TSTP Solution File: SWC327+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC327+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n007.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 : Wed Aug 31 18:40:27 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   91 (   8 unt;   0 def)
%            Number of atoms       :  647 ( 263 equ)
%            Maximal formula atoms :   52 (   7 avg)
%            Number of connectives :  883 ( 327   ~; 320   |; 204   &)
%                                         (   8 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   9 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  188 ( 106   !;  82   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f278,plain,
    $false,
    inference(avatar_sat_refutation,[],[f227,f235,f239,f243,f244,f245,f246,f247,f251,f252,f253,f254,f277]) ).

fof(f277,plain,
    ( ~ spl16_3
    | ~ spl16_5
    | ~ spl16_6
    | ~ spl16_7
    | ~ spl16_8 ),
    inference(avatar_contradiction_clause,[],[f276]) ).

fof(f276,plain,
    ( $false
    | ~ spl16_3
    | ~ spl16_5
    | ~ spl16_6
    | ~ spl16_7
    | ~ spl16_8 ),
    inference(subsumption_resolution,[],[f275,f263]) ).

fof(f263,plain,
    ( ssList(sK9(sK6))
    | ~ spl16_7 ),
    inference(subsumption_resolution,[],[f262,f180]) ).

fof(f180,plain,
    ssList(sK6),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ( ssList(sK2)
    & ssList(sK6)
    & sK5 = app(sK4,sK6)
    & ! [X5] :
        ( ~ ssItem(X5)
        | ! [X6] :
            ( ! [X7] :
                ( app(X7,cons(X5,nil)) != sK4
                | ~ ssList(X7) )
            | app(cons(X5,nil),X6) != sK6
            | ~ ssList(X6) ) )
    & equalelemsP(sK4)
    & ssList(sK5)
    & ( ! [X8] :
          ( ( ssItem(sK7(X8))
            & ssList(sK9(X8))
            & app(sK9(X8),cons(sK7(X8),nil)) = sK2
            & app(cons(sK7(X8),nil),sK8(X8)) = X8
            & ssList(sK8(X8)) )
          | ~ equalelemsP(sK2)
          | ~ ssList(X8)
          | app(sK2,X8) != sK3 )
      | ( nil != sK3
        & nil = sK2 ) )
    & ( nil = sK5
      | nil != sK4 )
    & sK5 = sK3
    & sK2 = sK4
    & ssList(sK4)
    & ssList(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f120,f133,f132,f131,f130,f129,f128,f127,f126]) ).

fof(f126,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ssList(X4)
                        & app(X2,X4) = X3
                        & ! [X5] :
                            ( ~ ssItem(X5)
                            | ! [X6] :
                                ( ! [X7] :
                                    ( app(X7,cons(X5,nil)) != X2
                                    | ~ ssList(X7) )
                                | app(cons(X5,nil),X6) != X4
                                | ~ ssList(X6) ) )
                        & equalelemsP(X2) )
                    & ssList(X3)
                    & ( ! [X8] :
                          ( ? [X9] :
                              ( ssItem(X9)
                              & ? [X10] :
                                  ( ? [X11] :
                                      ( ssList(X11)
                                      & app(X11,cons(X9,nil)) = X0 )
                                  & app(cons(X9,nil),X10) = X8
                                  & ssList(X10) ) )
                          | ~ equalelemsP(X0)
                          | ~ ssList(X8)
                          | app(X0,X8) != X1 )
                      | ( nil != X1
                        & nil = X0 ) )
                    & ( nil = X3
                      | nil != X2 )
                    & X1 = X3
                    & X0 = X2 )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK2)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ssList(X4)
                      & app(X2,X4) = X3
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) ) )
                      & equalelemsP(X2) )
                  & ssList(X3)
                  & ( ! [X8] :
                        ( ? [X9] :
                            ( ssItem(X9)
                            & ? [X10] :
                                ( ? [X11] :
                                    ( ssList(X11)
                                    & app(X11,cons(X9,nil)) = sK2 )
                                & app(cons(X9,nil),X10) = X8
                                & ssList(X10) ) )
                        | ~ equalelemsP(sK2)
                        | ~ ssList(X8)
                        | app(sK2,X8) != X1 )
                    | ( nil != X1
                      & nil = sK2 ) )
                  & ( nil = X3
                    | nil != X2 )
                  & X1 = X3
                  & sK2 = X2 )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ssList(X4)
                    & app(X2,X4) = X3
                    & ! [X5] :
                        ( ~ ssItem(X5)
                        | ! [X6] :
                            ( ! [X7] :
                                ( app(X7,cons(X5,nil)) != X2
                                | ~ ssList(X7) )
                            | app(cons(X5,nil),X6) != X4
                            | ~ ssList(X6) ) )
                    & equalelemsP(X2) )
                & ssList(X3)
                & ( ! [X8] :
                      ( ? [X9] :
                          ( ssItem(X9)
                          & ? [X10] :
                              ( ? [X11] :
                                  ( ssList(X11)
                                  & app(X11,cons(X9,nil)) = sK2 )
                              & app(cons(X9,nil),X10) = X8
                              & ssList(X10) ) )
                      | ~ equalelemsP(sK2)
                      | ~ ssList(X8)
                      | app(sK2,X8) != X1 )
                  | ( nil != X1
                    & nil = sK2 ) )
                & ( nil = X3
                  | nil != X2 )
                & X1 = X3
                & sK2 = X2 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ssList(X4)
                  & app(X2,X4) = X3
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ! [X7] :
                              ( app(X7,cons(X5,nil)) != X2
                              | ~ ssList(X7) )
                          | app(cons(X5,nil),X6) != X4
                          | ~ ssList(X6) ) )
                  & equalelemsP(X2) )
              & ssList(X3)
              & ( ! [X8] :
                    ( ? [X9] :
                        ( ssItem(X9)
                        & ? [X10] :
                            ( ? [X11] :
                                ( ssList(X11)
                                & app(X11,cons(X9,nil)) = sK2 )
                            & app(cons(X9,nil),X10) = X8
                            & ssList(X10) ) )
                    | ~ equalelemsP(sK2)
                    | ~ ssList(X8)
                    | app(sK2,X8) != sK3 )
                | ( nil != sK3
                  & nil = sK2 ) )
              & ( nil = X3
                | nil != X2 )
              & sK3 = X3
              & sK2 = X2 )
          & ssList(X2) )
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ssList(X4)
                & app(X2,X4) = X3
                & ! [X5] :
                    ( ~ ssItem(X5)
                    | ! [X6] :
                        ( ! [X7] :
                            ( app(X7,cons(X5,nil)) != X2
                            | ~ ssList(X7) )
                        | app(cons(X5,nil),X6) != X4
                        | ~ ssList(X6) ) )
                & equalelemsP(X2) )
            & ssList(X3)
            & ( ! [X8] :
                  ( ? [X9] :
                      ( ssItem(X9)
                      & ? [X10] :
                          ( ? [X11] :
                              ( ssList(X11)
                              & app(X11,cons(X9,nil)) = sK2 )
                          & app(cons(X9,nil),X10) = X8
                          & ssList(X10) ) )
                  | ~ equalelemsP(sK2)
                  | ~ ssList(X8)
                  | app(sK2,X8) != sK3 )
              | ( nil != sK3
                & nil = sK2 ) )
            & ( nil = X3
              | nil != X2 )
            & sK3 = X3
            & sK2 = X2 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ? [X4] :
              ( ssList(X4)
              & app(sK4,X4) = X3
              & ! [X5] :
                  ( ~ ssItem(X5)
                  | ! [X6] :
                      ( ! [X7] :
                          ( app(X7,cons(X5,nil)) != sK4
                          | ~ ssList(X7) )
                      | app(cons(X5,nil),X6) != X4
                      | ~ ssList(X6) ) )
              & equalelemsP(sK4) )
          & ssList(X3)
          & ( ! [X8] :
                ( ? [X9] :
                    ( ssItem(X9)
                    & ? [X10] :
                        ( ? [X11] :
                            ( ssList(X11)
                            & app(X11,cons(X9,nil)) = sK2 )
                        & app(cons(X9,nil),X10) = X8
                        & ssList(X10) ) )
                | ~ equalelemsP(sK2)
                | ~ ssList(X8)
                | app(sK2,X8) != sK3 )
            | ( nil != sK3
              & nil = sK2 ) )
          & ( nil = X3
            | nil != sK4 )
          & sK3 = X3
          & sK2 = sK4 )
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ssList(X4)
            & app(sK4,X4) = X3
            & ! [X5] :
                ( ~ ssItem(X5)
                | ! [X6] :
                    ( ! [X7] :
                        ( app(X7,cons(X5,nil)) != sK4
                        | ~ ssList(X7) )
                    | app(cons(X5,nil),X6) != X4
                    | ~ ssList(X6) ) )
            & equalelemsP(sK4) )
        & ssList(X3)
        & ( ! [X8] :
              ( ? [X9] :
                  ( ssItem(X9)
                  & ? [X10] :
                      ( ? [X11] :
                          ( ssList(X11)
                          & app(X11,cons(X9,nil)) = sK2 )
                      & app(cons(X9,nil),X10) = X8
                      & ssList(X10) ) )
              | ~ equalelemsP(sK2)
              | ~ ssList(X8)
              | app(sK2,X8) != sK3 )
          | ( nil != sK3
            & nil = sK2 ) )
        & ( nil = X3
          | nil != sK4 )
        & sK3 = X3
        & sK2 = sK4 )
   => ( ? [X4] :
          ( ssList(X4)
          & sK5 = app(sK4,X4)
          & ! [X5] :
              ( ~ ssItem(X5)
              | ! [X6] :
                  ( ! [X7] :
                      ( app(X7,cons(X5,nil)) != sK4
                      | ~ ssList(X7) )
                  | app(cons(X5,nil),X6) != X4
                  | ~ ssList(X6) ) )
          & equalelemsP(sK4) )
      & ssList(sK5)
      & ( ! [X8] :
            ( ? [X9] :
                ( ssItem(X9)
                & ? [X10] :
                    ( ? [X11] :
                        ( ssList(X11)
                        & app(X11,cons(X9,nil)) = sK2 )
                    & app(cons(X9,nil),X10) = X8
                    & ssList(X10) ) )
            | ~ equalelemsP(sK2)
            | ~ ssList(X8)
            | app(sK2,X8) != sK3 )
        | ( nil != sK3
          & nil = sK2 ) )
      & ( nil = sK5
        | nil != sK4 )
      & sK5 = sK3
      & sK2 = sK4 ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ( ? [X4] :
        ( ssList(X4)
        & sK5 = app(sK4,X4)
        & ! [X5] :
            ( ~ ssItem(X5)
            | ! [X6] :
                ( ! [X7] :
                    ( app(X7,cons(X5,nil)) != sK4
                    | ~ ssList(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) ) )
        & equalelemsP(sK4) )
   => ( ssList(sK6)
      & sK5 = app(sK4,sK6)
      & ! [X5] :
          ( ~ ssItem(X5)
          | ! [X6] :
              ( ! [X7] :
                  ( app(X7,cons(X5,nil)) != sK4
                  | ~ ssList(X7) )
              | app(cons(X5,nil),X6) != sK6
              | ~ ssList(X6) ) )
      & equalelemsP(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ! [X8] :
      ( ? [X9] :
          ( ssItem(X9)
          & ? [X10] :
              ( ? [X11] :
                  ( ssList(X11)
                  & app(X11,cons(X9,nil)) = sK2 )
              & app(cons(X9,nil),X10) = X8
              & ssList(X10) ) )
     => ( ssItem(sK7(X8))
        & ? [X10] :
            ( ? [X11] :
                ( ssList(X11)
                & sK2 = app(X11,cons(sK7(X8),nil)) )
            & app(cons(sK7(X8),nil),X10) = X8
            & ssList(X10) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ! [X8] :
      ( ? [X10] :
          ( ? [X11] :
              ( ssList(X11)
              & sK2 = app(X11,cons(sK7(X8),nil)) )
          & app(cons(sK7(X8),nil),X10) = X8
          & ssList(X10) )
     => ( ? [X11] :
            ( ssList(X11)
            & sK2 = app(X11,cons(sK7(X8),nil)) )
        & app(cons(sK7(X8),nil),sK8(X8)) = X8
        & ssList(sK8(X8)) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ! [X8] :
      ( ? [X11] :
          ( ssList(X11)
          & sK2 = app(X11,cons(sK7(X8),nil)) )
     => ( ssList(sK9(X8))
        & app(sK9(X8),cons(sK7(X8),nil)) = sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ssList(X4)
                      & app(X2,X4) = X3
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) ) )
                      & equalelemsP(X2) )
                  & ssList(X3)
                  & ( ! [X8] :
                        ( ? [X9] :
                            ( ssItem(X9)
                            & ? [X10] :
                                ( ? [X11] :
                                    ( ssList(X11)
                                    & app(X11,cons(X9,nil)) = X0 )
                                & app(cons(X9,nil),X10) = X8
                                & ssList(X10) ) )
                        | ~ equalelemsP(X0)
                        | ~ ssList(X8)
                        | app(X0,X8) != X1 )
                    | ( nil != X1
                      & nil = X0 ) )
                  & ( nil = X3
                    | nil != X2 )
                  & X1 = X3
                  & X0 = X2 )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f119]) ).

fof(f119,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & ( ! [X8] :
                        ( ? [X9] :
                            ( ? [X10] :
                                ( app(cons(X9,nil),X10) = X8
                                & ? [X11] :
                                    ( ssList(X11)
                                    & app(X11,cons(X9,nil)) = X0 )
                                & ssList(X10) )
                            & ssItem(X9) )
                        | ~ equalelemsP(X0)
                        | app(X0,X8) != X1
                        | ~ ssList(X8) )
                    | ( nil != X1
                      & nil = X0 ) )
                  & ( nil = X3
                    | nil != X2 )
                  & X1 = X3
                  & ? [X4] :
                      ( ! [X5] :
                          ( ~ ssItem(X5)
                          | ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) ) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & 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)
                   => ( X0 != X2
                      | ( ? [X8] :
                            ( ! [X9] :
                                ( ssItem(X9)
                               => ! [X10] :
                                    ( ssList(X10)
                                   => ( app(cons(X9,nil),X10) != X8
                                      | ! [X11] :
                                          ( ssList(X11)
                                         => app(X11,cons(X9,nil)) != X0 ) ) ) )
                            & equalelemsP(X0)
                            & app(X0,X8) = X1
                            & ssList(X8) )
                        & ( nil != X0
                          | nil = X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | X1 != X3
                      | ! [X4] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( app(cons(X5,nil),X6) = X4
                                    & ssList(X6)
                                    & ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) ) )
                                & ssItem(X5) )
                            | ~ equalelemsP(X2)
                            | app(X2,X4) != X3 ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f262,plain,
    ( ssList(sK9(sK6))
    | ~ ssList(sK6)
    | ~ spl16_7 ),
    inference(trivial_inequality_removal,[],[f261]) ).

fof(f261,plain,
    ( sK3 != sK3
    | ssList(sK9(sK6))
    | ~ ssList(sK6)
    | ~ spl16_7 ),
    inference(superposition,[],[f242,f199]) ).

fof(f199,plain,
    app(sK4,sK6) = sK3,
    inference(definition_unfolding,[],[f179,f164]) ).

fof(f164,plain,
    sK5 = sK3,
    inference(cnf_transformation,[],[f134]) ).

fof(f179,plain,
    sK5 = app(sK4,sK6),
    inference(cnf_transformation,[],[f134]) ).

fof(f242,plain,
    ( ! [X8] :
        ( app(sK4,X8) != sK3
        | ssList(sK9(X8))
        | ~ ssList(X8) )
    | ~ spl16_7 ),
    inference(avatar_component_clause,[],[f241]) ).

fof(f241,plain,
    ( spl16_7
  <=> ! [X8] :
        ( ssList(sK9(X8))
        | ~ ssList(X8)
        | app(sK4,X8) != sK3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).

fof(f275,plain,
    ( ~ ssList(sK9(sK6))
    | ~ spl16_3
    | ~ spl16_5
    | ~ spl16_6
    | ~ spl16_8 ),
    inference(trivial_inequality_removal,[],[f274]) ).

fof(f274,plain,
    ( ~ ssList(sK9(sK6))
    | sK4 != sK4
    | ~ spl16_3
    | ~ spl16_5
    | ~ spl16_6
    | ~ spl16_8 ),
    inference(superposition,[],[f273,f269]) ).

fof(f269,plain,
    ( app(sK9(sK6),cons(sK7(sK6),nil)) = sK4
    | ~ spl16_8 ),
    inference(subsumption_resolution,[],[f268,f180]) ).

fof(f268,plain,
    ( ~ ssList(sK6)
    | app(sK9(sK6),cons(sK7(sK6),nil)) = sK4
    | ~ spl16_8 ),
    inference(trivial_inequality_removal,[],[f267]) ).

fof(f267,plain,
    ( sK3 != sK3
    | app(sK9(sK6),cons(sK7(sK6),nil)) = sK4
    | ~ ssList(sK6)
    | ~ spl16_8 ),
    inference(superposition,[],[f250,f199]) ).

fof(f250,plain,
    ( ! [X8] :
        ( app(sK4,X8) != sK3
        | ~ ssList(X8)
        | app(sK9(X8),cons(sK7(X8),nil)) = sK4 )
    | ~ spl16_8 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f249,plain,
    ( spl16_8
  <=> ! [X8] :
        ( ~ ssList(X8)
        | app(sK4,X8) != sK3
        | app(sK9(X8),cons(sK7(X8),nil)) = sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).

fof(f273,plain,
    ( ! [X0] :
        ( app(X0,cons(sK7(sK6),nil)) != sK4
        | ~ ssList(X0) )
    | ~ spl16_3
    | ~ spl16_5
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f272,f257]) ).

fof(f257,plain,
    ( ssItem(sK7(sK6))
    | ~ spl16_5 ),
    inference(subsumption_resolution,[],[f256,f180]) ).

fof(f256,plain,
    ( ~ ssList(sK6)
    | ssItem(sK7(sK6))
    | ~ spl16_5 ),
    inference(trivial_inequality_removal,[],[f255]) ).

fof(f255,plain,
    ( ~ ssList(sK6)
    | sK3 != sK3
    | ssItem(sK7(sK6))
    | ~ spl16_5 ),
    inference(superposition,[],[f234,f199]) ).

fof(f234,plain,
    ( ! [X8] :
        ( app(sK4,X8) != sK3
        | ~ ssList(X8)
        | ssItem(sK7(X8)) )
    | ~ spl16_5 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f233,plain,
    ( spl16_5
  <=> ! [X8] :
        ( ~ ssList(X8)
        | app(sK4,X8) != sK3
        | ssItem(sK7(X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).

fof(f272,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | ~ ssItem(sK7(sK6))
        | app(X0,cons(sK7(sK6),nil)) != sK4 )
    | ~ spl16_3
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f271,f260]) ).

fof(f260,plain,
    ( ssList(sK8(sK6))
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f259,f180]) ).

fof(f259,plain,
    ( ssList(sK8(sK6))
    | ~ ssList(sK6)
    | ~ spl16_6 ),
    inference(trivial_inequality_removal,[],[f258]) ).

fof(f258,plain,
    ( ssList(sK8(sK6))
    | ~ ssList(sK6)
    | sK3 != sK3
    | ~ spl16_6 ),
    inference(superposition,[],[f238,f199]) ).

fof(f238,plain,
    ( ! [X8] :
        ( app(sK4,X8) != sK3
        | ~ ssList(X8)
        | ssList(sK8(X8)) )
    | ~ spl16_6 ),
    inference(avatar_component_clause,[],[f237]) ).

fof(f237,plain,
    ( spl16_6
  <=> ! [X8] :
        ( app(sK4,X8) != sK3
        | ssList(sK8(X8))
        | ~ ssList(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).

fof(f271,plain,
    ( ! [X0] :
        ( app(X0,cons(sK7(sK6),nil)) != sK4
        | ~ ssList(sK8(sK6))
        | ~ ssItem(sK7(sK6))
        | ~ ssList(X0) )
    | ~ spl16_3 ),
    inference(trivial_inequality_removal,[],[f270]) ).

fof(f270,plain,
    ( ! [X0] :
        ( app(X0,cons(sK7(sK6),nil)) != sK4
        | sK6 != sK6
        | ~ ssItem(sK7(sK6))
        | ~ ssList(sK8(sK6))
        | ~ ssList(X0) )
    | ~ spl16_3 ),
    inference(superposition,[],[f178,f266]) ).

fof(f266,plain,
    ( sK6 = app(cons(sK7(sK6),nil),sK8(sK6))
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f265,f180]) ).

fof(f265,plain,
    ( ~ ssList(sK6)
    | sK6 = app(cons(sK7(sK6),nil),sK8(sK6))
    | ~ spl16_3 ),
    inference(trivial_inequality_removal,[],[f264]) ).

fof(f264,plain,
    ( sK6 = app(cons(sK7(sK6),nil),sK8(sK6))
    | sK3 != sK3
    | ~ ssList(sK6)
    | ~ spl16_3 ),
    inference(superposition,[],[f226,f199]) ).

fof(f226,plain,
    ( ! [X8] :
        ( app(sK4,X8) != sK3
        | ~ ssList(X8)
        | app(cons(sK7(X8),nil),sK8(X8)) = X8 )
    | ~ spl16_3 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f225,plain,
    ( spl16_3
  <=> ! [X8] :
        ( app(sK4,X8) != sK3
        | app(cons(sK7(X8),nil),sK8(X8)) = X8
        | ~ ssList(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).

fof(f178,plain,
    ! [X6,X7,X5] :
      ( app(cons(X5,nil),X6) != sK6
      | ~ ssList(X6)
      | ~ ssItem(X5)
      | ~ ssList(X7)
      | app(X7,cons(X5,nil)) != sK4 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f254,plain,
    ( spl16_6
    | spl16_4
    | ~ spl16_2 ),
    inference(avatar_split_clause,[],[f210,f221,f229,f237]) ).

fof(f229,plain,
    ( spl16_4
  <=> nil = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).

fof(f221,plain,
    ( spl16_2
  <=> equalelemsP(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).

fof(f210,plain,
    ! [X8] :
      ( ~ equalelemsP(sK4)
      | nil = sK4
      | app(sK4,X8) != sK3
      | ssList(sK8(X8))
      | ~ ssList(X8) ),
    inference(definition_unfolding,[],[f166,f163,f163,f163]) ).

fof(f163,plain,
    sK2 = sK4,
    inference(cnf_transformation,[],[f134]) ).

fof(f166,plain,
    ! [X8] :
      ( ssList(sK8(X8))
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil = sK2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f253,plain,
    ( ~ spl16_4
    | spl16_1 ),
    inference(avatar_split_clause,[],[f211,f217,f229]) ).

fof(f217,plain,
    ( spl16_1
  <=> nil = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).

fof(f211,plain,
    ( nil = sK3
    | nil != sK4 ),
    inference(definition_unfolding,[],[f165,f164]) ).

fof(f165,plain,
    ( nil = sK5
    | nil != sK4 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f252,plain,
    ( spl16_4
    | ~ spl16_2
    | spl16_8 ),
    inference(avatar_split_clause,[],[f206,f249,f221,f229]) ).

fof(f206,plain,
    ! [X8] :
      ( app(sK4,X8) != sK3
      | ~ equalelemsP(sK4)
      | nil = sK4
      | ~ ssList(X8)
      | app(sK9(X8),cons(sK7(X8),nil)) = sK4 ),
    inference(definition_unfolding,[],[f170,f163,f163,f163,f163]) ).

fof(f170,plain,
    ! [X8] :
      ( app(sK9(X8),cons(sK7(X8),nil)) = sK2
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil = sK2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f251,plain,
    ( ~ spl16_2
    | ~ spl16_1
    | spl16_8 ),
    inference(avatar_split_clause,[],[f205,f249,f217,f221]) ).

fof(f205,plain,
    ! [X8] :
      ( ~ ssList(X8)
      | nil != sK3
      | app(sK9(X8),cons(sK7(X8),nil)) = sK4
      | app(sK4,X8) != sK3
      | ~ equalelemsP(sK4) ),
    inference(definition_unfolding,[],[f171,f163,f163,f163]) ).

fof(f171,plain,
    ! [X8] :
      ( app(sK9(X8),cons(sK7(X8),nil)) = sK2
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil != sK3 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f247,plain,
    spl16_2,
    inference(avatar_split_clause,[],[f177,f221]) ).

fof(f177,plain,
    equalelemsP(sK4),
    inference(cnf_transformation,[],[f134]) ).

fof(f246,plain,
    ( ~ spl16_2
    | spl16_4
    | spl16_7 ),
    inference(avatar_split_clause,[],[f204,f241,f229,f221]) ).

fof(f204,plain,
    ! [X8] :
      ( ssList(sK9(X8))
      | nil = sK4
      | ~ equalelemsP(sK4)
      | ~ ssList(X8)
      | app(sK4,X8) != sK3 ),
    inference(definition_unfolding,[],[f172,f163,f163,f163]) ).

fof(f172,plain,
    ! [X8] :
      ( ssList(sK9(X8))
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil = sK2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f245,plain,
    ( ~ spl16_2
    | spl16_5
    | ~ spl16_1 ),
    inference(avatar_split_clause,[],[f201,f217,f233,f221]) ).

fof(f201,plain,
    ! [X8] :
      ( nil != sK3
      | ssItem(sK7(X8))
      | ~ equalelemsP(sK4)
      | ~ ssList(X8)
      | app(sK4,X8) != sK3 ),
    inference(definition_unfolding,[],[f175,f163,f163]) ).

fof(f175,plain,
    ! [X8] :
      ( ssItem(sK7(X8))
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil != sK3 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f244,plain,
    ( spl16_3
    | ~ spl16_2
    | spl16_4 ),
    inference(avatar_split_clause,[],[f208,f229,f221,f225]) ).

fof(f208,plain,
    ! [X8] :
      ( nil = sK4
      | ~ equalelemsP(sK4)
      | ~ ssList(X8)
      | app(sK4,X8) != sK3
      | app(cons(sK7(X8),nil),sK8(X8)) = X8 ),
    inference(definition_unfolding,[],[f168,f163,f163,f163]) ).

fof(f168,plain,
    ! [X8] :
      ( app(cons(sK7(X8),nil),sK8(X8)) = X8
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil = sK2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f243,plain,
    ( ~ spl16_1
    | ~ spl16_2
    | spl16_7 ),
    inference(avatar_split_clause,[],[f203,f241,f221,f217]) ).

fof(f203,plain,
    ! [X8] :
      ( ssList(sK9(X8))
      | ~ equalelemsP(sK4)
      | app(sK4,X8) != sK3
      | ~ ssList(X8)
      | nil != sK3 ),
    inference(definition_unfolding,[],[f173,f163,f163]) ).

fof(f173,plain,
    ! [X8] :
      ( ssList(sK9(X8))
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil != sK3 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f239,plain,
    ( ~ spl16_1
    | ~ spl16_2
    | spl16_6 ),
    inference(avatar_split_clause,[],[f209,f237,f221,f217]) ).

fof(f209,plain,
    ! [X8] :
      ( app(sK4,X8) != sK3
      | ~ equalelemsP(sK4)
      | nil != sK3
      | ~ ssList(X8)
      | ssList(sK8(X8)) ),
    inference(definition_unfolding,[],[f167,f163,f163]) ).

fof(f167,plain,
    ! [X8] :
      ( ssList(sK8(X8))
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil != sK3 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f235,plain,
    ( spl16_4
    | ~ spl16_2
    | spl16_5 ),
    inference(avatar_split_clause,[],[f202,f233,f221,f229]) ).

fof(f202,plain,
    ! [X8] :
      ( ~ ssList(X8)
      | ~ equalelemsP(sK4)
      | nil = sK4
      | ssItem(sK7(X8))
      | app(sK4,X8) != sK3 ),
    inference(definition_unfolding,[],[f174,f163,f163,f163]) ).

fof(f174,plain,
    ! [X8] :
      ( ssItem(sK7(X8))
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil = sK2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f227,plain,
    ( ~ spl16_1
    | ~ spl16_2
    | spl16_3 ),
    inference(avatar_split_clause,[],[f207,f225,f221,f217]) ).

fof(f207,plain,
    ! [X8] :
      ( app(sK4,X8) != sK3
      | ~ ssList(X8)
      | ~ equalelemsP(sK4)
      | app(cons(sK7(X8),nil),sK8(X8)) = X8
      | nil != sK3 ),
    inference(definition_unfolding,[],[f169,f163,f163]) ).

fof(f169,plain,
    ! [X8] :
      ( app(cons(sK7(X8),nil),sK8(X8)) = X8
      | ~ equalelemsP(sK2)
      | ~ ssList(X8)
      | app(sK2,X8) != sK3
      | nil != sK3 ),
    inference(cnf_transformation,[],[f134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC327+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 18:32:16 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (15653)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (15669)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (15660)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50  % (15661)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.50  % (15657)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (15668)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52  % (15668)Instruction limit reached!
% 0.19/0.52  % (15668)------------------------------
% 0.19/0.52  % (15668)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (15665)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.52  % (15668)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (15668)Termination reason: Unknown
% 0.19/0.52  % (15668)Termination phase: Property scanning
% 0.19/0.52  
% 0.19/0.52  % (15668)Memory used [KB]: 1791
% 0.19/0.52  % (15668)Time elapsed: 0.005 s
% 0.19/0.52  % (15668)Instructions burned: 7 (million)
% 0.19/0.52  % (15668)------------------------------
% 0.19/0.52  % (15668)------------------------------
% 0.19/0.52  % (15677)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52  % (15679)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52  % (15658)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.52  % (15681)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.52  % (15680)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.53  % (15676)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.53  % (15655)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.53  % (15654)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53  % (15681)Instruction limit reached!
% 0.19/0.53  % (15681)------------------------------
% 0.19/0.53  % (15681)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (15681)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (15681)Termination reason: Unknown
% 0.19/0.53  % (15681)Termination phase: Property scanning
% 0.19/0.53  
% 0.19/0.53  % (15681)Memory used [KB]: 1791
% 0.19/0.53  % (15681)Time elapsed: 0.005 s
% 0.19/0.53  % (15681)Instructions burned: 10 (million)
% 0.19/0.53  % (15681)------------------------------
% 0.19/0.53  % (15681)------------------------------
% 0.19/0.53  % (15656)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (15655)Instruction limit reached!
% 0.19/0.53  % (15655)------------------------------
% 0.19/0.53  % (15655)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (15655)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (15655)Termination reason: Unknown
% 0.19/0.53  % (15655)Termination phase: Preprocessing 3
% 0.19/0.53  
% 0.19/0.53  % (15655)Memory used [KB]: 1663
% 0.19/0.53  % (15655)Time elapsed: 0.004 s
% 0.19/0.53  % (15655)Instructions burned: 4 (million)
% 0.19/0.53  % (15655)------------------------------
% 0.19/0.53  % (15655)------------------------------
% 0.19/0.53  % (15675)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.53  % (15657)First to succeed.
% 0.19/0.53  % (15671)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.53  % (15682)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.53  % (15654)Instruction limit reached!
% 0.19/0.53  % (15654)------------------------------
% 0.19/0.53  % (15654)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (15654)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (15654)Termination reason: Unknown
% 0.19/0.53  % (15654)Termination phase: Saturation
% 0.19/0.53  
% 0.19/0.53  % (15654)Memory used [KB]: 6396
% 0.19/0.53  % (15654)Time elapsed: 0.134 s
% 0.19/0.53  % (15654)Instructions burned: 13 (million)
% 0.19/0.53  % (15654)------------------------------
% 0.19/0.53  % (15654)------------------------------
% 0.19/0.53  % (15657)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (15657)------------------------------
% 0.19/0.53  % (15657)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (15657)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (15657)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (15657)Memory used [KB]: 6140
% 0.19/0.53  % (15657)Time elapsed: 0.137 s
% 0.19/0.53  % (15657)Instructions burned: 6 (million)
% 0.19/0.53  % (15657)------------------------------
% 0.19/0.53  % (15657)------------------------------
% 0.19/0.53  % (15652)Success in time 0.185 s
%------------------------------------------------------------------------------