formulas(assumptions).

% Find a smallest noncommutative group (by finding the
% conterexample to the statement that all groups are commutative).

% Mace4 should produce a counterexample immediately.

% Group Theory

  (x * y) * z = x * (y * z)  # label(associativity).

% There is a left identity element, and every element has a left inverse.

  exists e ((all x (e * x = x)) &
            (all x exists y (y * x = e))).

end_of_list.

formulas(goals).

x * y = y * x  # label(commutativity).

end_of_list.

