Consider the following premises. For all x_10, if x_10 were a bartender, then x_10 is running. It is raining. If David goes running, then it is not raining. Can we infer the following from them? If we can, name the inference rule being used: David is not a bartender.
 From the fact that for all x_10, if x_10 were a bartender, then x_10 is running we can infer that if David were a bartender, then David is running via universal instantiation. From the fact that if David goes running, then it is not raining, and that it is raining we can infer that David is not running via modus tollens. Finally, from the fact that if David were a bartender, then David is running, and that David is not running we can infer that David is not a bartender via modus tollens. Therefore, the answer is yes.