%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET838-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:39:00 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   14 (   8 unt;   0 def)
%            Number of atoms       :   20 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   14 (   8   ~;   6   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :    6 (   0 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
    ! [A] :
      ( $equal(v_g(v_f(v_xa(A))),v_xa(A))
      | ~ $equal(v_g(v_f(A)),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
    [] ).

cnf(145616072,plain,
    ( $equal(v_g(v_f(v_xa(A))),v_xa(A))
    | ~ $equal(v_g(v_f(A)),A) ),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

fof(cls_conjecture_0,plain,
    $equal(v_f(v_g(v_x)),v_x),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
    [] ).

cnf(145604688,plain,
    $equal(v_f(v_g(v_x)),v_x),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

cnf(161456000,plain,
    $equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x))),
    inference(paramodulation,[status(thm)],[145616072,145604688,theory(equality)]),
    [] ).

fof(cls_conjecture_1,plain,
    ! [A] :
      ( $equal(v_x,A)
      | ~ $equal(v_f(v_g(A)),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
    [] ).

cnf(145610352,plain,
    ( $equal(v_x,A)
    | ~ $equal(v_f(v_g(A)),A) ),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

cnf(161623968,plain,
    $equal(v_x,v_f(v_xa(v_g(v_x)))),
    inference(paramodulation,[status(thm)],[161456000,145610352,theory(equality)]),
    [] ).

cnf(161862208,plain,
    $equal(v_g(v_x),v_xa(v_g(v_x))),
    inference(paramodulation,[status(thm)],[161623968,161456000,theory(equality)]),
    [] ).

cnf(161927536,plain,
    $equal(v_x,v_f(v_xa(v_xa(v_g(v_x))))),
    inference(paramodulation,[status(thm)],[161862208,161623968,theory(equality)]),
    [] ).

cnf(162431776,plain,
    $equal(v_g(v_x),v_xa(v_xa(v_g(v_x)))),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161927536,145616072,theory(equality)]),
    [] ).

fof(cls_conjecture_3,plain,
    ! [A] :
      ( ~ $equal(v_xa(A),A)
      | ~ $equal(v_g(v_f(A)),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),
    [] ).

cnf(145622544,plain,
    ( ~ $equal(v_xa(A),A)
    | ~ $equal(v_g(v_f(A)),A) ),
    inference(rewrite,[status(thm)],[cls_conjecture_3]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161862208,162431776,145622544,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,($equal(v_g(v_f(v_xa(A))),v_xa(A))|~$equal(v_g(v_f(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
% 
% cnf(145616072,plain,($equal(v_g(v_f(v_xa(A))),v_xa(A))|~$equal(v_g(v_f(A)),A)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% fof(cls_conjecture_0,plain,($equal(v_f(v_g(v_x)),v_x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
% 
% cnf(145604688,plain,($equal(v_f(v_g(v_x)),v_x)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% cnf(161456000,plain,($equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x)))),inference(paramodulation,[status(thm)],[145616072,145604688,theory(equality)]),[]).
% 
% fof(cls_conjecture_1,plain,($equal(v_x,A)|~$equal(v_f(v_g(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
% 
% cnf(145610352,plain,($equal(v_x,A)|~$equal(v_f(v_g(A)),A)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% cnf(161623968,plain,($equal(v_x,v_f(v_xa(v_g(v_x))))),inference(paramodulation,[status(thm)],[161456000,145610352,theory(equality)]),[]).
% 
% cnf(161862208,plain,($equal(v_g(v_x),v_xa(v_g(v_x)))),inference(paramodulation,[status(thm)],[161623968,161456000,theory(equality)]),[]).
% 
% cnf(161927536,plain,($equal(v_x,v_f(v_xa(v_xa(v_g(v_x)))))),inference(paramodulation,[status(thm)],[161862208,161623968,theory(equality)]),[]).
% 
% cnf(162431776,plain,($equal(v_g(v_x),v_xa(v_xa(v_g(v_x))))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161927536,145616072,theory(equality)]),[]).
% 
% fof(cls_conjecture_3,plain,(~$equal(v_xa(A),A)|~$equal(v_g(v_f(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET838-2.tptp',unknown),[]).
% 
% cnf(145622544,plain,(~$equal(v_xa(A),A)|~$equal(v_g(v_f(A)),A)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[161456000,161862208,162431776,145622544,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------