Consider the following premises. For all x_22, if x_22 were a cashier, then x_22 is playing squash. For all x_22, x_22 will cook or x_22 will listen to a song. For all x_22, x_22 will play squash if and only if x_22 is happy. For all x_22, if x_22 listens to a song, then x_22 is a cashier. There is at least one x_22 for which x_22 will not cook. Can we infer the following from them? There is at least one x_22 for which x_22 is happy.
 From the fact that for all x_22, x_22 will cook or x_22 will listen to a song, and that there is at least one x_22 for which x_22 will not cook we can infer that there is at least one x_22 for which x_22 will listen to a song. From the fact that for all x_22, if x_22 listens to a song, then x_22 is a cashier, and that for all x_22, if x_22 were a cashier, then x_22 is playing squash we can infer that for all x_22, if x_22 listens to a song, then x_22 is playing squash. From the fact that for all x_22, x_22 will play squash if and only if x_22 is happy we can infer that for all x_22, if x_22 plays squash, then x_22 is happy. From the fact that for all x_22, if x_22 listens to a song, then x_22 is playing squash, and that there is at least one x_22 for which x_22 will listen to a song we can infer that there is at least one x_22 for which x_22 will play squash. Finally, from the fact that for all x_22, if x_22 plays squash, then x_22 is happy, and that there is at least one x_22 for which x_22 will play squash we can infer that there is at least one x_22 for which x_22 is happy. Therefore, the answer is yes.