Consider the following premises. For all x_6, if x_6 were bored, then x_6 is curious. For all x_6, x_6 is curious or x_6 will not sleep. For all x_6, x_6 will sleep or x_6 is bored. There is at least one x_6 for which if x_6 were curious, then x_6 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will play tennis.
 From the fact that for all x_6, x_6 is curious or x_6 will not sleep we can infer that for all x_6, if x_6 sleeps, then x_6 is curious via universal rewriting. From the fact that for all x_6, if x_6 sleeps, then x_6 is curious, that for all x_6, if x_6 were bored, then x_6 is curious, and that for all x_6, x_6 will sleep or x_6 is bored we can infer that for all x_6, x_6 is curious via universal disjunction elimination. Finally, from the fact that there is at least one x_6 for which if x_6 were curious, then x_6 is playing tennis, and that for all x_6, x_6 is curious we can infer that there is at least one x_6 for which x_6 will play tennis via existential modus ponens. Therefore, the answer is yes.