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Even though my dataset is very small, I think it's sufficient to conclude that LLMs can't consistently reason. Also their reasoning performance gets worse as the SAT instance grows, which may be due to the context window becoming too large as the model reasoning progresses, and it gets harder to remember original clauses at the top of the context. A friend of mine made an observation that how complex SAT instances are similar to working with many rules in large codebases. As we add more rules, it gets more and more likely for LLMs to forget some of them, which can be insidious. Of course that doesn't mean LLMs are useless. They can be definitely useful without being able to reason, but due to lack of reasoning, we can't just write down the rules and expect that LLMs will always follow them. For critical requirements there needs to be some other process in place to ensure that these are met.
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Currently, if you're stuck, the game only offers to reveal the entire puzzle, forcing you to move onto the next difficulty level and start over. However, we have you covered! Below are piecemeal answers that will serve as hints so that you can find your way through each difficulty level.