Consider the following premises. For all x_4, x_4 is curious or x_4 will drink water. There is at least one x_4 for which if x_4 works, then x_4 is sleeping. For all x_4, if x_4 were curious, then x_4 is working. For all x_4, if x_4 drinks water, then x_4 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will sleep.
 From the fact that for all x_4, if x_4 were curious, then x_4 is working, and that there is at least one x_4 for which if x_4 works, then x_4 is sleeping we can infer that there is at least one x_4 for which if x_4 were curious, then x_4 is sleeping via existential transitivity. Finally, from the fact that there is at least one x_4 for which if x_4 were curious, then x_4 is sleeping, that for all x_4, if x_4 drinks water, then x_4 is sleeping, and that for all x_4, x_4 is curious or x_4 will drink water we can infer that there is at least one x_4 for which x_4 will sleep via existential disjunction elimination. Therefore, the answer is yes.