I wanted to test this claim with SAT problems. Why SAT? Because solving SAT problems require applying very few rules consistently. The principle stays the same even if you have millions of variables or just a couple. So if you know how to reason properly any SAT instances is solvable given enough time. Also, it's easy to generate completely random SAT problems that make it less likely for LLM to solve the problem based on pure pattern recognition. Therefore, I think it is a good problem type to test whether LLMs can generalize basic rules beyond their training data.
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Recent examination of some ancient rocks from the west coast of Scotland has now overturned that thinking, suggesting there were periods during snowball Earth when the climate woke up.