Consider the following premises. If it is cold, then Jennifer is a sailor. For all x_3, x_3 is a bartender if and only if x_3 is a sailor. Jennifer is not a bartender. If Richard plays squash, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: Richard is not playing squash.
 From the fact that for all x_3, x_3 is a bartender if and only if x_3 is a sailor we can infer that Jennifer is a bartender if and only if Jennifer is a sailor via universal instantiation. From the fact that Jennifer is a bartender if and only if Jennifer is a sailor, and that Jennifer is not a bartender we can infer that Jennifer is not a sailor via biconditional elimination. From the fact that if Richard plays squash, then it is cold, and that if it is cold, then Jennifer is a sailor we can infer that if Richard plays squash, then Jennifer is a sailor via transitivity. Finally, from the fact that if Richard plays squash, then Jennifer is a sailor, and that Jennifer is not a sailor we can infer that Richard is not playing squash via modus tollens. Therefore, the answer is yes.