We just installed cat doors on the interior of our house so that Lily can access the basement and our bedroom when the doors are closed. I haven't trained her at all yet because I'm still doing research on how to do it. Well, tonight, I thought I heard the one to the basement close from the family room. I go into the kitchen, where the door to the basement is, and there's no Lily. I open the basement door, and there she is, on the bottom of the stairs! She figured it out all on her own! What a smart kitty!
I think she thinks she's not supposed to go down there, because she scooted right back up when I opened the door. I did praise her, though, so maybe that helped.