Goblet of Fire Chapter 26
“There’s a way of doing it!” Hermione said crossly. “There just has to be!”
She seemed to be taking the library’s lack of useful information on the subject as a personal insult; it had never failed her before.
Half Blood Prince Chapter 18
Meanwhile, the Hogwarts library had failed Hermione for the first time in living memory. She was so shocked, she even forgot that she was annoyed at Harry for his trick with the bezoar.
If Half Blood Prince was the first time that the library failed Hermione, was the search for a method of breathing underwater in Goblet of Fire considered successful? In what sense? And if it was successful why does it say that the library had never failed her before, implying that it failed her now?
Or was Goblet of Fire not "in living memory" by the time of Half Blood Prince?
(Of course there's also the time in Philosopher's Stone that the library failed her when looking for Nicholas Flamel, although perhaps that doesn't count as a failure because she did eventually find him, albeit accidentally).