> As I understand it, the point of reducing a problem to SAT is because there's a proof that SAT is NP-Complete which in turn would prove that your problem is N

> As I understand it, the point of reducing a problem to SAT is because there's a proof that SAT is NP-Complete which in turn would prove that your problem is NP-Complete. That's kind of backwards: reducing any problem in NP (not just NP-complete ones) to SAT is possible and mathematically straightforward because SAT is NP-complete. You do reductions from SAT to other problems in order to show that they are NP-complete (which involves cleverness in working out how to represent propositional logic in e.g. Sudoku).