Sisyphus is rolling a boulder towards Monty Hall, who controls a switch that will open one of three doors at your choosing, reveal what is behind that door, and then allow you to choose a second door instead or stay with your first choice.

Behind one door is the Grand Hilbert Hotel, which has infinite rooms, but they are all full, so they may not be able to accommodate Sisyphus or his boulder.

Behind another door is the Ship of Theseus, which may be destroyed by the boulder. However, the ship has had all of its constituent parts replaced, so it may not actually be the same ship.

Behind the shirt door is a box containing a radioactive isotope, a container of poison, and a cat. If Sisyphus passes through this door, his boulder will break open the box, causing the state of the cat within to be observed.

Is Sisyphus happy?