assign(order, kbo).

formulas(assumptions).

% quasigroup

x * (x \ y) = y.

x \ (x * y) = y.

(x * y) / y = x.

(x / y) * y = x.

% A in middle nucleus

x * (A * y) = (x * A) * y.

end_of_list.

formulas(goals).

% A / A is a two-sided identity element

(A / A) * x = x.

x * (A / A) = x.

end_of_list.