Consider the following premises. For all x_6, if x_6 goes running, then x_6 is a taxi driver. For all x_6, if x_6 were a taxi driver, then x_6 is a soldier. For all x_6, if x_6 sleeps, then x_6 is a cashier. There is at least one x_6 for which if x_6 were a cashier, then x_6 is running. Can we infer the following from them? For all x_6, if x_6 were a taxi driver, then x_6 is a soldier.
That is one of the premises. Therefore, the answer is yes.