Consider the following premises. For all x_13, x_13 is fast if and only if x_13 will listen to a song. There is at least one x_13 for which x_13 is not fast. For all x_13, if x_13 makes tea, then x_13 is listening to a song. For all x_13, if x_13 were fast, then x_13 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which x_13 will not make tea.
 From the fact that for all x_13, x_13 is fast if and only if x_13 will listen to a song we can infer that for all x_13, if x_13 listens to a song, then x_13 is fast via universal biconditional elimination. From the fact that for all x_13, if x_13 were fast, then x_13 is listening to a song, and that for all x_13, if x_13 listens to a song, then x_13 is fast we can infer that for all x_13, x_13 is fast if and only if x_13 will listen to a song via universal biconditional introduction. From the fact that for all x_13, x_13 is fast if and only if x_13 will listen to a song, and that there is at least one x_13 for which x_13 is not fast we can infer that there is at least one x_13 for which x_13 will not listen to a song via existential biconditional elimination. Finally, from the fact that for all x_13, if x_13 makes tea, then x_13 is listening to a song, and that there is at least one x_13 for which x_13 will not listen to a song we can infer that there is at least one x_13 for which x_13 will not make tea via existential modus tollens. Therefore, the answer is yes.