Consider the following premises. For all x_1, if x_1 were a sailor, then x_1 is sleeping. There is at least one x_1 for which if x_1 were a janitor, then x_1 is sleeping. For all x_1, x_1 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will not sleep.
 From the fact that for all x_1, x_1 is a sailor we can infer that for all x_1, x_1 is a sailor or x_1 is a janitor via universal addition. Finally, from the fact that for all x_1, if x_1 were a sailor, then x_1 is sleeping, that there is at least one x_1 for which if x_1 were a janitor, then x_1 is sleeping, and that for all x_1, x_1 is a sailor or x_1 is a janitor we can infer that there is at least one x_1 for which x_1 will sleep via existential disjunction elimination, which contradicts that For all x_1, x_1 will not sleep. Therefore, the answer is no.