Consider the following premises. For all x_7, x_7 is rich or x_7 is an astronaut. For all x_7, x_7 is rich if and only if x_7 will sleep. For all x_7, if x_7 were an astronaut, then x_7 is sleeping. For all x_7, if x_7 sleeps, then x_7 is playing squash. 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 not play squash.
 From the fact that for all x_7, x_7 is rich if and only if x_7 will sleep we can infer that for all x_7, if x_7 were rich, then x_7 is sleeping via universal biconditional elimination. From the fact that for all x_7, if x_7 were rich, then x_7 is sleeping, that for all x_7, if x_7 were an astronaut, then x_7 is sleeping, and that for all x_7, x_7 is rich or x_7 is an astronaut we can infer that for all x_7, x_7 will sleep via universal disjunction elimination. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is playing squash, and that for all x_7, x_7 will sleep we can infer that for all x_7, x_7 will play squash via universal modus ponens, which contradicts that There is at least one x_7 for which x_7 will not play squash. Therefore, the answer is no.