Consider the following premises. For all x_16, if x_16 sleeps, then x_16 is playing squash. For all x_16, if x_16 were bored, then x_16 is a writer. For all x_16, x_16 is bored if and only if x_16 will play squash. For all x_16, if x_16 were an artist, then x_16 is sleeping. For all x_16, x_16 is not a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 is not an artist.
 From the fact that for all x_16, x_16 is bored if and only if x_16 will play squash we can infer that for all x_16, if x_16 plays squash, then x_16 is bored via universal biconditional elimination. From the fact that for all x_16, if x_16 were bored, then x_16 is a writer, and that for all x_16, x_16 is not a writer we can infer that for all x_16, x_16 is not bored via universal modus tollens. From the fact that for all x_16, if x_16 sleeps, then x_16 is playing squash, and that for all x_16, if x_16 plays squash, then x_16 is bored we can infer that for all x_16, if x_16 sleeps, then x_16 is bored via universal transitivity. From the fact that for all x_16, if x_16 sleeps, then x_16 is bored, and that for all x_16, x_16 is not bored we can infer that for all x_16, x_16 will not sleep via universal modus tollens. Finally, from the fact that for all x_16, if x_16 were an artist, then x_16 is sleeping, and that for all x_16, x_16 will not sleep we can infer that for all x_16, x_16 is not an artist via universal modus tollens. Therefore, the answer is yes.