This study is concerned with the Boolean satisfiability (SAT) problem and its solution in setting a hybrid computational intelligence environment of genetic and fuzzy computing. In this framework, fuzzy sets realize an embedding principle meaning that original two-valued (Boolean) functions under investigation are extended to their continuous counterparts resulting in the form of fuzzy (multivalued) functions. In the sequel, the SAT problem is reformulated for the fuzzy functions and solved using a genetic algorithm (GA). It is shown that a GA, especially its recursive version, is an efficient tool for handling multivariable SAT problems. Thorough experiments revealed that the recursive version of the GA can solve SAT problems with more than 1000 variables.