TPTP Axioms File: GRP004-1.ax


%--------------------------------------------------------------------------
% File     : GRP004-1 : TPTP v7.5.0. 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 non-Horn;   0 unit;   2 RR)
%            Number of atoms      :    6 (   1 equality)
%            Maximal clause size  :    4 (   3 average)
%            Number of predicates :    2 (   0 propositional; 1-2 arity)
%            Number of functors   :    2 (   0 constant; 1-2 arity)
%            Number of variables  :    4 (   0 singleton)
%            Maximal term depth   :    2 (   1 average)
% 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) )).

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