Propositional Parlor Puzzle

There's a game available on STEAM called "Mimic Logic" which consists of these kinds of puzzles.

If you like these puzzles, you want to check out books by the late, great Raymond Smullyan:

https://www.amazon.com/Lady-Tiger-Other-Puzzles-Recreational...

Interesting to see, I was wondering how to encode this puzzle for a logic solver.

One nit, this doesn't seem to handle the case where a box can have both true and false statements. As per the rules only one box needs to have only false and one only true statements, the third can have both.

Maybe this is also in the next part.

I just played this at the weekend - Blue Prince on the PS5.