%------------------------------------------------------------------------------
% File     : GRP007+0 : TPTP v9.0.0. 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 unt;   0 def)
%            Number of atoms       :    7 (   1 equ)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :    5 (   0   ~;   0   |;   3   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 3-3 aty)
%            Number of variables   :    7 (   7   !;   0   ?)
% SPC      : 

% Comments :
%------------------------------------------------------------------------------
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)) ) ).

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