Consider the following premises. There is at least one x_10 for which x_10 will sleep. For all x_10, if x_10 plays a game, then x_10 is an artist. For all x_10, if x_10 sleeps, then x_10 is an artist. For all x_10, if x_10 were an artist, then x_10 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not play squash.
 From the fact that there is at least one x_10 for which x_10 will sleep we can infer that there is at least one x_10 for which x_10 will sleep or x_10 will play a game via existential addition. From the fact that for all x_10, if x_10 sleeps, then x_10 is an artist, that for all x_10, if x_10 plays a game, then x_10 is an artist, and that there is at least one x_10 for which x_10 will sleep or x_10 will play a game we can infer that there is at least one x_10 for which x_10 is an artist via existential disjunction elimination. Finally, from the fact that for all x_10, if x_10 were an artist, then x_10 is playing squash, and that there is at least one x_10 for which x_10 is an artist we can infer that there is at least one x_10 for which x_10 will play squash via existential modus ponens, which contradicts that For all x_10, x_10 will not play squash. Therefore, the answer is no.