Consider the following premises. For all x_8, x_8 will drive a car or x_8 is a poet. If Joseph were a poet, then Barbara is rich. Barbara is rich or Joseph is not driving a car. Can we infer the following from them? If we can, name the inference rule being used: Barbara is rich.
 From the fact that for all x_8, x_8 will drive a car or x_8 is a poet we can infer that Joseph is driving a car or Joseph is a poet via universal instantiation. From the fact that Barbara is rich or Joseph is not driving a car we can infer that if Joseph drives a car, then Barbara is rich via rewriting. Finally, from the fact that if Joseph drives a car, then Barbara is rich, that if Joseph were a poet, then Barbara is rich, and that Joseph is driving a car or Joseph is a poet we can infer that Barbara is rich via disjunction elimination. Therefore, the answer is yes.