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I've learned about tableau calculus which is a decision procedure solving the problem of satisfiability of a first order logic formula. Now I'm wondering why this technique can't be used to solve the satisfiability problem (SAT)?

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up vote 6 down vote accepted

It can be, but the solution process is equivalent to converting a CNF formula to DNF, which is NP-hard. You will at worst end up exploring an exponential number of disjunction branches.

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