Consider the following premises. For all x_11, x_11 will climb a mountain or x_11 will work. There is at least one x_11 for which if x_11 climbs a mountain, then x_11 is not sleeping. For all x_11, x_11 will sleep and x_11 will write a letter. Can we infer the following from them? There is at least one x_11 for which x_11 will work.
 From the fact that for all x_11, x_11 will sleep and x_11 will write a letter we can infer that for all x_11, x_11 will sleep. From the fact that there is at least one x_11 for which if x_11 climbs a mountain, then x_11 is not sleeping, and that for all x_11, x_11 will sleep we can infer that there is at least one x_11 for which x_11 will not climb a mountain. Finally, from the fact that for all x_11, x_11 will climb a mountain or x_11 will work, and that there is at least one x_11 for which x_11 will not climb a mountain we can infer that there is at least one x_11 for which x_11 will work. Therefore, the answer is yes.