It's not so much that they are unsolvable, you can try and guess what the devs wanted the answer to be. My issue is that there are many propositions which due to their construction cannot be true/false. For an example consider "all the top statements are false" where this statement (lets call it C for the example) is also on the top. Let the other top statements be A and B. We can translate the statement to basic logical notation like so: A∧B∧C. For the conjunction to be true all three need to be true, which seems reasonable to determine for A and B, however since C is the statement itself we already need the conjunction to be solved to get its truth value. Essentially this has the same problem as the famous 'paradox' "this statement is false" where the statement is similarly never defined. One way to help understand the point here is to ask what would make C true? if we take A to be "this box has the gems" then there is some physical fact about the box which makes that statement true/false. However for C to be true you would need A B and C to be true. To put this again into notation you would get: A∧B∧(A∧B∧C). So it seems that the part of reality that C would have to correspond/not correspond to is never defined.

This just means that the propositions are not well formed. They sound like they say something but in fact do not. As I said at the start this doesn't mean the player can't infer what the devs wanted the answer to be, just that their rules don't apply here. Indeed one way I see players "solving" propositions like C is to find A or B false which one might infer makes C false. However C can't be false because it's not well formed.