TSTP Solution File: SWC002+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC002+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 : n005.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 18:38:09 EDT 2022

% Result   : Theorem 0.21s 0.54s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   99 (   5 unt;   0 def)
%            Number of atoms       :  551 (  59 equ)
%            Maximal formula atoms :   27 (   5 avg)
%            Number of connectives :  837 ( 385   ~; 371   |;  52   &)
%                                         (  13 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   20 (  18 usr;  13 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :  117 (  93   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f967,plain,
    $false,
    inference(avatar_sat_refutation,[],[f569,f578,f583,f588,f605,f606,f607,f608,f615,f617,f619,f945,f966]) ).

fof(f966,plain,
    ( ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_8
    | ~ spl56_11
    | ~ spl56_36 ),
    inference(avatar_contradiction_clause,[],[f965]) ).

fof(f965,plain,
    ( $false
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_8
    | ~ spl56_11
    | ~ spl56_36 ),
    inference(subsumption_resolution,[],[f960,f835]) ).

fof(f835,plain,
    ( ~ sQ55_eqProxy(sK54(sK51),sK51)
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_8
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f834,f592]) ).

fof(f592,plain,
    ( sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ spl56_7 ),
    inference(avatar_component_clause,[],[f590]) ).

fof(f590,plain,
    ( spl56_7
  <=> sQ55_eqProxy(app(sK52,sK53),sK49) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_7])]) ).

fof(f834,plain,
    ( ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ sQ55_eqProxy(sK54(sK51),sK51)
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_8
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f833,f613]) ).

fof(f613,plain,
    ( ssList(sK52)
    | ~ spl56_11 ),
    inference(avatar_component_clause,[],[f611]) ).

fof(f611,plain,
    ( spl56_11
  <=> ssList(sK52) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_11])]) ).

fof(f833,plain,
    ( ~ ssList(sK52)
    | ~ sQ55_eqProxy(sK54(sK51),sK51)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_8 ),
    inference(subsumption_resolution,[],[f832,f582]) ).

fof(f582,plain,
    ( ssItem(sK51)
    | ~ spl56_5 ),
    inference(avatar_component_clause,[],[f580]) ).

fof(f580,plain,
    ( spl56_5
  <=> ssItem(sK51) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_5])]) ).

fof(f832,plain,
    ( ~ ssItem(sK51)
    | ~ ssList(sK52)
    | ~ sQ55_eqProxy(sK54(sK51),sK51)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ spl56_2
    | ~ spl56_6
    | ~ spl56_8 ),
    inference(subsumption_resolution,[],[f819,f568]) ).

fof(f568,plain,
    ( ssList(sK53)
    | ~ spl56_2 ),
    inference(avatar_component_clause,[],[f566]) ).

fof(f566,plain,
    ( spl56_2
  <=> ssList(sK53) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_2])]) ).

fof(f819,plain,
    ( ~ ssList(sK53)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ ssList(sK52)
    | ~ ssItem(sK51)
    | ~ sQ55_eqProxy(sK54(sK51),sK51)
    | ~ spl56_6
    | ~ spl56_8 ),
    inference(resolution,[],[f793,f596]) ).

fof(f596,plain,
    ( ! [X6,X4,X5] :
        ( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | ~ sQ55_eqProxy(app(X5,X6),sK49)
        | ~ ssList(X5)
        | ~ sQ55_eqProxy(sK54(X4),X4)
        | ~ ssItem(X4)
        | ~ ssList(X6) )
    | ~ spl56_8 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f595,plain,
    ( spl56_8
  <=> ! [X6,X4,X5] :
        ( ~ sQ55_eqProxy(app(X5,X6),sK49)
        | ~ sQ55_eqProxy(sK54(X4),X4)
        | ~ ssList(X5)
        | ~ ssItem(X4)
        | ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | ~ ssList(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_8])]) ).

fof(f793,plain,
    ( sQ55_eqProxy(app(app(sK52,cons(sK51,nil)),sK53),sK48)
    | ~ spl56_6 ),
    inference(resolution,[],[f560,f587]) ).

fof(f587,plain,
    ( sQ55_eqProxy(sK48,app(app(sK52,cons(sK51,nil)),sK53))
    | ~ spl56_6 ),
    inference(avatar_component_clause,[],[f585]) ).

fof(f585,plain,
    ( spl56_6
  <=> sQ55_eqProxy(sK48,app(app(sK52,cons(sK51,nil)),sK53)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_6])]) ).

fof(f560,plain,
    ! [X0,X1] :
      ( ~ sQ55_eqProxy(X0,X1)
      | sQ55_eqProxy(X1,X0) ),
    inference(equality_proxy_axiom,[],[f458]) ).

fof(f458,plain,
    ! [X0,X1] :
      ( sQ55_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ55_eqProxy])]) ).

fof(f960,plain,
    ( sQ55_eqProxy(sK54(sK51),sK51)
    | ~ spl56_36 ),
    inference(resolution,[],[f914,f560]) ).

fof(f914,plain,
    ( sQ55_eqProxy(sK51,sK54(sK51))
    | ~ spl56_36 ),
    inference(avatar_component_clause,[],[f912]) ).

fof(f912,plain,
    ( spl56_36
  <=> sQ55_eqProxy(sK51,sK54(sK51)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_36])]) ).

fof(f945,plain,
    ( spl56_36
    | ~ spl56_2
    | ~ spl56_3
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_9
    | ~ spl56_10
    | ~ spl56_11 ),
    inference(avatar_split_clause,[],[f900,f611,f603,f599,f590,f585,f580,f575,f571,f566,f912]) ).

fof(f571,plain,
    ( spl56_3
  <=> ! [X11] :
        ( ~ geq(X11,sK51)
        | ~ ssItem(X11)
        | sQ55_eqProxy(sK51,X11)
        | ~ memberP(sK48,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_3])]) ).

fof(f575,plain,
    ( spl56_4
  <=> ! [X6,X4,X5] :
        ( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | ssItem(sK54(X4))
        | ~ ssItem(X4)
        | ~ ssList(X6)
        | ~ sQ55_eqProxy(app(X5,X6),sK49)
        | ~ ssList(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_4])]) ).

fof(f599,plain,
    ( spl56_9
  <=> ! [X6,X4,X5] :
        ( geq(sK54(X4),X4)
        | ~ ssItem(X4)
        | ~ sQ55_eqProxy(app(X5,X6),sK49)
        | ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | ~ ssList(X5)
        | ~ ssList(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_9])]) ).

fof(f603,plain,
    ( spl56_10
  <=> ! [X6,X4,X5] :
        ( memberP(sK48,sK54(X4))
        | ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | ~ ssItem(X4)
        | ~ ssList(X6)
        | ~ ssList(X5)
        | ~ sQ55_eqProxy(app(X5,X6),sK49) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_10])]) ).

fof(f900,plain,
    ( sQ55_eqProxy(sK51,sK54(sK51))
    | ~ spl56_2
    | ~ spl56_3
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_9
    | ~ spl56_10
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f899,f827]) ).

fof(f827,plain,
    ( memberP(sK48,sK54(sK51))
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_10
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f826,f568]) ).

fof(f826,plain,
    ( ~ ssList(sK53)
    | memberP(sK48,sK54(sK51))
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_10
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f825,f592]) ).

fof(f825,plain,
    ( memberP(sK48,sK54(sK51))
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ ssList(sK53)
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_10
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f824,f613]) ).

fof(f824,plain,
    ( ~ ssList(sK52)
    | ~ ssList(sK53)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | memberP(sK48,sK54(sK51))
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_10 ),
    inference(subsumption_resolution,[],[f817,f582]) ).

fof(f817,plain,
    ( ~ ssItem(sK51)
    | ~ ssList(sK52)
    | ~ ssList(sK53)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | memberP(sK48,sK54(sK51))
    | ~ spl56_6
    | ~ spl56_10 ),
    inference(resolution,[],[f793,f604]) ).

fof(f604,plain,
    ( ! [X6,X4,X5] :
        ( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | memberP(sK48,sK54(X4))
        | ~ ssItem(X4)
        | ~ ssList(X6)
        | ~ sQ55_eqProxy(app(X5,X6),sK49)
        | ~ ssList(X5) )
    | ~ spl56_10 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f899,plain,
    ( sQ55_eqProxy(sK51,sK54(sK51))
    | ~ memberP(sK48,sK54(sK51))
    | ~ spl56_2
    | ~ spl56_3
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_9
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f895,f831]) ).

fof(f831,plain,
    ( ssItem(sK54(sK51))
    | ~ spl56_2
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f830,f613]) ).

fof(f830,plain,
    ( ~ ssList(sK52)
    | ssItem(sK54(sK51))
    | ~ spl56_2
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7 ),
    inference(subsumption_resolution,[],[f829,f592]) ).

fof(f829,plain,
    ( ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ssItem(sK54(sK51))
    | ~ ssList(sK52)
    | ~ spl56_2
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6 ),
    inference(subsumption_resolution,[],[f828,f568]) ).

fof(f828,plain,
    ( ~ ssList(sK53)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ ssList(sK52)
    | ssItem(sK54(sK51))
    | ~ spl56_4
    | ~ spl56_5
    | ~ spl56_6 ),
    inference(subsumption_resolution,[],[f820,f582]) ).

fof(f820,plain,
    ( ~ ssItem(sK51)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ ssList(sK53)
    | ssItem(sK54(sK51))
    | ~ ssList(sK52)
    | ~ spl56_4
    | ~ spl56_6 ),
    inference(resolution,[],[f793,f576]) ).

fof(f576,plain,
    ( ! [X6,X4,X5] :
        ( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | ~ ssList(X5)
        | ssItem(sK54(X4))
        | ~ ssList(X6)
        | ~ ssItem(X4)
        | ~ sQ55_eqProxy(app(X5,X6),sK49) )
    | ~ spl56_4 ),
    inference(avatar_component_clause,[],[f575]) ).

fof(f895,plain,
    ( sQ55_eqProxy(sK51,sK54(sK51))
    | ~ ssItem(sK54(sK51))
    | ~ memberP(sK48,sK54(sK51))
    | ~ spl56_2
    | ~ spl56_3
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_9
    | ~ spl56_11 ),
    inference(resolution,[],[f845,f572]) ).

fof(f572,plain,
    ( ! [X11] :
        ( ~ geq(X11,sK51)
        | ~ memberP(sK48,X11)
        | ~ ssItem(X11)
        | sQ55_eqProxy(sK51,X11) )
    | ~ spl56_3 ),
    inference(avatar_component_clause,[],[f571]) ).

fof(f845,plain,
    ( geq(sK54(sK51),sK51)
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_9
    | ~ spl56_11 ),
    inference(subsumption_resolution,[],[f844,f613]) ).

fof(f844,plain,
    ( ~ ssList(sK52)
    | geq(sK54(sK51),sK51)
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_7
    | ~ spl56_9 ),
    inference(subsumption_resolution,[],[f843,f592]) ).

fof(f843,plain,
    ( geq(sK54(sK51),sK51)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ ssList(sK52)
    | ~ spl56_2
    | ~ spl56_5
    | ~ spl56_6
    | ~ spl56_9 ),
    inference(subsumption_resolution,[],[f842,f582]) ).

fof(f842,plain,
    ( ~ ssItem(sK51)
    | geq(sK54(sK51),sK51)
    | ~ ssList(sK52)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ spl56_2
    | ~ spl56_6
    | ~ spl56_9 ),
    inference(subsumption_resolution,[],[f818,f568]) ).

fof(f818,plain,
    ( ~ ssList(sK53)
    | ~ ssList(sK52)
    | ~ ssItem(sK51)
    | ~ sQ55_eqProxy(app(sK52,sK53),sK49)
    | geq(sK54(sK51),sK51)
    | ~ spl56_6
    | ~ spl56_9 ),
    inference(resolution,[],[f793,f600]) ).

fof(f600,plain,
    ( ! [X6,X4,X5] :
        ( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
        | geq(sK54(X4),X4)
        | ~ sQ55_eqProxy(app(X5,X6),sK49)
        | ~ ssList(X5)
        | ~ ssItem(X4)
        | ~ ssList(X6) )
    | ~ spl56_9 ),
    inference(avatar_component_clause,[],[f599]) ).

fof(f619,plain,
    ( ~ spl56_1
    | spl56_9 ),
    inference(avatar_split_clause,[],[f552,f599,f562]) ).

fof(f562,plain,
    ( spl56_1
  <=> neq(sK48,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl56_1])]) ).

fof(f552,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X5)
      | ~ sQ55_eqProxy(app(X5,X6),sK49)
      | ~ ssList(X6)
      | ~ ssItem(X4)
      | ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
      | ~ neq(sK48,nil)
      | geq(sK54(X4),X4) ),
    inference(equality_proxy_replacement,[],[f454,f458,f458]) ).

fof(f454,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK49
      | geq(sK54(X4),X4)
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f407,f427,f426]) ).

fof(f426,plain,
    sK50 = sK48,
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ( neq(X1,nil)
                      & ~ neq(X3,nil) )
                    | ( neq(X1,nil)
                      & ? [X8] :
                          ( ? [X9] :
                              ( ? [X10] :
                                  ( app(app(X9,cons(X8,nil)),X10) = X3
                                  & app(X9,X10) = X2
                                  & ! [X11] :
                                      ( ~ geq(X11,X8)
                                      | ~ memberP(X3,X11)
                                      | ~ ssItem(X11)
                                      | X8 = X11 )
                                  & ssList(X10) )
                              & ssList(X9) )
                          & ssItem(X8) )
                      & ! [X4] :
                          ( ~ ssItem(X4)
                          | ! [X5] :
                              ( ~ ssList(X5)
                              | ! [X6] :
                                  ( app(app(X5,cons(X4,nil)),X6) != X1
                                  | ? [X7] :
                                      ( X4 != X7
                                      & ssItem(X7)
                                      & geq(X7,X4)
                                      & memberP(X1,X7) )
                                  | app(X5,X6) != X0
                                  | ~ ssList(X6) ) ) ) ) )
                  & X0 = X2
                  & X1 = X3 ) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & ( ( neq(X1,nil)
                      & ~ neq(X3,nil) )
                    | ( neq(X1,nil)
                      & ! [X4] :
                          ( ! [X5] :
                              ( ! [X6] :
                                  ( ~ ssList(X6)
                                  | app(app(X5,cons(X4,nil)),X6) != X1
                                  | app(X5,X6) != X0
                                  | ? [X7] :
                                      ( geq(X7,X4)
                                      & X4 != X7
                                      & memberP(X1,X7)
                                      & ssItem(X7) ) )
                              | ~ ssList(X5) )
                          | ~ ssItem(X4) )
                      & ? [X8] :
                          ( ? [X9] :
                              ( ? [X10] :
                                  ( app(app(X9,cons(X8,nil)),X10) = X3
                                  & ! [X11] :
                                      ( ~ geq(X11,X8)
                                      | ~ memberP(X3,X11)
                                      | ~ ssItem(X11)
                                      | X8 = X11 )
                                  & app(X9,X10) = X2
                                  & ssList(X10) )
                              & ssList(X9) )
                          & ssItem(X8) ) ) )
                  & 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)
                   => ( X1 != X3
                      | X0 != X2
                      | ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ~ neq(X1,nil)
                          | ? [X4] :
                              ( ? [X5] :
                                  ( ? [X6] :
                                      ( ssList(X6)
                                      & app(app(X5,cons(X4,nil)),X6) = X1
                                      & app(X5,X6) = X0
                                      & ! [X7] :
                                          ( ssItem(X7)
                                         => ( ~ geq(X7,X4)
                                            | X4 = X7
                                            | ~ memberP(X1,X7) ) ) )
                                  & ssList(X5) )
                              & ssItem(X4) )
                          | ! [X8] :
                              ( ssItem(X8)
                             => ! [X9] :
                                  ( ssList(X9)
                                 => ! [X10] :
                                      ( ssList(X10)
                                     => ( app(app(X9,cons(X8,nil)),X10) != X3
                                        | ? [X11] :
                                            ( memberP(X3,X11)
                                            & X8 != X11
                                            & ssItem(X11)
                                            & geq(X11,X8) )
                                        | app(X9,X10) != X2 ) ) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X1 != X3
                    | X0 != X2
                    | ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ~ neq(X1,nil)
                        | ? [X4] :
                            ( ? [X5] :
                                ( ? [X6] :
                                    ( ssList(X6)
                                    & app(app(X5,cons(X4,nil)),X6) = X1
                                    & app(X5,X6) = X0
                                    & ! [X7] :
                                        ( ssItem(X7)
                                       => ( ~ geq(X7,X4)
                                          | X4 = X7
                                          | ~ memberP(X1,X7) ) ) )
                                & ssList(X5) )
                            & ssItem(X4) )
                        | ! [X8] :
                            ( ssItem(X8)
                           => ! [X9] :
                                ( ssList(X9)
                               => ! [X10] :
                                    ( ssList(X10)
                                   => ( app(app(X9,cons(X8,nil)),X10) != X3
                                      | ? [X11] :
                                          ( memberP(X3,X11)
                                          & X8 != X11
                                          & ssItem(X11)
                                          & geq(X11,X8) )
                                      | app(X9,X10) != X2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f427,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f99]) ).

fof(f407,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK47
      | geq(sK54(X4),X4)
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f617,plain,
    spl56_1,
    inference(avatar_split_clause,[],[f425,f562]) ).

fof(f425,plain,
    neq(sK48,nil),
    inference(cnf_transformation,[],[f99]) ).

fof(f615,plain,
    ( spl56_11
    | ~ spl56_1 ),
    inference(avatar_split_clause,[],[f443,f562,f611]) ).

fof(f443,plain,
    ( ~ neq(sK48,nil)
    | ssList(sK52) ),
    inference(definition_unfolding,[],[f420,f426]) ).

fof(f420,plain,
    ( ssList(sK52)
    | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f608,plain,
    ( ~ spl56_1
    | spl56_8 ),
    inference(avatar_split_clause,[],[f550,f595,f562]) ).

fof(f550,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X5)
      | ~ ssList(X6)
      | ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
      | ~ neq(sK48,nil)
      | ~ ssItem(X4)
      | ~ sQ55_eqProxy(app(X5,X6),sK49)
      | ~ sQ55_eqProxy(sK54(X4),X4) ),
    inference(equality_proxy_replacement,[],[f452,f458,f458,f458]) ).

fof(f452,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK49
      | sK54(X4) != X4
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f409,f427,f426]) ).

fof(f409,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK47
      | sK54(X4) != X4
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f607,plain,
    ( ~ spl56_1
    | spl56_4 ),
    inference(avatar_split_clause,[],[f551,f575,f562]) ).

fof(f551,plain,
    ! [X6,X4,X5] :
      ( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
      | ~ ssItem(X4)
      | ssItem(sK54(X4))
      | ~ ssList(X6)
      | ~ neq(sK48,nil)
      | ~ ssList(X5)
      | ~ sQ55_eqProxy(app(X5,X6),sK49) ),
    inference(equality_proxy_replacement,[],[f453,f458,f458]) ).

fof(f453,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK49
      | ssItem(sK54(X4))
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f408,f427,f426]) ).

fof(f408,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK47
      | ssItem(sK54(X4))
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f606,plain,
    ( ~ spl56_1
    | spl56_7 ),
    inference(avatar_split_clause,[],[f543,f590,f562]) ).

fof(f543,plain,
    ( sQ55_eqProxy(app(sK52,sK53),sK49)
    | ~ neq(sK48,nil) ),
    inference(equality_proxy_replacement,[],[f445,f458]) ).

fof(f445,plain,
    ( app(sK52,sK53) = sK49
    | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f418,f426]) ).

fof(f418,plain,
    ( app(sK52,sK53) = sK49
    | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f605,plain,
    ( ~ spl56_1
    | spl56_10 ),
    inference(avatar_split_clause,[],[f553,f603,f562]) ).

fof(f553,plain,
    ! [X6,X4,X5] :
      ( memberP(sK48,sK54(X4))
      | ~ ssList(X6)
      | ~ ssItem(X4)
      | ~ ssList(X5)
      | ~ sQ55_eqProxy(app(X5,X6),sK49)
      | ~ neq(sK48,nil)
      | ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48) ),
    inference(equality_proxy_replacement,[],[f455,f458,f458]) ).

fof(f455,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK49
      | memberP(sK48,sK54(X4))
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f406,f427,f426]) ).

fof(f406,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X6)
      | app(X5,X6) != sK47
      | memberP(sK48,sK54(X4))
      | app(app(X5,cons(X4,nil)),X6) != sK48
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f588,plain,
    ( ~ spl56_1
    | spl56_6 ),
    inference(avatar_split_clause,[],[f542,f585,f562]) ).

fof(f542,plain,
    ( sQ55_eqProxy(sK48,app(app(sK52,cons(sK51,nil)),sK53))
    | ~ neq(sK48,nil) ),
    inference(equality_proxy_replacement,[],[f444,f458]) ).

fof(f444,plain,
    ( sK48 = app(app(sK52,cons(sK51,nil)),sK53)
    | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f419,f426,f426]) ).

fof(f419,plain,
    ( sK50 = app(app(sK52,cons(sK51,nil)),sK53)
    | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f583,plain,
    ( ~ spl56_1
    | spl56_5 ),
    inference(avatar_split_clause,[],[f442,f580,f562]) ).

fof(f442,plain,
    ( ssItem(sK51)
    | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f423,f426]) ).

fof(f423,plain,
    ( ssItem(sK51)
    | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f578,plain,
    ( ~ spl56_1
    | spl56_3 ),
    inference(avatar_split_clause,[],[f555,f571,f562]) ).

fof(f555,plain,
    ! [X11] :
      ( sQ55_eqProxy(sK51,X11)
      | ~ ssItem(X11)
      | ~ memberP(sK48,X11)
      | ~ neq(sK48,nil)
      | ~ geq(X11,sK51) ),
    inference(equality_proxy_replacement,[],[f457,f458]) ).

fof(f457,plain,
    ! [X11] :
      ( sK51 = X11
      | ~ ssItem(X11)
      | ~ memberP(sK48,X11)
      | ~ geq(X11,sK51)
      | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f404,f426,f426]) ).

fof(f404,plain,
    ! [X11] :
      ( sK51 = X11
      | ~ ssItem(X11)
      | ~ memberP(sK50,X11)
      | ~ geq(X11,sK51)
      | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f569,plain,
    ( ~ spl56_1
    | spl56_2 ),
    inference(avatar_split_clause,[],[f446,f566,f562]) ).

fof(f446,plain,
    ( ssList(sK53)
    | ~ neq(sK48,nil) ),
    inference(definition_unfolding,[],[f417,f426]) ).

fof(f417,plain,
    ( ssList(sK53)
    | ~ neq(sK50,nil) ),
    inference(cnf_transformation,[],[f99]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC002+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.36  % Computer : n005.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Tue Aug 30 17:52:48 EDT 2022
% 0.13/0.36  % CPUTime    : 
% 0.21/0.49  % (22357)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)
% 0.21/0.49  % (22372)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)
% 0.21/0.50  % (22365)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.21/0.51  % (22357)Instruction limit reached!
% 0.21/0.51  % (22357)------------------------------
% 0.21/0.51  % (22357)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (22357)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (22357)Termination reason: Unknown
% 0.21/0.52  % (22357)Termination phase: Saturation
% 0.21/0.52  
% 0.21/0.52  % (22357)Memory used [KB]: 2046
% 0.21/0.52  % (22357)Time elapsed: 0.102 s
% 0.21/0.52  % (22357)Instructions burned: 16 (million)
% 0.21/0.52  % (22357)------------------------------
% 0.21/0.52  % (22357)------------------------------
% 0.21/0.52  % (22345)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.54  % (22372)Instruction limit reached!
% 0.21/0.54  % (22372)------------------------------
% 0.21/0.54  % (22372)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (22359)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.54  % (22365)First to succeed.
% 0.21/0.54  % (22372)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (22372)Termination reason: Unknown
% 0.21/0.54  % (22372)Termination phase: Saturation
% 0.21/0.54  
% 0.21/0.54  % (22372)Memory used [KB]: 6652
% 0.21/0.54  % (22372)Time elapsed: 0.117 s
% 0.21/0.54  % (22372)Instructions burned: 25 (million)
% 0.21/0.54  % (22372)------------------------------
% 0.21/0.54  % (22372)------------------------------
% 0.21/0.54  % (22359)Instruction limit reached!
% 0.21/0.54  % (22359)------------------------------
% 0.21/0.54  % (22359)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (22359)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (22359)Termination reason: Unknown
% 0.21/0.54  % (22359)Termination phase: Naming
% 0.21/0.54  
% 0.21/0.54  % (22359)Memory used [KB]: 1535
% 0.21/0.54  % (22359)Time elapsed: 0.003 s
% 0.21/0.54  % (22359)Instructions burned: 3 (million)
% 0.21/0.54  % (22359)------------------------------
% 0.21/0.54  % (22359)------------------------------
% 0.21/0.54  % (22365)Refutation found. Thanks to Tanya!
% 0.21/0.54  % SZS status Theorem for theBenchmark
% 0.21/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54  % (22365)------------------------------
% 0.21/0.54  % (22365)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (22365)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (22365)Termination reason: Refutation
% 0.21/0.54  
% 0.21/0.54  % (22365)Memory used [KB]: 6524
% 0.21/0.54  % (22365)Time elapsed: 0.128 s
% 0.21/0.54  % (22365)Instructions burned: 25 (million)
% 0.21/0.54  % (22365)------------------------------
% 0.21/0.54  % (22365)------------------------------
% 0.21/0.54  % (22344)Success in time 0.172 s
%------------------------------------------------------------------------------