%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP005-1 : 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 12:17:30 EDT 2009

% Result   : Unsatisfiable 0.0s
% Output   : Refutation 0.0s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   7 unt;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (  11   ~;   8   |;   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   :   10 (   0 sgn   4   !;   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/GRP005-1.tptp',unknown),
    [] ).

cnf(143542960,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/GRP005-1.tptp',unknown),
    [] ).

cnf(143560920,plain,
    ( ~ an_element(A)
    | ~ an_element(B)
    | ~ product(A,inverse(B),C)
    | an_element(C) ),
    inference(rewrite,[status(thm)],[condition]),
    [] ).

fof(prove_identity_is_an_element,plain,
    ~ an_element(identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP005-1.tptp',unknown),
    [] ).

cnf(143582608,plain,
    ~ an_element(identity),
    inference(rewrite,[status(thm)],[prove_identity_is_an_element]),
    [] ).

cnf(151406872,plain,
    ( ~ an_element(A)
    | ~ an_element(B)
    | ~ product(A,inverse(B),identity) ),
    inference(resolution,[status(thm)],[143560920,143582608]),
    [] ).

fof(element_of_set,plain,
    an_element(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP005-1.tptp',unknown),
    [] ).

cnf(143551048,plain,
    an_element(a),
    inference(rewrite,[status(thm)],[element_of_set]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[143542960,151406872,143551048]),
    [] ).

%------------------------------------------------------------------------------
%----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/GRP005-1.tptp',unknown),[]).
% 
% cnf(143542960,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/GRP005-1.tptp',unknown),[]).
% 
% cnf(143560920,plain,(~an_element(A)|~an_element(B)|~product(A,inverse(B),C)|an_element(C)),inference(rewrite,[status(thm)],[condition]),[]).
% 
% fof(prove_identity_is_an_element,plain,(~an_element(identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP005-1.tptp',unknown),[]).
% 
% cnf(143582608,plain,(~an_element(identity)),inference(rewrite,[status(thm)],[prove_identity_is_an_element]),[]).
% 
% cnf(151406872,plain,(~an_element(A)|~an_element(B)|~product(A,inverse(B),identity)),inference(resolution,[status(thm)],[143560920,143582608]),[]).
% 
% fof(element_of_set,plain,(an_element(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP005-1.tptp',unknown),[]).
% 
% cnf(143551048,plain,(an_element(a)),inference(rewrite,[status(thm)],[element_of_set]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[143542960,151406872,143551048]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------