Consider the following premises. For all x_13, x_13 is sad if and only if x_13 will play tennis. For all x_13, if x_13 were a writer, then x_13 is climbing a mountain. For all x_13, if x_13 climbs a mountain, then x_13 is playing tennis. For all x_13, x_13 is not poor or x_13 is a writer. For all x_13, x_13 is poor or x_13 is an artist. For all x_13, if x_13 were an artist, then x_13 is sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 will play tennis.
 From the fact that for all x_13, x_13 is sad if and only if x_13 will play tennis we can infer that for all x_13, if x_13 were sad, then x_13 is playing tennis via universal biconditional elimination. From the fact that for all x_13, if x_13 were a writer, then x_13 is climbing a mountain, and that for all x_13, if x_13 climbs a mountain, then x_13 is playing tennis we can infer that for all x_13, if x_13 were a writer, then x_13 is playing tennis via universal transitivity. From the fact that for all x_13, x_13 is poor or x_13 is an artist, and that for all x_13, x_13 is not poor or x_13 is a writer we can infer that for all x_13, x_13 is an artist or x_13 is a writer via universal resolution. From the fact that for all x_13, if x_13 were an artist, then x_13 is sad, and that for all x_13, if x_13 were sad, then x_13 is playing tennis we can infer that for all x_13, if x_13 were an artist, then x_13 is playing tennis via universal transitivity. Finally, from the fact that for all x_13, if x_13 were an artist, then x_13 is playing tennis, that for all x_13, if x_13 were a writer, then x_13 is playing tennis, and that for all x_13, x_13 is an artist or x_13 is a writer we can infer that for all x_13, x_13 will play tennis via universal disjunction elimination. Therefore, the answer is yes.