Consider the following premises. There is at least one x_10 for which x_10 will go running if and only if x_10 will cook. For all x_10, if x_10 were a cashier, then x_10 is fast. For all x_10, if x_10 were fast, then x_10 is cooking. Can we infer the following from them? For all x_10, the fact that x_10 were a cashier does not imply that x_10 is running.
That contradicts the premises. Therefore the answer is no.