Consider the following premises. There is at least one x_18 for which if x_18 sleeps, then x_18 is drinking water. For all x_18, if x_18 were a writer, then x_18 is not drinking water. For all x_18, x_18 is a bartender or x_18 will sleep. For all x_18, if x_18 were a writer, then x_18 is an astronaut. For all x_18, if x_18 were an astronaut, then x_18 is a writer. For all x_18, if x_18 were a bartender, then x_18 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_18 for which x_18 is not an astronaut.
 From the fact that for all x_18, if x_18 were an astronaut, then x_18 is a writer, and that for all x_18, if x_18 were a writer, then x_18 is an astronaut we can infer that for all x_18, x_18 is an astronaut if and only if x_18 is a writer via universal biconditional introduction. From the fact that for all x_18, if x_18 were a bartender, then x_18 is drinking water, that there is at least one x_18 for which if x_18 sleeps, then x_18 is drinking water, and that for all x_18, x_18 is a bartender or x_18 will sleep we can infer that there is at least one x_18 for which x_18 will drink water via existential disjunction elimination. From the fact that for all x_18, if x_18 were a writer, then x_18 is not drinking water, and that there is at least one x_18 for which x_18 will drink water we can infer that there is at least one x_18 for which x_18 is not a writer via existential modus tollens. Finally, from the fact that for all x_18, x_18 is an astronaut if and only if x_18 is a writer, and that there is at least one x_18 for which x_18 is not a writer we can infer that there is at least one x_18 for which x_18 is not an astronaut via existential biconditional elimination. Therefore, the answer is yes.