Consider the following premises. For all x_6, x_6 will not work. There is at least one x_6 for which if x_6 works, then x_6 is climbing a mountain. For all x_6, x_6 will work if and only if x_6 will climb a mountain. Can we infer the following from them? For all x_6, x_6 will climb a mountain.
 From the fact that for all x_6, x_6 will work if and only if x_6 will climb a mountain we can infer that for all x_6, if x_6 climbs a mountain, then x_6 is working. From the fact that for all x_6, if x_6 climbs a mountain, then x_6 is working, and that there is at least one x_6 for which if x_6 works, then x_6 is climbing a mountain we can infer that there is at least one x_6 for which x_6 will climb a mountain if and only if x_6 will work. Finally, from the fact that there is at least one x_6 for which x_6 will climb a mountain if and only if x_6 will work, and that for all x_6, x_6 will not work we can infer that there is at least one x_6 for which x_6 will not climb a mountain, which contradicts that For all x_6, x_6 will climb a mountain. Therefore, the answer is no.