Consider the following premises. For all x_7, x_7 will read a book or x_7 will drive a car. There is at least one x_7 for which if x_7 listens to a song, then x_7 is playing tennis. For all x_7, if x_7 drives a car, then x_7 is listening to a song. For all x_7, x_7 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not play tennis.
 From the fact that for all x_7, x_7 will read a book or x_7 will drive a car, and that for all x_7, x_7 will not read a book we can infer that for all x_7, x_7 will drive a car via universal disjunctive syllogism. From the fact that for all x_7, if x_7 drives a car, then x_7 is listening to a song, and that there is at least one x_7 for which if x_7 listens to a song, then x_7 is playing tennis we can infer that there is at least one x_7 for which if x_7 drives a car, then x_7 is playing tennis via existential transitivity. Finally, from the fact that there is at least one x_7 for which if x_7 drives a car, then x_7 is playing tennis, and that for all x_7, x_7 will drive a car we can infer that there is at least one x_7 for which x_7 will play tennis via existential modus ponens, which contradicts that For all x_7, x_7 will not play tennis. Therefore, the answer is no.