assign(iterate_up_to, 12). set(verbose). % This list of formulas specifies a noncommutative group. % % Normally we would write the group axioms with clauses % (as in the example ncg-48.in). Here we use quantified % formulas. formulas(theory). % Associativity all x all y all z ((x * y) * z = x * (y * z)). % 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))). % So far, we have group theory. Now, state that % there are two noncommuting elements. exists a exists b (a * b != b * a). end_of_list.