Consider the following premises. There is at least one x_11 for which x_11 will not listen to a song. For all x_11, x_11 is bored if and only if x_11 will listen to a song. For all x_11, if x_11 were an office clerk, then x_11 is bored. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is an office clerk.
 From the fact that for all x_11, x_11 is bored if and only if x_11 will listen to a song we can infer that for all x_11, if x_11 were bored, then x_11 is listening to a song via universal biconditional elimination. From the fact that for all x_11, if x_11 were bored, then x_11 is listening to a song, and that there is at least one x_11 for which x_11 will not listen to a song we can infer that there is at least one x_11 for which x_11 is not bored via existential modus tollens. Finally, from the fact that for all x_11, if x_11 were an office clerk, then x_11 is bored, and that there is at least one x_11 for which x_11 is not bored we can infer that there is at least one x_11 for which x_11 is not an office clerk via existential modus tollens, which contradicts that For all x_11, x_11 is an office clerk. Therefore, the answer is no.