Consider the following premises. For all x_7, x_7 will sleep if and only if x_7 will drink water. For all x_7, if x_7 were bored, then x_7 is sleeping. For all x_7, x_7 will take a plane or x_7 will drink water. There is at least one x_7 for which x_7 will not take a plane or x_7 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will sleep.
 From the fact that for all x_7, x_7 will take a plane or x_7 will drink water, and that there is at least one x_7 for which x_7 will not take a plane or x_7 is bored we can infer that there is at least one x_7 for which x_7 will drink water or x_7 is bored via existential resolution. From the fact that for all x_7, x_7 will sleep if and only if x_7 will drink water we can infer that for all x_7, if x_7 drinks water, then x_7 is sleeping via universal biconditional elimination. Finally, from the fact that for all x_7, if x_7 drinks water, then x_7 is sleeping, that for all x_7, if x_7 were bored, then x_7 is sleeping, and that there is at least one x_7 for which x_7 will drink water or x_7 is bored we can infer that there is at least one x_7 for which x_7 will sleep via existential disjunction elimination. Therefore, the answer is yes.