Consider the following premises. For all y, if y drives a car, then y is playing tennis. For all y, if y takes a plane, then y is playing tennis. For all y, y is a cashier or y will drive a car. For all y, y is not a cashier or y will take a plane. For all y, y is a politician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which either y will play tennis or y is a politician are not true.
 From the fact that for all y, y is a cashier or y will drive a car, and that for all y, y is not a cashier or y will take a plane we can infer that for all y, y will drive a car or y will take a plane via universal resolution. From the fact that for all y, if y drives a car, then y is playing tennis, that for all y, if y takes a plane, then y is playing tennis, and that for all y, y will drive a car or y will take a plane we can infer that for all y, y will play tennis via universal disjunction elimination. Finally, from the fact that for all y, y will play tennis, and that for all y, y is a politician we can infer that for all y, y will play tennis and y is a politician via universal conjunction, which contradicts that There is at least one y for which either y will play tennis or y is a politician are not true. Therefore, the answer is no.