Consider the following premises. For all x_8, x_8 is not happy. For all x_8, x_8 will listen to a song if and only if x_8 is happy. For all x_8, x_8 will cook if and only if x_8 will play squash. For all x_8, x_8 will cook if and only if x_8 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not play squash.
 From the fact that for all x_8, x_8 will listen to a song if and only if x_8 is happy, and that for all x_8, x_8 is not happy we can infer that for all x_8, x_8 will not listen to a song via universal biconditional elimination. From the fact that for all x_8, x_8 will cook if and only if x_8 will listen to a song, and that for all x_8, x_8 will not listen to a song we can infer that for all x_8, x_8 will not cook via universal biconditional elimination. Finally, from the fact that for all x_8, x_8 will cook if and only if x_8 will play squash, and that for all x_8, x_8 will not cook we can infer that for all x_8, x_8 will not play squash via universal biconditional elimination. Therefore, the answer is yes.