Consider the following premises. For all y, y will not go running. There is at least one y for which if y were a poet, then y is working. For all y, if y works, then y is a poet. For all y, if y were a poet, then y is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will not work.
 From the fact that for all y, if y were a poet, then y is running, and that for all y, y will not go running we can infer that for all y, y is not a poet via universal modus tollens. From the fact that for all y, if y works, then y is a poet, and that there is at least one y for which if y were a poet, then y is working we can infer that there is at least one y for which y will work if and only if y is a poet via existential biconditional introduction. From the fact that there is at least one y for which y will work if and only if y is a poet we can infer that there is at least one y for which if y works, then y is a poet via existential biconditional elimination. Finally, from the fact that there is at least one y for which if y works, then y is a poet, and that for all y, y is not a poet we can infer that there is at least one y for which y will not work via existential modus tollens. Therefore, the answer is yes.