%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET855-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 15:39:41 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   7 unt;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   8   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_3,plain,
    c_lessequals(c_union(v_y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),
    [] ).

cnf(173272696,plain,
    c_lessequals(c_union(v_y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_3]),
    [] ).

fof(cls_Set_Osubset__antisym_0,plain,
    ! [A,B,C] :
      ( ~ c_lessequals(A,B,tc_set(C))
      | ~ c_lessequals(B,A,tc_set(C))
      | $equal(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),
    [] ).

cnf(173263544,plain,
    ( ~ c_lessequals(A,B,tc_set(C))
    | ~ c_lessequals(B,A,tc_set(C))
    | $equal(A,B) ),
    inference(rewrite,[status(thm)],[cls_Set_Osubset__antisym_0]),
    [] ).

fof(cls_conjecture_4,plain,
    ~ $equal(c_union(v_y,tc_set(t_a)),v_n),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),
    [] ).

cnf(173276984,plain,
    ~ $equal(c_union(v_y,tc_set(t_a)),v_n),
    inference(rewrite,[status(thm)],[cls_conjecture_4]),
    [] ).

cnf(186322456,plain,
    ( ~ c_lessequals(c_union(v_y,tc_set(t_a)),v_n,tc_set(A))
    | ~ c_lessequals(v_n,c_union(v_y,tc_set(t_a)),tc_set(A)) ),
    inference(resolution,[status(thm)],[173263544,173276984]),
    [] ).

fof(cls_conjecture_2,plain,
    c_lessequals(v_n,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),
    [] ).

cnf(173268424,plain,
    c_lessequals(v_n,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[173272696,186322456,173268424]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_3,plain,(c_lessequals(c_union(v_y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),[]).
% 
% cnf(173272696,plain,(c_lessequals(c_union(v_y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
% 
% fof(cls_Set_Osubset__antisym_0,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(B,A,tc_set(C))|$equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),[]).
% 
% cnf(173263544,plain,(~c_lessequals(A,B,tc_set(C))|~c_lessequals(B,A,tc_set(C))|$equal(A,B)),inference(rewrite,[status(thm)],[cls_Set_Osubset__antisym_0]),[]).
% 
% fof(cls_conjecture_4,plain,(~$equal(c_union(v_y,tc_set(t_a)),v_n)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),[]).
% 
% cnf(173276984,plain,(~$equal(c_union(v_y,tc_set(t_a)),v_n)),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
% 
% cnf(186322456,plain,(~c_lessequals(c_union(v_y,tc_set(t_a)),v_n,tc_set(A))|~c_lessequals(v_n,c_union(v_y,tc_set(t_a)),tc_set(A))),inference(resolution,[status(thm)],[173263544,173276984]),[]).
% 
% fof(cls_conjecture_2,plain,(c_lessequals(v_n,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET855-2.tptp',unknown),[]).
% 
% cnf(173268424,plain,(c_lessequals(v_n,c_union(v_y,tc_set(t_a)),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[173272696,186322456,173268424]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------