Consider the following premises. For all y_4, y_4 will climb a mountain or y_4 is not a server. For all y_4, if y_4 climbs a mountain, then y_4 is a server. There is at least one y_4 for which y_4 will not climb a mountain. Can we infer the following from them? There is at least one y_4 for which y_4 is not a server.
 From the fact that for all y_4, y_4 will climb a mountain or y_4 is not a server we can infer that for all y_4, if y_4 were a server, then y_4 is climbing a mountain. From the fact that for all y_4, if y_4 climbs a mountain, then y_4 is a server, and that for all y_4, if y_4 were a server, then y_4 is climbing a mountain we can infer that for all y_4, y_4 will climb a mountain if and only if y_4 is a server. Finally, from the fact that for all y_4, y_4 will climb a mountain if and only if y_4 is a server, and that there is at least one y_4 for which y_4 will not climb a mountain we can infer that there is at least one y_4 for which y_4 is not a server. Therefore, the answer is yes.