Consider the following premises. For all x_6, if x_6 were a soldier, then x_6 is running. For all x_6, x_6 is not a writer. For all x_6, x_6 is a writer or x_6 is a soldier. Can we infer the following from them? Barbara is running.
 From the fact that for all x_6, x_6 is a writer or x_6 is a soldier, and that for all x_6, x_6 is not a writer we can infer that for all x_6, x_6 is a soldier. From the fact that for all x_6, if x_6 were a soldier, then x_6 is running, and that for all x_6, x_6 is a soldier we can infer that for all x_6, x_6 will go running. Finally, from the fact that for all x_6, x_6 will go running we can infer that Barbara is running. Therefore, the answer is yes.