I'd prefer counter-examples over damaged formulas. For example, consider the theorem that a continuous function on the interval [a,b] is bounded. The damaged formula might read "If f is continuous on (a,b), then it is bounded." There is some merit in spotting that (a,b) doesn't include the end point a. There is greater merit in noticing that if we leave off the end point we have f(x) = 1/(x-a) as a continuous function that is unbounded.

That leads on to the difference between what one might call syntactic memorisation and semantic memorisation. Confronted with the claim "If f is continuous on (a,b), then it is bounded." one might know it is supposed to be [a,b] as a matter of rote memorisation, but such knowledge is only a stepping stone. One wants to press on to a deeper understanding so that even if one forgets whether it is supposed to be (a,b) or [a,b] one can quickly reconstruct the memory by running over a counter-example (a,b) and providing a proof for [a,b]