%--------------------------------------------------------------------------
% File     : GRP004-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Group Theory (Subgroups)
% Axioms   : Subgroup (equality) axioms
% Version  : [MOW76] (equality) axioms :
%            Reduced > Complete.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    2 (   0 unt;   0 nHn;   2 RR)
%            Number of literals    :    6 (   1 equ;   4 neg)
%            Maximal clause size   :    4 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :    4 (   0 sgn)
% SPC      : 

% Comments : Requires GRP004-0.ax
%          : The redundant axiom that states that the identity element is in
%            the subgroup, present in the [MOW76] presentation, is omitted
%            here.
%--------------------------------------------------------------------------
cnf(closure_of_inverse,axiom,
    ( ~ subgroup_member(X)
    | subgroup_member(inverse(X)) ) ).

cnf(closure_of_multiply,axiom,
    ( ~ subgroup_member(X)
    | ~ subgroup_member(Y)
    | multiply(X,Y) != Z
    | subgroup_member(Z) ) ).

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