Consider the following premises. Thomas is not cooking. If it is late, then Thomas is running. For all z_3, z_3 will go running if and only if z_3 will cook. Can we infer the following from them? It is not late.
 From the fact that for all z_3, z_3 will go running if and only if z_3 will cook we can infer that Thomas is running if and only if Thomas is cooking. From the fact that Thomas is running if and only if Thomas is cooking, and that Thomas is not cooking we can infer that Thomas is not running. Finally, from the fact that if it is late, then Thomas is running, and that Thomas is not running we can infer that it is not late. Therefore, the answer is yes.