Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has motivated researchers to adopt phylogenetic networks and other general models to study genome evolution. One important problem arising from reconstruction and verification of phylogenetic networks is the cluster containment problem, namely determining whether or not a cluster of taxa is displayed in a phylogenetic network. In this work, a new upper bound for this NP-complete problem is established through an efficient reduction to the SAT problem. Two efficient (albeit exponential time) methods are also implemented. It is developed on the basis of generalization of the so-called reticulation-visible property of phylogenetic networks.