP(X0,sk3)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_71 ),
    inference(superposition,[],[f570,f257]) ).

fof(f570,plain,
    ( ! [X0] :
        ( segmentP(X0,nil)
        | ~ ssList(X0) )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f569]) ).

fof(f1036,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f103,f1034]) ).

fof(f1034,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

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

fof(f1032,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f102,f1030]) ).

fof(f1030,plain,
    ( spl0_141
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

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

fof(f1028,plain,
    ( spl0_140
    | ~ spl0_3
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1024,f1021,f256,f1026]) ).

fof(f1026,plain,
    ( spl0_140
  <=> ! [X0] :
        ( cons(skaf44(X0),sk3) = X0
        | ~ singletonP(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1021,plain,
    ( spl0_139
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f1024,plain,
    ( ! [X0] :
        ( cons(skaf44(X0),sk3) = X0
        | ~ singletonP(X0)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_139 ),
    inference(forward_demodulation,[],[f1022,f257]) ).

fof(f1022,plain,
    ( ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1021]) ).

fof(f1023,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f101,f1021]) ).

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

fof(f1019,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f100,f1017]) ).

fof(f1017,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

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

fof(f1015,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f97,f1013]) ).

fof(f1013,plain,
    ( spl0_137
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

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

fof(f1011,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f96,f1009]) ).

fof(f1009,plain,
    ( spl0_136
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

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

fof(f1007,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f238,f1005]) ).

fof(f1005,plain,
    ( spl0_135
  <=> ! [X2,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f238,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f221]) ).

fof(f221,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(equality_resolution,[],[f138]) ).

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

fof(f1003,plain,
    ( spl0_134
    | ~ spl0_15
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f789,f756,f331,f1000]) ).

fof(f1000,plain,
    ( spl0_134
  <=> duplicatefreeP(sk6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f756,plain,
    ( spl0_105
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f789,plain,
    ( duplicatefreeP(sk6)
    | ~ spl0_15
    | ~ spl0_105 ),
    inference(resolution,[],[f757,f333]) ).

fof(f757,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) )
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f756]) ).

fof(f998,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f99,f996]) ).

fof(f996,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

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

fof(f994,plain,
    ( spl0_132
    | ~ spl0_3
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f990,f987,f256,f992]) ).

fof(f992,plain,
    ( spl0_132
  <=> ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssItem(X0)
        | ~ ssList(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f987,plain,
    ( spl0_131
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f990,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssItem(X0)
        | ~ ssList(X1) )
    | ~ spl0_3
    | ~ spl0_131 ),
    inference(forward_demodulation,[],[f988,f257]) ).

fof(f988,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f987]) ).

fof(f989,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f98,f987]) ).

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

fof(f985,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f95,f983]) ).

fof(f983,plain,
    ( spl0_130
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

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

fof(f981,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f94,f979]) ).

fof(f979,plain,
    ( spl0_129
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

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

fof(f977,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f93,f975]) ).

fof(f975,plain,
    ( spl0_128
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

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

fof(f973,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f92,f971]) ).

fof(f971,plain,
    ( spl0_127
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

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

fof(f969,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f91,f967]) ).

fof(f967,plain,
    ( spl0_126
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

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

fof(f965,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f90,f963]) ).

fof(f963,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

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

fof(f961,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f89,f959]) ).

fof(f959,plain,
    ( spl0_124
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

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

fof(f957,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f88,f955]) ).

fof(f955,plain,
    ( spl0_123
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

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

fof(f953,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f87,f951]) ).

fof(f951,plain,
    ( spl0_122
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

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

fof(f942,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f86,f940]) ).

fof(f940,plain,
    ( spl0_121
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

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

fof(f938,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f85,f936]) ).

fof(f936,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

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

fof(f931,plain,
    ( spl0_119
    | ~ spl0_3
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f927,f923,f256,f929]) ).

fof(f929,plain,
    ( spl0_119
  <=> ! [X0] :
        ( sk3 = X0
        | ~ frontsegP(sk3,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f923,plain,
    ( spl0_118
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f927,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ frontsegP(sk3,X0)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_118 ),
    inference(forward_demodulation,[],[f926,f257]) ).

fof(f926,plain,
    ( ! [X0] :
        ( ~ frontsegP(sk3,X0)
        | ~ ssList(X0)
        | nil = X0 )
    | ~ spl0_3
    | ~ spl0_118 ),
    inference(forward_demodulation,[],[f924,f257]) ).

fof(f924,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 )
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f923]) ).

fof(f925,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f84,f923]) ).

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

fof(f918,plain,
    ( spl0_117
    | ~ spl0_3
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f914,f910,f256,f916]) ).

fof(f916,plain,
    ( spl0_117
  <=> ! [X0] :
        ( sk3 = X0
        | ~ rearsegP(sk3,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f910,plain,
    ( spl0_116
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f914,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ rearsegP(sk3,X0)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f913,f257]) ).

fof(f913,plain,
    ( ! [X0] :
        ( ~ rearsegP(sk3,X0)
        | ~ ssList(X0)
        | nil = X0 )
    | ~ spl0_3
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f911,f257]) ).

fof(f911,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f910]) ).

fof(f912,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f82,f910]) ).

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

fof(f905,plain,
    ( spl0_115
    | ~ spl0_3
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f901,f897,f256,f903]) ).

fof(f903,plain,
    ( spl0_115
  <=> ! [X0] :
        ( sk3 = X0
        | ~ segmentP(sk3,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f897,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f901,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ segmentP(sk3,X0)
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_114 ),
    inference(forward_demodulation,[],[f900,f257]) ).

fof(f900,plain,
    ( ! [X0] :
        ( ~ segmentP(sk3,X0)
        | ~ ssList(X0)
        | nil = X0 )
    | ~ spl0_3
    | ~ spl0_114 ),
    inference(forward_demodulation,[],[f898,f257]) ).

fof(f898,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f897]) ).

fof(f899,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f80,f897]) ).

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

fof(f895,plain,
    ( spl0_113
    | ~ spl0_3
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f891,f888,f256,f893]) ).

fof(f893,plain,
    ( spl0_113
  <=> ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | ssItem(hd(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f888,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssItem(hd(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f891,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | ssItem(hd(X0)) )
    | ~ spl0_3
    | ~ spl0_112 ),
    inference(forward_demodulation,[],[f889,f257]) ).

fof(f889,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssItem(hd(X0)) )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f888]) ).

fof(f890,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f78,f888]) ).

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

fof(f883,plain,
    ( spl0_111
    | ~ spl0_3
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f879,f876,f256,f881]) ).

fof(f881,plain,
    ( spl0_111
  <=> ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f876,plain,
    ( spl0_110
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f879,plain,
    ( ! [X0] :
        ( sk3 = X0
        | ~ ssList(X0)
        | ssList(tl(X0)) )
    | ~ spl0_3
    | ~ spl0_110 ),
    inference(forward_demodulation,[],[f877,f257]) ).

fof(f877,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f876]) ).

fof(f878,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f77,f876]) ).

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

fof(f841,plain,
    ( spl0_109
    | ~ spl0_3
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f837,f834,f256,f839]) ).

fof(f834,plain,
    ( spl0_108
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f837,plain,
    ( ! [X0] :
        ( app(sk3,X0) = X0
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_108 ),
    inference(forward_demodulation,[],[f835,f257]) ).

fof(f835,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f834]) ).

fof(f836,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f74,f834]) ).

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

fof(f799,plain,
    ( spl0_107
    | ~ spl0_3
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f795,f792,f256,f797]) ).

fof(f792,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f795,plain,
    ( ! [X0] :
        ( app(X0,sk3) = X0
        | ~ ssList(X0) )
    | ~ spl0_3
    | ~ spl0_106 ),
    inference(forward_demodulation,[],[f793,f257]) ).

fof(f793,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f792]) ).

fof(f794,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f73,f792]) ).

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

fof(f758,plain,
    ( spl0_104
    | spl0_105 ),
    inference(avatar_split_clause,[],[f72,f756,f753]) ).

fof(f753,plain,
    ( spl0_104
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

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

fof(f751,plain,
    ( spl0_103
    | ~ spl0_3
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f747,f744,f256,f749]) ).

fof(f749,plain,
    ( spl0_103
  <=> ! [X0] :
        ( cyclefreeP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f744,plain,
    ( spl0_102
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f747,plain,
    ( ! [X0] :
        ( cyclefreeP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_102 ),
    inference(forward_demodulation,[],[f745,f257]) ).

fof(f745,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) )
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f744]) ).

fof(f746,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f70,f744]) ).

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

fof(f742,plain,
    ( spl0_101
    | ~ spl0_3
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f738,f735,f256,f740]) ).

fof(f740,plain,
    ( spl0_101
  <=> ! [X0] :
        ( totalorderP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f735,plain,
    ( spl0_100
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f738,plain,
    ( ! [X0] :
        ( totalorderP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_100 ),
    inference(forward_demodulation,[],[f736,f257]) ).

fof(f736,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f735]) ).

fof(f737,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f69,f735]) ).

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

fof(f733,plain,
    ( spl0_99
    | ~ spl0_3
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f729,f726,f256,f731]) ).

fof(f731,plain,
    ( spl0_99
  <=> ! [X0] :
        ( strictorderP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f726,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f729,plain,
    ( ! [X0] :
        ( strictorderP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_98 ),
    inference(forward_demodulation,[],[f727,f257]) ).

fof(f727,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f726]) ).

fof(f728,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f68,f726]) ).

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

fof(f724,plain,
    ( ~ spl0_97
    | ~ spl0_3
    | spl0_22 ),
    inference(avatar_split_clause,[],[f618,f366,f256,f721]) ).

fof(f721,plain,
    ( spl0_97
  <=> singletonP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f366,plain,
    ( spl0_22
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f618,plain,
    ( ~ singletonP(sk3)
    | ~ spl0_3
    | spl0_22 ),
    inference(superposition,[],[f368,f257]) ).

fof(f368,plain,
    ( ~ singletonP(nil)
    | spl0_22 ),
    inference(avatar_component_clause,[],[f366]) ).

fof(f719,plain,
    ( spl0_96
    | ~ spl0_3
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f715,f712,f256,f717]) ).

fof(f717,plain,
    ( spl0_96
  <=> ! [X0] :
        ( totalorderedP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f712,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f715,plain,
    ( ! [X0] :
        ( totalorderedP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_95 ),
    inference(forward_demodulation,[],[f713,f257]) ).

fof(f713,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f712]) ).

fof(f714,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f67,f712]) ).

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

fof(f710,plain,
    ( spl0_94
    | ~ spl0_3
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f706,f703,f256,f708]) ).

fof(f708,plain,
    ( spl0_94
  <=> ! [X0] :
        ( strictorderedP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f703,plain,
    ( spl0_93
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f706,plain,
    ( ! [X0] :
        ( strictorderedP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_93 ),
    inference(forward_demodulation,[],[f704,f257]) ).

fof(f704,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f703]) ).

fof(f705,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f66,f703]) ).

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

fof(f701,plain,
    ( spl0_92
    | ~ spl0_3
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f697,f694,f256,f699]) ).

fof(f699,plain,
    ( spl0_92
  <=> ! [X0] :
        ( duplicatefreeP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

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

fof(f697,plain,
    ( ! [X0] :
        ( duplicatefreeP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_91 ),
    inference(forward_demodulation,[],[f695,f257]) ).

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

fof(f696,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f65,f694]) ).

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

fof(f692,plain,
    ( spl0_90
    | ~ spl0_3
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f683,f680,f256,f690]) ).

fof(f690,plain,
    ( spl0_90
  <=> ! [X0] :
        ( equalelemsP(cons(X0,sk3))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f680,plain,
    ( spl0_88
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f683,plain,
    ( ! [X0] :
        ( equalelemsP(cons(X0,sk3))
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_88 ),
    inference(forward_demodulation,[],[f681,f257]) ).

fof(f681,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f680]) ).

fof(f688,plain,
    ( spl0_89
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f616,f346,f256,f685]) ).

fof(f685,plain,
    ( spl0_89
  <=> cyclefreeP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f346,plain,
    ( spl0_18
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f616,plain,
    ( cyclefreeP(sk3)
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(superposition,[],[f348,f257]) ).

fof(f348,plain,
    ( cyclefreeP(nil)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f346]) ).

fof(f682,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f64,f680]) ).

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

fof(f676,plain,
    ( spl0_87
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f615,f341,f256,f673]) ).

fof(f673,plain,
    ( spl0_87
  <=> totalorderP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f341,plain,
    ( spl0_17
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f615,plain,
    ( totalorderP(sk3)
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(superposition,[],[f343,f257]) ).

fof(f343,plain,
    ( totalorderP(nil)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f670,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f241,f668]) ).

fof(f668,plain,
    ( spl0_86
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f241,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f215]) ).

fof(f215,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(f666,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f239,f664]) ).

fof(f664,plain,
    ( spl0_85
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f239,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f220]) ).

fof(f220,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(f662,plain,
    ( spl0_84
    | ~ spl0_3
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f658,f655,f256,f660]) ).

fof(f660,plain,
    ( spl0_84
  <=> ! [X0] :
        ( ~ memberP(sk3,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f655,plain,
    ( spl0_83
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f658,plain,
    ( ! [X0] :
        ( ~ memberP(sk3,X0)
        | ~ ssItem(X0) )
    | ~ spl0_3
    | ~ spl0_83 ),
    inference(forward_demodulation,[],[f656,f257]) ).

fof(f656,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f655]) ).

fof(f657,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f71,f655]) ).

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

fof(f653,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f63,f651]) ).

fof(f651,plain,
    ( spl0_82
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

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

fof(f649,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f62,f647]) ).

fof(f647,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

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

fof(f645,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f61,f643]) ).

fof(f643,plain,
    ( spl0_80
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

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

fof(f641,plain,
    ( spl0_79
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f614,f336,f256,f638]) ).

fof(f638,plain,
    ( spl0_79
  <=> strictorderP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f336,plain,
    ( spl0_16
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f614,plain,
    ( strictorderP(sk3)
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(superposition,[],[f338,f257]) ).

fof(f338,plain,
    ( strictorderP(nil)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f336]) ).

fof(f636,plain,
    ( spl0_78
    | ~ spl0_6
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f631,f627,f271,f633]) ).

fof(f271,plain,
    ( spl0_6
  <=> sk3 = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f627,plain,
    ( spl0_77
  <=> sk4 = app(sk6,cons(sk5,sk3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f631,plain,
    ( sk3 = app(sk6,cons(sk5,sk3))
    | ~ spl0_6
    | ~ spl0_77 ),
    inference(forward_demodulation,[],[f629,f273]) ).

fof(f273,plain,
    ( sk3 = sk4
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f629,plain,
    ( sk4 = app(sk6,cons(sk5,sk3))
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f627]) ).

fof(f630,plain,
    ( spl0_77
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f244,f256,f627]) ).

fof(f244,plain,
    ( nil != sk3
    | sk4 = app(sk6,cons(sk5,sk3)) ),
    inference(inner_rewriting,[],[f209]) ).

fof(f209,plain,
    ( nil != sk3
    | sk4 = app(sk6,cons(sk5,nil)) ),
    inference(definition_unfolding,[],[f200,f191,f190]) ).

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

fof(f200,axiom,
    ( nil != sk1
    | sk2 = app(sk6,cons(sk5,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).

fof(f609,plain,
    ( spl0_3
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f607,f271,f265,f256]) ).

fof(f265,plain,
    ( spl0_5
  <=> nil = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f607,plain,
    ( nil = sk3
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f267,f273]) ).

fof(f267,plain,
    ( nil = sk4
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f602,plain,
    ( spl0_5
    | spl0_15 ),
    inference(avatar_split_clause,[],[f207,f331,f265]) ).

fof(f207,plain,
    ( ssList(sk6)
    | nil = sk4 ),
    inference(definition_unfolding,[],[f196,f190]) ).

fof(f196,axiom,
    ( ssList(sk6)
    | nil = sk2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).

fof(f601,plain,
    ( spl0_24
    | ~ spl0_4
    | ~ spl0_15
    | ~ spl0_68
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f600,f593,f554,f331,f260,f376]) ).

fof(f260,plain,
    ( spl0_4
  <=> ssItem(sk5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f554,plain,
    ( spl0_68
  <=> ! [X6,X7] :
        ( ~ ssItem(X6)
        | ~ ssList(X7)
        | sk4 != app(X7,cons(X6,nil))
        | sk3 = app(cons(X6,nil),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f593,plain,
    ( spl0_76
  <=> sk4 = app(sk6,cons(sk5,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f600,plain,
    ( ~ ssList(sk6)
    | ~ ssItem(sk5)
    | sk3 = app(cons(sk5,nil),sk6)
    | ~ spl0_68
    | ~ spl0_76 ),
    inference(trivial_inequality_removal,[],[f599]) ).

fof(f599,plain,
    ( sk4 != sk4
    | ~ ssList(sk6)
    | ~ ssItem(sk5)
    | sk3 = app(cons(sk5,nil),sk6)
    | ~ spl0_68
    | ~ spl0_76 ),
    inference(superposition,[],[f555,f595]) ).

fof(f595,plain,
    ( sk4 = app(sk6,cons(sk5,nil))
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f593]) ).

fof(f555,plain,
    ( ! [X6,X7] :
        ( sk4 != app(X7,cons(X6,nil))
        | ~ ssList(X7)
        | ~ ssItem(X6)
        | sk3 = app(cons(X6,nil),X7) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f554]) ).

fof(f596,plain,
    ( spl0_76
    | spl0_5 ),
    inference(avatar_split_clause,[],[f211,f265,f593]) ).

fof(f211,plain,
    ( nil = sk4
    | sk4 = app(sk6,cons(sk5,nil)) ),
    inference(definition_unfolding,[],[f197,f190,f190]) ).

fof(f197,axiom,
    ( nil = sk2
    | sk2 = app(sk6,cons(sk5,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).

fof(f591,plain,
    ( ~ spl0_24
    | spl0_5 ),
    inference(avatar_split_clause,[],[f210,f265,f376]) ).

fof(f210,plain,
    ( nil = sk4
    | sk3 != app(cons(sk5,nil),sk6) ),
    inference(definition_unfolding,[],[f198,f190,f191]) ).

fof(f198,axiom,
    ( nil = sk2
    | sk1 != app(cons(sk5,nil),sk6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).

fof(f590,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f589,f371,f271,f265]) ).

fof(f589,plain,
    ( sk3 = sk4
    | nil = sk4
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f211,f373]) ).

fof(f373,plain,
    ( sk3 = app(sk6,cons(sk5,nil))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f588,plain,
    ( spl0_24
    | ~ spl0_15
    | ~ spl0_4
    | ~ spl0_23
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f563,f559,f371,f260,f331,f376]) ).

fof(f559,plain,
    ( spl0_69
  <=> ! [X6,X7] :
        ( sk3 != app(X7,cons(X6,nil))
        | ~ ssItem(X6)
        | ~ ssList(X7)
        | sk3 = app(cons(X6,nil),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f563,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(sk6)
    | sk3 = app(cons(sk5,nil),sk6)
    | ~ spl0_23
    | ~ spl0_69 ),
    inference(trivial_inequality_removal,[],[f562]) ).

fof(f562,plain,
    ( sk3 != sk3
    | ~ ssItem(sk5)
    | ~ ssList(sk6)
    | sk3 = app(cons(sk5,nil),sk6)
    | ~ spl0_23
    | ~ spl0_69 ),
    inference(superposition,[],[f560,f373]) ).

fof(f560,plain,
    ( ! [X6,X7] :
        ( sk3 != app(X7,cons(X6,nil))
        | ~ ssItem(X6)
        | ~ ssList(X7)
        | sk3 = app(cons(X6,nil),X7) )
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f559]) ).

fof(f587,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f60,f585]) ).

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

fof(f583,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f59,f581]) ).

fof(f581,plain,
    ( spl0_74
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

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

fof(f579,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f58,f577]) ).

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

fof(f575,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f57,f573]) ).

fof(f573,plain,
    ( spl0_72
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

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

fof(f571,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f56,f569]) ).

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

fof(f567,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f55,f565]) ).

fof(f565,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

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

fof(f561,plain,
    ( spl0_69
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f557,f554,f271,f559]) ).

fof(f557,plain,
    ( ! [X6,X7] :
        ( sk3 != app(X7,cons(X6,nil))
        | ~ ssItem(X6)
        | ~ ssList(X7)
        | sk3 = app(cons(X6,nil),X7) )
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(forward_demodulation,[],[f555,f273]) ).

fof(f556,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f192,f554]) ).

fof(f192,axiom,
    ! [X6,X7] :
      ( ~ ssItem(X6)
      | ~ ssList(X7)
      | sk4 != app(X7,cons(X6,nil))
      | sk3 = app(cons(X6,nil),X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

fof(f552,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f53,f550]) ).

fof(f550,plain,
    ( spl0_67
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

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

fof(f548,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f52,f546]) ).

fof(f546,plain,
    ( spl0_66
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

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

fof(f544,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f51,f542]) ).

fof(f542,plain,
    ( spl0_65
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

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

fof(f540,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f50,f538]) ).

fof(f538,plain,
    ( spl0_64
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

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

fof(f536,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f49,f534]) ).

fof(f534,plain,
    ( spl0_63
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

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

fof(f532,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f48,f530]) ).

fof(f530,plain,
    ( spl0_62
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

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

fof(f528,plain,
    ~ spl0_61,
    inference(avatar_split_clause,[],[f54,f525]) ).

fof(f525,plain,
    ( spl0_61
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

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

fof(f523,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f47,f521]) ).

fof(f521,plain,
    ( spl0_60
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

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

fof(f519,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f46,f517]) ).

fof(f517,plain,
    ( spl0_59
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

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

fof(f515,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f45,f513]) ).

fof(f513,plain,
    ( spl0_58
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

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

fof(f511,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f44,f509]) ).

fof(f509,plain,
    ( spl0_57
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

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

fof(f507,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f43,f505]) ).

fof(f505,plain,
    ( spl0_56
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

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

fof(f503,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f42,f501]) ).

fof(f501,plain,
    ( spl0_55
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

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

fof(f499,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f41,f497]) ).

fof(f497,plain,
    ( spl0_54
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

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

fof(f495,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f40,f493]) ).

fof(f493,plain,
    ( spl0_53
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

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

fof(f491,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f39,f489]) ).

fof(f489,plain,
    ( spl0_52
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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

fof(f487,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f38,f485]) ).

fof(f485,plain,
    ( spl0_51
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

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

fof(f483,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f37,f481]) ).

fof(f481,plain,
    ( spl0_50
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

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

fof(f479,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f36,f477]) ).

fof(f477,plain,
    ( spl0_49
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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

fof(f475,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f35,f473]) ).

fof(f473,plain,
    ( spl0_48
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

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

fof(f471,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f34,f469]) ).

fof(f469,plain,
    ( spl0_47
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

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

fof(f467,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f33,f465]) ).

fof(f465,plain,
    ( spl0_46
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

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

fof(f463,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f32,f461]) ).

fof(f461,plain,
    ( spl0_45
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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

fof(f459,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f31,f457]) ).

fof(f457,plain,
    ( spl0_44
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

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

fof(f455,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f30,f453]) ).

fof(f453,plain,
    ( spl0_43
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f451,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f29,f449]) ).

fof(f449,plain,
    ( spl0_42
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

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

fof(f447,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f28,f445]) ).

fof(f445,plain,
    ( spl0_41
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

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

fof(f443,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f27,f441]) ).

fof(f441,plain,
    ( spl0_40
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

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

fof(f439,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f26,f437]) ).

fof(f437,plain,
    ( spl0_39
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f435,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f25,f433]) ).

fof(f433,plain,
    ( spl0_38
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

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

fof(f431,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f24,f429]) ).

fof(f429,plain,
    ( spl0_37
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

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

fof(f427,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f23,f425]) ).

fof(f425,plain,
    ( spl0_36
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

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

fof(f423,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f22,f421]) ).

fof(f421,plain,
    ( spl0_35
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

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

fof(f419,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f21,f417]) ).

fof(f417,plain,
    ( spl0_34
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

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

fof(f415,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f20,f413]) ).

fof(f413,plain,
    ( spl0_33
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

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

fof(f411,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f19,f409]) ).

fof(f409,plain,
    ( spl0_32
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

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

fof(f407,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f18,f405]) ).

fof(f405,plain,
    ( spl0_31
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

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

fof(f403,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f17,f401]) ).

fof(f401,plain,
    ( spl0_30
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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

fof(f399,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f16,f397]) ).

fof(f397,plain,
    ( spl0_29
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

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

fof(f395,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f15,f393]) ).

fof(f393,plain,
    ( spl0_28
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f391,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f14,f389]) ).

fof(f389,plain,
    ( spl0_27
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

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

fof(f387,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f13,f385]) ).

fof(f385,plain,
    ( spl0_26
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

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

fof(f383,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f12,f381]) ).

fof(f381,plain,
    ( spl0_25
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

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

fof(f379,plain,
    ( ~ spl0_24
    | spl0_3
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f327,f271,f256,f376]) ).

fof(f327,plain,
    ( nil = sk3
    | sk3 != app(cons(sk5,nil),sk6)
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f210,f273]) ).

fof(f374,plain,
    ( spl0_3
    | spl0_23
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f326,f271,f371,f256]) ).

fof(f326,plain,
    ( sk3 = app(sk6,cons(sk5,nil))
    | nil = sk3
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f325,f273]) ).

fof(f325,plain,
    ( nil = sk3
    | sk4 = app(sk6,cons(sk5,nil))
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f211,f273]) ).

fof(f369,plain,
    ~ spl0_22,
    inference(avatar_split_clause,[],[f11,f366]) ).

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

fof(f364,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f10,f361]) ).

fof(f361,plain,
    ( spl0_21
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

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

fof(f359,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f9,f356]) ).

fof(f356,plain,
    ( spl0_20
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

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

fof(f354,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f8,f351]) ).

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

fof(f349,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f7,f346]) ).

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

fof(f344,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f6,f341]) ).

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

fof(f339,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f5,f336]) ).

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

fof(f334,plain,
    ( spl0_15
    | spl0_3
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f328,f271,f256,f331]) ).

fof(f328,plain,
    ( nil = sk3
    | ssList(sk6)
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f207,f273]) ).

fof(f324,plain,
    ( ~ spl0_6
    | spl0_3
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f269,f265,f256,f271]) ).

fof(f269,plain,
    ( sk3 != sk4
    | spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f258,f267]) ).

fof(f258,plain,
    ( nil != sk3
    | spl0_3 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f323,plain,
    ( spl0_14
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f318,f313,f271,f265,f320]) ).

fof(f320,plain,
    ( spl0_14
  <=> totalorderedP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f313,plain,
    ( spl0_13
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f318,plain,
    ( totalorderedP(sk3)
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_13 ),
    inference(forward_demodulation,[],[f317,f273]) ).

fof(f317,plain,
    ( totalorderedP(sk4)
    | ~ spl0_5
    | ~ spl0_13 ),
    inference(forward_demodulation,[],[f315,f267]) ).

fof(f315,plain,
    ( totalorderedP(nil)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f313]) ).

fof(f316,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f4,f313]) ).

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

fof(f311,plain,
    ( spl0_12
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f306,f301,f271,f265,f308]) ).

fof(f308,plain,
    ( spl0_12
  <=> strictorderedP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f301,plain,
    ( spl0_11
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f306,plain,
    ( strictorderedP(sk3)
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(forward_demodulation,[],[f305,f273]) ).

fof(f305,plain,
    ( strictorderedP(sk4)
    | ~ spl0_5
    | ~ spl0_11 ),
    inference(forward_demodulation,[],[f303,f267]) ).

fof(f303,plain,
    ( strictorderedP(nil)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f304,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f3,f301]) ).

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

fof(f299,plain,
    ( spl0_10
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f294,f289,f271,f265,f296]) ).

fof(f296,plain,
    ( spl0_10
  <=> duplicatefreeP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f289,plain,
    ( spl0_9
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f294,plain,
    ( duplicatefreeP(sk3)
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_9 ),
    inference(forward_demodulation,[],[f293,f273]) ).

fof(f293,plain,
    ( duplicatefreeP(sk4)
    | ~ spl0_5
    | ~ spl0_9 ),
    inference(forward_demodulation,[],[f291,f267]) ).

fof(f291,plain,
    ( duplicatefreeP(nil)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f292,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f2,f289]) ).

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

fof(f287,plain,
    ( spl0_8
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f282,f277,f271,f265,f284]) ).

fof(f284,plain,
    ( spl0_8
  <=> equalelemsP(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f277,plain,
    ( spl0_7
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f282,plain,
    ( equalelemsP(sk3)
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f281,f273]) ).

fof(f281,plain,
    ( equalelemsP(sk4)
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f279,f267]) ).

fof(f279,plain,
    ( equalelemsP(nil)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f277]) ).

fof(f280,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f1,f277]) ).

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

fof(f274,plain,
    ( spl0_6
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f242,f265,f271]) ).

fof(f242,plain,
    ( nil != sk4
    | sk3 = sk4 ),
    inference(inner_rewriting,[],[f193]) ).

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

fof(f268,plain,
    ( spl0_5
    | spl0_4 ),
    inference(avatar_split_clause,[],[f205,f260,f265]) ).

fof(f205,plain,
    ( ssItem(sk5)
    | nil = sk4 ),
    inference(definition_unfolding,[],[f194,f190]) ).

fof(f194,axiom,
    ( ssItem(sk5)
    | nil = sk2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

fof(f263,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f204,f260,f256]) ).

fof(f204,plain,
    ( ssItem(sk5)
    | nil != sk3 ),
    inference(definition_unfolding,[],[f195,f191]) ).

fof(f195,axiom,
    ( ssItem(sk5)
    | nil != sk1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).

fof(f254,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f189,f251]) ).

fof(f251,plain,
    ( spl0_2
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

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

fof(f249,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f188,f246]) ).

fof(f246,plain,
    ( spl0_1
  <=> ssList(sk3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f188,axiom,
    ssList(sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SWC322-1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun May 19 03:55:53 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (26522)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.36  % (26525)WARNING: value z3 for option sas not known
% 0.19/0.36  % (26525)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)
% 0.19/0.36  % (26524)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.36  % (26528)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)
% 0.19/0.36  % (26527)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)
% 0.19/0.36  % (26526)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.37  % (26529)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)
% 0.19/0.37  % (26523)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.38  TRYING [1]
% 0.19/0.38  TRYING [2]
% 0.19/0.39  TRYING [3]
% 0.19/0.40  % (26527)First to succeed.
% 0.19/0.41  % (26527)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26522"
% 0.19/0.41  % (26527)Refutation found. Thanks to Tanya!
% 0.19/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.42  % (26527)------------------------------
% 0.19/0.42  % (26527)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.42  % (26527)Termination reason: Refutation
% 0.19/0.42  
% 0.19/0.42  % (26527)Memory used [KB]: 1870
% 0.19/0.42  % (26527)Time elapsed: 0.046 s
% 0.19/0.42  % (26527)Instructions burned: 83 (million)
% 0.19/0.42  % (26522)Success in time 0.067 s
%------------------------------------------------------------------------------