Conflict Resolution

We introduce a new method for solving systems of linear inequalities over the rationals--the conflict resolution method. Themethod successively refines an initial assignment with the help of newly derived constraints until either the assignment becomes a solution of the system or a trivially unsatisfiable constraint is derived. We show that this method is correct and terminating. Our experimental results show that conflict resolution outperforms the Fourier-Motzkin method and the Chernikov algorithm, in some cases by orders of magnitude.