Consider the following premises. For all x_13, x_13 will read a book or x_13 will climb a mountain. For all x_13, if x_13 reads a book, then x_13 is rich. For all x_13, x_13 is rich if and only if x_13 will cook. For all x_13, x_13 is rich or x_13 will not climb a mountain. For all x_13, if x_13 listens to a song, then x_13 is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 will cook.
 From the fact that for all x_13, x_13 is rich if and only if x_13 will cook we can infer that for all x_13, if x_13 were rich, then x_13 is cooking via universal biconditional elimination. From the fact that for all x_13, x_13 is rich or x_13 will not climb a mountain we can infer that for all x_13, if x_13 climbs a mountain, then x_13 is rich via universal rewriting. From the fact that for all x_13, if x_13 reads a book, then x_13 is rich, that for all x_13, if x_13 climbs a mountain, then x_13 is rich, and that for all x_13, x_13 will read a book or x_13 will climb a mountain we can infer that for all x_13, x_13 is rich via universal disjunction elimination. From the fact that for all x_13, x_13 is rich we can infer that for all x_13, x_13 is rich or x_13 will listen to a song via universal addition. Finally, from the fact that for all x_13, if x_13 were rich, then x_13 is cooking, that for all x_13, if x_13 listens to a song, then x_13 is cooking, and that for all x_13, x_13 is rich or x_13 will listen to a song we can infer that for all x_13, x_13 will cook via universal disjunction elimination. Therefore, the answer is yes.