Consider the following premises. For all y_1, if y_1 were a janitor, then y_1 is taking a plane. For all y_1, y_1 will play squash. For all y_1, y_1 will take a plane if and only if y_1 will play squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which neither y_1 will take a plane nor y_1 will sleep.
 From the fact that for all y_1, y_1 will take a plane if and only if y_1 will play squash we can infer that for all y_1, if y_1 plays squash, then y_1 is taking a plane via universal biconditional elimination. From the fact that for all y_1, y_1 will play squash we can infer that for all y_1, y_1 will play squash or y_1 is a janitor via universal addition. From the fact that for all y_1, if y_1 plays squash, then y_1 is taking a plane, that for all y_1, if y_1 were a janitor, then y_1 is taking a plane, and that for all y_1, y_1 will play squash or y_1 is a janitor we can infer that for all y_1, y_1 will take a plane via universal disjunction elimination. Finally, from the fact that for all y_1, y_1 will take a plane we can infer that for all y_1, y_1 will take a plane or y_1 will sleep via universal addition, which contradicts that There is at least one y_1 for which neither y_1 will take a plane nor y_1 will sleep. Therefore, the answer is no.