Consider the following premises. For all x_12, if x_12 plays squash, then x_12 is listening to a song. For all x_12, x_12 is a carpenter. For all x_12, x_12 will listen to a song if and only if x_12 will play squash. There is at least one x_12 for which if x_12 plays squash, then x_12 is not a carpenter. Can we infer the following from them? There is at least one x_12 for which x_12 will not listen to a song.
 From the fact that for all x_12, x_12 will listen to a song if and only if x_12 will play squash we can infer that for all x_12, if x_12 listens to a song, then x_12 is playing squash. From the fact that there is at least one x_12 for which if x_12 plays squash, then x_12 is not a carpenter, and that for all x_12, x_12 is a carpenter we can infer that there is at least one x_12 for which x_12 will not play squash. From the fact that for all x_12, if x_12 listens to a song, then x_12 is playing squash, and that for all x_12, if x_12 plays squash, then x_12 is listening to a song we can infer that for all x_12, x_12 will listen to a song if and only if x_12 will play squash. Finally, from the fact that for all x_12, x_12 will listen to a song if and only if x_12 will play squash, and that there is at least one x_12 for which x_12 will not play squash we can infer that there is at least one x_12 for which x_12 will not listen to a song. Therefore, the answer is yes.