Consider the following premises. For all x_3, x_3 is not a cashier. For all x_3, if x_3 were a sailor, then x_3 is playing squash. For all x_3, if x_3 plays squash, then x_3 is a cashier. There is at least one x_3 for which if x_3 were a cashier, then x_3 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is not a sailor.
 From the fact that for all x_3, if x_3 were a sailor, then x_3 is playing squash, and that for all x_3, if x_3 plays squash, then x_3 is a cashier we can infer that for all x_3, if x_3 were a sailor, then x_3 is a cashier via universal transitivity. From the fact that there is at least one x_3 for which if x_3 were a cashier, then x_3 is a sailor, and that for all x_3, if x_3 were a sailor, then x_3 is a cashier we can infer that there is at least one x_3 for which x_3 is a cashier if and only if x_3 is a sailor via existential biconditional introduction. Finally, from the fact that there is at least one x_3 for which x_3 is a cashier if and only if x_3 is a sailor, and that for all x_3, x_3 is not a cashier we can infer that there is at least one x_3 for which x_3 is not a sailor via existential biconditional elimination. Therefore, the answer is yes.