formulas(assumptions).

% Noncommutative ring with unit.

% Mace4 should produce a counterexample immediately.

% <+,-,0> is an Abelian group:

0 + x = x.
-x + x = 0.
(x+y)+z = x+(y+z).
x+y = y+x.

% Product is associative:

(x*y)*z = x*(y*z).

% Left and right distributivity:

x*(y+z) = (x*y)+(x*z).
(y+z)*x = (y*x)+(z*x).

% Let the ring have a unit.

1 * x = x.
x * 1 = x.

end_of_list.

formulas(goals).

x * y = y * x  # answer(commtativity_of_product).

end_of_list.

