%--------------------------------------------------------------------------
% File     : GRP003-2 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Group Theory (Subgroups)
% Axioms   : Subgroup axioms for the GRP003 group theory axioms
% Version  : [Wos65] axioms.
% English  :

% Refs     : [Wos65] Wos (1965), Unpublished Note
% Source   : [SPRFN]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    1 (   0 unt;   0 nHn;   1 RR)
%            Number of literals    :    4 (   0 equ;   3 neg)
%            Maximal clause size   :    4 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 1-3 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 1-1 aty)
%            Number of variables   :    3 (   0 sgn)
% SPC      : 

% Comments : Requires GRP003-0.ax
%            The closure_of_product_and_inverse axiom is derived from the
%            two basic subgroup axioms - closure of product and
%            closure_of_inverse - by resolution.
%--------------------------------------------------------------------------
cnf(closure_of_product_and_inverse,axiom,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,inverse(B),C)
    | subgroup_member(C) ) ).

%--------------------------------------------------------------------------