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