Consider the following premises. For all x_6, if x_6 makes tea, then x_6 is playing a game. For all x_6, if x_6 were a politician, then x_6 is playing a game. For all x_6, x_6 will not read a book or x_6 will make tea. For all x_6, x_6 will read a book or x_6 is a politician. 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 neither x_6 will play a game nor x_6 will drive a car.
 From the fact that for all x_6, x_6 will read a book or x_6 is a politician, and that for all x_6, x_6 will not read a book or x_6 will make tea we can infer that for all x_6, x_6 is a politician or x_6 will make tea via universal resolution. From the fact that for all x_6, if x_6 were a politician, then x_6 is playing a game, that for all x_6, if x_6 makes tea, then x_6 is playing a game, and that for all x_6, x_6 is a politician or x_6 will make tea we can infer that for all x_6, x_6 will play a game via universal disjunction elimination. Finally, from the fact that for all x_6, x_6 will play a game we can infer that for all x_6, x_6 will play a game or x_6 will drive a car via universal addition, which contradicts that There is at least one x_6 for which neither x_6 will play a game nor x_6 will drive a car. Therefore, the answer is no.