1. A method, in a data processing system, for efficiently determining Boolean satisfiability (SAT) using lazy constraints, the method comprising: determining, by a processor in the data processing system, whether a SAT problem is satisfied without applying constraints in a list of constraints; responsive to the SAT problem being satisfied without applying the constraints in the list of constraints, fixing, by the processor, a set of variable assignments determined in satisfying the SAT problem without applying the constraints in the list of constraints; for each constraint in the list of constraints, determining, by the processor, whether the set of variable assignments remain constant when applying the constraint to the SAT problem; responsive to the set of variable assignments remaining constant when applying the constraint to the SAT problem: adding, by the processor, the constraint to a list of non-affecting constraints to track constraints from the list of constraints that do not directly affect the SAT problem; and returning, by the processor, a satisfied result; and responsive to the set of variable assignments changing when applying the constraint to the SAT problem: adding, by the processor, the constraint to a list of affecting constraints to track constraints from the list of constraints that directly affect the SAT problem; unfixing, by the processor, the set of variable assignments determined in satisfying the SAT problem without applying the constraints in the list of constraints; determining, by the processor, whether the SAT problem is satisfiable with the constraint being applied; responsive to the SAT problem being satisfied with the constraint, fixing, by the processor, a new set of variable assignments determined in satisfying the SAT problem with the constraint being applied; and for each remaining constraint in the list of constraints, continuing, by the processor, with determining whether the SAT problem with the constraint results in the new set of variable assignments remain constant, change, or are inconclusive.