%--------------------------------------------------------------------------
% File     : GRP003-1 : TPTP v7.2.0. Released v1.0.0.
% Domain   : Group Theory (Subgroups)
% Axioms   : Subgroup axioms for the GRP003 group theory axioms
% Version  : [MOW76] axioms : Reduced > Complete.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
%          : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% Source   : [MOW76]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    2 (   0 non-Horn;   0 unit;   2 RR)
%            Number of atoms      :    6 (   0 equality)
%            Maximal clause size  :    4 (   3 average)
%            Number of predicates :    2 (   0 propositional; 1-3 arity)
%            Number of functors   :    1 (   0 constant; 1-1 arity)
%            Number of variables  :    4 (   0 singleton)
%            Maximal term depth   :    2 (   1 average)
% SPC      : 

% Comments : Requires GRP003-0.ax
%          : The dependent axiom, that identity is in every subgroup, is
%            omitted.
%          : These axioms are used in [Wos88] p.187, but with the dependent
%            axiom.
%--------------------------------------------------------------------------
cnf(closure_of_inverse,axiom,
    ( ~ subgroup_member(X)
    | subgroup_member(inverse(X)) )).

cnf(closure_of_product,axiom,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,B,C)
    | subgroup_member(C) )).

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