Consider the following premises. For all x_8, x_8 is a mechanic if and only if x_8 will go running. For all x_8, x_8 will go running. Can we infer the following from them? There is at least one x_8 for which neither x_8 is a mechanic nor x_8 will cook.
 From the fact that for all x_8, x_8 is a mechanic if and only if x_8 will go running we can infer that for all x_8, if x_8 goes running, then x_8 is a mechanic. From the fact that for all x_8, if x_8 goes running, then x_8 is a mechanic, and that for all x_8, x_8 will go running we can infer that for all x_8, x_8 is a mechanic. Finally, from the fact that for all x_8, x_8 is a mechanic we can infer that for all x_8, x_8 is a mechanic or x_8 will cook, which contradicts that There is at least one x_8 for which neither x_8 is a mechanic nor x_8 will cook. Therefore, the answer is no.