At the end of X-Men: Days of Future Past, Professor X asks Wolverine what he remembers, and he replies "Everything".
However, the Trask incident happened in 1973 and the events of X-Men Origins: Wolverine happened after 1975.
It was shown in Origins that Stryker put adamantium inside his body and wiped his memory. Therefore, how could Wolverine say that he remembers everything that happened in 1973?
Kitty says only someone who time-travels remembers everything. Does this mean that Wolverine came from 1973 to 2023 directly, or did he live through those years again?