Consider the following premises. For all x_6, x_6 is a janitor. For all x_6, x_6 is sad or x_6 is not a janitor. There is at least one x_6 for which if x_6 plays squash, then x_6 is not sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will play squash.
 From the fact that for all x_6, x_6 is sad or x_6 is not a janitor we can infer that for all x_6, if x_6 were a janitor, then x_6 is sad via universal rewriting. From the fact that for all x_6, if x_6 were a janitor, then x_6 is sad, and that for all x_6, x_6 is a janitor we can infer that for all x_6, x_6 is sad via universal modus ponens. Finally, from the fact that there is at least one x_6 for which if x_6 plays squash, then x_6 is not sad, and that for all x_6, x_6 is sad we can infer that there is at least one x_6 for which x_6 will not play squash via existential modus tollens, which contradicts that For all x_6, x_6 will play squash. Therefore, the answer is no.