Consider the following premises. For all x_6, if x_6 cooks, then x_6 is working. For all x_6, x_6 will work if and only if x_6 will cook. Can we infer the following from them? If Robert works, then Robert is cooking.
 From the fact that for all x_6, x_6 will work if and only if x_6 will cook we can infer that for all x_6, if x_6 works, then x_6 is cooking. From the fact that for all x_6, if x_6 works, then x_6 is cooking, and that for all x_6, if x_6 cooks, then x_6 is working we can infer that for all x_6, x_6 will work if and only if x_6 will cook. From the fact that for all x_6, x_6 will work if and only if x_6 will cook we can infer that Robert is working if and only if Robert is cooking. Finally, from the fact that Robert is working if and only if Robert is cooking we can infer that if Robert works, then Robert is cooking. Therefore, the answer is yes.