Consider the following premises. If Richard were a musician, then William is excited. For all x_22, if x_22 drives a car, then x_22 is a musician. For all x_22, x_22 will drive a car or x_22 is a bartender. For all x_22, if x_22 were a bartender, then x_22 is a musician. Can we infer the following from them? If we can, name the inference rule being used: William is excited or David is cooking.
 From the fact that for all x_22, if x_22 drives a car, then x_22 is a musician, that for all x_22, if x_22 were a bartender, then x_22 is a musician, and that for all x_22, x_22 will drive a car or x_22 is a bartender we can infer that for all x_22, x_22 is a musician via universal disjunction elimination. From the fact that for all x_22, x_22 is a musician we can infer that Richard is a musician via universal instantiation. From the fact that if Richard were a musician, then William is excited, and that Richard is a musician we can infer that William is excited via modus ponens. Finally, from the fact that William is excited we can infer that William is excited or David is cooking via addition. Therefore, the answer is yes.