%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC041+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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 May 31 12:38:59 EDT 2023

% Result   : Theorem 0.06s 0.27s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (  14 unt;   0 def)
%            Number of atoms       :  168 (  77 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  188 (  62   ~;  57   |;  50   &)
%                                         (   6 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   46 (;  30   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f83,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( nil = app(U,V)
          <=> ( nil = V
              & nil = U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f84,axiom,
    ! [U] :
      ( ssList(U)
     => app(U,nil) = U ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( nil != V
                    | V != X
                    | U != W
                    | nil = U
                    | ! [Y] :
                        ( ssList(Y)
                       => ( app(W,Y) != X
                          | ~ equalelemsP(W)
                          | ? [Z] :
                              ( ssItem(Z)
                              & ? [X1] :
                                  ( ssList(X1)
                                  & app(cons(Z,nil),X1) = Y
                                  & ? [X2] :
                                      ( ssList(X2)
                                      & app(X2,cons(Z,nil)) = W ) ) ) ) )
                    | ( nil != X
                      & nil = W ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f97,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( nil != V
                      | V != X
                      | U != W
                      | nil = U
                      | ! [Y] :
                          ( ssList(Y)
                         => ( app(W,Y) != X
                            | ~ equalelemsP(W)
                            | ? [Z] :
                                ( ssItem(Z)
                                & ? [X1] :
                                    ( ssList(X1)
                                    & app(cons(Z,nil),X1) = Y
                                    & ? [X2] :
                                        ( ssList(X2)
                                        & app(X2,cons(Z,nil)) = W ) ) ) ) )
                      | ( nil != X
                        & nil = W ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f383,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( nil = app(U,V)
          <=> ( nil = V
              & nil = U ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f83]) ).

fof(f384,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( nil != app(U,V)
              | ( nil = V
                & nil = U ) )
            & ( nil = app(U,V)
              | nil != V
              | nil != U ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f383]) ).

fof(f385,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | nil != app(X0,X1)
      | nil = X1 ),
    inference(cnf_transformation,[status(esa)],[f384]) ).

fof(f388,plain,
    ! [U] :
      ( ~ ssList(U)
      | app(U,nil) = U ),
    inference(pre_NNF_transformation,[status(esa)],[f84]) ).

fof(f389,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[status(esa)],[f388]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & nil = V
                  & V = X
                  & U = W
                  & nil != U
                  & ? [Y] :
                      ( ssList(Y)
                      & app(W,Y) = X
                      & equalelemsP(W)
                      & ! [Z] :
                          ( ~ ssItem(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(cons(Z,nil),X1) != Y
                              | ! [X2] :
                                  ( ~ ssList(X2)
                                  | app(X2,cons(Z,nil)) != W ) ) ) )
                  & ( nil = X
                    | nil != W ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & nil = V
                  & V = X
                  & U = W
                  & nil != U
                  & ? [Y] :
                      ( ssList(Y)
                      & app(W,Y) = X
                      & equalelemsP(W)
                      & ! [Z] :
                          ( ~ ssItem(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(cons(Z,nil),X1) != Y )
                          | ! [X2] :
                              ( ~ ssList(X2)
                              | app(X2,cons(Z,nil)) != W ) ) )
                  & ( nil = X
                    | nil != W ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f415]) ).

fof(f417,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & nil = sk0_48
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & nil != sk0_47
    & ssList(sk0_51)
    & app(sk0_49,sk0_51) = sk0_50
    & equalelemsP(sk0_49)
    & ! [Z] :
        ( ~ ssItem(Z)
        | ! [X1] :
            ( ~ ssList(X1)
            | app(cons(Z,nil),X1) != sk0_51 )
        | ! [X2] :
            ( ~ ssList(X2)
            | app(X2,cons(Z,nil)) != sk0_49 ) )
    & ( nil = sk0_50
      | nil != sk0_49 ) ),
    inference(skolemization,[status(esa)],[f416]) ).

fof(f418,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f422,plain,
    nil = sk0_48,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f423,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f424,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f425,plain,
    nil != sk0_47,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f426,plain,
    ssList(sk0_51),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f427,plain,
    app(sk0_49,sk0_51) = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f469,plain,
    nil = sk0_50,
    inference(forward_demodulation,[status(thm)],[f422,f423]) ).

fof(f473,plain,
    app(sk0_47,sk0_51) = sk0_50,
    inference(forward_demodulation,[status(thm)],[f424,f427]) ).

fof(f474,plain,
    app(sk0_47,sk0_51) = nil,
    inference(forward_demodulation,[status(thm)],[f469,f473]) ).

fof(f488,plain,
    ( spl0_4
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f490,plain,
    ( ~ ssList(sk0_47)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f488]) ).

fof(f491,plain,
    ( spl0_5
  <=> ssList(sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f493,plain,
    ( ~ ssList(sk0_51)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f491]) ).

fof(f499,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f493,f426]) ).

fof(f500,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f499]) ).

fof(f501,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f490,f418]) ).

fof(f502,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f501]) ).

fof(f516,plain,
    ( spl0_10
  <=> nil = sk0_51 ),
    introduced(split_symbol_definition) ).

fof(f517,plain,
    ( nil = sk0_51
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f516]) ).

fof(f519,plain,
    ( ~ ssList(sk0_47)
    | ~ ssList(sk0_51)
    | nil = sk0_51 ),
    inference(resolution,[status(thm)],[f385,f474]) ).

fof(f520,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f519,f488,f491,f516]) ).

fof(f527,plain,
    ( app(sk0_47,nil) = nil
    | ~ spl0_10 ),
    inference(backward_demodulation,[status(thm)],[f517,f474]) ).

fof(f530,plain,
    ( spl0_11
  <=> nil = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f531,plain,
    ( nil = sk0_47
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f530]) ).

fof(f533,plain,
    ( ~ ssList(sk0_47)
    | nil = sk0_47
    | ~ spl0_10 ),
    inference(paramodulation,[status(thm)],[f527,f389]) ).

fof(f534,plain,
    ( ~ spl0_4
    | spl0_11
    | ~ spl0_10 ),
    inference(split_clause,[status(thm)],[f533,f488,f530,f516]) ).

fof(f539,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f531,f425]) ).

fof(f540,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f539]) ).

fof(f541,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f500,f502,f520,f534,f540]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.06  % Problem  : SWC041+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25  % Computer : n007.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 300
% 0.06/0.25  % DateTime : Tue May 30 11:11:01 EDT 2023
% 0.06/0.25  % CPUTime  : 
% 0.06/0.26  % Drodi V3.5.1
% 0.06/0.27  % Refutation found
% 0.06/0.27  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.28  % Elapsed time: 0.020377 seconds
% 0.09/0.28  % CPU time: 0.032664 seconds
% 0.09/0.28  % Memory used: 16.183 MB
%------------------------------------------------------------------------------