## TPTP Axioms File: GRP007+0.ax

```%------------------------------------------------------------------------------
% File     : GRP007+0 : TPTP v7.5.0. Released v2.0.0.
% Domain   : Group Theory (Named Semigroups)
% Axioms   : Group theory (Named Semigroups) axioms
% Version  : [Gol93] axioms.
% English  :

% Refs     : [Gol93] Goller (1993), Anwendung des Theorembeweisers SETHEO a
% Source   : [Gol93]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    2 (   0 unit)
%            Number of atoms       :    7 (   1 equality)
%            Maximal formula depth :    8 (   7 average)
%            Number of connectives :    5 (   0 ~  ;   0  |;   3  &)
%                                         (   0 <=>;   2 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :    1 (   0 constant; 3-3 arity)
%            Number of variables   :    7 (   0 singleton;   7 !;   0 ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      :

%------------------------------------------------------------------------------
fof(total_function,axiom,
( ! [G,X,Y] :
( ( group_member(X,G)
& group_member(Y,G) )
=> group_member(multiply(G,X,Y),G) ) )).

fof(associativity,axiom,
( ! [G,X,Y,Z] :
( ( group_member(X,G)
& group_member(Y,G)
& group_member(Z,G) )
=> multiply(G,multiply(G,X,Y),Z) = multiply(G,X,multiply(G,Y,Z)) ) )).

%------------------------------------------------------------------------------
```