%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP034-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.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 12:18:56 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (  11 unt;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  12   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 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 (   1 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_a_inverse_is_in_subgroup,plain,
    ~ subgroup_member(inverse(a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),
    [] ).

cnf(166602776,plain,
    ~ subgroup_member(inverse(a)),
    inference(rewrite,[status(thm)],[prove_a_inverse_is_in_subgroup]),
    [] ).

fof(closure_of_product_and_inverse,plain,
    ! [A,B,C] :
      ( ~ subgroup_member(A)
      | ~ subgroup_member(B)
      | ~ product(A,inverse(B),C)
      | subgroup_member(C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),
    [] ).

cnf(166594064,plain,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,inverse(B),C)
    | subgroup_member(C) ),
    inference(rewrite,[status(thm)],[closure_of_product_and_inverse]),
    [] ).

fof(a_is_in_subgroup,plain,
    subgroup_member(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),
    [] ).

cnf(166598776,plain,
    subgroup_member(a),
    inference(rewrite,[status(thm)],[a_is_in_subgroup]),
    [] ).

cnf(174424224,plain,
    ( ~ subgroup_member(A)
    | ~ product(A,inverse(a),B)
    | subgroup_member(B) ),
    inference(resolution,[status(thm)],[166594064,166598776]),
    [] ).

fof(left_identity,plain,
    ! [A] : product(identity,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),
    [] ).

cnf(166543312,plain,
    product(identity,A,A),
    inference(rewrite,[status(thm)],[left_identity]),
    [] ).

cnf(174456512,plain,
    ~ subgroup_member(identity),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[166602776,174424224,166543312]),
    [] ).

fof(right_inverse,plain,
    ! [A] : product(A,inverse(A),identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),
    [] ).

cnf(166554896,plain,
    product(A,inverse(A),identity),
    inference(rewrite,[status(thm)],[right_inverse]),
    [] ).

cnf(176841376,plain,
    ~ subgroup_member(A),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[174456512,166594064,166554896]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[176841376,166598776]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_a_inverse_is_in_subgroup,plain,(~subgroup_member(inverse(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),[]).
% 
% cnf(166602776,plain,(~subgroup_member(inverse(a))),inference(rewrite,[status(thm)],[prove_a_inverse_is_in_subgroup]),[]).
% 
% fof(closure_of_product_and_inverse,plain,(~subgroup_member(A)|~subgroup_member(B)|~product(A,inverse(B),C)|subgroup_member(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),[]).
% 
% cnf(166594064,plain,(~subgroup_member(A)|~subgroup_member(B)|~product(A,inverse(B),C)|subgroup_member(C)),inference(rewrite,[status(thm)],[closure_of_product_and_inverse]),[]).
% 
% fof(a_is_in_subgroup,plain,(subgroup_member(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),[]).
% 
% cnf(166598776,plain,(subgroup_member(a)),inference(rewrite,[status(thm)],[a_is_in_subgroup]),[]).
% 
% cnf(174424224,plain,(~subgroup_member(A)|~product(A,inverse(a),B)|subgroup_member(B)),inference(resolution,[status(thm)],[166594064,166598776]),[]).
% 
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),[]).
% 
% cnf(166543312,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
% 
% cnf(174456512,plain,(~subgroup_member(identity)),inference(forward_subsumption_resolution__resolution,[status(thm)],[166602776,174424224,166543312]),[]).
% 
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-3.tptp',unknown),[]).
% 
% cnf(166554896,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
% 
% cnf(176841376,plain,(~subgroup_member(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174456512,166594064,166554896]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[176841376,166598776]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------