Consider the following premises. There is at least one x_4 for which x_4 will play a game. For all x_4, if x_4 were a taxi driver, then x_4 is listening to a song. For all x_4, if x_4 listens to a song, then x_4 is not playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is a taxi driver.
 From the fact that for all x_4, if x_4 listens to a song, then x_4 is not playing a game, and that there is at least one x_4 for which x_4 will play a game we can infer that there is at least one x_4 for which x_4 will not listen to a song via existential modus tollens. Finally, from the fact that for all x_4, if x_4 were a taxi driver, then x_4 is listening to a song, and that there is at least one x_4 for which x_4 will not listen to a song we can infer that there is at least one x_4 for which x_4 is not a taxi driver via existential modus tollens, which contradicts that For all x_4, x_4 is a taxi driver. Therefore, the answer is no.