Consider the following premises. For all x_11, x_11 is not a politician. For all x_11, x_11 will make tea. There is at least one x_11 for which if x_11 makes tea, then x_11 is a janitor. For all x_11, x_11 is a politician or x_11 will sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will sleep and x_11 is a janitor.
 From the fact that for all x_11, x_11 is a politician or x_11 will sleep, and that for all x_11, x_11 is not a politician we can infer that for all x_11, x_11 will sleep via universal disjunctive syllogism. From the fact that there is at least one x_11 for which if x_11 makes tea, then x_11 is a janitor, and that for all x_11, x_11 will make tea we can infer that there is at least one x_11 for which x_11 is a janitor via existential modus ponens. Finally, from the fact that for all x_11, x_11 will sleep, and that there is at least one x_11 for which x_11 is a janitor we can infer that there is at least one x_11 for which x_11 will sleep and x_11 is a janitor via existential conjunction. Therefore, the answer is yes.