Consider the following premises. For all x_13, if x_13 were a poet, then x_13 is cooking. For all x_13, if x_13 cooks, then x_13 is a poet. For all x_13, x_13 is not a poet. For all x_13, x_13 will cook or x_13 will go running. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 will go running or x_13 will play tennis.
 From the fact that for all x_13, if x_13 were a poet, then x_13 is cooking, and that for all x_13, if x_13 cooks, then x_13 is a poet we can infer that for all x_13, x_13 is a poet if and only if x_13 will cook via universal biconditional introduction. From the fact that for all x_13, x_13 is a poet if and only if x_13 will cook we can infer that for all x_13, if x_13 cooks, then x_13 is a poet via universal biconditional elimination. From the fact that for all x_13, if x_13 cooks, then x_13 is a poet, and that for all x_13, x_13 is not a poet we can infer that for all x_13, x_13 will not cook via universal modus tollens. From the fact that for all x_13, x_13 will cook or x_13 will go running, and that for all x_13, x_13 will not cook we can infer that for all x_13, x_13 will go running via universal disjunctive syllogism. Finally, from the fact that for all x_13, x_13 will go running we can infer that for all x_13, x_13 will go running or x_13 will play tennis via universal addition. Therefore, the answer is yes.