MATH.6:9 - Consequences

A countermodel gives a conclusive failure of the stated implication and a concrete object for further work. It can reveal a useful narrower theorem, a needed distinction, or a replacement construction. Its direct result is refutation on the stated interpretation; choosing and proving the repair remains further work.

An unsuccessful attempt can still identify an incompatible set of assignments or a limited class with no failure. Its usefulness depends on how that result changes the next mathematical move.