%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP155-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% 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 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:29:51 EDT 2009

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

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(monotony_glb2,plain,
    ! [A,C,B] : $equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP155-1.tptp',unknown),
    [] ).

cnf(164482320,plain,
    $equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
    inference(rewrite,[status(thm)],[monotony_glb2]),
    [] ).

fof(prove_ax_mono1b,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP155-1.tptp',unknown),
    [] ).

cnf(164494936,plain,
    ~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c)),
    inference(rewrite,[status(thm)],[prove_ax_mono1b]),
    [] ).

fof(ax_mono1b,plain,
    $equal(greatest_lower_bound(a,b),a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP155-1.tptp',unknown),
    [] ).

cnf(164490064,plain,
    $equal(greatest_lower_bound(a,b),a),
    inference(rewrite,[status(thm)],[ax_mono1b]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164482320,164494936,164490064,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(monotony_glb2,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP155-1.tptp',unknown),[]).
% 
% cnf(164482320,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_glb2]),[]).
% 
% fof(prove_ax_mono1b,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP155-1.tptp',unknown),[]).
% 
% cnf(164494936,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c))),inference(rewrite,[status(thm)],[prove_ax_mono1b]),[]).
% 
% fof(ax_mono1b,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP155-1.tptp',unknown),[]).
% 
% cnf(164490064,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[ax_mono1b]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164482320,164494936,164490064,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------