%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP136-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 12:29:06 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 (  11 unt;   0 def)
%            Number of atoms       :   11 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP136-1.tptp',unknown),
    [] ).

cnf(145510728,plain,
    $equal(least_upper_bound(B,A),least_upper_bound(A,B)),
    inference(rewrite,[status(thm)],[symmetry_of_lub]),
    [] ).

fof(prove_ax_antisyma,plain,
    ~ $equal(b,a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),
    [] ).

cnf(145482616,plain,
    ~ $equal(b,a),
    inference(rewrite,[status(thm)],[prove_ax_antisyma]),
    [] ).

fof(ax_antisyma_2,plain,
    $equal(least_upper_bound(a,b),a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),
    [] ).

cnf(145612296,plain,
    $equal(least_upper_bound(a,b),a),
    inference(rewrite,[status(thm)],[ax_antisyma_2]),
    [] ).

cnf(153425808,plain,
    ~ $equal(b,least_upper_bound(a,b)),
    inference(paramodulation,[status(thm)],[145482616,145612296,theory(equality)]),
    [] ).

cnf(153495104,plain,
    ~ $equal(b,least_upper_bound(b,a)),
    inference(paramodulation,[status(thm)],[153425808,145510728,theory(equality)]),
    [] ).

fof(ax_antisyma_1,plain,
    $equal(least_upper_bound(a,b),b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),
    [] ).

cnf(145608384,plain,
    $equal(least_upper_bound(a,b),b),
    inference(rewrite,[status(thm)],[ax_antisyma_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145510728,153495104,145608384,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(symmetry_of_lub,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),[]).
% 
% cnf(145510728,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_lub]),[]).
% 
% fof(prove_ax_antisyma,plain,(~$equal(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),[]).
% 
% cnf(145482616,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[prove_ax_antisyma]),[]).
% 
% fof(ax_antisyma_2,plain,($equal(least_upper_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),[]).
% 
% cnf(145612296,plain,($equal(least_upper_bound(a,b),a)),inference(rewrite,[status(thm)],[ax_antisyma_2]),[]).
% 
% cnf(153425808,plain,(~$equal(b,least_upper_bound(a,b))),inference(paramodulation,[status(thm)],[145482616,145612296,theory(equality)]),[]).
% 
% cnf(153495104,plain,(~$equal(b,least_upper_bound(b,a))),inference(paramodulation,[status(thm)],[153425808,145510728,theory(equality)]),[]).
% 
% fof(ax_antisyma_1,plain,($equal(least_upper_bound(a,b),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP136-1.tptp',unknown),[]).
% 
% cnf(145608384,plain,($equal(least_upper_bound(a,b),b)),inference(rewrite,[status(thm)],[ax_antisyma_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145510728,153495104,145608384,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------