Consider the following premises. For all y_4, y_4 will write a letter or y_4 will not climb a mountain. There is at least one y_4 for which if y_4 were a bartender, then y_4 is an office clerk. For all y_4, if y_4 were an office clerk, then y_4 is climbing a mountain. Can we infer the following from them? For all y_4, the fact that y_4 were a bartender does not imply that y_4 is writing a letter.
That contradicts the premises. Therefore the answer is no.