%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : HEN007-4 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.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 13:15:43 EDT 2009

% Result   : Unsatisfiable 1.3s
% Output   : Refutation 1.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  11 unt;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_c_divide_b_LE_c_divide_a,plain,
    ~ less_equal(divide(c,b),divide(c,a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),
    [] ).

cnf(148639432,plain,
    ~ less_equal(divide(c,b),divide(c,a)),
    inference(rewrite,[status(thm)],[prove_c_divide_b_LE_c_divide_a]),
    [] ).

fof(property_of_divide1,plain,
    ! [A,B,C] :
      ( ~ less_equal(divide(A,B),C)
      | less_equal(divide(A,C),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),
    [] ).

cnf(148631624,plain,
    ( ~ less_equal(divide(A,B),C)
    | less_equal(divide(A,C),B) ),
    inference(rewrite,[status(thm)],[property_of_divide1]),
    [] ).

fof(transitivity_of_less_equal,plain,
    ! [A,B,C] :
      ( ~ less_equal(A,B)
      | ~ less_equal(B,C)
      | less_equal(A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),
    [] ).

cnf(148621912,plain,
    ( ~ less_equal(A,B)
    | ~ less_equal(B,C)
    | less_equal(A,C) ),
    inference(rewrite,[status(thm)],[transitivity_of_less_equal]),
    [] ).

fof(a_LE_b,plain,
    less_equal(a,b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),
    [] ).

cnf(148635432,plain,
    less_equal(a,b),
    inference(rewrite,[status(thm)],[a_LE_b]),
    [] ).

cnf(163252840,plain,
    ( ~ less_equal(A,a)
    | less_equal(A,b) ),
    inference(resolution,[status(thm)],[148621912,148635432]),
    [] ).

fof(quotient_less_equal2,plain,
    ! [A,B] :
      ( ~ $equal(zero,divide(A,B))
      | less_equal(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),
    [] ).

cnf(148566888,plain,
    ( ~ $equal(zero,divide(A,B))
    | less_equal(A,B) ),
    inference(rewrite,[status(thm)],[quotient_less_equal2]),
    [] ).

fof(x_divide_x_is_zero,plain,
    ! [A] : $equal(zero,divide(A,A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),
    [] ).

cnf(148556080,plain,
    $equal(zero,divide(A,A)),
    inference(rewrite,[status(thm)],[x_divide_x_is_zero]),
    [] ).

cnf(158671048,plain,
    less_equal(A,A),
    inference(resolution,[status(thm)],[148566888,148556080]),
    [] ).

cnf(163549080,plain,
    less_equal(divide(A,divide(A,B)),B),
    inference(resolution,[status(thm)],[148631624,158671048]),
    [] ).

cnf(166336280,plain,
    less_equal(divide(A,divide(A,a)),b),
    inference(resolution,[status(thm)],[163252840,163549080]),
    [] ).

cnf(177371048,plain,
    less_equal(divide(A,b),divide(A,a)),
    inference(resolution,[status(thm)],[148631624,166336280]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[148639432,177371048]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_c_divide_b_LE_c_divide_a,plain,(~less_equal(divide(c,b),divide(c,a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),[]).
% 
% cnf(148639432,plain,(~less_equal(divide(c,b),divide(c,a))),inference(rewrite,[status(thm)],[prove_c_divide_b_LE_c_divide_a]),[]).
% 
% fof(property_of_divide1,plain,(~less_equal(divide(A,B),C)|less_equal(divide(A,C),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),[]).
% 
% cnf(148631624,plain,(~less_equal(divide(A,B),C)|less_equal(divide(A,C),B)),inference(rewrite,[status(thm)],[property_of_divide1]),[]).
% 
% fof(transitivity_of_less_equal,plain,(~less_equal(A,B)|~less_equal(B,C)|less_equal(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),[]).
% 
% cnf(148621912,plain,(~less_equal(A,B)|~less_equal(B,C)|less_equal(A,C)),inference(rewrite,[status(thm)],[transitivity_of_less_equal]),[]).
% 
% fof(a_LE_b,plain,(less_equal(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),[]).
% 
% cnf(148635432,plain,(less_equal(a,b)),inference(rewrite,[status(thm)],[a_LE_b]),[]).
% 
% cnf(163252840,plain,(~less_equal(A,a)|less_equal(A,b)),inference(resolution,[status(thm)],[148621912,148635432]),[]).
% 
% fof(quotient_less_equal2,plain,(~$equal(zero,divide(A,B))|less_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),[]).
% 
% cnf(148566888,plain,(~$equal(zero,divide(A,B))|less_equal(A,B)),inference(rewrite,[status(thm)],[quotient_less_equal2]),[]).
% 
% fof(x_divide_x_is_zero,plain,($equal(zero,divide(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN007-4.tptp',unknown),[]).
% 
% cnf(148556080,plain,($equal(zero,divide(A,A))),inference(rewrite,[status(thm)],[x_divide_x_is_zero]),[]).
% 
% cnf(158671048,plain,(less_equal(A,A)),inference(resolution,[status(thm)],[148566888,148556080]),[]).
% 
% cnf(163549080,plain,(less_equal(divide(A,divide(A,B)),B)),inference(resolution,[status(thm)],[148631624,158671048]),[]).
% 
% cnf(166336280,plain,(less_equal(divide(A,divide(A,a)),b)),inference(resolution,[status(thm)],[163252840,163549080]),[]).
% 
% cnf(177371048,plain,(less_equal(divide(A,b),divide(A,a))),inference(resolution,[status(thm)],[148631624,166336280]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[148639432,177371048]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------