Consider the following premises. For all x_12, x_12 will listen to a song. For all x_12, x_12 will cook if and only if x_12 is a carpenter. There is at least one x_12 for which if x_12 were a carpenter, then x_12 is not listening to a song. For all x_12, if x_12 were a carpenter, then x_12 is cooking. Can we infer the following from them? For all x_12, x_12 will cook.
 From the fact that for all x_12, x_12 will cook if and only if x_12 is a carpenter we can infer that for all x_12, if x_12 cooks, then x_12 is a carpenter. From the fact that there is at least one x_12 for which if x_12 were a carpenter, then x_12 is not listening to a song, and that for all x_12, x_12 will listen to a song we can infer that there is at least one x_12 for which x_12 is not a carpenter. From the fact that for all x_12, if x_12 cooks, then x_12 is a carpenter, and that for all x_12, if x_12 were a carpenter, then x_12 is cooking we can infer that for all x_12, x_12 will cook if and only if x_12 is a carpenter. Finally, from the fact that for all x_12, x_12 will cook if and only if x_12 is a carpenter, and that there is at least one x_12 for which x_12 is not a carpenter we can infer that there is at least one x_12 for which x_12 will not cook, which contradicts that For all x_12, x_12 will cook. Therefore, the answer is no.