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Do you think that it is possible to compile a propositional formula towards a SAT problem of similar size whose solution allows us to find a valuation which satisfies the starting formula? If so, explain the method you would use. Thanks in advance.

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This questions seems to be already answered here: How to convert a propositional formula to conjunctive normal form (CNF)? SAT-solvers usually take a CNF in dimcas format as input.