Consider the following premises. There is at least one x_12 for which x_12 is not a poet or x_12 will cook. For all x_12, x_12 is a poet or x_12 is excited. For all x_12, if x_12 cooks, then x_12 is a doctor. For all x_12, x_12 is a doctor or x_12 is not excited. For all x_12, if x_12 were a doctor, then x_12 is cooking. Can we infer the following from them? There is at least one x_12 for which x_12 is a doctor.
 From the fact that for all x_12, if x_12 cooks, then x_12 is a doctor, and that for all x_12, if x_12 were a doctor, 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 doctor. From the fact that for all x_12, x_12 is a doctor or x_12 is not excited we can infer that for all x_12, if x_12 were excited, then x_12 is a doctor. From the fact that for all x_12, x_12 is a poet or x_12 is excited, and that there is at least one x_12 for which x_12 is not a poet or x_12 will cook we can infer that there is at least one x_12 for which x_12 is excited or x_12 will cook. From the fact that for all x_12, x_12 will cook if and only if x_12 is a doctor we can infer that for all x_12, if x_12 cooks, then x_12 is a doctor. Finally, from the fact that for all x_12, if x_12 were excited, then x_12 is a doctor, that for all x_12, if x_12 cooks, then x_12 is a doctor, and that there is at least one x_12 for which x_12 is excited or x_12 will cook we can infer that there is at least one x_12 for which x_12 is a doctor. Therefore, the answer is yes.