Consider the following premises. It is late if and only if Joseph is cooking. For all x_6, x_6 is not a nurse. For all x_6, if x_6 cooks, then x_6 is a nurse. Can we infer the following from them? It is late.
 From the fact that for all x_6, if x_6 cooks, then x_6 is a nurse, and that for all x_6, x_6 is not a nurse we can infer that for all x_6, x_6 will not cook. From the fact that for all x_6, x_6 will not cook we can infer that Joseph is not cooking. Finally, from the fact that it is late if and only if Joseph is cooking, and that Joseph is not cooking we can infer that it is not late, which contradicts that It is late. Therefore, the answer is no.