Consider the following premises. For all x_6, if x_6 listens to a song, then x_6 is an office clerk. For all x_6, if x_6 were bored, then x_6 is listening to a song. Barbara is bored. Can we infer the following from them? If we can, name the inference rule being used: Barbara is an office clerk.
 From the fact that for all x_6, if x_6 were bored, then x_6 is listening to a song, and that for all x_6, if x_6 listens to a song, then x_6 is an office clerk we can infer that for all x_6, if x_6 were bored, then x_6 is an office clerk via universal transitivity. From the fact that for all x_6, if x_6 were bored, then x_6 is an office clerk we can infer that if Barbara were bored, then Barbara is an office clerk via universal instantiation. Finally, from the fact that if Barbara were bored, then Barbara is an office clerk, and that Barbara is bored we can infer that Barbara is an office clerk via modus ponens. Therefore, the answer is yes.