Ac we nought free ne sindon, for-thy-the we never ne mighton from Wulfsfleet yewitan, nefne we thone Hlaford finden and hine ofslain. Se Hlaford hath thisne stede mid searocraftum yebounden, that none ne may hine forletan. We sindon here so fuglas on nete, so fishes on weir.
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I used z3 theorem prover to assess LLM output, which is a pretty decent SAT solver. I considered the LLM output successful if it determines the formula is SAT or UNSAT correctly, and for SAT case it needs to provide a valid assignment. Testing the assignment is easy, given an assignment you can add a single variable clause to the formula. If the resulting formula is still SAT, that means the assignment is valid otherwise it means that the assignment contradicts with the formula, and it is invalid.