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The inference of gene predictors in the gene regulatory network (GRN) has become an important research area in the genomics and medical disciplines. Accurate predicators are necessary for constructing the GRN model and to enable targeted biological experiments that attempt to validate or control the regulation process. In this paper, we implement a SAT-based algorithm to determine the gene predictor set from steady state gene expression data (attractor states). Using the attractor states as input, the states are ordered into attractor cycles. For each attractor cycle ordering, all possible predictors are enumerated and a conjunctive normal form (CNF) expression is generated which encodes these predictors and their biological constraints. Each CNF is solved using a SAT solver to find candidate predictor sets. Statistical analysis of the resulting predictor sets selects the most likely predictor set of the GRN, corresponding to the attractor data. We demonstrate our algorithm on attractor state data from a melanoma study and present our predictor set results.