Consider the following premises. If Joseph were a nurse, then Mary is running. Joseph is a nurse or William is curious. For all x_10, x_10 will not go running. Can we infer the following from them? If we can, name the inference rule being used: William is curious.
 From the fact that for all x_10, x_10 will not go running we can infer that Mary is not running via universal instantiation. From the fact that if Joseph were a nurse, then Mary is running, and that Mary is not running we can infer that Joseph is not a nurse via modus tollens. Finally, from the fact that Joseph is a nurse or William is curious, and that Joseph is not a nurse we can infer that William is curious via disjunctive syllogism. Therefore, the answer is yes.