%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP189-2 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:33:37 EDT 2009

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

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_p38b,plain,
    ~ $equal(greatest_lower_bound(b,least_upper_bound(a,b)),b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP189-2.tptp',unknown),
    [] ).

cnf(142535424,plain,
    ~ $equal(greatest_lower_bound(b,least_upper_bound(a,b)),b),
    inference(rewrite,[status(thm)],[prove_p38b]),
    [] ).

fof(symmetry_of_lub,plain,
    ! [B,A] : $equal(least_upper_bound(B,A),least_upper_bound(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP189-2.tptp',unknown),
    [] ).

cnf(142407456,plain,
    $equal(least_upper_bound(B,A),least_upper_bound(A,B)),
    inference(rewrite,[status(thm)],[symmetry_of_lub]),
    [] ).

cnf(150380040,plain,
    ~ $equal(greatest_lower_bound(b,least_upper_bound(b,a)),b),
    inference(paramodulation,[status(thm)],[142535424,142407456,theory(equality)]),
    [] ).

fof(glb_absorbtion,plain,
    ! [A,B] : $equal(greatest_lower_bound(A,least_upper_bound(A,B)),A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP189-2.tptp',unknown),
    [] ).

cnf(142438784,plain,
    $equal(greatest_lower_bound(A,least_upper_bound(A,B)),A),
    inference(rewrite,[status(thm)],[glb_absorbtion]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[150380040,142438784]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_p38b,plain,(~$equal(greatest_lower_bound(b,least_upper_bound(a,b)),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP189-2.tptp',unknown),[]).
% 
% cnf(142535424,plain,(~$equal(greatest_lower_bound(b,least_upper_bound(a,b)),b)),inference(rewrite,[status(thm)],[prove_p38b]),[]).
% 
% fof(symmetry_of_lub,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP189-2.tptp',unknown),[]).
% 
% cnf(142407456,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_lub]),[]).
% 
% cnf(150380040,plain,(~$equal(greatest_lower_bound(b,least_upper_bound(b,a)),b)),inference(paramodulation,[status(thm)],[142535424,142407456,theory(equality)]),[]).
% 
% fof(glb_absorbtion,plain,($equal(greatest_lower_bound(A,least_upper_bound(A,B)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP189-2.tptp',unknown),[]).
% 
% cnf(142438784,plain,($equal(greatest_lower_bound(A,least_upper_bound(A,B)),A)),inference(rewrite,[status(thm)],[glb_absorbtion]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[150380040,142438784]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------