The automated detection of faults on variability analysis tools is a challenging task often infeasible due to the combinatorial complexity of the analyses. In previous works, we successfully automated the generation of test data for feature model analysis tools using metamorphic testing. The positive results obtained have encouraged us to explore the applicability of this technique for the efficient detection of faults in other variability-intensive domains. In this paper, we present an automated test data generator for SAT solvers that enables the generation of random propositional formulas (inputs) and their solutions (expected output). In order to show the feasibility of our approach, we introduced 100 artificial faults (i.e. mutants) in an open source SAT solver and compared the ability of our generator and three related benchmarks to detect them. Our results are promising and encourage us to generalize the technique, which could be potentially applicable to any tool dealing with variability such as Eclipse repositories or Maven dependencies analyzers.