%--------------------------------------------------
% groups of exponent two
%--------------------------------------------------

:- option(ac(off)).

axiom( [ [], [ X+Y 	= Y+X 		] ] ).
axiom( [ [], [ (X+Y)+Z	= X+(Y+Z)	] ] ).
axiom( [ [], [ X+X 	= e 		] ] ).
axiom( [ [], [ X+e 	= X 		] ] ).

% axiom( [ [], [ X+(Y+Z)	= Y+(X+Z)	] ] ).
% axiom( [ [], [ e+X 		= X 		] ] ).
% axiom( [ [], [ X+(X+Y) 	= Y 		] ] ).

precedence( [+, e] ).
predicates( [] ).

:-sarp([1-9,13-14]).   % turning on case analysis