TPTP Axioms File: GRP003-2.ax


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% File     : GRP003-2 : TPTP v7.5.0. 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% Refs     : [Wos65] Wos (1965), Unpublished Note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 non-Horn;   0 unit;   1 RR)
%            Number of atoms      :    4 (   0 equality)
%            Maximal clause size  :    4 (   4 average)
%            Number of predicates :    2 (   0 propositional; 1-3 arity)
%            Number of functors   :    1 (   0 constant; 1-1 arity)
%            Number of variables  :    3 (   0 singleton)
%            Maximal term depth   :    2 (   1 average)
% 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) )).

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