We introduce a direct polynomial reduction from BLP to DGP1 that reduces instance size increase in the target problem with respect to the existing chain BLP -> SAT -> 3SAT -> DGP1 based on existing literature. Based on this reduction, we can easily model any problem in NP as a DGP1. We therefore present a set of methods for solving DGP1 instances: exact, leading to certificates for YES instances; relaxed, leading to bounds on an error function for NO instances; and heuristic, based on continuous optimization methods.