Consider the following premises. For all x_4, if x_4 were a doctor, then x_4 is a lawyer. There is at least one x_4 for which if x_4 takes a plane, then x_4 is a doctor. For all x_4, x_4 is not a lawyer. For all x_4, if x_4 were a lawyer, then x_4 is taking a plane. Can we infer the following from them? There is at least one x_4 for which x_4 is not a doctor.
 From the fact that for all x_4, if x_4 were a lawyer, then x_4 is taking a plane, and that there is at least one x_4 for which if x_4 takes a plane, then x_4 is a doctor we can infer that there is at least one x_4 for which if x_4 were a lawyer, then x_4 is a doctor. From the fact that for all x_4, if x_4 were a doctor, then x_4 is a lawyer, and that there is at least one x_4 for which if x_4 were a lawyer, then x_4 is a doctor we can infer that there is at least one x_4 for which x_4 is a doctor if and only if x_4 is a lawyer. Finally, from the fact that there is at least one x_4 for which x_4 is a doctor if and only if x_4 is a lawyer, and that for all x_4, x_4 is not a lawyer we can infer that there is at least one x_4 for which x_4 is not a doctor. Therefore, the answer is yes.