Consider the following premises. For all x_17, x_17 will not sleep. There is at least one x_17 for which if x_17 were a nurse, then x_17 is sleeping. For all x_17, if x_17 were a nurse, then x_17 is a bartender. For all x_17, if x_17 were a bartender, then x_17 is a nurse. For all x_17, x_17 will make tea if and only if x_17 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_17 for which x_17 will not make tea.
 From the fact that for all x_17, if x_17 were a nurse, then x_17 is a bartender, and that for all x_17, if x_17 were a bartender, then x_17 is a nurse we can infer that for all x_17, x_17 is a nurse if and only if x_17 is a bartender via universal biconditional introduction. From the fact that there is at least one x_17 for which if x_17 were a nurse, then x_17 is sleeping, and that for all x_17, x_17 will not sleep we can infer that there is at least one x_17 for which x_17 is not a nurse via existential modus tollens. From the fact that for all x_17, x_17 is a nurse if and only if x_17 is a bartender, and that there is at least one x_17 for which x_17 is not a nurse we can infer that there is at least one x_17 for which x_17 is not a bartender via existential biconditional elimination. Finally, from the fact that for all x_17, x_17 will make tea if and only if x_17 is a bartender, and that there is at least one x_17 for which x_17 is not a bartender we can infer that there is at least one x_17 for which x_17 will not make tea via existential biconditional elimination. Therefore, the answer is yes.