Consider the following premises. For all x_2, if x_2 plays squash, then x_2 is a poet. For all x_2, if x_2 goes running, then x_2 is playing squash. There is at least one x_2 for which if x_2 plays squash, then x_2 is running. For all x_2, x_2 is not a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will go running.
 From the fact that for all x_2, if x_2 plays squash, then x_2 is a poet, and that for all x_2, x_2 is not a poet we can infer that for all x_2, x_2 will not play squash via universal modus tollens. From the fact that for all x_2, if x_2 goes running, then x_2 is playing squash, and that there is at least one x_2 for which if x_2 plays squash, then x_2 is running we can infer that there is at least one x_2 for which x_2 will go running if and only if x_2 will play squash via existential biconditional introduction. Finally, from the fact that there is at least one x_2 for which x_2 will go running if and only if x_2 will play squash, and that for all x_2, x_2 will not play squash we can infer that there is at least one x_2 for which x_2 will not go running via existential biconditional elimination, which contradicts that For all x_2, x_2 will go running. Therefore, the answer is no.