Consider the following premises. For all x_5, if x_5 were a soldier, then x_5 is a poet. For all x_5, x_5 will go running. For all x_5, if x_5 were a poet, then x_5 is not running. There is at least one x_5 for which if x_5 were a poet, then x_5 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a soldier.
 From the fact that there is at least one x_5 for which if x_5 were a poet, then x_5 is a soldier, and that for all x_5, if x_5 were a soldier, then x_5 is a poet we can infer that there is at least one x_5 for which x_5 is a poet if and only if x_5 is a soldier via existential biconditional introduction. From the fact that for all x_5, if x_5 were a poet, then x_5 is not running, and that for all x_5, x_5 will go running we can infer that for all x_5, x_5 is not a poet via universal modus tollens. Finally, from the fact that there is at least one x_5 for which x_5 is a poet if and only if x_5 is a soldier, and that for all x_5, x_5 is not a poet we can infer that there is at least one x_5 for which x_5 is not a soldier via existential biconditional elimination, which contradicts that For all x_5, x_5 is a soldier. Therefore, the answer is no.