Consider the following premises. There is at least one x_4 for which x_4 will not climb a mountain. For all x_4, x_4 will climb a mountain if and only if x_4 is excited. Can we infer the following from them? For all x_4, x_4 is excited.
 From the fact that for all x_4, x_4 will climb a mountain if and only if x_4 is excited we can infer that for all x_4, if x_4 were excited, then x_4 is climbing a mountain. Finally, from the fact that for all x_4, if x_4 were excited, then x_4 is climbing a mountain, and that there is at least one x_4 for which x_4 will not climb a mountain we can infer that there is at least one x_4 for which x_4 is not excited, which contradicts that For all x_4, x_4 is excited. Therefore, the answer is no.