Consider the following premises. For all x_7, x_7 will go running. Patricia is a doctor if and only if Richard is cooking. For all x_7, if x_7 cooks, then x_7 is not running. Can we infer the following from them? Patricia is a doctor.
 From the fact that for all x_7, if x_7 cooks, then x_7 is not running, and that for all x_7, x_7 will go running we can infer that for all x_7, x_7 will not cook. From the fact that for all x_7, x_7 will not cook we can infer that Richard is not cooking. Finally, from the fact that Patricia is a doctor if and only if Richard is cooking, and that Richard is not cooking we can infer that Patricia is not a doctor, which contradicts that Patricia is a doctor. Therefore, the answer is no.