%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : HEN002-1 : 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 13:14:52 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 (   6 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    7 (   2 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(quotient_less_equal,plain,
    ! [A,B] :
      ( ~ less_equal(A,B)
      | quotient(A,B,zero) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-1.tptp',unknown),
    [] ).

cnf(159711832,plain,
    ( ~ less_equal(A,B)
    | quotient(A,B,zero) ),
    inference(rewrite,[status(thm)],[quotient_less_equal]),
    [] ).

fof(zero_is_smallest,plain,
    ! [A] : less_equal(zero,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-1.tptp',unknown),
    [] ).

cnf(159740112,plain,
    less_equal(zero,A),
    inference(rewrite,[status(thm)],[zero_is_smallest]),
    [] ).

cnf(167549376,plain,
    quotient(zero,A,zero),
    inference(resolution,[status(thm)],[159711832,159740112]),
    [] ).

fof(prove_zero_divide_anything_is_zero,plain,
    ~ quotient(zero,x,zero),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-1.tptp',unknown),
    [] ).

cnf(159771168,plain,
    ~ quotient(zero,x,zero),
    inference(rewrite,[status(thm)],[prove_zero_divide_anything_is_zero]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[167549376,159771168]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(quotient_less_equal,plain,(~less_equal(A,B)|quotient(A,B,zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-1.tptp',unknown),[]).
% 
% cnf(159711832,plain,(~less_equal(A,B)|quotient(A,B,zero)),inference(rewrite,[status(thm)],[quotient_less_equal]),[]).
% 
% fof(zero_is_smallest,plain,(less_equal(zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-1.tptp',unknown),[]).
% 
% cnf(159740112,plain,(less_equal(zero,A)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
% 
% cnf(167549376,plain,(quotient(zero,A,zero)),inference(resolution,[status(thm)],[159711832,159740112]),[]).
% 
% fof(prove_zero_divide_anything_is_zero,plain,(~quotient(zero,x,zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN002-1.tptp',unknown),[]).
% 
% cnf(159771168,plain,(~quotient(zero,x,zero)),inference(rewrite,[status(thm)],[prove_zero_divide_anything_is_zero]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[167549376,159771168]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------