TSTP Solution File: SWC019-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC019-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:51:37 EDT 2024

% Result   : Unsatisfiable 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  248
% Syntax   : Number of formulae    :  402 ( 181 unt;   0 def)
%            Number of atoms       :  864 (  85 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  807 ( 345   ~; 337   |;   0   &)
%                                         ( 125 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :  146 ( 144 usr; 126 prp; 0-2 aty)
%            Number of functors    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :  298 ( 298   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f986,plain,
    $false,
    inference(avatar_sat_refutation,[],[f237,f242,f246,f251,f256,f261,f266,f271,f276,f281,f286,f291,f296,f301,f305,f309,f313,f317,f321,f325,f329,f333,f337,f341,f345,f349,f353,f357,f361,f365,f369,f373,f377,f381,f385,f389,f393,f397,f401,f405,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f450,f454,f458,f462,f466,f470,f474,f478,f482,f486,f490,f494,f498,f502,f506,f510,f514,f518,f522,f526,f530,f534,f538,f542,f546,f550,f557,f590,f595,f599,f661,f665,f669,f673,f677,f681,f685,f710,f714,f718,f723,f727,f731,f735,f739,f743,f747,f751,f755,f759,f764,f769,f773,f777,f781,f785,f789,f793,f797,f801,f806,f810,f814,f818,f869,f881,f885,f889,f896,f968,f972,f976,f980,f984,f985]) ).

fof(f985,plain,
    ( ~ spl0_1
    | spl0_2
    | ~ spl0_64
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f892,f867,f500,f239,f234]) ).

fof(f234,plain,
    ( spl0_1
  <=> ssList(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f239,plain,
    ( spl0_2
  <=> nil = sk4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f500,plain,
    ( spl0_64
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f867,plain,
    ( spl0_116
  <=> ! [X0] :
        ( nil = X0
        | ~ frontsegP(sk4,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f892,plain,
    ( nil = sk4
    | ~ ssList(sk4)
    | ~ spl0_64
    | ~ spl0_116 ),
    inference(duplicate_literal_removal,[],[f891]) ).

fof(f891,plain,
    ( nil = sk4
    | ~ ssList(sk4)
    | ~ ssList(sk4)
    | ~ spl0_64
    | ~ spl0_116 ),
    inference(resolution,[],[f868,f501]) ).

fof(f501,plain,
    ( ! [X0] :
        ( frontsegP(X0,X0)
        | ~ ssList(X0) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f500]) ).

fof(f868,plain,
    ( ! [X0] :
        ( ~ frontsegP(sk4,X0)
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f867]) ).

fof(f984,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f126,f982]) ).

fof(f982,plain,
    ( spl0_125
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

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

fof(f980,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f125,f978]) ).

fof(f978,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | totalorderedP(X1)
        | nil = X1
        | ~ totalorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

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

fof(f976,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f124,f974]) ).

fof(f974,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | strictorderedP(X1)
        | nil = X1
        | ~ strictorderedP(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

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

fof(f972,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f121,f970]) ).

fof(f970,plain,
    ( spl0_122
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ leq(X0,X1)
        | X0 = X1
        | lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

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

fof(f968,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f120,f966]) ).

fof(f966,plain,
    ( spl0_121
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) = app(cons(X0,nil),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

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

fof(f896,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f119,f894]) ).

fof(f894,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X1
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

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

fof(f889,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f118,f887]) ).

fof(f887,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | nil = X0
        | nil != app(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

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

fof(f885,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f109,f883]) ).

fof(f883,plain,
    ( spl0_118
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(skaf83(X0),skaf82(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

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

fof(f881,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f104,f879]) ).

fof(f879,plain,
    ( spl0_117
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

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

fof(f869,plain,
    ( spl0_116
    | ~ spl0_11
    | ~ spl0_3
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f860,f775,f244,f283,f867]) ).

fof(f283,plain,
    ( spl0_11
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f244,plain,
    ( spl0_3
  <=> ! [X6] :
        ( ~ ssList(X6)
        | ~ neq(X6,nil)
        | ~ frontsegP(sk4,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f775,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( ~ ssList(X1)
        | ~ ssList(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f860,plain,
    ( ! [X0] :
        ( ~ ssList(nil)
        | nil = X0
        | ~ ssList(X0)
        | ~ frontsegP(sk4,X0) )
    | ~ spl0_3
    | ~ spl0_105 ),
    inference(duplicate_literal_removal,[],[f855]) ).

fof(f855,plain,
    ( ! [X0] :
        ( ~ ssList(nil)
        | nil = X0
        | ~ ssList(X0)
        | ~ ssList(X0)
        | ~ frontsegP(sk4,X0) )
    | ~ spl0_3
    | ~ spl0_105 ),
    inference(resolution,[],[f776,f245]) ).

fof(f245,plain,
    ( ! [X6] :
        ( ~ neq(X6,nil)
        | ~ ssList(X6)
        | ~ frontsegP(sk4,X6) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f776,plain,
    ( ! [X0,X1] :
        ( neq(X1,X0)
        | ~ ssList(X0)
        | X0 = X1
        | ~ ssList(X1) )
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f775]) ).

fof(f818,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f206,f816]) ).

fof(f816,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ ssList(cons(X0,nil))
        | singletonP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f206,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | singletonP(cons(X0,nil)) ),
    inference(equality_resolution,[],[f116]) ).

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

fof(f814,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f114,f812]) ).

fof(f812,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X1,X0)
        | ~ lt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

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

fof(f810,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f110,f808]) ).

fof(f808,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X1,X0)
        | ~ gt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

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

fof(f806,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f108,f804]) ).

fof(f804,plain,
    ( spl0_112
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ leq(X0,X1)
        | geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

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

fof(f801,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f107,f799]) ).

fof(f799,plain,
    ( spl0_111
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ geq(X0,X1)
        | leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

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

fof(f797,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f106,f795]) ).

fof(f795,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X1)
        | ~ lt(X0,X1)
        | gt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

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

fof(f793,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f105,f791]) ).

fof(f791,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ gt(X0,X1)
        | lt(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

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

fof(f789,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f103,f787]) ).

fof(f787,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | ~ lt(X0,X1)
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

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

fof(f785,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f102,f783]) ).

fof(f783,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( ~ ssItem(X1)
        | ~ ssItem(X0)
        | X0 = X1
        | neq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

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

fof(f781,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f101,f779]) ).

fof(f779,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ singletonP(X0)
        | ~ ssList(X0)
        | cons(skaf44(X0),nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

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

fof(f777,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f100,f775]) ).

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

fof(f773,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f97,f771]) ).

fof(f771,plain,
    ( spl0_104
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | hd(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

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

fof(f769,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f96,f767]) ).

fof(f767,plain,
    ( spl0_103
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | tl(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

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

fof(f764,plain,
    ( spl0_102
    | ~ spl0_1
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f657,f597,f234,f761]) ).

fof(f761,plain,
    ( spl0_102
  <=> sk4 = app(nil,sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f597,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f657,plain,
    ( sk4 = app(nil,sk4)
    | ~ spl0_1
    | ~ spl0_81 ),
    inference(resolution,[],[f598,f236]) ).

fof(f236,plain,
    ( ssList(sk4)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f598,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f759,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f227,f757]) ).

fof(f757,plain,
    ( spl0_101
  <=> ! [X2,X1] :
        ( ~ ssItem(X1)
        | ~ ssList(X2)
        | memberP(cons(X1,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f227,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(duplicate_literal_removal,[],[f210]) ).

fof(f210,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(equality_resolution,[],[f138]) ).

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

fof(f755,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f99,f753]) ).

fof(f753,plain,
    ( spl0_100
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

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

fof(f751,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f98,f749]) ).

fof(f749,plain,
    ( spl0_99
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | nil != cons(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

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

fof(f747,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f95,f745]) ).

fof(f745,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf54(X0),skaf55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

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

fof(f743,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f94,f741]) ).

fof(f741,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderP(X0)
        | ~ leq(skaf55(X0),skaf54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

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

fof(f739,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f93,f737]) ).

fof(f737,plain,
    ( spl0_96
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf59(X0),skaf60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

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

fof(f735,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f92,f733]) ).

fof(f733,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderP(X0)
        | ~ lt(skaf60(X0),skaf59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

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

fof(f731,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f91,f729]) ).

fof(f729,plain,
    ( spl0_94
  <=> ! [X0] :
        ( ~ ssList(X0)
        | totalorderedP(X0)
        | ~ leq(skaf64(X0),skaf65(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

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

fof(f727,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f90,f725]) ).

fof(f725,plain,
    ( spl0_93
  <=> ! [X0] :
        ( ~ ssList(X0)
        | strictorderedP(X0)
        | ~ lt(skaf69(X0),skaf70(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

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

fof(f723,plain,
    ( spl0_92
    | ~ spl0_1
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f628,f588,f234,f720]) ).

fof(f720,plain,
    ( spl0_92
  <=> sk4 = app(sk4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f588,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f628,plain,
    ( sk4 = app(sk4,nil)
    | ~ spl0_1
    | ~ spl0_79 ),
    inference(resolution,[],[f589,f236]) ).

fof(f589,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f588]) ).

fof(f718,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f89,f716]) ).

fof(f716,plain,
    ( spl0_91
  <=> ! [X0] :
        ( ~ ssList(X0)
        | equalelemsP(X0)
        | skaf79(X0) != skaf78(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

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

fof(f714,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f88,f712]) ).

fof(f712,plain,
    ( spl0_90
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf49(X0),skaf50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

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

fof(f710,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f87,f708]) ).

fof(f708,plain,
    ( spl0_89
  <=> ! [X0] :
        ( ~ ssList(X0)
        | cyclefreeP(X0)
        | leq(skaf50(X0),skaf49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

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

fof(f685,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f86,f683]) ).

fof(f683,plain,
    ( spl0_88
  <=> ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssList(X1)
        | ssList(cons(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

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

fof(f681,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f85,f679]) ).

fof(f679,plain,
    ( spl0_87
  <=> ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ssList(app(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

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

fof(f677,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f84,f675]) ).

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

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

fof(f673,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f82,f671]) ).

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

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

fof(f669,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f80,f667]) ).

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

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

fof(f665,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f76,f663]) ).

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

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

fof(f661,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f75,f659]) ).

fof(f659,plain,
    ( spl0_82
  <=> ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | ssList(tl(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

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

fof(f599,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f74,f597]) ).

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

fof(f595,plain,
    ( spl0_80
    | ~ spl0_1
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f586,f555,f234,f592]) ).

fof(f592,plain,
    ( spl0_80
  <=> duplicatefreeP(sk4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f555,plain,
    ( spl0_78
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f586,plain,
    ( duplicatefreeP(sk4)
    | ~ spl0_1
    | ~ spl0_78 ),
    inference(resolution,[],[f556,f236]) ).

fof(f556,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f555]) ).

fof(f590,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f73,f588]) ).

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

fof(f557,plain,
    ( spl0_77
    | spl0_78 ),
    inference(avatar_split_clause,[],[f72,f555,f552]) ).

fof(f552,plain,
    ( spl0_77
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

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

fof(f550,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f70,f548]) ).

fof(f548,plain,
    ( spl0_76
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cyclefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

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

fof(f546,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f69,f544]) ).

fof(f544,plain,
    ( spl0_75
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

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

fof(f542,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f68,f540]) ).

fof(f540,plain,
    ( spl0_74
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

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

fof(f538,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f67,f536]) ).

fof(f536,plain,
    ( spl0_73
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | totalorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

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

fof(f534,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f66,f532]) ).

fof(f532,plain,
    ( spl0_72
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | strictorderedP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

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

fof(f530,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f65,f528]) ).

fof(f528,plain,
    ( spl0_71
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | duplicatefreeP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

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

fof(f526,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f64,f524]) ).

fof(f524,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | equalelemsP(cons(X0,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

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

fof(f522,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f230,f520]) ).

fof(f520,plain,
    ( spl0_69
  <=> ! [X1] :
        ( ~ ssItem(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f230,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f204]) ).

fof(f204,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f117]) ).

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

fof(f518,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f228,f516]) ).

fof(f516,plain,
    ( spl0_68
  <=> ! [X1] :
        ( ~ ssList(X1)
        | ~ neq(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f228,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(duplicate_literal_removal,[],[f209]) ).

fof(f209,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f115]) ).

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

fof(f514,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f71,f512]) ).

fof(f512,plain,
    ( spl0_67
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ memberP(nil,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

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

fof(f510,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f63,f508]) ).

fof(f508,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | ~ lt(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

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

fof(f506,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f62,f504]) ).

fof(f504,plain,
    ( spl0_65
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | leq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

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

fof(f502,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f61,f500]) ).

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

fof(f498,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f60,f496]) ).

fof(f496,plain,
    ( spl0_63
  <=> ! [X0] :
        ( ~ ssList(X0)
        | frontsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

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

fof(f494,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f59,f492]) ).

fof(f492,plain,
    ( spl0_62
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

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

fof(f490,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f58,f488]) ).

fof(f488,plain,
    ( spl0_61
  <=> ! [X0] :
        ( ~ ssList(X0)
        | rearsegP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

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

fof(f486,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f57,f484]) ).

fof(f484,plain,
    ( spl0_60
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

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

fof(f482,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f56,f480]) ).

fof(f480,plain,
    ( spl0_59
  <=> ! [X0] :
        ( ~ ssList(X0)
        | segmentP(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

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

fof(f478,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f55,f476]) ).

fof(f476,plain,
    ( spl0_58
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | geq(X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

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

fof(f474,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f53,f472]) ).

fof(f472,plain,
    ( spl0_57
  <=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

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

fof(f470,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f52,f468]) ).

fof(f468,plain,
    ( spl0_56
  <=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

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

fof(f466,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f51,f464]) ).

fof(f464,plain,
    ( spl0_55
  <=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

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

fof(f462,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f50,f460]) ).

fof(f460,plain,
    ( spl0_54
  <=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

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

fof(f458,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f49,f456]) ).

fof(f456,plain,
    ( spl0_53
  <=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

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

fof(f454,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f48,f452]) ).

fof(f452,plain,
    ( spl0_52
  <=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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

fof(f450,plain,
    ~ spl0_51,
    inference(avatar_split_clause,[],[f54,f447]) ).

fof(f447,plain,
    ( spl0_51
  <=> skac3 = skac2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

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

fof(f445,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f47,f443]) ).

fof(f443,plain,
    ( spl0_50
  <=> ! [X0] : ssItem(skaf44(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

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

fof(f441,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f46,f439]) ).

fof(f439,plain,
    ( spl0_49
  <=> ! [X0] : ssItem(skaf49(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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

fof(f437,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f45,f435]) ).

fof(f435,plain,
    ( spl0_48
  <=> ! [X0] : ssItem(skaf50(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

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

fof(f433,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f44,f431]) ).

fof(f431,plain,
    ( spl0_47
  <=> ! [X0] : ssList(skaf51(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

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

fof(f429,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f43,f427]) ).

fof(f427,plain,
    ( spl0_46
  <=> ! [X0] : ssList(skaf52(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

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

fof(f425,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f42,f423]) ).

fof(f423,plain,
    ( spl0_45
  <=> ! [X0] : ssList(skaf53(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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

fof(f421,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f41,f419]) ).

fof(f419,plain,
    ( spl0_44
  <=> ! [X0] : ssItem(skaf54(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

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

fof(f417,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f40,f415]) ).

fof(f415,plain,
    ( spl0_43
  <=> ! [X0] : ssItem(skaf55(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f413,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f39,f411]) ).

fof(f411,plain,
    ( spl0_42
  <=> ! [X0] : ssList(skaf56(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

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

fof(f409,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f38,f407]) ).

fof(f407,plain,
    ( spl0_41
  <=> ! [X0] : ssList(skaf57(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

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

fof(f405,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f37,f403]) ).

fof(f403,plain,
    ( spl0_40
  <=> ! [X0] : ssList(skaf58(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

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

fof(f401,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f36,f399]) ).

fof(f399,plain,
    ( spl0_39
  <=> ! [X0] : ssItem(skaf59(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f397,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f35,f395]) ).

fof(f395,plain,
    ( spl0_38
  <=> ! [X0] : ssItem(skaf60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

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

fof(f393,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f34,f391]) ).

fof(f391,plain,
    ( spl0_37
  <=> ! [X0] : ssList(skaf61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

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

fof(f389,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f33,f387]) ).

fof(f387,plain,
    ( spl0_36
  <=> ! [X0] : ssList(skaf62(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

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

fof(f385,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f32,f383]) ).

fof(f383,plain,
    ( spl0_35
  <=> ! [X0] : ssList(skaf63(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

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

fof(f381,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f31,f379]) ).

fof(f379,plain,
    ( spl0_34
  <=> ! [X0] : ssItem(skaf64(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

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

fof(f377,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f30,f375]) ).

fof(f375,plain,
    ( spl0_33
  <=> ! [X0] : ssItem(skaf65(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

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

fof(f373,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f29,f371]) ).

fof(f371,plain,
    ( spl0_32
  <=> ! [X0] : ssList(skaf66(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

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

fof(f369,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f28,f367]) ).

fof(f367,plain,
    ( spl0_31
  <=> ! [X0] : ssList(skaf67(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

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

fof(f365,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f27,f363]) ).

fof(f363,plain,
    ( spl0_30
  <=> ! [X0] : ssList(skaf68(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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

fof(f361,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f26,f359]) ).

fof(f359,plain,
    ( spl0_29
  <=> ! [X0] : ssItem(skaf69(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

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

fof(f357,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f25,f355]) ).

fof(f355,plain,
    ( spl0_28
  <=> ! [X0] : ssItem(skaf70(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f353,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f24,f351]) ).

fof(f351,plain,
    ( spl0_27
  <=> ! [X0] : ssList(skaf71(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

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

fof(f349,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f23,f347]) ).

fof(f347,plain,
    ( spl0_26
  <=> ! [X0] : ssList(skaf72(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

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

fof(f345,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f22,f343]) ).

fof(f343,plain,
    ( spl0_25
  <=> ! [X0] : ssList(skaf73(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

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

fof(f341,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f21,f339]) ).

fof(f339,plain,
    ( spl0_24
  <=> ! [X0] : ssItem(skaf74(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

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

fof(f337,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f20,f335]) ).

fof(f335,plain,
    ( spl0_23
  <=> ! [X0] : ssList(skaf75(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

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

fof(f333,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f19,f331]) ).

fof(f331,plain,
    ( spl0_22
  <=> ! [X0] : ssList(skaf76(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

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

fof(f329,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f18,f327]) ).

fof(f327,plain,
    ( spl0_21
  <=> ! [X0] : ssList(skaf77(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

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

fof(f325,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f17,f323]) ).

fof(f323,plain,
    ( spl0_20
  <=> ! [X0] : ssItem(skaf78(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

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

fof(f321,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f16,f319]) ).

fof(f319,plain,
    ( spl0_19
  <=> ! [X0] : ssItem(skaf79(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

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

fof(f317,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f15,f315]) ).

fof(f315,plain,
    ( spl0_18
  <=> ! [X0] : ssList(skaf80(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

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

fof(f313,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f14,f311]) ).

fof(f311,plain,
    ( spl0_17
  <=> ! [X0] : ssList(skaf81(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

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

fof(f309,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f13,f307]) ).

fof(f307,plain,
    ( spl0_16
  <=> ! [X0] : ssList(skaf82(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

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

fof(f305,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f12,f303]) ).

fof(f303,plain,
    ( spl0_15
  <=> ! [X0] : ssItem(skaf83(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

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

fof(f301,plain,
    ~ spl0_14,
    inference(avatar_split_clause,[],[f11,f298]) ).

fof(f298,plain,
    ( spl0_14
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

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

fof(f296,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f10,f293]) ).

fof(f293,plain,
    ( spl0_13
  <=> ssItem(skac2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

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

fof(f291,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f9,f288]) ).

fof(f288,plain,
    ( spl0_12
  <=> ssItem(skac3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

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

fof(f286,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f8,f283]) ).

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

fof(f281,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f7,f278]) ).

fof(f278,plain,
    ( spl0_10
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

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

fof(f276,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f6,f273]) ).

fof(f273,plain,
    ( spl0_9
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

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

fof(f271,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f5,f268]) ).

fof(f268,plain,
    ( spl0_8
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

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

fof(f266,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f4,f263]) ).

fof(f263,plain,
    ( spl0_7
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

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

fof(f261,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f3,f258]) ).

fof(f258,plain,
    ( spl0_6
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

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

fof(f256,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f2,f253]) ).

fof(f253,plain,
    ( spl0_5
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

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

fof(f251,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f1,f248]) ).

fof(f248,plain,
    ( spl0_4
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

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

fof(f246,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f231,f244]) ).

fof(f231,plain,
    ! [X6] :
      ( ~ ssList(X6)
      | ~ neq(X6,nil)
      | ~ frontsegP(sk4,X6) ),
    inference(duplicate_literal_removal,[],[f200]) ).

fof(f200,plain,
    ! [X6] :
      ( ~ ssList(X6)
      | ~ neq(X6,nil)
      | ~ frontsegP(sk4,X6)
      | ~ frontsegP(sk4,X6) ),
    inference(definition_unfolding,[],[f193,f195,f190]) ).

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

fof(f195,plain,
    sk1 = sk4,
    inference(definition_unfolding,[],[f191,f192]) ).

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

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

fof(f193,axiom,
    ! [X6] :
      ( ~ ssList(X6)
      | ~ neq(X6,nil)
      | ~ frontsegP(sk1,X6)
      | ~ frontsegP(sk2,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

fof(f242,plain,
    ~ spl0_2,
    inference(avatar_split_clause,[],[f232,f239]) ).

fof(f232,plain,
    nil != sk4,
    inference(duplicate_literal_removal,[],[f199]) ).

fof(f199,plain,
    ( nil != sk4
    | nil != sk4 ),
    inference(definition_unfolding,[],[f194,f195,f190]) ).

fof(f194,axiom,
    ( nil != sk1
    | nil != sk2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

fof(f237,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f196,f234]) ).

fof(f196,plain,
    ssList(sk4),
    inference(definition_unfolding,[],[f188,f192]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWC019-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.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   : Fri May  3 20:24:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (14985)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (14988)WARNING: value z3 for option sas not known
% 0.14/0.38  % (14989)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (14987)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (14990)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)
% 0.14/0.38  % (14991)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)
% 0.14/0.38  % (14992)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)
% 0.14/0.38  % (14988)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)
% 0.14/0.38  % (14986)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.40  % (14990)First to succeed.
% 0.14/0.40  % (14991)Also succeeded, but the first one will report.
% 0.14/0.40  % (14988)Also succeeded, but the first one will report.
% 0.14/0.40  % (14990)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14985"
% 0.14/0.40  % (14990)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41  % (14990)------------------------------
% 0.14/0.41  % (14990)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41  % (14990)Termination reason: Refutation
% 0.14/0.41  
% 0.14/0.41  % (14990)Memory used [KB]: 1385
% 0.14/0.41  % (14990)Time elapsed: 0.023 s
% 0.14/0.41  % (14990)Instructions burned: 35 (million)
% 0.14/0.41  % (14985)Success in time 0.043 s
%------------------------------------------------------------------------------