Suppose we have a Turing machine $M$ as black box that decide $SAT$ problem. Now suppse we have a $CNF$ formula $\phi$ with $n$ variables. How it possible checking satisfiblity of $\phi$ and then finding that assignment with at most $2n+1$ times using $M$?
I know that every $SAT$ instance can comverted to $CNF$ clauses so i think we can do it recursively to checking satisfiblity and then finding it, but i get stuck to formulate it that how we can do it.
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