%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET832-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.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 15:38:40 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (   8 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :    9 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_Set_OsubsetD_0,plain,
    ! [A,B,C,D] :
      ( ~ c_in(A,B,C)
      | ~ c_lessequals(B,D,tc_set(C))
      | c_in(A,D,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),
    [] ).

cnf(172519408,plain,
    ( ~ c_in(A,B,C)
    | ~ c_lessequals(B,D,tc_set(C))
    | c_in(A,D,C) ),
    inference(rewrite,[status(thm)],[cls_Set_OsubsetD_0]),
    [] ).

fof(cls_conjecture_0,plain,
    c_lessequals(v_y,v_v,tc_set(t_a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),
    [] ).

cnf(172524256,plain,
    c_lessequals(v_y,v_v,tc_set(t_a)),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

cnf(185599456,plain,
    ( ~ c_in(A,v_y,t_a)
    | c_in(A,v_v,t_a) ),
    inference(resolution,[status(thm)],[172519408,172524256]),
    [] ).

fof(cls_conjecture_2,plain,
    c_in(v_x,v_y,t_a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),
    [] ).

cnf(172529088,plain,
    c_in(v_x,v_y,t_a),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

cnf(185604192,plain,
    c_in(v_x,v_v,t_a),
    inference(resolution,[status(thm)],[185599456,172529088]),
    [] ).

fof(cls_conjecture_3,plain,
    ~ c_in(v_x,v_v,t_a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),
    [] ).

cnf(172533080,plain,
    ~ c_in(v_x,v_v,t_a),
    inference(rewrite,[status(thm)],[cls_conjecture_3]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[185604192,172533080]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_Set_OsubsetD_0,plain,(~c_in(A,B,C)|~c_lessequals(B,D,tc_set(C))|c_in(A,D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),[]).
% 
% cnf(172519408,plain,(~c_in(A,B,C)|~c_lessequals(B,D,tc_set(C))|c_in(A,D,C)),inference(rewrite,[status(thm)],[cls_Set_OsubsetD_0]),[]).
% 
% fof(cls_conjecture_0,plain,(c_lessequals(v_y,v_v,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),[]).
% 
% cnf(172524256,plain,(c_lessequals(v_y,v_v,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% cnf(185599456,plain,(~c_in(A,v_y,t_a)|c_in(A,v_v,t_a)),inference(resolution,[status(thm)],[172519408,172524256]),[]).
% 
% fof(cls_conjecture_2,plain,(c_in(v_x,v_y,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),[]).
% 
% cnf(172529088,plain,(c_in(v_x,v_y,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% cnf(185604192,plain,(c_in(v_x,v_v,t_a)),inference(resolution,[status(thm)],[185599456,172529088]),[]).
% 
% fof(cls_conjecture_3,plain,(~c_in(v_x,v_v,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET832-2.tptp',unknown),[]).
% 
% cnf(172533080,plain,(~c_in(v_x,v_v,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[185604192,172533080]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------