I once used Sentient[0] to solve a similar puzzle in a different game that I think made a puzzle that required a constraint solver as a joke on the player. I'm a bit saddened to see that the repo hasn't been updated in 6 years, and a node update broke the binary installed on my computer, I find it a much more ergonomic environment than Prolog, hopefully someone else will pick up the mantle.

[0]: https://sentient-lang.org/