TSTP Solution File: SWC094-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC094-1 : 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 : n029.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 04:47:08 EDT 2024

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  250
% Syntax   : Number of formulae    :  401 ( 181 unt;   0 def)
%            Number of atoms       :  873 (  91 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  829 ( 357   ~; 346   |;   0   &)
%                                         ( 126 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :  147 ( 145 usr; 127 prp; 0-2 aty)
%            Number of functors    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :  310 ( 310   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f984,plain,
    $false,
    inference(avatar_sat_refutation,[],[f233,f238,f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f292,f296,f300,f304,f308,f312,f316,f320,f324,f328,f332,f336,f340,f344,f348,f352,f356,f360,f364,f368,f372,f376,f380,f384,f388,f392,f396,f400,f404,f408,f412,f416,f420,f424,f428,f432,f437,f441,f445,f449,f453,f457,f461,f465,f469,f473,f477,f481,f485,f489,f493,f497,f501,f505,f509,f513,f517,f521,f525,f529,f533,f537,f541,f548,f581,f585,f619,f652,f656,f660,f664,f668,f672,f676,f701,f705,f709,f713,f717,f722,f726,f730,f734,f738,f742,f746,f750,f755,f759,f766,f770,f774,f778,f782,f786,f790,f794,f798,f802,f808,f812,f860,f872,f876,f880,f884,f958,f962,f966,f970,f974,f978,f982,f983]) ).

fof(f983,plain,
    ( ~ spl0_9
    | ~ spl0_93
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f918,f858,f719,f270]) ).

fof(f270,plain,
    ( spl0_9
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f719,plain,
    ( spl0_93
  <=> sk4 = app(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f858,plain,
    ( spl0_115
  <=> ! [X0] :
        ( sk4 != app(sk4,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f918,plain,
    ( ~ ssList(nil)
    | ~ spl0_93
    | ~ spl0_115 ),
    inference(trivial_inequality_removal,[],[f917]) ).

fof(f917,plain,
    ( sk4 != sk4
    | ~ ssList(nil)
    | ~ spl0_93
    | ~ spl0_115 ),
    inference(superposition,[],[f859,f721]) ).

fof(f721,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f719]) ).

fof(f859,plain,
    ( ! [X0] :
        ( sk4 != app(sk4,X0)
        | ~ ssList(X0) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f858]) ).

fof(f982,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f128,f980]) ).

fof(f980,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

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(f978,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f127,f976]) ).

fof(f976,plain,
    ( spl0_125
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

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(f974,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f126,f972]) ).

fof(f972,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

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(f970,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f125,f968]) ).

fof(f968,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

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(f966,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f124,f964]) ).

fof(f964,plain,
    ( spl0_122
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

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(f962,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f121,f960]) ).

fof(f960,plain,
    ( spl0_121
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

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

fof(f958,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f120,f956]) ).

fof(f956,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

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(f884,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f119,f882]) ).

fof(f882,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

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

fof(f880,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f118,f878]) ).

fof(f878,plain,
    ( spl0_118
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

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

fof(f876,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f109,f874]) ).

fof(f874,plain,
    ( spl0_117
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

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

fof(f872,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f104,f870]) ).

fof(f870,plain,
    ( spl0_116
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

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

fof(f860,plain,
    ( ~ spl0_1
    | ~ spl0_9
    | spl0_115
    | ~ spl0_56
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f762,f719,f463,f858,f270,f230]) ).

fof(f230,plain,
    ( spl0_1
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f463,plain,
    ( spl0_56
  <=> ! [X6,X7,X8] :
        ( ~ ssList(X6)
        | ~ ssList(X7)
        | ~ ssList(X8)
        | sk4 != app(X6,X8)
        | sk4 != app(app(X6,X7),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f762,plain,
    ( ! [X0] :
        ( sk4 != app(sk4,X0)
        | ~ ssList(nil)
        | ~ ssList(X0)
        | ~ ssList(sk4) )
    | ~ spl0_56
    | ~ spl0_93 ),
    inference(duplicate_literal_removal,[],[f761]) ).

fof(f761,plain,
    ( ! [X0] :
        ( sk4 != app(sk4,X0)
        | ~ ssList(nil)
        | ~ ssList(X0)
        | sk4 != app(sk4,X0)
        | ~ ssList(sk4) )
    | ~ spl0_56
    | ~ spl0_93 ),
    inference(superposition,[],[f464,f721]) ).

fof(f464,plain,
    ( ! [X8,X6,X7] :
        ( sk4 != app(app(X6,X7),X8)
        | ~ ssList(X7)
        | ~ ssList(X8)
        | sk4 != app(X6,X8)
        | ~ ssList(X6) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f463]) ).

fof(f812,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f204,f810]) ).

fof(f810,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f204,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(f808,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f114,f806]) ).

fof(f806,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

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

fof(f802,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f110,f800]) ).

fof(f800,plain,
    ( spl0_112
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

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

fof(f798,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f108,f796]) ).

fof(f796,plain,
    ( spl0_111
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

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

fof(f794,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f107,f792]) ).

fof(f792,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

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

fof(f790,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f106,f788]) ).

fof(f788,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

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

fof(f786,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f105,f784]) ).

fof(f784,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

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

fof(f782,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f103,f780]) ).

fof(f780,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

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

fof(f778,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f102,f776]) ).

fof(f776,plain,
    ( spl0_106
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

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

fof(f774,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f101,f772]) ).

fof(f772,plain,
    ( spl0_105
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

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

fof(f770,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f100,f768]) ).

fof(f768,plain,
    ( spl0_104
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

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

fof(f766,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f97,f764]) ).

fof(f764,plain,
    ( spl0_103
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

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

fof(f759,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f96,f757]) ).

fof(f757,plain,
    ( spl0_102
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

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

fof(f755,plain,
    ( spl0_101
    | ~ spl0_1
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f648,f583,f230,f752]) ).

fof(f752,plain,
    ( spl0_101
  <=> sk4 = app(nil,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f583,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f648,plain,
    ( sk4 = app(nil,sk4)
    | ~ spl0_1
    | ~ spl0_79 ),
    inference(resolution,[],[f584,f232]) ).

fof(f232,plain,
    ( ssList(sk4)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f584,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f583]) ).

fof(f750,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f225,f748]) ).

fof(f748,plain,
    ( spl0_100
  <=> ! [X2,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f225,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f208]) ).

fof(f208,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(f746,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f99,f744]) ).

fof(f744,plain,
    ( spl0_99
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

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

fof(f742,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f98,f740]) ).

fof(f740,plain,
    ( spl0_98
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

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

fof(f738,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f95,f736]) ).

fof(f736,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

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

fof(f734,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f94,f732]) ).

fof(f732,plain,
    ( spl0_96
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

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

fof(f730,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f93,f728]) ).

fof(f728,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

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

fof(f726,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f92,f724]) ).

fof(f724,plain,
    ( spl0_94
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

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

fof(f722,plain,
    ( spl0_93
    | ~ spl0_1
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f614,f579,f230,f719]) ).

fof(f579,plain,
    ( spl0_78
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f614,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_1
    | ~ spl0_78 ),
    inference(resolution,[],[f580,f232]) ).

fof(f580,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f579]) ).

fof(f717,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f91,f715]) ).

fof(f715,plain,
    ( spl0_92
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

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

fof(f713,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f90,f711]) ).

fof(f711,plain,
    ( spl0_91
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

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

fof(f709,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f89,f707]) ).

fof(f707,plain,
    ( spl0_90
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

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

fof(f705,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f88,f703]) ).

fof(f703,plain,
    ( spl0_89
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

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

fof(f701,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f87,f699]) ).

fof(f699,plain,
    ( spl0_88
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

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

fof(f676,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f86,f674]) ).

fof(f674,plain,
    ( spl0_87
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

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

fof(f672,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f85,f670]) ).

fof(f670,plain,
    ( spl0_86
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

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

fof(f668,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f84,f666]) ).

fof(f666,plain,
    ( spl0_85
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ frontsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

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

fof(f664,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f82,f662]) ).

fof(f662,plain,
    ( spl0_84
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ rearsegP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

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

fof(f660,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f80,f658]) ).

fof(f658,plain,
    ( spl0_83
  <=> ! [X0] :
        ( ~ ssList(X0)
        | ~ segmentP(nil,X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

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

fof(f656,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f78,f654]) ).

fof(f654,plain,
    ( spl0_82
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssItem(hd(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

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

fof(f652,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f75,f650]) ).

fof(f650,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

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

fof(f619,plain,
    ( spl0_80
    | ~ spl0_1
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f577,f546,f230,f616]) ).

fof(f616,plain,
    ( spl0_80
  <=> duplicatefreeP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f546,plain,
    ( spl0_77
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f577,plain,
    ( duplicatefreeP(sk4)
    | ~ spl0_1
    | ~ spl0_77 ),
    inference(resolution,[],[f547,f232]) ).

fof(f547,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f546]) ).

fof(f585,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f74,f583]) ).

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

fof(f581,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f73,f579]) ).

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

fof(f548,plain,
    ( spl0_76
    | spl0_77 ),
    inference(avatar_split_clause,[],[f72,f546,f543]) ).

fof(f543,plain,
    ( spl0_76
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

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

fof(f541,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f70,f539]) ).

fof(f539,plain,
    ( spl0_75
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

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

fof(f537,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f69,f535]) ).

fof(f535,plain,
    ( spl0_74
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

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

fof(f533,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f68,f531]) ).

fof(f531,plain,
    ( spl0_73
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

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

fof(f529,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f67,f527]) ).

fof(f527,plain,
    ( spl0_72
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

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

fof(f525,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f66,f523]) ).

fof(f523,plain,
    ( spl0_71
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

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

fof(f521,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f65,f519]) ).

fof(f519,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | duplicatefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

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

fof(f517,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f64,f515]) ).

fof(f515,plain,
    ( spl0_69
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

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

fof(f513,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f228,f511]) ).

fof(f511,plain,
    ( spl0_68
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f228,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f202]) ).

fof(f202,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(f509,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f226,f507]) ).

fof(f507,plain,
    ( spl0_67
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f226,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f207]) ).

fof(f207,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(f505,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f71,f503]) ).

fof(f503,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

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

fof(f501,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f63,f499]) ).

fof(f499,plain,
    ( spl0_65
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

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

fof(f497,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f62,f495]) ).

fof(f495,plain,
    ( spl0_64
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

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

fof(f493,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f61,f491]) ).

fof(f491,plain,
    ( spl0_63
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

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

fof(f489,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f60,f487]) ).

fof(f487,plain,
    ( spl0_62
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

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

fof(f485,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f59,f483]) ).

fof(f483,plain,
    ( spl0_61
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

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

fof(f481,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f58,f479]) ).

fof(f479,plain,
    ( spl0_60
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

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

fof(f477,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f57,f475]) ).

fof(f475,plain,
    ( spl0_59
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

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

fof(f473,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f56,f471]) ).

fof(f471,plain,
    ( spl0_58
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

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

fof(f469,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f55,f467]) ).

fof(f467,plain,
    ( spl0_57
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

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

fof(f465,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f198,f463]) ).

fof(f198,plain,
    ! [X8,X6,X7] :
      ( ~ ssList(X6)
      | ~ ssList(X7)
      | ~ ssList(X8)
      | sk4 != app(X6,X8)
      | sk4 != app(app(X6,X7),X8) ),
    inference(definition_unfolding,[],[f193,f190,f194]) ).

fof(f194,plain,
    sk1 = sk4,
    inference(definition_unfolding,[],[f191,f192]) ).

fof(f192,axiom,
    sk3 = sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

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

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

fof(f193,axiom,
    ! [X8,X6,X7] :
      ( ~ ssList(X6)
      | ~ ssList(X7)
      | ~ ssList(X8)
      | sk2 != app(X6,X8)
      | sk1 != app(app(X6,X7),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).

fof(f461,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f53,f459]) ).

fof(f459,plain,
    ( spl0_55
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

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

fof(f457,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f52,f455]) ).

fof(f455,plain,
    ( spl0_54
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

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

fof(f453,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f51,f451]) ).

fof(f451,plain,
    ( spl0_53
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

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

fof(f449,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f50,f447]) ).

fof(f447,plain,
    ( spl0_52
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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

fof(f445,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f49,f443]) ).

fof(f443,plain,
    ( spl0_51
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

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

fof(f441,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f48,f439]) ).

fof(f439,plain,
    ( spl0_50
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

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

fof(f437,plain,
    ~ spl0_49,
    inference(avatar_split_clause,[],[f54,f434]) ).

fof(f434,plain,
    ( spl0_49
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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

fof(f432,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f47,f430]) ).

fof(f430,plain,
    ( spl0_48
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

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

fof(f428,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f46,f426]) ).

fof(f426,plain,
    ( spl0_47
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

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

fof(f424,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f45,f422]) ).

fof(f422,plain,
    ( spl0_46
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

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

fof(f420,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f44,f418]) ).

fof(f418,plain,
    ( spl0_45
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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

fof(f416,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f43,f414]) ).

fof(f414,plain,
    ( spl0_44
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

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

fof(f412,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f42,f410]) ).

fof(f410,plain,
    ( spl0_43
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f408,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f41,f406]) ).

fof(f406,plain,
    ( spl0_42
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

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

fof(f404,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f40,f402]) ).

fof(f402,plain,
    ( spl0_41
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

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

fof(f400,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f39,f398]) ).

fof(f398,plain,
    ( spl0_40
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

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

fof(f396,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f38,f394]) ).

fof(f394,plain,
    ( spl0_39
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f392,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f37,f390]) ).

fof(f390,plain,
    ( spl0_38
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

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

fof(f388,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f36,f386]) ).

fof(f386,plain,
    ( spl0_37
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

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

fof(f384,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f35,f382]) ).

fof(f382,plain,
    ( spl0_36
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

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

fof(f380,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f34,f378]) ).

fof(f378,plain,
    ( spl0_35
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

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

fof(f376,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f33,f374]) ).

fof(f374,plain,
    ( spl0_34
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

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

fof(f372,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f32,f370]) ).

fof(f370,plain,
    ( spl0_33
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

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

fof(f368,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f31,f366]) ).

fof(f366,plain,
    ( spl0_32
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

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

fof(f364,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f30,f362]) ).

fof(f362,plain,
    ( spl0_31
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

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

fof(f360,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f29,f358]) ).

fof(f358,plain,
    ( spl0_30
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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

fof(f356,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f28,f354]) ).

fof(f354,plain,
    ( spl0_29
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

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

fof(f352,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f27,f350]) ).

fof(f350,plain,
    ( spl0_28
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f348,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f26,f346]) ).

fof(f346,plain,
    ( spl0_27
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

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

fof(f344,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f25,f342]) ).

fof(f342,plain,
    ( spl0_26
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

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

fof(f340,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f24,f338]) ).

fof(f338,plain,
    ( spl0_25
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

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

fof(f336,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f23,f334]) ).

fof(f334,plain,
    ( spl0_24
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

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

fof(f332,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f22,f330]) ).

fof(f330,plain,
    ( spl0_23
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

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

fof(f328,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f21,f326]) ).

fof(f326,plain,
    ( spl0_22
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

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

fof(f324,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f20,f322]) ).

fof(f322,plain,
    ( spl0_21
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

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

fof(f320,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f19,f318]) ).

fof(f318,plain,
    ( spl0_20
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

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

fof(f316,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f18,f314]) ).

fof(f314,plain,
    ( spl0_19
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

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

fof(f312,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f17,f310]) ).

fof(f310,plain,
    ( spl0_18
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

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

fof(f308,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f16,f306]) ).

fof(f306,plain,
    ( spl0_17
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

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

fof(f304,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f15,f302]) ).

fof(f302,plain,
    ( spl0_16
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

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

fof(f300,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f14,f298]) ).

fof(f298,plain,
    ( spl0_15
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

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

fof(f296,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f13,f294]) ).

fof(f294,plain,
    ( spl0_14
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

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

fof(f292,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f12,f290]) ).

fof(f290,plain,
    ( spl0_13
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

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

fof(f288,plain,
    ~ spl0_12,
    inference(avatar_split_clause,[],[f11,f285]) ).

fof(f285,plain,
    ( spl0_12
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

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

fof(f283,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f10,f280]) ).

fof(f280,plain,
    ( spl0_11
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

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

fof(f278,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f9,f275]) ).

fof(f275,plain,
    ( spl0_10
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

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

fof(f273,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f8,f270]) ).

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

fof(f268,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f7,f265]) ).

fof(f265,plain,
    ( spl0_8
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

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

fof(f263,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f6,f260]) ).

fof(f260,plain,
    ( spl0_7
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

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

fof(f258,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f5,f255]) ).

fof(f255,plain,
    ( spl0_6
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

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

fof(f253,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f4,f250]) ).

fof(f250,plain,
    ( spl0_5
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

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

fof(f248,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f3,f245]) ).

fof(f245,plain,
    ( spl0_4
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

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

fof(f243,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f2,f240]) ).

fof(f240,plain,
    ( spl0_3
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

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

fof(f238,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f1,f235]) ).

fof(f235,plain,
    ( spl0_2
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

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

fof(f233,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f195,f230]) ).

fof(f195,plain,
    ssList(sk4),
    inference(definition_unfolding,[],[f186,f194]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWC094-1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 03:44:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (18142)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (18145)WARNING: value z3 for option sas not known
% 0.20/0.38  % (18144)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (18146)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38  % (18143)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38  % (18148)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)
% 0.20/0.38  % (18149)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)
% 0.20/0.38  % (18145)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)
% 0.20/0.38  % (18147)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)
% 0.20/0.39  TRYING [1]
% 0.20/0.39  TRYING [2]
% 0.20/0.39  % (18147)First to succeed.
% 0.20/0.40  % (18147)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18142"
% 0.20/0.40  % (18146)Also succeeded, but the first one will report.
% 0.20/0.40  % (18147)Refutation found. Thanks to Tanya!
% 0.20/0.40  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40  % (18147)------------------------------
% 0.20/0.40  % (18147)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.40  % (18147)Termination reason: Refutation
% 0.20/0.40  
% 0.20/0.40  % (18147)Memory used [KB]: 1386
% 0.20/0.40  % (18147)Time elapsed: 0.022 s
% 0.20/0.40  % (18147)Instructions burned: 35 (million)
% 0.20/0.40  % (18142)Success in time 0.021 s
%------------------------------------------------------------------------------