Consider the following premises. There is at least one x_6 for which if x_6 were sad, then x_6 is cooking. For all x_6, x_6 will listen to a song or x_6 is a carpenter. For all x_6, x_6 will cook if and only if x_6 will listen to a song. For all x_6, if x_6 were a carpenter, then x_6 is sad. Can we infer the following from them? There is at least one x_6 for which x_6 will cook.
 From the fact that for all x_6, if x_6 were a carpenter, then x_6 is sad, and that there is at least one x_6 for which if x_6 were sad, then x_6 is cooking we can infer that there is at least one x_6 for which if x_6 were a carpenter, then x_6 is cooking. From the fact that for all x_6, x_6 will cook if and only if x_6 will listen to a song we can infer that for all x_6, if x_6 listens to a song, then x_6 is cooking. Finally, from the fact that for all x_6, if x_6 listens to a song, then x_6 is cooking, that there is at least one x_6 for which if x_6 were a carpenter, then x_6 is cooking, and that for all x_6, x_6 will listen to a song or x_6 is a carpenter we can infer that there is at least one x_6 for which x_6 will cook. Therefore, the answer is yes.