Consider the following premises. If it is late, then Barbara is not writing a letter. For all x_9, x_9 will write a letter. Can we infer the following from them? It is late.
 From the fact that for all x_9, x_9 will write a letter we can infer that Barbara is writing a letter. Finally, from the fact that if it is late, then Barbara is not writing a letter, and that Barbara is writing a letter we can infer that it is not late, which contradicts that It is late. Therefore, the answer is no.