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 constraints in a list of constraints; responsive to the SAT problem being satisfied without constraints, fixing, by the processor, a set of variable assignments determined in satisfying the SAT problem without constraints; for each constraint in the list of constraints, determining, by the processor, whether the SAT problem with the constraint results in the set of variable assignments remain constant; responsive to the SAT problem with the constraint resulting in the set of variable assignments remaining constant, adding, by the processor, the constraint to a list of non-affecting constraints; and returning, by the processor, a satisfied result.