Consider the following premises. For all x_15, if x_15 were an electrician, then x_15 is sleeping. For all x_15, x_15 is not a cashier. For all x_15, x_15 is an electrician if and only if x_15 will play squash. There is at least one x_15 for which x_15 will sleep if and only if x_15 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which x_15 will not play squash.
 From the fact that there is at least one x_15 for which x_15 will sleep if and only if x_15 is a cashier, and that for all x_15, x_15 is not a cashier we can infer that there is at least one x_15 for which x_15 will not sleep via existential biconditional elimination. From the fact that for all x_15, if x_15 were an electrician, then x_15 is sleeping, and that there is at least one x_15 for which x_15 will not sleep we can infer that there is at least one x_15 for which x_15 is not an electrician via existential modus tollens. Finally, from the fact that for all x_15, x_15 is an electrician if and only if x_15 will play squash, and that there is at least one x_15 for which x_15 is not an electrician we can infer that there is at least one x_15 for which x_15 will not play squash via existential biconditional elimination. Therefore, the answer is yes.