Consider the following premises. There is at least one x_9 for which if x_9 cooks, then x_9 is a soldier. For all x_9, if x_9 cooks, then x_9 is a soldier. For all x_9, x_9 will cook or x_9 is not a soldier. Can we infer the following from them? For all x_9, the fact that x_9 were a soldier does not imply that x_9 is cooking.
That contradicts the premises. Therefore the answer is no.