TSTP Solution File: SWC038+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC038+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 : n017.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 09:52:22 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  112
% Syntax   : Number of formulae    :  361 (  94 unt;   0 def)
%            Number of atoms       : 1089 ( 353 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives : 1096 ( 368   ~; 413   |; 183   &)
%                                         (  73 <=>;  59  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   82 (  80 usr;  62 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-2 aty)
%            Number of variables   :  348 ( 295   !;  53   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1031,plain,
    $false,
    inference(avatar_sat_refutation,[],[f707,f712,f717,f722,f727,f732,f737,f742,f747,f752,f757,f761,f765,f769,f773,f777,f781,f786,f791,f795,f799,f803,f807,f811,f815,f819,f823,f827,f836,f840,f844,f848,f852,f856,f860,f864,f868,f872,f876,f881,f885,f900,f910,f915,f919,f923,f927,f931,f935,f939,f943,f957,f961,f965,f969,f973,f977,f1002,f1006,f1015,f1024,f1030]) ).

fof(f1030,plain,
    ( ~ spl69_1
    | spl69_11
    | ~ spl69_18
    | ~ spl69_41 ),
    inference(avatar_split_clause,[],[f903,f883,f783,f754,f704]) ).

fof(f704,plain,
    ( spl69_1
  <=> ssList(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).

fof(f754,plain,
    ( spl69_11
  <=> sK20 = sK21 ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_11])]) ).

fof(f783,plain,
    ( spl69_18
  <=> frontsegP(sK21,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_18])]) ).

fof(f883,plain,
    ( spl69_41
  <=> ! [X0] :
        ( sK21 = X0
        | ~ frontsegP(sK21,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_41])]) ).

fof(f903,plain,
    ( sK20 = sK21
    | ~ ssList(sK20)
    | ~ spl69_18
    | ~ spl69_41 ),
    inference(resolution,[],[f884,f785]) ).

fof(f785,plain,
    ( frontsegP(sK21,sK20)
    | ~ spl69_18 ),
    inference(avatar_component_clause,[],[f783]) ).

fof(f884,plain,
    ( ! [X0] :
        ( ~ frontsegP(sK21,X0)
        | sK21 = X0
        | ~ ssList(X0) )
    | ~ spl69_41 ),
    inference(avatar_component_clause,[],[f883]) ).

fof(f1024,plain,
    spl69_61,
    inference(avatar_split_clause,[],[f664,f1022]) ).

fof(f1022,plain,
    ( spl69_61
  <=> ! [X0,X1] :
        ( tl(app(X0,X1)) = app(tl(X0),X1)
        | sK21 = X0
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_61])]) ).

fof(f664,plain,
    ! [X0,X1] :
      ( tl(app(X0,X1)) = app(tl(X0),X1)
      | sK21 = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f568,f603]) ).

fof(f603,plain,
    nil = sK21,
    inference(definition_unfolding,[],[f378,f379]) ).

fof(f379,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ( ( ( frontsegP(sK21,sK20)
        & neq(sK20,nil) )
      | ( nil = sK20
        & nil = sK21 ) )
    & nil != sK18
    & sK18 = sK20
    & sK19 = sK21
    & nil = sK19
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( frontsegP(X3,X2)
                        & neq(X2,nil) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & nil = X1
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & nil != sK18
                  & sK18 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( frontsegP(X3,X2)
                    & neq(X2,nil) )
                  | ( nil = X2
                    & nil = X3 ) )
                & nil != sK18
                & sK18 = X2
                & X1 = X3
                & nil = X1
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( frontsegP(X3,X2)
                  & neq(X2,nil) )
                | ( nil = X2
                  & nil = X3 ) )
              & nil != sK18
              & sK18 = X2
              & sK19 = X3
              & nil = sK19
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( frontsegP(X3,X2)
                & neq(X2,nil) )
              | ( nil = X2
                & nil = X3 ) )
            & nil != sK18
            & sK18 = X2
            & sK19 = X3
            & nil = sK19
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( frontsegP(X3,sK20)
              & neq(sK20,nil) )
            | ( nil = sK20
              & nil = X3 ) )
          & nil != sK18
          & sK18 = sK20
          & sK19 = X3
          & nil = sK19
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ( ( frontsegP(X3,sK20)
            & neq(sK20,nil) )
          | ( nil = sK20
            & nil = X3 ) )
        & nil != sK18
        & sK18 = sK20
        & sK19 = X3
        & nil = sK19
        & ssList(X3) )
   => ( ( ( frontsegP(sK21,sK20)
          & neq(sK20,nil) )
        | ( nil = sK20
          & nil = sK21 ) )
      & nil != sK18
      & sK18 = sK20
      & sK19 = sK21
      & nil = sK19
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( ~ frontsegP(X3,X2)
                          | ~ neq(X2,nil) )
                        & ( nil != X2
                          | nil != X3 ) )
                      | nil = X0
                      | X0 != X2
                      | X1 != X3
                      | nil != X1 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ~ frontsegP(X3,X2)
                        | ~ neq(X2,nil) )
                      & ( nil != X2
                        | nil != X3 ) )
                    | nil = X0
                    | X0 != X2
                    | X1 != X3
                    | nil != X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f378,plain,
    nil = sK19,
    inference(cnf_transformation,[],[f254]) ).

fof(f568,plain,
    ! [X0,X1] :
      ( tl(app(X0,X1)) = app(tl(X0),X1)
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f189,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(app(X0,X1)) = app(tl(X0),X1)
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(app(X0,X1)) = app(tl(X0),X1)
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f86]) ).

fof(f86,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil != X0
           => tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).

fof(f1015,plain,
    spl69_60,
    inference(avatar_split_clause,[],[f663,f1013]) ).

fof(f1013,plain,
    ( spl69_60
  <=> ! [X0,X1] :
        ( hd(X0) = hd(app(X0,X1))
        | sK21 = X0
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_60])]) ).

fof(f663,plain,
    ! [X0,X1] :
      ( hd(X0) = hd(app(X0,X1))
      | sK21 = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f567,f603]) ).

fof(f567,plain,
    ! [X0,X1] :
      ( hd(X0) = hd(app(X0,X1))
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f187]) ).

fof(f187,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f186]) ).

fof(f186,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f85,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil != X0
           => hd(X0) = hd(app(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).

fof(f1006,plain,
    spl69_59,
    inference(avatar_split_clause,[],[f662,f1004]) ).

fof(f1004,plain,
    ( spl69_59
  <=> ! [X0,X1] :
        ( cons(X1,X0) = app(cons(X1,sK21),X0)
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_59])]) ).

fof(f662,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,sK21),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f561,f603]) ).

fof(f561,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).

fof(f1002,plain,
    ~ spl69_58,
    inference(avatar_split_clause,[],[f602,f999]) ).

fof(f999,plain,
    ( spl69_58
  <=> sK67 = sK68 ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_58])]) ).

fof(f602,plain,
    sK67 != sK68,
    inference(cnf_transformation,[],[f373]) ).

fof(f373,plain,
    ( sK67 != sK68
    & ssItem(sK68)
    & ssItem(sK67) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f2,f372,f371]) ).

fof(f371,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( X0 != X1
            & ssItem(X1) )
        & ssItem(X0) )
   => ( ? [X1] :
          ( sK67 != X1
          & ssItem(X1) )
      & ssItem(sK67) ) ),
    introduced(choice_axiom,[]) ).

fof(f372,plain,
    ( ? [X1] :
        ( sK67 != X1
        & ssItem(X1) )
   => ( sK67 != sK68
      & ssItem(sK68) ) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ? [X0] :
      ( ? [X1] :
          ( X0 != X1
          & ssItem(X1) )
      & ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

fof(f977,plain,
    spl69_57,
    inference(avatar_split_clause,[],[f668,f975]) ).

fof(f975,plain,
    ( spl69_57
  <=> ! [X0,X1] :
        ( sK21 = X1
        | app(X0,X1) != sK21
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_57])]) ).

fof(f668,plain,
    ! [X0,X1] :
      ( sK21 = X1
      | app(X0,X1) != sK21
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f585,f603,f603]) ).

fof(f585,plain,
    ! [X0,X1] :
      ( nil = X1
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f370]) ).

fof(f370,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f369]) ).

fof(f369,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f202]) ).

fof(f202,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).

fof(f973,plain,
    spl69_56,
    inference(avatar_split_clause,[],[f667,f971]) ).

fof(f971,plain,
    ( spl69_56
  <=> ! [X0,X1] :
        ( sK21 = X0
        | app(X0,X1) != sK21
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_56])]) ).

fof(f667,plain,
    ! [X0,X1] :
      ( sK21 = X0
      | app(X0,X1) != sK21
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f586,f603,f603]) ).

fof(f586,plain,
    ! [X0,X1] :
      ( nil = X0
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f370]) ).

fof(f969,plain,
    spl69_55,
    inference(avatar_split_clause,[],[f648,f967]) ).

fof(f967,plain,
    ( spl69_55
  <=> ! [X0] :
        ( cons(hd(X0),tl(X0)) = X0
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_55])]) ).

fof(f648,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f463,f603]) ).

fof(f463,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).

fof(f965,plain,
    spl69_54,
    inference(avatar_split_clause,[],[f643,f963]) ).

fof(f963,plain,
    ( spl69_54
  <=> ! [X0] :
        ( cons(sK23(X0),sK22(X0)) = X0
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_54])]) ).

fof(f643,plain,
    ! [X0] :
      ( cons(sK23(X0),sK22(X0)) = X0
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f460,f603]) ).

fof(f460,plain,
    ! [X0] :
      ( cons(sK23(X0),sK22(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f276,plain,
    ! [X0] :
      ( ( cons(sK23(X0),sK22(X0)) = X0
        & ssItem(sK23(X0))
        & ssList(sK22(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f149,f275,f274]) ).

fof(f274,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
     => ( ? [X2] :
            ( cons(X2,sK22(X0)) = X0
            & ssItem(X2) )
        & ssList(sK22(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f275,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK22(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK23(X0),sK22(X0)) = X0
        & ssItem(sK23(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ? [X1] :
            ( ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) )
            & ssList(X1) )
        | nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).

fof(f961,plain,
    spl69_53,
    inference(avatar_split_clause,[],[f633,f959]) ).

fof(f959,plain,
    ( spl69_53
  <=> ! [X0,X1] :
        ( sP2(X0,X1)
        | ~ lt(X1,hd(X0))
        | ~ strictorderedP(X0)
        | sK21 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_53])]) ).

fof(f633,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | ~ lt(X1,hd(X0))
      | ~ strictorderedP(X0)
      | sK21 = X0 ),
    inference(definition_unfolding,[],[f445,f603]) ).

fof(f445,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | ~ lt(X1,hd(X0))
      | ~ strictorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ( ~ lt(X1,hd(X0))
            | ~ strictorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( lt(X1,hd(X0))
          & strictorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f270]) ).

fof(f270,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f269]) ).

fof(f269,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f226]) ).

fof(f226,plain,
    ! [X1,X0] :
      ( sP2(X1,X0)
    <=> ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f957,plain,
    spl69_52,
    inference(avatar_split_clause,[],[f628,f955]) ).

fof(f955,plain,
    ( spl69_52
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | ~ leq(X1,hd(X0))
        | ~ totalorderedP(X0)
        | sK21 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_52])]) ).

fof(f628,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | ~ leq(X1,hd(X0))
      | ~ totalorderedP(X0)
      | sK21 = X0 ),
    inference(definition_unfolding,[],[f437,f603]) ).

fof(f437,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | ~ leq(X1,hd(X0))
      | ~ totalorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f267]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ leq(X1,hd(X0))
            | ~ totalorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( leq(X1,hd(X0))
          & totalorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f266]) ).

fof(f266,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(flattening,[],[f265]) ).

fof(f265,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f223,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f943,plain,
    spl69_51,
    inference(avatar_split_clause,[],[f677,f941]) ).

fof(f941,plain,
    ( spl69_51
  <=> ! [X1] :
        ( singletonP(cons(X1,sK21))
        | ~ ssItem(X1)
        | ~ ssList(cons(X1,sK21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_51])]) ).

fof(f677,plain,
    ! [X1] :
      ( singletonP(cons(X1,sK21))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,sK21)) ),
    inference(equality_resolution,[],[f653]) ).

fof(f653,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,sK21) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f470,f603]) ).

fof(f470,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f284]) ).

fof(f284,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK26(X0),nil) = X0
            & ssItem(sK26(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f282,f283]) ).

fof(f283,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK26(X0),nil) = X0
        & ssItem(sK26(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f282,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f281]) ).

fof(f281,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f939,plain,
    spl69_50,
    inference(avatar_split_clause,[],[f654,f937]) ).

fof(f937,plain,
    ( spl69_50
  <=> ! [X0] :
        ( cons(sK26(X0),sK21) = X0
        | ~ singletonP(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_50])]) ).

fof(f654,plain,
    ! [X0] :
      ( cons(sK26(X0),sK21) = X0
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f469,f603]) ).

fof(f469,plain,
    ! [X0] :
      ( cons(sK26(X0),nil) = X0
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f284]) ).

fof(f935,plain,
    spl69_49,
    inference(avatar_split_clause,[],[f651,f933]) ).

fof(f933,plain,
    ( spl69_49
  <=> ! [X0] :
        ( tl(X0) = sK25(X0)
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_49])]) ).

fof(f651,plain,
    ! [X0] :
      ( tl(X0) = sK25(X0)
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f467,f603]) ).

fof(f467,plain,
    ! [X0] :
      ( tl(X0) = sK25(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f280]) ).

fof(f280,plain,
    ! [X0] :
      ( ( tl(X0) = sK25(X0)
        & ssList(sK25(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f159,f279]) ).

fof(f279,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK25(X0)
        & ssList(sK25(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).

fof(f931,plain,
    spl69_48,
    inference(avatar_split_clause,[],[f649,f929]) ).

fof(f929,plain,
    ( spl69_48
  <=> ! [X0] :
        ( hd(X0) = sK24(X0)
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_48])]) ).

fof(f649,plain,
    ! [X0] :
      ( hd(X0) = sK24(X0)
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f465,f603]) ).

fof(f465,plain,
    ! [X0] :
      ( hd(X0) = sK24(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f278,plain,
    ! [X0] :
      ( ( hd(X0) = sK24(X0)
        & ssItem(sK24(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f157,f277]) ).

fof(f277,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK24(X0)
        & ssItem(sK24(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).

fof(f927,plain,
    spl69_47,
    inference(avatar_split_clause,[],[f635,f925]) ).

fof(f925,plain,
    ( spl69_47
  <=> ! [X0,X1] :
        ( lt(X1,hd(X0))
        | sK21 = X0
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_47])]) ).

fof(f635,plain,
    ! [X0,X1] :
      ( lt(X1,hd(X0))
      | sK21 = X0
      | ~ sP2(X0,X1) ),
    inference(definition_unfolding,[],[f443,f603]) ).

fof(f443,plain,
    ! [X0,X1] :
      ( lt(X1,hd(X0))
      | nil = X0
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f923,plain,
    spl69_46,
    inference(avatar_split_clause,[],[f630,f921]) ).

fof(f921,plain,
    ( spl69_46
  <=> ! [X0,X1] :
        ( leq(X1,hd(X0))
        | sK21 = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_46])]) ).

fof(f630,plain,
    ! [X0,X1] :
      ( leq(X1,hd(X0))
      | sK21 = X0
      | ~ sP0(X0,X1) ),
    inference(definition_unfolding,[],[f435,f603]) ).

fof(f435,plain,
    ! [X0,X1] :
      ( leq(X1,hd(X0))
      | nil = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f919,plain,
    spl69_45,
    inference(avatar_split_clause,[],[f661,f917]) ).

fof(f917,plain,
    ( spl69_45
  <=> ! [X0,X1] :
        ( cons(X1,X0) != sK21
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_45])]) ).

fof(f661,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != sK21
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f557,f603]) ).

fof(f557,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

fof(f915,plain,
    spl69_44,
    inference(avatar_split_clause,[],[f601,f912]) ).

fof(f912,plain,
    ( spl69_44
  <=> ssItem(sK68) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_44])]) ).

fof(f601,plain,
    ssItem(sK68),
    inference(cnf_transformation,[],[f373]) ).

fof(f910,plain,
    spl69_43,
    inference(avatar_split_clause,[],[f600,f907]) ).

fof(f907,plain,
    ( spl69_43
  <=> ssItem(sK67) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_43])]) ).

fof(f600,plain,
    ssItem(sK67),
    inference(cnf_transformation,[],[f373]) ).

fof(f900,plain,
    ( spl69_42
    | ~ spl69_1
    | ~ spl69_28 ),
    inference(avatar_split_clause,[],[f830,f825,f704,f897]) ).

fof(f897,plain,
    ( spl69_42
  <=> sK20 = app(sK21,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_42])]) ).

fof(f825,plain,
    ( spl69_28
  <=> ! [X0] :
        ( app(sK21,X0) = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_28])]) ).

fof(f830,plain,
    ( sK20 = app(sK21,sK20)
    | ~ spl69_1
    | ~ spl69_28 ),
    inference(resolution,[],[f826,f706]) ).

fof(f706,plain,
    ( ssList(sK20)
    | ~ spl69_1 ),
    inference(avatar_component_clause,[],[f704]) ).

fof(f826,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(sK21,X0) = X0 )
    | ~ spl69_28 ),
    inference(avatar_component_clause,[],[f825]) ).

fof(f885,plain,
    spl69_41,
    inference(avatar_split_clause,[],[f660,f883]) ).

fof(f660,plain,
    ! [X0] :
      ( sK21 = X0
      | ~ frontsegP(sK21,X0)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f554,f603,f603]) ).

fof(f554,plain,
    ! [X0] :
      ( nil = X0
      | ~ frontsegP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f349,plain,
    ! [X0] :
      ( ( ( frontsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ frontsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ( frontsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).

fof(f881,plain,
    ( spl69_40
    | ~ spl69_2
    | ~ spl69_27 ),
    inference(avatar_split_clause,[],[f829,f821,f709,f878]) ).

fof(f878,plain,
    ( spl69_40
  <=> sK21 = app(sK21,sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_40])]) ).

fof(f709,plain,
    ( spl69_2
  <=> ssList(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).

fof(f821,plain,
    ( spl69_27
  <=> ! [X0] :
        ( app(X0,sK21) = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_27])]) ).

fof(f829,plain,
    ( sK21 = app(sK21,sK21)
    | ~ spl69_2
    | ~ spl69_27 ),
    inference(resolution,[],[f822,f711]) ).

fof(f711,plain,
    ( ssList(sK21)
    | ~ spl69_2 ),
    inference(avatar_component_clause,[],[f709]) ).

fof(f822,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,sK21) = X0 )
    | ~ spl69_27 ),
    inference(avatar_component_clause,[],[f821]) ).

fof(f876,plain,
    spl69_39,
    inference(avatar_split_clause,[],[f658,f874]) ).

fof(f874,plain,
    ( spl69_39
  <=> ! [X0] :
        ( sK21 = X0
        | ~ rearsegP(sK21,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_39])]) ).

fof(f658,plain,
    ! [X0] :
      ( sK21 = X0
      | ~ rearsegP(sK21,X0)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f552,f603,f603]) ).

fof(f552,plain,
    ! [X0] :
      ( nil = X0
      | ~ rearsegP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f348,plain,
    ! [X0] :
      ( ( ( rearsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ rearsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( ( rearsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( rearsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).

fof(f872,plain,
    spl69_38,
    inference(avatar_split_clause,[],[f656,f870]) ).

fof(f870,plain,
    ( spl69_38
  <=> ! [X0] :
        ( sK21 = X0
        | ~ segmentP(sK21,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_38])]) ).

fof(f656,plain,
    ! [X0] :
      ( sK21 = X0
      | ~ segmentP(sK21,X0)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f550,f603,f603]) ).

fof(f550,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f347,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).

fof(f868,plain,
    spl69_37,
    inference(avatar_split_clause,[],[f652,f866]) ).

fof(f866,plain,
    ( spl69_37
  <=> ! [X0] :
        ( ssList(sK25(X0))
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_37])]) ).

fof(f652,plain,
    ! [X0] :
      ( ssList(sK25(X0))
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f466,f603]) ).

fof(f466,plain,
    ! [X0] :
      ( ssList(sK25(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f280]) ).

fof(f864,plain,
    spl69_36,
    inference(avatar_split_clause,[],[f650,f862]) ).

fof(f862,plain,
    ( spl69_36
  <=> ! [X0] :
        ( ssItem(sK24(X0))
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_36])]) ).

fof(f650,plain,
    ! [X0] :
      ( ssItem(sK24(X0))
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f464,f603]) ).

fof(f464,plain,
    ! [X0] :
      ( ssItem(sK24(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f860,plain,
    spl69_35,
    inference(avatar_split_clause,[],[f647,f858]) ).

fof(f858,plain,
    ( spl69_35
  <=> ! [X0] :
        ( ssList(tl(X0))
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_35])]) ).

fof(f647,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f462,f603]) ).

fof(f462,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).

fof(f856,plain,
    spl69_34,
    inference(avatar_split_clause,[],[f646,f854]) ).

fof(f854,plain,
    ( spl69_34
  <=> ! [X0] :
        ( ssItem(hd(X0))
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_34])]) ).

fof(f646,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f461,f603]) ).

fof(f461,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).

fof(f852,plain,
    spl69_33,
    inference(avatar_split_clause,[],[f645,f850]) ).

fof(f850,plain,
    ( spl69_33
  <=> ! [X0] :
        ( ssList(sK22(X0))
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_33])]) ).

fof(f645,plain,
    ! [X0] :
      ( ssList(sK22(X0))
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f458,f603]) ).

fof(f458,plain,
    ! [X0] :
      ( ssList(sK22(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f848,plain,
    spl69_32,
    inference(avatar_split_clause,[],[f644,f846]) ).

fof(f846,plain,
    ( spl69_32
  <=> ! [X0] :
        ( ssItem(sK23(X0))
        | sK21 = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_32])]) ).

fof(f644,plain,
    ! [X0] :
      ( ssItem(sK23(X0))
      | sK21 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f459,f603]) ).

fof(f459,plain,
    ! [X0] :
      ( ssItem(sK23(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f844,plain,
    spl69_31,
    inference(avatar_split_clause,[],[f636,f842]) ).

fof(f842,plain,
    ( spl69_31
  <=> ! [X0,X1] :
        ( strictorderedP(X0)
        | sK21 = X0
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_31])]) ).

fof(f636,plain,
    ! [X0,X1] :
      ( strictorderedP(X0)
      | sK21 = X0
      | ~ sP2(X0,X1) ),
    inference(definition_unfolding,[],[f442,f603]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( strictorderedP(X0)
      | nil = X0
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f840,plain,
    spl69_30,
    inference(avatar_split_clause,[],[f631,f838]) ).

fof(f838,plain,
    ( spl69_30
  <=> ! [X0,X1] :
        ( totalorderedP(X0)
        | sK21 = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_30])]) ).

fof(f631,plain,
    ! [X0,X1] :
      ( totalorderedP(X0)
      | sK21 = X0
      | ~ sP0(X0,X1) ),
    inference(definition_unfolding,[],[f434,f603]) ).

fof(f434,plain,
    ! [X0,X1] :
      ( totalorderedP(X0)
      | nil = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f836,plain,
    ( spl69_29
    | ~ spl69_1
    | ~ spl69_27 ),
    inference(avatar_split_clause,[],[f828,f821,f704,f833]) ).

fof(f833,plain,
    ( spl69_29
  <=> sK20 = app(sK20,sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_29])]) ).

fof(f828,plain,
    ( sK20 = app(sK20,sK21)
    | ~ spl69_1
    | ~ spl69_27 ),
    inference(resolution,[],[f822,f706]) ).

fof(f827,plain,
    spl69_28,
    inference(avatar_split_clause,[],[f642,f825]) ).

fof(f642,plain,
    ! [X0] :
      ( app(sK21,X0) = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f457,f603]) ).

fof(f457,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f823,plain,
    spl69_27,
    inference(avatar_split_clause,[],[f641,f821]) ).

fof(f641,plain,
    ! [X0] :
      ( app(X0,sK21) = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f456,f603]) ).

fof(f456,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).

fof(f819,plain,
    spl69_26,
    inference(avatar_split_clause,[],[f627,f817]) ).

fof(f817,plain,
    ( spl69_26
  <=> ! [X0] :
        ( totalorderedP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_26])]) ).

fof(f627,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f405,f603]) ).

fof(f405,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).

fof(f815,plain,
    spl69_25,
    inference(avatar_split_clause,[],[f626,f813]) ).

fof(f813,plain,
    ( spl69_25
  <=> ! [X0] :
        ( strictorderedP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_25])]) ).

fof(f626,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f404,f603]) ).

fof(f404,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).

fof(f811,plain,
    spl69_24,
    inference(avatar_split_clause,[],[f625,f809]) ).

fof(f809,plain,
    ( spl69_24
  <=> ! [X0] :
        ( strictorderP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_24])]) ).

fof(f625,plain,
    ! [X0] :
      ( strictorderP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f403,f603]) ).

fof(f403,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).

fof(f807,plain,
    spl69_23,
    inference(avatar_split_clause,[],[f624,f805]) ).

fof(f805,plain,
    ( spl69_23
  <=> ! [X0] :
        ( totalorderP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_23])]) ).

fof(f624,plain,
    ! [X0] :
      ( totalorderP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f402,f603]) ).

fof(f402,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).

fof(f803,plain,
    spl69_22,
    inference(avatar_split_clause,[],[f623,f801]) ).

fof(f801,plain,
    ( spl69_22
  <=> ! [X0] :
        ( cyclefreeP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_22])]) ).

fof(f623,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f401,f603]) ).

fof(f401,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( ssItem(X0)
     => cyclefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).

fof(f799,plain,
    spl69_21,
    inference(avatar_split_clause,[],[f622,f797]) ).

fof(f797,plain,
    ( spl69_21
  <=> ! [X0] :
        ( duplicatefreeP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_21])]) ).

fof(f622,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f400,f603]) ).

fof(f400,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0] :
      ( ssItem(X0)
     => duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).

fof(f795,plain,
    spl69_20,
    inference(avatar_split_clause,[],[f621,f793]) ).

fof(f793,plain,
    ( spl69_20
  <=> ! [X0] :
        ( equalelemsP(cons(X0,sK21))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_20])]) ).

fof(f621,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,sK21))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f399,f603]) ).

fof(f399,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,axiom,
    ! [X0] :
      ( ssItem(X0)
     => equalelemsP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).

fof(f791,plain,
    ( spl69_11
    | spl69_19 ),
    inference(avatar_split_clause,[],[f606,f788,f754]) ).

fof(f788,plain,
    ( spl69_19
  <=> neq(sK20,sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_19])]) ).

fof(f606,plain,
    ( neq(sK20,sK21)
    | sK20 = sK21 ),
    inference(definition_unfolding,[],[f383,f603,f603]) ).

fof(f383,plain,
    ( neq(sK20,nil)
    | nil = sK20 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f786,plain,
    ( spl69_11
    | spl69_18 ),
    inference(avatar_split_clause,[],[f604,f783,f754]) ).

fof(f604,plain,
    ( frontsegP(sK21,sK20)
    | sK20 = sK21 ),
    inference(definition_unfolding,[],[f385,f603]) ).

fof(f385,plain,
    ( frontsegP(sK21,sK20)
    | nil = sK20 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f781,plain,
    spl69_17,
    inference(avatar_split_clause,[],[f640,f779]) ).

fof(f779,plain,
    ( spl69_17
  <=> ! [X0] :
        ( frontsegP(X0,sK21)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_17])]) ).

fof(f640,plain,
    ! [X0] :
      ( frontsegP(X0,sK21)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f453,f603]) ).

fof(f453,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).

fof(f777,plain,
    spl69_16,
    inference(avatar_split_clause,[],[f639,f775]) ).

fof(f775,plain,
    ( spl69_16
  <=> ! [X0] :
        ( rearsegP(X0,sK21)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_16])]) ).

fof(f639,plain,
    ! [X0] :
      ( rearsegP(X0,sK21)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f451,f603]) ).

fof(f451,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).

fof(f773,plain,
    spl69_15,
    inference(avatar_split_clause,[],[f638,f771]) ).

fof(f771,plain,
    ( spl69_15
  <=> ! [X0] :
        ( segmentP(X0,sK21)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_15])]) ).

fof(f638,plain,
    ! [X0] :
      ( segmentP(X0,sK21)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f450,f603]) ).

fof(f450,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).

fof(f769,plain,
    spl69_14,
    inference(avatar_split_clause,[],[f620,f767]) ).

fof(f767,plain,
    ( spl69_14
  <=> ! [X0] :
        ( ~ memberP(sK21,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_14])]) ).

fof(f620,plain,
    ! [X0] :
      ( ~ memberP(sK21,X0)
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f395,f603]) ).

fof(f395,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).

fof(f765,plain,
    spl69_13,
    inference(avatar_split_clause,[],[f675,f763]) ).

fof(f763,plain,
    ( spl69_13
  <=> ! [X1] : sP2(sK21,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_13])]) ).

fof(f675,plain,
    ! [X1] : sP2(sK21,X1),
    inference(equality_resolution,[],[f634]) ).

fof(f634,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | sK21 != X0 ),
    inference(definition_unfolding,[],[f444,f603]) ).

fof(f444,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f271]) ).

fof(f761,plain,
    spl69_12,
    inference(avatar_split_clause,[],[f673,f759]) ).

fof(f759,plain,
    ( spl69_12
  <=> ! [X1] : sP0(sK21,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_12])]) ).

fof(f673,plain,
    ! [X1] : sP0(sK21,X1),
    inference(equality_resolution,[],[f629]) ).

fof(f629,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK21 != X0 ),
    inference(definition_unfolding,[],[f436,f603]) ).

fof(f436,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f267]) ).

fof(f757,plain,
    ~ spl69_11,
    inference(avatar_split_clause,[],[f608,f754]) ).

fof(f608,plain,
    sK20 != sK21,
    inference(definition_unfolding,[],[f381,f603,f380]) ).

fof(f380,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f254]) ).

fof(f381,plain,
    nil != sK18,
    inference(cnf_transformation,[],[f254]) ).

fof(f752,plain,
    spl69_10,
    inference(avatar_split_clause,[],[f618,f749]) ).

fof(f749,plain,
    ( spl69_10
  <=> totalorderedP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_10])]) ).

fof(f618,plain,
    totalorderedP(sK21),
    inference(definition_unfolding,[],[f393,f603]) ).

fof(f393,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).

fof(f747,plain,
    spl69_9,
    inference(avatar_split_clause,[],[f617,f744]) ).

fof(f744,plain,
    ( spl69_9
  <=> strictorderedP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).

fof(f617,plain,
    strictorderedP(sK21),
    inference(definition_unfolding,[],[f392,f603]) ).

fof(f392,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).

fof(f742,plain,
    spl69_8,
    inference(avatar_split_clause,[],[f616,f739]) ).

fof(f739,plain,
    ( spl69_8
  <=> totalorderP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_8])]) ).

fof(f616,plain,
    totalorderP(sK21),
    inference(definition_unfolding,[],[f391,f603]) ).

fof(f391,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).

fof(f737,plain,
    spl69_7,
    inference(avatar_split_clause,[],[f615,f734]) ).

fof(f734,plain,
    ( spl69_7
  <=> strictorderP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_7])]) ).

fof(f615,plain,
    strictorderP(sK21),
    inference(definition_unfolding,[],[f390,f603]) ).

fof(f390,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).

fof(f732,plain,
    spl69_6,
    inference(avatar_split_clause,[],[f614,f729]) ).

fof(f729,plain,
    ( spl69_6
  <=> cyclefreeP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).

fof(f614,plain,
    cyclefreeP(sK21),
    inference(definition_unfolding,[],[f389,f603]) ).

fof(f389,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).

fof(f727,plain,
    spl69_5,
    inference(avatar_split_clause,[],[f613,f724]) ).

fof(f724,plain,
    ( spl69_5
  <=> duplicatefreeP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).

fof(f613,plain,
    duplicatefreeP(sK21),
    inference(definition_unfolding,[],[f388,f603]) ).

fof(f388,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).

fof(f722,plain,
    spl69_4,
    inference(avatar_split_clause,[],[f612,f719]) ).

fof(f719,plain,
    ( spl69_4
  <=> equalelemsP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).

fof(f612,plain,
    equalelemsP(sK21),
    inference(definition_unfolding,[],[f387,f603]) ).

fof(f387,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).

fof(f717,plain,
    ~ spl69_3,
    inference(avatar_split_clause,[],[f611,f714]) ).

fof(f714,plain,
    ( spl69_3
  <=> singletonP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).

fof(f611,plain,
    ~ singletonP(sK21),
    inference(definition_unfolding,[],[f386,f603]) ).

fof(f386,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).

fof(f712,plain,
    spl69_2,
    inference(avatar_split_clause,[],[f377,f709]) ).

fof(f377,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f254]) ).

fof(f707,plain,
    spl69_1,
    inference(avatar_split_clause,[],[f376,f704]) ).

fof(f376,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWC038+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 20:27:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (3821)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (3826)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)
% 0.13/0.37  % (3824)WARNING: value z3 for option sas not known
% 0.13/0.37  % (3822)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (3823)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (3825)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (3824)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)
% 0.13/0.37  % (3827)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)
% 0.13/0.37  % (3828)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)
% 0.13/0.37  % (3826)First to succeed.
% 0.13/0.38  % (3826)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3821"
% 0.13/0.38  % (3826)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (3826)------------------------------
% 0.13/0.38  % (3826)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38  % (3826)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (3826)Memory used [KB]: 1463
% 0.13/0.38  % (3826)Time elapsed: 0.012 s
% 0.13/0.38  % (3826)Instructions burned: 33 (million)
% 0.13/0.38  % (3821)Success in time 0.025 s
%------------------------------------------------------------------------------