Enigmarch 2023: Day 11

[tahnan]

Here we are again: PDF, text below. You can check your answer here.

Enigmarch, Day 11: Trapped in A Smullyan Room

When I saw the prompt for Day 11, BOLD, my first thought was "Knights are bold, unlike knaves". After struggling with a truth-teller puzzle, I considered the warning over doors that shouldn't be opened: "Be bold, be bold, but not too bold...". I still wasn't getting anywhere, so I went for a walk.

I was a little deep in thought, because when I looked up, I'd somehow wandered into a room with 26 doors in a circle (this is a common danger for puzzle-writers). A sign posted in the center read:

Some of the doors in this room are dangerous to open, and some are safe. Some of their signs are telling the truth, and some are lying. But to keep things fair, every honorable sign is bolded (and only the honorable signs are); a sign is honorable if it is safe and truth-telling, or dangerous and lying, and dishonorable if it is safe and lying or dangerous and truthtelling.^* -RS

^*Except for door R. Never could figure out whether it was lying or not.

Sure enough, the doors had the following signs, in order:

A: At least one door in the second half of the alphabet is safe.
B: Of the next door and myself, one is safe and one is dangerous.
C: Of the previous door and myself, both are safe or both are dangerous.
D: Of myself, E, and F, exactly one is telling the truth.
E: All doors alphabetically before me are lying.
F: The doors adjacent to me are both truthtellers or both liars.
G: The doors adjacent to me are both safe or both deadly.
H: The doors adjacent to me are both safe or both deadly.
I: Either all three of the previous doors are lying, or all three are telling the truth.
J: There is a sequence of at least six doors that alternate truthtelling and lying.
K: Every door with the word "safe" on its sign is safe.
L: Every safe door has the word "safe" on its sign.
M: All lying doors are bolded.
N: All safe doors are telling the truth.
O: All vowels are telling the truth.
P: There is at least one sequence of five doors that are all truthtellers or all liars.
Q: At least half of the doors alphabetically before me are telling the truth.
R: "I am safe" is just as true for me as "I am telling the truth."
S: None of D, Q, and myself are safe.
T: No door after me alphabetically is safe.
U: No more than two consecutive doors are lying.
V: Of the next door and myself, one is a truthteller and one is a liar.
W: Of the previous door and myself, both are truthtellers or both are liars.
X: No bolded door among the last six doors alphabetically is safe.
Y: More of the last six doors alphabetically are telling the truth than lying.
Z: At least one door in the first half of the alphabet is safe.

Of course, I only need one safe door, but when you've wandered into a Smullyan Room, it's hard to resist working out all of the options. So...which doors are safe?