That is, both "He knows that the answer is 5" and "He does not know that the answer is 5" imply that "The answer is 5".
a verb like "manage to" has the signature +/− since, in a positive environment, the complement projects ("I managed to pass"→"I passed") but, in a negative environment, the negation of the complement projects ("I did not manage to pass"→ ¬"I passed").