Resolution Tunnels for Improved SAT Solver Performance

We show how to aggressively add uninferred constraints, in a controlled manner, to formulae for finding Van der Waerden numbers during search. We show that doing so can improve the performance of standard SAT solvers on these formulae by orders of magnitude. We obtain a new and much greater lower bound for one of the Van der Waerden numbers, specifically a bound of 1132 for W(2,6). We believe this bound to actually be the number we seek. The structure of propositional formulae for solving Van der Waerden numbers is similar to that of formulae arising from Bounded Model Checking. Therefore, we view this as a preliminary investigation into solving hard formulae in the area of Formal Verification.