Solving SAT using tableau calculus 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)?
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.