Consider the following premises. For all x_12, if x_12 plays tennis, then x_12 is not cooking. For all x_12, x_12 is poor or x_12 will cook. For all x_12, if x_12 were poor, then x_12 is an electrician. For all x_12, x_12 is not excited. For all x_12, x_12 is an electrician if and only if x_12 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will play tennis.
 From the fact that for all x_12, x_12 is an electrician if and only if x_12 is excited, and that for all x_12, x_12 is not excited we can infer that for all x_12, x_12 is not an electrician via universal biconditional elimination. From the fact that for all x_12, if x_12 were poor, then x_12 is an electrician, and that for all x_12, x_12 is not an electrician we can infer that for all x_12, x_12 is not poor via universal modus tollens. From the fact that for all x_12, x_12 is poor or x_12 will cook, and that for all x_12, x_12 is not poor we can infer that for all x_12, x_12 will cook via universal disjunctive syllogism. Finally, from the fact that for all x_12, if x_12 plays tennis, then x_12 is not cooking, and that for all x_12, x_12 will cook we can infer that for all x_12, x_12 will not play tennis via universal modus tollens, which contradicts that There is at least one x_12 for which x_12 will play tennis. Therefore, the answer is no.