TSTP Solution File: SWC327+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC327+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 04:38:11 EDT 2024

% Result   : Theorem 0.66s 0.82s
% Output   : Refutation 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  147 (   8 unt;   0 def)
%            Number of atoms       :  889 ( 326 equ)
%            Maximal formula atoms :   52 (   6 avg)
%            Number of connectives : 1229 ( 487   ~; 476   |; 213   &)
%                                         (  21 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   26 (  24 usr;  22 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  222 ( 136   !;  86   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f754,plain,
    $false,
    inference(avatar_sat_refutation,[],[f610,f615,f620,f625,f630,f638,f642,f646,f650,f654,f655,f656,f667,f674,f676,f683,f690,f697,f703,f706,f732,f733,f744,f750,f751,f753]) ).

fof(f753,plain,
    ( ~ spl55_15
    | spl55_19
    | ~ spl55_3
    | ~ spl55_5
    | ~ spl55_9 ),
    inference(avatar_split_clause,[],[f737,f635,f618,f607,f694,f664]) ).

fof(f664,plain,
    ( spl55_15
  <=> ssList(sK54) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_15])]) ).

fof(f694,plain,
    ( spl55_19
  <=> sK54 = app(cons(sK51(sK54),nil),sK52(sK54)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_19])]) ).

fof(f607,plain,
    ( spl55_3
  <=> nil = sK50 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_3])]) ).

fof(f618,plain,
    ( spl55_5
  <=> ! [X4] :
        ( app(cons(sK51(X4),nil),sK52(X4)) = X4
        | ~ ssList(X4)
        | nil != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_5])]) ).

fof(f635,plain,
    ( spl55_9
  <=> nil = sK49 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_9])]) ).

fof(f737,plain,
    ( sK54 = app(cons(sK51(sK54),nil),sK52(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_5
    | ~ spl55_9 ),
    inference(trivial_inequality_removal,[],[f736]) ).

fof(f736,plain,
    ( nil != nil
    | sK54 = app(cons(sK51(sK54),nil),sK52(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_5
    | ~ spl55_9 ),
    inference(superposition,[],[f709,f721]) ).

fof(f721,plain,
    ( nil = app(nil,sK54)
    | ~ spl55_3
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f715,f608]) ).

fof(f608,plain,
    ( nil = sK50
    | ~ spl55_3 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f715,plain,
    ( sK50 = app(nil,sK54)
    | ~ spl55_9 ),
    inference(superposition,[],[f538,f637]) ).

fof(f637,plain,
    ( nil = sK49
    | ~ spl55_9 ),
    inference(avatar_component_clause,[],[f635]) ).

fof(f538,plain,
    sK50 = app(sK49,sK54),
    inference(cnf_transformation,[],[f340]) ).

fof(f340,plain,
    ( ( ( nil != sK48
        & nil = sK47 )
      | ! [X4] :
          ( ~ equalelemsP(sK47)
          | ( sK47 = app(sK53(X4),cons(sK51(X4),nil))
            & ssList(sK53(X4))
            & app(cons(sK51(X4),nil),sK52(X4)) = X4
            & ssList(sK52(X4))
            & ssItem(sK51(X4)) )
          | app(sK47,X4) != sK48
          | ~ ssList(X4) ) )
    & ( nil != sK49
      | nil = sK50 )
    & ! [X9] :
        ( ! [X10] :
            ( ! [X11] :
                ( app(X11,cons(X9,nil)) != sK49
                | ~ ssList(X11) )
            | app(cons(X9,nil),X10) != sK54
            | ~ ssList(X10) )
        | ~ ssItem(X9) )
    & equalelemsP(sK49)
    & sK50 = app(sK49,sK54)
    & ssList(sK54)
    & sK47 = sK49
    & sK48 = sK50
    & ssList(sK50)
    & ssList(sK49)
    & ssList(sK48)
    & ssList(sK47) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49,sK50,sK51,sK52,sK53,sK54])],[f223,f339,f338,f337,f336,f335,f334,f333,f332]) ).

fof(f332,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil != X1
                        & nil = X0 )
                      | ! [X4] :
                          ( ~ equalelemsP(X0)
                          | ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( app(X7,cons(X5,nil)) = X0
                                      & ssList(X7) )
                                  & app(cons(X5,nil),X6) = X4
                                  & ssList(X6) )
                              & ssItem(X5) )
                          | app(X0,X4) != X1
                          | ~ ssList(X4) ) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X8] :
                        ( ! [X9] :
                            ( ! [X10] :
                                ( ! [X11] :
                                    ( app(X11,cons(X9,nil)) != X2
                                    | ~ ssList(X11) )
                                | app(cons(X9,nil),X10) != X8
                                | ~ ssList(X10) )
                            | ~ ssItem(X9) )
                        & equalelemsP(X2)
                        & app(X2,X8) = X3
                        & ssList(X8) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = sK47 )
                    | ! [X4] :
                        ( ~ equalelemsP(sK47)
                        | ? [X5] :
                            ( ? [X6] :
                                ( ? [X7] :
                                    ( app(X7,cons(X5,nil)) = sK47
                                    & ssList(X7) )
                                & app(cons(X5,nil),X6) = X4
                                & ssList(X6) )
                            & ssItem(X5) )
                        | app(sK47,X4) != X1
                        | ~ ssList(X4) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ! [X11] :
                                  ( app(X11,cons(X9,nil)) != X2
                                  | ~ ssList(X11) )
                              | app(cons(X9,nil),X10) != X8
                              | ~ ssList(X10) )
                          | ~ ssItem(X9) )
                      & equalelemsP(X2)
                      & app(X2,X8) = X3
                      & ssList(X8) )
                  & sK47 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK47) ) ),
    introduced(choice_axiom,[]) ).

fof(f333,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil != X1
                    & nil = sK47 )
                  | ! [X4] :
                      ( ~ equalelemsP(sK47)
                      | ? [X5] :
                          ( ? [X6] :
                              ( ? [X7] :
                                  ( app(X7,cons(X5,nil)) = sK47
                                  & ssList(X7) )
                              & app(cons(X5,nil),X6) = X4
                              & ssList(X6) )
                          & ssItem(X5) )
                      | app(sK47,X4) != X1
                      | ~ ssList(X4) ) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ! [X11] :
                                ( app(X11,cons(X9,nil)) != X2
                                | ~ ssList(X11) )
                            | app(cons(X9,nil),X10) != X8
                            | ~ ssList(X10) )
                        | ~ ssItem(X9) )
                    & equalelemsP(X2)
                    & app(X2,X8) = X3
                    & ssList(X8) )
                & sK47 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil != sK48
                  & nil = sK47 )
                | ! [X4] :
                    ( ~ equalelemsP(sK47)
                    | ? [X5] :
                        ( ? [X6] :
                            ( ? [X7] :
                                ( app(X7,cons(X5,nil)) = sK47
                                & ssList(X7) )
                            & app(cons(X5,nil),X6) = X4
                            & ssList(X6) )
                        & ssItem(X5) )
                    | app(sK47,X4) != sK48
                    | ~ ssList(X4) ) )
              & ( nil != X2
                | nil = X3 )
              & ? [X8] :
                  ( ! [X9] :
                      ( ! [X10] :
                          ( ! [X11] :
                              ( app(X11,cons(X9,nil)) != X2
                              | ~ ssList(X11) )
                          | app(cons(X9,nil),X10) != X8
                          | ~ ssList(X10) )
                      | ~ ssItem(X9) )
                  & equalelemsP(X2)
                  & app(X2,X8) = X3
                  & ssList(X8) )
              & sK47 = X2
              & sK48 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK48) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil != sK48
                & nil = sK47 )
              | ! [X4] :
                  ( ~ equalelemsP(sK47)
                  | ? [X5] :
                      ( ? [X6] :
                          ( ? [X7] :
                              ( app(X7,cons(X5,nil)) = sK47
                              & ssList(X7) )
                          & app(cons(X5,nil),X6) = X4
                          & ssList(X6) )
                      & ssItem(X5) )
                  | app(sK47,X4) != sK48
                  | ~ ssList(X4) ) )
            & ( nil != X2
              | nil = X3 )
            & ? [X8] :
                ( ! [X9] :
                    ( ! [X10] :
                        ( ! [X11] :
                            ( app(X11,cons(X9,nil)) != X2
                            | ~ ssList(X11) )
                        | app(cons(X9,nil),X10) != X8
                        | ~ ssList(X10) )
                    | ~ ssItem(X9) )
                & equalelemsP(X2)
                & app(X2,X8) = X3
                & ssList(X8) )
            & sK47 = X2
            & sK48 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil != sK48
              & nil = sK47 )
            | ! [X4] :
                ( ~ equalelemsP(sK47)
                | ? [X5] :
                    ( ? [X6] :
                        ( ? [X7] :
                            ( app(X7,cons(X5,nil)) = sK47
                            & ssList(X7) )
                        & app(cons(X5,nil),X6) = X4
                        & ssList(X6) )
                    & ssItem(X5) )
                | app(sK47,X4) != sK48
                | ~ ssList(X4) ) )
          & ( nil != sK49
            | nil = X3 )
          & ? [X8] :
              ( ! [X9] :
                  ( ! [X10] :
                      ( ! [X11] :
                          ( app(X11,cons(X9,nil)) != sK49
                          | ~ ssList(X11) )
                      | app(cons(X9,nil),X10) != X8
                      | ~ ssList(X10) )
                  | ~ ssItem(X9) )
              & equalelemsP(sK49)
              & app(sK49,X8) = X3
              & ssList(X8) )
          & sK47 = sK49
          & sK48 = X3
          & ssList(X3) )
      & ssList(sK49) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ( ? [X3] :
        ( ( ( nil != sK48
            & nil = sK47 )
          | ! [X4] :
              ( ~ equalelemsP(sK47)
              | ? [X5] :
                  ( ? [X6] :
                      ( ? [X7] :
                          ( app(X7,cons(X5,nil)) = sK47
                          & ssList(X7) )
                      & app(cons(X5,nil),X6) = X4
                      & ssList(X6) )
                  & ssItem(X5) )
              | app(sK47,X4) != sK48
              | ~ ssList(X4) ) )
        & ( nil != sK49
          | nil = X3 )
        & ? [X8] :
            ( ! [X9] :
                ( ! [X10] :
                    ( ! [X11] :
                        ( app(X11,cons(X9,nil)) != sK49
                        | ~ ssList(X11) )
                    | app(cons(X9,nil),X10) != X8
                    | ~ ssList(X10) )
                | ~ ssItem(X9) )
            & equalelemsP(sK49)
            & app(sK49,X8) = X3
            & ssList(X8) )
        & sK47 = sK49
        & sK48 = X3
        & ssList(X3) )
   => ( ( ( nil != sK48
          & nil = sK47 )
        | ! [X4] :
            ( ~ equalelemsP(sK47)
            | ? [X5] :
                ( ? [X6] :
                    ( ? [X7] :
                        ( app(X7,cons(X5,nil)) = sK47
                        & ssList(X7) )
                    & app(cons(X5,nil),X6) = X4
                    & ssList(X6) )
                & ssItem(X5) )
            | app(sK47,X4) != sK48
            | ~ ssList(X4) ) )
      & ( nil != sK49
        | nil = sK50 )
      & ? [X8] :
          ( ! [X9] :
              ( ! [X10] :
                  ( ! [X11] :
                      ( app(X11,cons(X9,nil)) != sK49
                      | ~ ssList(X11) )
                  | app(cons(X9,nil),X10) != X8
                  | ~ ssList(X10) )
              | ~ ssItem(X9) )
          & equalelemsP(sK49)
          & app(sK49,X8) = sK50
          & ssList(X8) )
      & sK47 = sK49
      & sK48 = sK50
      & ssList(sK50) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X4] :
      ( ? [X5] :
          ( ? [X6] :
              ( ? [X7] :
                  ( app(X7,cons(X5,nil)) = sK47
                  & ssList(X7) )
              & app(cons(X5,nil),X6) = X4
              & ssList(X6) )
          & ssItem(X5) )
     => ( ? [X6] :
            ( ? [X7] :
                ( sK47 = app(X7,cons(sK51(X4),nil))
                & ssList(X7) )
            & app(cons(sK51(X4),nil),X6) = X4
            & ssList(X6) )
        & ssItem(sK51(X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ! [X4] :
      ( ? [X6] :
          ( ? [X7] :
              ( sK47 = app(X7,cons(sK51(X4),nil))
              & ssList(X7) )
          & app(cons(sK51(X4),nil),X6) = X4
          & ssList(X6) )
     => ( ? [X7] :
            ( sK47 = app(X7,cons(sK51(X4),nil))
            & ssList(X7) )
        & app(cons(sK51(X4),nil),sK52(X4)) = X4
        & ssList(sK52(X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ! [X4] :
      ( ? [X7] :
          ( sK47 = app(X7,cons(sK51(X4),nil))
          & ssList(X7) )
     => ( sK47 = app(sK53(X4),cons(sK51(X4),nil))
        & ssList(sK53(X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f339,plain,
    ( ? [X8] :
        ( ! [X9] :
            ( ! [X10] :
                ( ! [X11] :
                    ( app(X11,cons(X9,nil)) != sK49
                    | ~ ssList(X11) )
                | app(cons(X9,nil),X10) != X8
                | ~ ssList(X10) )
            | ~ ssItem(X9) )
        & equalelemsP(sK49)
        & app(sK49,X8) = sK50
        & ssList(X8) )
   => ( ! [X9] :
          ( ! [X10] :
              ( ! [X11] :
                  ( app(X11,cons(X9,nil)) != sK49
                  | ~ ssList(X11) )
              | app(cons(X9,nil),X10) != sK54
              | ~ ssList(X10) )
          | ~ ssItem(X9) )
      & equalelemsP(sK49)
      & sK50 = app(sK49,sK54)
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | ! [X4] :
                        ( ~ equalelemsP(X0)
                        | ? [X5] :
                            ( ? [X6] :
                                ( ? [X7] :
                                    ( app(X7,cons(X5,nil)) = X0
                                    & ssList(X7) )
                                & app(cons(X5,nil),X6) = X4
                                & ssList(X6) )
                            & ssItem(X5) )
                        | app(X0,X4) != X1
                        | ~ ssList(X4) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ! [X11] :
                                  ( app(X11,cons(X9,nil)) != X2
                                  | ~ ssList(X11) )
                              | app(cons(X9,nil),X10) != X8
                              | ~ ssList(X10) )
                          | ~ ssItem(X9) )
                      & equalelemsP(X2)
                      & app(X2,X8) = X3
                      & ssList(X8) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | ! [X4] :
                        ( ~ equalelemsP(X0)
                        | ? [X5] :
                            ( ? [X6] :
                                ( ? [X7] :
                                    ( app(X7,cons(X5,nil)) = X0
                                    & ssList(X7) )
                                & app(cons(X5,nil),X6) = X4
                                & ssList(X6) )
                            & ssItem(X5) )
                        | app(X0,X4) != X1
                        | ~ ssList(X4) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ! [X11] :
                                  ( app(X11,cons(X9,nil)) != X2
                                  | ~ ssList(X11) )
                              | app(cons(X9,nil),X10) != X8
                              | ~ ssList(X10) )
                          | ~ ssItem(X9) )
                      & equalelemsP(X2)
                      & app(X2,X8) = X3
                      & ssList(X8) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil = X1
                          | nil != X0 )
                        & ? [X4] :
                            ( equalelemsP(X0)
                            & ! [X5] :
                                ( ssItem(X5)
                               => ! [X6] :
                                    ( ssList(X6)
                                   => ( ! [X7] :
                                          ( ssList(X7)
                                         => app(X7,cons(X5,nil)) != X0 )
                                      | app(cons(X5,nil),X6) != X4 ) ) )
                            & app(X0,X4) = X1
                            & ssList(X4) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X8] :
                          ( ssList(X8)
                         => ( ? [X9] :
                                ( ? [X10] :
                                    ( ? [X11] :
                                        ( app(X11,cons(X9,nil)) = X2
                                        & ssList(X11) )
                                    & app(cons(X9,nil),X10) = X8
                                    & ssList(X10) )
                                & ssItem(X9) )
                            | ~ equalelemsP(X2)
                            | app(X2,X8) != X3 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil = X1
                          | nil != X0 )
                        & ? [X8] :
                            ( equalelemsP(X0)
                            & ! [X9] :
                                ( ssItem(X9)
                               => ! [X10] :
                                    ( ssList(X10)
                                   => ( ! [X11] :
                                          ( ssList(X11)
                                         => app(X11,cons(X9,nil)) != X0 )
                                      | app(cons(X9,nil),X10) != X8 ) ) )
                            & app(X0,X8) = X1
                            & ssList(X8) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) )
                                    & app(cons(X5,nil),X6) = X4
                                    & ssList(X6) )
                                & ssItem(X5) )
                            | ~ equalelemsP(X2)
                            | app(X2,X4) != X3 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil = X1
                        | nil != X0 )
                      & ? [X8] :
                          ( equalelemsP(X0)
                          & ! [X9] :
                              ( ssItem(X9)
                             => ! [X10] :
                                  ( ssList(X10)
                                 => ( ! [X11] :
                                        ( ssList(X11)
                                       => app(X11,cons(X9,nil)) != X0 )
                                    | app(cons(X9,nil),X10) != X8 ) ) )
                          & app(X0,X8) = X1
                          & ssList(X8) ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( app(X7,cons(X5,nil)) = X2
                                      & ssList(X7) )
                                  & app(cons(X5,nil),X6) = X4
                                  & ssList(X6) )
                              & ssItem(X5) )
                          | ~ equalelemsP(X2)
                          | app(X2,X4) != X3 ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f709,plain,
    ( ! [X4] :
        ( nil != app(nil,X4)
        | app(cons(sK51(X4),nil),sK52(X4)) = X4
        | ~ ssList(X4) )
    | ~ spl55_5
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f619,f637]) ).

fof(f619,plain,
    ( ! [X4] :
        ( app(cons(sK51(X4),nil),sK52(X4)) = X4
        | ~ ssList(X4)
        | nil != app(sK49,X4) )
    | ~ spl55_5 ),
    inference(avatar_component_clause,[],[f618]) ).

fof(f751,plain,
    ( ~ spl55_15
    | spl55_17
    | ~ spl55_3
    | ~ spl55_7
    | ~ spl55_9 ),
    inference(avatar_split_clause,[],[f727,f635,f628,f607,f680,f664]) ).

fof(f680,plain,
    ( spl55_17
  <=> ssItem(sK51(sK54)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_17])]) ).

fof(f628,plain,
    ( spl55_7
  <=> ! [X4] :
        ( ssItem(sK51(X4))
        | ~ ssList(X4)
        | nil != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_7])]) ).

fof(f727,plain,
    ( ssItem(sK51(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_7
    | ~ spl55_9 ),
    inference(trivial_inequality_removal,[],[f726]) ).

fof(f726,plain,
    ( nil != nil
    | ssItem(sK51(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_7
    | ~ spl55_9 ),
    inference(superposition,[],[f707,f721]) ).

fof(f707,plain,
    ( ! [X4] :
        ( nil != app(nil,X4)
        | ssItem(sK51(X4))
        | ~ ssList(X4) )
    | ~ spl55_7
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f629,f637]) ).

fof(f629,plain,
    ( ! [X4] :
        ( ssItem(sK51(X4))
        | ~ ssList(X4)
        | nil != app(sK49,X4) )
    | ~ spl55_7 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f750,plain,
    ( ~ spl55_14
    | ~ spl55_9
    | ~ spl55_20
    | ~ spl55_21 ),
    inference(avatar_split_clause,[],[f747,f741,f701,f635,f660]) ).

fof(f660,plain,
    ( spl55_14
  <=> ssList(sK53(sK54)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_14])]) ).

fof(f701,plain,
    ( spl55_20
  <=> ! [X0] :
        ( ~ ssList(X0)
        | sK49 != app(X0,cons(sK51(sK54),nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_20])]) ).

fof(f741,plain,
    ( spl55_21
  <=> nil = app(sK53(sK54),cons(sK51(sK54),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_21])]) ).

fof(f747,plain,
    ( ~ ssList(sK53(sK54))
    | ~ spl55_9
    | ~ spl55_20
    | ~ spl55_21 ),
    inference(trivial_inequality_removal,[],[f746]) ).

fof(f746,plain,
    ( nil != nil
    | ~ ssList(sK53(sK54))
    | ~ spl55_9
    | ~ spl55_20
    | ~ spl55_21 ),
    inference(superposition,[],[f734,f743]) ).

fof(f743,plain,
    ( nil = app(sK53(sK54),cons(sK51(sK54),nil))
    | ~ spl55_21 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f734,plain,
    ( ! [X0] :
        ( nil != app(X0,cons(sK51(sK54),nil))
        | ~ ssList(X0) )
    | ~ spl55_9
    | ~ spl55_20 ),
    inference(forward_demodulation,[],[f702,f637]) ).

fof(f702,plain,
    ( ! [X0] :
        ( sK49 != app(X0,cons(sK51(sK54),nil))
        | ~ ssList(X0) )
    | ~ spl55_20 ),
    inference(avatar_component_clause,[],[f701]) ).

fof(f744,plain,
    ( ~ spl55_15
    | spl55_21
    | ~ spl55_1
    | ~ spl55_3
    | ~ spl55_9 ),
    inference(avatar_split_clause,[],[f739,f635,f607,f600,f741,f664]) ).

fof(f600,plain,
    ( spl55_1
  <=> ! [X4] :
        ( sK49 = app(sK53(X4),cons(sK51(X4),nil))
        | ~ ssList(X4)
        | nil != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_1])]) ).

fof(f739,plain,
    ( nil = app(sK53(sK54),cons(sK51(sK54),nil))
    | ~ ssList(sK54)
    | ~ spl55_1
    | ~ spl55_3
    | ~ spl55_9 ),
    inference(trivial_inequality_removal,[],[f738]) ).

fof(f738,plain,
    ( nil != nil
    | nil = app(sK53(sK54),cons(sK51(sK54),nil))
    | ~ ssList(sK54)
    | ~ spl55_1
    | ~ spl55_3
    | ~ spl55_9 ),
    inference(superposition,[],[f712,f721]) ).

fof(f712,plain,
    ( ! [X4] :
        ( nil != app(nil,X4)
        | nil = app(sK53(X4),cons(sK51(X4),nil))
        | ~ ssList(X4) )
    | ~ spl55_1
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f711,f637]) ).

fof(f711,plain,
    ( ! [X4] :
        ( nil = app(sK53(X4),cons(sK51(X4),nil))
        | ~ ssList(X4)
        | nil != app(sK49,X4) )
    | ~ spl55_1
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f601,f637]) ).

fof(f601,plain,
    ( ! [X4] :
        ( sK49 = app(sK53(X4),cons(sK51(X4),nil))
        | ~ ssList(X4)
        | nil != app(sK49,X4) )
    | ~ spl55_1 ),
    inference(avatar_component_clause,[],[f600]) ).

fof(f733,plain,
    ( ~ spl55_15
    | spl55_16
    | ~ spl55_3
    | ~ spl55_6
    | ~ spl55_9 ),
    inference(avatar_split_clause,[],[f729,f635,f623,f607,f671,f664]) ).

fof(f671,plain,
    ( spl55_16
  <=> ssList(sK52(sK54)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_16])]) ).

fof(f623,plain,
    ( spl55_6
  <=> ! [X4] :
        ( ssList(sK52(X4))
        | ~ ssList(X4)
        | nil != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_6])]) ).

fof(f729,plain,
    ( ssList(sK52(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_6
    | ~ spl55_9 ),
    inference(trivial_inequality_removal,[],[f728]) ).

fof(f728,plain,
    ( nil != nil
    | ssList(sK52(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_6
    | ~ spl55_9 ),
    inference(superposition,[],[f708,f721]) ).

fof(f708,plain,
    ( ! [X4] :
        ( nil != app(nil,X4)
        | ssList(sK52(X4))
        | ~ ssList(X4) )
    | ~ spl55_6
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f624,f637]) ).

fof(f624,plain,
    ( ! [X4] :
        ( ssList(sK52(X4))
        | ~ ssList(X4)
        | nil != app(sK49,X4) )
    | ~ spl55_6 ),
    inference(avatar_component_clause,[],[f623]) ).

fof(f732,plain,
    ( ~ spl55_15
    | spl55_14
    | ~ spl55_3
    | ~ spl55_4
    | ~ spl55_9 ),
    inference(avatar_split_clause,[],[f731,f635,f613,f607,f660,f664]) ).

fof(f613,plain,
    ( spl55_4
  <=> ! [X4] :
        ( ssList(sK53(X4))
        | ~ ssList(X4)
        | nil != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_4])]) ).

fof(f731,plain,
    ( ssList(sK53(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_4
    | ~ spl55_9 ),
    inference(trivial_inequality_removal,[],[f730]) ).

fof(f730,plain,
    ( nil != nil
    | ssList(sK53(sK54))
    | ~ ssList(sK54)
    | ~ spl55_3
    | ~ spl55_4
    | ~ spl55_9 ),
    inference(superposition,[],[f710,f721]) ).

fof(f710,plain,
    ( ! [X4] :
        ( nil != app(nil,X4)
        | ssList(sK53(X4))
        | ~ ssList(X4) )
    | ~ spl55_4
    | ~ spl55_9 ),
    inference(forward_demodulation,[],[f614,f637]) ).

fof(f614,plain,
    ( ! [X4] :
        ( ssList(sK53(X4))
        | ~ ssList(X4)
        | nil != app(sK49,X4) )
    | ~ spl55_4 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f706,plain,
    ( ~ spl55_14
    | ~ spl55_18
    | ~ spl55_20 ),
    inference(avatar_split_clause,[],[f705,f701,f687,f660]) ).

fof(f687,plain,
    ( spl55_18
  <=> sK49 = app(sK53(sK54),cons(sK51(sK54),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_18])]) ).

fof(f705,plain,
    ( ~ ssList(sK53(sK54))
    | ~ spl55_18
    | ~ spl55_20 ),
    inference(trivial_inequality_removal,[],[f704]) ).

fof(f704,plain,
    ( sK49 != sK49
    | ~ ssList(sK53(sK54))
    | ~ spl55_18
    | ~ spl55_20 ),
    inference(superposition,[],[f702,f689]) ).

fof(f689,plain,
    ( sK49 = app(sK53(sK54),cons(sK51(sK54),nil))
    | ~ spl55_18 ),
    inference(avatar_component_clause,[],[f687]) ).

fof(f703,plain,
    ( ~ spl55_17
    | ~ spl55_16
    | spl55_20
    | ~ spl55_19 ),
    inference(avatar_split_clause,[],[f699,f694,f701,f671,f680]) ).

fof(f699,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sK49 != app(X0,cons(sK51(sK54),nil))
        | ~ ssList(sK52(sK54))
        | ~ ssItem(sK51(sK54)) )
    | ~ spl55_19 ),
    inference(trivial_inequality_removal,[],[f698]) ).

fof(f698,plain,
    ( ! [X0] :
        ( sK54 != sK54
        | ~ ssList(X0)
        | sK49 != app(X0,cons(sK51(sK54),nil))
        | ~ ssList(sK52(sK54))
        | ~ ssItem(sK51(sK54)) )
    | ~ spl55_19 ),
    inference(superposition,[],[f540,f696]) ).

fof(f696,plain,
    ( sK54 = app(cons(sK51(sK54),nil),sK52(sK54))
    | ~ spl55_19 ),
    inference(avatar_component_clause,[],[f694]) ).

fof(f540,plain,
    ! [X10,X11,X9] :
      ( app(cons(X9,nil),X10) != sK54
      | ~ ssList(X11)
      | app(X11,cons(X9,nil)) != sK49
      | ~ ssList(X10)
      | ~ ssItem(X9) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f697,plain,
    ( spl55_19
    | ~ spl55_15
    | ~ spl55_11 ),
    inference(avatar_split_clause,[],[f692,f644,f664,f694]) ).

fof(f644,plain,
    ( spl55_11
  <=> ! [X4] :
        ( app(cons(sK51(X4),nil),sK52(X4)) = X4
        | ~ ssList(X4)
        | sK50 != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_11])]) ).

fof(f692,plain,
    ( ~ ssList(sK54)
    | sK54 = app(cons(sK51(sK54),nil),sK52(sK54))
    | ~ spl55_11 ),
    inference(trivial_inequality_removal,[],[f691]) ).

fof(f691,plain,
    ( sK50 != sK50
    | ~ ssList(sK54)
    | sK54 = app(cons(sK51(sK54),nil),sK52(sK54))
    | ~ spl55_11 ),
    inference(superposition,[],[f645,f538]) ).

fof(f645,plain,
    ( ! [X4] :
        ( sK50 != app(sK49,X4)
        | ~ ssList(X4)
        | app(cons(sK51(X4),nil),sK52(X4)) = X4 )
    | ~ spl55_11 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f690,plain,
    ( spl55_18
    | ~ spl55_15
    | ~ spl55_8 ),
    inference(avatar_split_clause,[],[f685,f632,f664,f687]) ).

fof(f632,plain,
    ( spl55_8
  <=> ! [X4] :
        ( sK49 = app(sK53(X4),cons(sK51(X4),nil))
        | ~ ssList(X4)
        | sK50 != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_8])]) ).

fof(f685,plain,
    ( ~ ssList(sK54)
    | sK49 = app(sK53(sK54),cons(sK51(sK54),nil))
    | ~ spl55_8 ),
    inference(trivial_inequality_removal,[],[f684]) ).

fof(f684,plain,
    ( sK50 != sK50
    | ~ ssList(sK54)
    | sK49 = app(sK53(sK54),cons(sK51(sK54),nil))
    | ~ spl55_8 ),
    inference(superposition,[],[f633,f538]) ).

fof(f633,plain,
    ( ! [X4] :
        ( sK50 != app(sK49,X4)
        | ~ ssList(X4)
        | sK49 = app(sK53(X4),cons(sK51(X4),nil)) )
    | ~ spl55_8 ),
    inference(avatar_component_clause,[],[f632]) ).

fof(f683,plain,
    ( spl55_17
    | ~ spl55_15
    | ~ spl55_13 ),
    inference(avatar_split_clause,[],[f678,f652,f664,f680]) ).

fof(f652,plain,
    ( spl55_13
  <=> ! [X4] :
        ( ssItem(sK51(X4))
        | ~ ssList(X4)
        | sK50 != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_13])]) ).

fof(f678,plain,
    ( ~ ssList(sK54)
    | ssItem(sK51(sK54))
    | ~ spl55_13 ),
    inference(trivial_inequality_removal,[],[f677]) ).

fof(f677,plain,
    ( sK50 != sK50
    | ~ ssList(sK54)
    | ssItem(sK51(sK54))
    | ~ spl55_13 ),
    inference(superposition,[],[f653,f538]) ).

fof(f653,plain,
    ( ! [X4] :
        ( sK50 != app(sK49,X4)
        | ~ ssList(X4)
        | ssItem(sK51(X4)) )
    | ~ spl55_13 ),
    inference(avatar_component_clause,[],[f652]) ).

fof(f676,plain,
    spl55_15,
    inference(avatar_contradiction_clause,[],[f675]) ).

fof(f675,plain,
    ( $false
    | spl55_15 ),
    inference(resolution,[],[f666,f537]) ).

fof(f537,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f340]) ).

fof(f666,plain,
    ( ~ ssList(sK54)
    | spl55_15 ),
    inference(avatar_component_clause,[],[f664]) ).

fof(f674,plain,
    ( spl55_16
    | ~ spl55_15
    | ~ spl55_12 ),
    inference(avatar_split_clause,[],[f669,f648,f664,f671]) ).

fof(f648,plain,
    ( spl55_12
  <=> ! [X4] :
        ( ssList(sK52(X4))
        | ~ ssList(X4)
        | sK50 != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_12])]) ).

fof(f669,plain,
    ( ~ ssList(sK54)
    | ssList(sK52(sK54))
    | ~ spl55_12 ),
    inference(trivial_inequality_removal,[],[f668]) ).

fof(f668,plain,
    ( sK50 != sK50
    | ~ ssList(sK54)
    | ssList(sK52(sK54))
    | ~ spl55_12 ),
    inference(superposition,[],[f649,f538]) ).

fof(f649,plain,
    ( ! [X4] :
        ( sK50 != app(sK49,X4)
        | ~ ssList(X4)
        | ssList(sK52(X4)) )
    | ~ spl55_12 ),
    inference(avatar_component_clause,[],[f648]) ).

fof(f667,plain,
    ( spl55_14
    | ~ spl55_15
    | ~ spl55_10 ),
    inference(avatar_split_clause,[],[f658,f640,f664,f660]) ).

fof(f640,plain,
    ( spl55_10
  <=> ! [X4] :
        ( ssList(sK53(X4))
        | ~ ssList(X4)
        | sK50 != app(sK49,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_10])]) ).

fof(f658,plain,
    ( ~ ssList(sK54)
    | ssList(sK53(sK54))
    | ~ spl55_10 ),
    inference(trivial_inequality_removal,[],[f657]) ).

fof(f657,plain,
    ( sK50 != sK50
    | ~ ssList(sK54)
    | ssList(sK53(sK54))
    | ~ spl55_10 ),
    inference(superposition,[],[f641,f538]) ).

fof(f641,plain,
    ( ! [X4] :
        ( sK50 != app(sK49,X4)
        | ~ ssList(X4)
        | ssList(sK53(X4)) )
    | ~ spl55_10 ),
    inference(avatar_component_clause,[],[f640]) ).

fof(f656,plain,
    spl55_2,
    inference(avatar_split_clause,[],[f539,f603]) ).

fof(f603,plain,
    ( spl55_2
  <=> equalelemsP(sK49) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_2])]) ).

fof(f539,plain,
    equalelemsP(sK49),
    inference(cnf_transformation,[],[f340]) ).

fof(f655,plain,
    ( spl55_3
    | ~ spl55_9 ),
    inference(avatar_split_clause,[],[f541,f635,f607]) ).

fof(f541,plain,
    ( nil != sK49
    | nil = sK50 ),
    inference(cnf_transformation,[],[f340]) ).

fof(f654,plain,
    ( spl55_13
    | ~ spl55_2
    | spl55_9 ),
    inference(avatar_split_clause,[],[f561,f635,f603,f652]) ).

fof(f561,plain,
    ! [X4] :
      ( nil = sK49
      | ~ equalelemsP(sK49)
      | ssItem(sK51(X4))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f542,f536,f536,f536,f535]) ).

fof(f535,plain,
    sK48 = sK50,
    inference(cnf_transformation,[],[f340]) ).

fof(f536,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f340]) ).

fof(f542,plain,
    ! [X4] :
      ( nil = sK47
      | ~ equalelemsP(sK47)
      | ssItem(sK51(X4))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f650,plain,
    ( spl55_12
    | ~ spl55_2
    | spl55_9 ),
    inference(avatar_split_clause,[],[f560,f635,f603,f648]) ).

fof(f560,plain,
    ! [X4] :
      ( nil = sK49
      | ~ equalelemsP(sK49)
      | ssList(sK52(X4))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f543,f536,f536,f536,f535]) ).

fof(f543,plain,
    ! [X4] :
      ( nil = sK47
      | ~ equalelemsP(sK47)
      | ssList(sK52(X4))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f646,plain,
    ( spl55_11
    | ~ spl55_2
    | spl55_9 ),
    inference(avatar_split_clause,[],[f559,f635,f603,f644]) ).

fof(f559,plain,
    ! [X4] :
      ( nil = sK49
      | ~ equalelemsP(sK49)
      | app(cons(sK51(X4),nil),sK52(X4)) = X4
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f544,f536,f536,f536,f535]) ).

fof(f544,plain,
    ! [X4] :
      ( nil = sK47
      | ~ equalelemsP(sK47)
      | app(cons(sK51(X4),nil),sK52(X4)) = X4
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f642,plain,
    ( spl55_10
    | ~ spl55_2
    | spl55_9 ),
    inference(avatar_split_clause,[],[f558,f635,f603,f640]) ).

fof(f558,plain,
    ! [X4] :
      ( nil = sK49
      | ~ equalelemsP(sK49)
      | ssList(sK53(X4))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f545,f536,f536,f536,f535]) ).

fof(f545,plain,
    ! [X4] :
      ( nil = sK47
      | ~ equalelemsP(sK47)
      | ssList(sK53(X4))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f638,plain,
    ( spl55_8
    | ~ spl55_2
    | spl55_9 ),
    inference(avatar_split_clause,[],[f557,f635,f603,f632]) ).

fof(f557,plain,
    ! [X4] :
      ( nil = sK49
      | ~ equalelemsP(sK49)
      | sK49 = app(sK53(X4),cons(sK51(X4),nil))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f546,f536,f536,f536,f536,f535]) ).

fof(f546,plain,
    ! [X4] :
      ( nil = sK47
      | ~ equalelemsP(sK47)
      | sK47 = app(sK53(X4),cons(sK51(X4),nil))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f630,plain,
    ( spl55_7
    | ~ spl55_2
    | ~ spl55_3 ),
    inference(avatar_split_clause,[],[f626,f607,f603,f628]) ).

fof(f626,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | ssItem(sK51(X4))
      | nil != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(inner_rewriting,[],[f556]) ).

fof(f556,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | ssItem(sK51(X4))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f547,f535,f536,f536,f535]) ).

fof(f547,plain,
    ! [X4] :
      ( nil != sK48
      | ~ equalelemsP(sK47)
      | ssItem(sK51(X4))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f625,plain,
    ( spl55_6
    | ~ spl55_2
    | ~ spl55_3 ),
    inference(avatar_split_clause,[],[f621,f607,f603,f623]) ).

fof(f621,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | ssList(sK52(X4))
      | nil != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(inner_rewriting,[],[f555]) ).

fof(f555,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | ssList(sK52(X4))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f548,f535,f536,f536,f535]) ).

fof(f548,plain,
    ! [X4] :
      ( nil != sK48
      | ~ equalelemsP(sK47)
      | ssList(sK52(X4))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f620,plain,
    ( spl55_5
    | ~ spl55_2
    | ~ spl55_3 ),
    inference(avatar_split_clause,[],[f616,f607,f603,f618]) ).

fof(f616,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | app(cons(sK51(X4),nil),sK52(X4)) = X4
      | nil != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(inner_rewriting,[],[f554]) ).

fof(f554,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | app(cons(sK51(X4),nil),sK52(X4)) = X4
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f549,f535,f536,f536,f535]) ).

fof(f549,plain,
    ! [X4] :
      ( nil != sK48
      | ~ equalelemsP(sK47)
      | app(cons(sK51(X4),nil),sK52(X4)) = X4
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f615,plain,
    ( spl55_4
    | ~ spl55_2
    | ~ spl55_3 ),
    inference(avatar_split_clause,[],[f611,f607,f603,f613]) ).

fof(f611,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | ssList(sK53(X4))
      | nil != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(inner_rewriting,[],[f553]) ).

fof(f553,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | ssList(sK53(X4))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f550,f535,f536,f536,f535]) ).

fof(f550,plain,
    ! [X4] :
      ( nil != sK48
      | ~ equalelemsP(sK47)
      | ssList(sK53(X4))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f610,plain,
    ( spl55_1
    | ~ spl55_2
    | ~ spl55_3 ),
    inference(avatar_split_clause,[],[f598,f607,f603,f600]) ).

fof(f598,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | sK49 = app(sK53(X4),cons(sK51(X4),nil))
      | nil != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(inner_rewriting,[],[f552]) ).

fof(f552,plain,
    ! [X4] :
      ( nil != sK50
      | ~ equalelemsP(sK49)
      | sK49 = app(sK53(X4),cons(sK51(X4),nil))
      | sK50 != app(sK49,X4)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f551,f535,f536,f536,f536,f535]) ).

fof(f551,plain,
    ! [X4] :
      ( nil != sK48
      | ~ equalelemsP(sK47)
      | sK47 = app(sK53(X4),cons(sK51(X4),nil))
      | app(sK47,X4) != sK48
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f340]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : SWC327+1 : TPTP v8.2.0. Released v2.4.0.
% 0.05/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31  % Computer : n024.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Sun May 19 02:50:37 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  This is a FOF_THM_RFO_SEQ problem
% 0.10/0.31  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.81  % (3999)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.61/0.81  % (3996)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2995ds/34Mi)
% 0.61/0.81  % (3998)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.61/0.81  % (3997)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2995ds/51Mi)
% 0.61/0.81  % (4000)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2995ds/34Mi)
% 0.61/0.81  % (4002)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2995ds/83Mi)
% 0.61/0.81  % (4001)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.61/0.81  % (4003)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.61/0.82  % (3997)First to succeed.
% 0.61/0.82  % (3997)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3995"
% 0.66/0.82  % (3997)Refutation found. Thanks to Tanya!
% 0.66/0.82  % SZS status Theorem for theBenchmark
% 0.66/0.82  % SZS output start Proof for theBenchmark
% See solution above
% 0.66/0.83  % (3997)------------------------------
% 0.66/0.83  % (3997)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.66/0.83  % (3997)Termination reason: Refutation
% 0.66/0.83  
% 0.66/0.83  % (3997)Memory used [KB]: 1488
% 0.66/0.83  % (3997)Time elapsed: 0.015 s
% 0.66/0.83  % (3997)Instructions burned: 26 (million)
% 0.66/0.83  % (3995)Success in time 0.506 s
% 0.66/0.83  % Vampire---4.8 exiting
%------------------------------------------------------------------------------