Consider the following premises. For all x_17, x_17 will make tea if and only if x_17 will sleep. For all x_17, if x_17 were a janitor, then x_17 is sleeping. Mary is making tea. 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 sleep or x_17 is a taxi driver.
 From the fact that Mary is making tea we can infer that there is at least one x_17 for which x_17 will make tea via existential generalization. From the fact that there is at least one x_17 for which x_17 will make tea we can infer that there is at least one x_17 for which x_17 will make tea or x_17 is a janitor via existential addition. From the fact that for all x_17, x_17 will make tea if and only if x_17 will sleep we can infer that for all x_17, if x_17 makes tea, then x_17 is sleeping via universal biconditional elimination. From the fact that for all x_17, if x_17 makes tea, then x_17 is sleeping, that for all x_17, if x_17 were a janitor, then x_17 is sleeping, and that there is at least one x_17 for which x_17 will make tea or x_17 is a janitor we can infer that there is at least one x_17 for which x_17 will sleep via existential disjunction elimination. Finally, from the fact that there is at least one x_17 for which x_17 will sleep we can infer that there is at least one x_17 for which x_17 will sleep or x_17 is a taxi driver via existential addition. Therefore, the answer is yes.