%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP146-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 12:29:29 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 (  10 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   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;   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(ax_lub1a_1,plain,
    $equal(least_upper_bound(a,c),c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),
    [] ).

cnf(159391624,plain,
    $equal(least_upper_bound(a,c),c),
    inference(rewrite,[status(thm)],[ax_lub1a_1]),
    [] ).

fof(prove_ax_lub1a,plain,
    ~ $equal(least_upper_bound(least_upper_bound(a,b),c),c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),
    [] ).

cnf(159266008,plain,
    ~ $equal(least_upper_bound(least_upper_bound(a,b),c),c),
    inference(rewrite,[status(thm)],[prove_ax_lub1a]),
    [] ).

fof(associativity_of_lub,plain,
    ! [A,B,C] : $equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),
    [] ).

cnf(159305976,plain,
    $equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C))),
    inference(rewrite,[status(thm)],[associativity_of_lub]),
    [] ).

cnf(167337272,plain,
    ~ $equal(least_upper_bound(a,least_upper_bound(b,c)),c),
    inference(paramodulation,[status(thm)],[159266008,159305976,theory(equality)]),
    [] ).

fof(ax_lub1a_2,plain,
    $equal(least_upper_bound(b,c),c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),
    [] ).

cnf(159395568,plain,
    $equal(least_upper_bound(b,c),c),
    inference(rewrite,[status(thm)],[ax_lub1a_2]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[159391624,167337272,159395568,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(ax_lub1a_1,plain,($equal(least_upper_bound(a,c),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),[]).
% 
% cnf(159391624,plain,($equal(least_upper_bound(a,c),c)),inference(rewrite,[status(thm)],[ax_lub1a_1]),[]).
% 
% fof(prove_ax_lub1a,plain,(~$equal(least_upper_bound(least_upper_bound(a,b),c),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),[]).
% 
% cnf(159266008,plain,(~$equal(least_upper_bound(least_upper_bound(a,b),c),c)),inference(rewrite,[status(thm)],[prove_ax_lub1a]),[]).
% 
% fof(associativity_of_lub,plain,($equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),[]).
% 
% cnf(159305976,plain,($equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[associativity_of_lub]),[]).
% 
% cnf(167337272,plain,(~$equal(least_upper_bound(a,least_upper_bound(b,c)),c)),inference(paramodulation,[status(thm)],[159266008,159305976,theory(equality)]),[]).
% 
% fof(ax_lub1a_2,plain,($equal(least_upper_bound(b,c),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP146-1.tptp',unknown),[]).
% 
% cnf(159395568,plain,($equal(least_upper_bound(b,c),c)),inference(rewrite,[status(thm)],[ax_lub1a_2]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[159391624,167337272,159395568,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------