Consider the following premises. There is at least one x_12 for which if x_12 plays a game, then x_12 is poor. For all x_12, if x_12 were poor, then x_12 is playing a game. For all x_12, if x_12 were a poet, then x_12 is poor. For all x_12, if x_12 were poor, then x_12 is a soldier. For all x_12, if x_12 were a soldier, then x_12 is a poet. For all x_12, x_12 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 is a poet.
 From the fact that for all x_12, if x_12 were poor, then x_12 is a soldier, and that for all x_12, if x_12 were a soldier, then x_12 is a poet we can infer that for all x_12, if x_12 were poor, then x_12 is a poet via universal transitivity. From the fact that for all x_12, if x_12 were poor, then x_12 is playing a game, and that there is at least one x_12 for which if x_12 plays a game, then x_12 is poor we can infer that there is at least one x_12 for which x_12 is poor if and only if x_12 will play a game via existential biconditional introduction. From the fact that for all x_12, if x_12 were a poet, then x_12 is poor, and that for all x_12, if x_12 were poor, then x_12 is a poet we can infer that for all x_12, x_12 is a poet if and only if x_12 is poor via universal biconditional introduction. From the fact that there is at least one x_12 for which x_12 is poor if and only if x_12 will play a game, and that for all x_12, x_12 will not play a game we can infer that there is at least one x_12 for which x_12 is not poor via existential biconditional elimination. Finally, from the fact that for all x_12, x_12 is a poet if and only if x_12 is poor, and that there is at least one x_12 for which x_12 is not poor we can infer that there is at least one x_12 for which x_12 is not a poet via existential biconditional elimination, which contradicts that For all x_12, x_12 is a poet. Therefore, the answer is no.