%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP006-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.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 12:17:32 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (  10 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   21 (  12   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   13 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(right_inverse,plain,
    ! [A] : product(A,inverse(A),identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),
    [] ).

cnf(156129200,plain,
    product(A,inverse(A),identity),
    inference(rewrite,[status(thm)],[right_inverse]),
    [] ).

fof(condition,plain,
    ! [A,B,C] :
      ( ~ an_element(A)
      | ~ an_element(B)
      | ~ product(A,inverse(B),C)
      | an_element(C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),
    [] ).

cnf(156142528,plain,
    ( ~ an_element(A)
    | ~ an_element(B)
    | ~ product(A,inverse(B),C)
    | an_element(C) ),
    inference(rewrite,[status(thm)],[condition]),
    [] ).

fof(element_of_set,plain,
    an_element(the_element),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),
    [] ).

cnf(156160440,plain,
    an_element(the_element),
    inference(rewrite,[status(thm)],[element_of_set]),
    [] ).

cnf(163951968,plain,
    ( ~ product(the_element,inverse(the_element),A)
    | an_element(A) ),
    inference(resolution,[status(thm)],[156142528,156160440]),
    [] ).

fof(prove_b_inverse_is_in_set,plain,
    ~ an_element(inverse(the_element)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),
    [] ).

cnf(156168792,plain,
    ~ an_element(inverse(the_element)),
    inference(rewrite,[status(thm)],[prove_b_inverse_is_in_set]),
    [] ).

cnf(163971536,plain,
    ( ~ an_element(A)
    | ~ product(A,inverse(the_element),B)
    | an_element(B) ),
    inference(resolution,[status(thm)],[156142528,156160440]),
    [] ).

fof(left_identity,plain,
    ! [A] : product(identity,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),
    [] ).

cnf(156121544,plain,
    product(identity,A,A),
    inference(rewrite,[status(thm)],[left_identity]),
    [] ).

cnf(163988936,plain,
    ~ an_element(identity),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[156168792,163971536,156121544]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[156129200,163951968,163988936]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),[]).
% 
% cnf(156129200,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
% 
% fof(condition,plain,(~an_element(A)|~an_element(B)|~product(A,inverse(B),C)|an_element(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),[]).
% 
% cnf(156142528,plain,(~an_element(A)|~an_element(B)|~product(A,inverse(B),C)|an_element(C)),inference(rewrite,[status(thm)],[condition]),[]).
% 
% fof(element_of_set,plain,(an_element(the_element)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),[]).
% 
% cnf(156160440,plain,(an_element(the_element)),inference(rewrite,[status(thm)],[element_of_set]),[]).
% 
% cnf(163951968,plain,(~product(the_element,inverse(the_element),A)|an_element(A)),inference(resolution,[status(thm)],[156142528,156160440]),[]).
% 
% fof(prove_b_inverse_is_in_set,plain,(~an_element(inverse(the_element))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),[]).
% 
% cnf(156168792,plain,(~an_element(inverse(the_element))),inference(rewrite,[status(thm)],[prove_b_inverse_is_in_set]),[]).
% 
% cnf(163971536,plain,(~an_element(A)|~product(A,inverse(the_element),B)|an_element(B)),inference(resolution,[status(thm)],[156142528,156160440]),[]).
% 
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP006-1.tptp',unknown),[]).
% 
% cnf(156121544,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
% 
% cnf(163988936,plain,(~an_element(identity)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156168792,163971536,156121544]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[156129200,163951968,163988936]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------