Consider the following premises. For all x_6, x_6 is a server if and only if x_6 will climb a mountain. For all x_6, x_6 is a server or x_6 will not climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which if is not true that x_6 is a server if and only if x_6 will climb a mountain.
 From the fact that for all x_6, x_6 is a server or x_6 will not climb a mountain we can infer that for all x_6, if x_6 climbs a mountain, then x_6 is a server via universal rewriting. From the fact that for all x_6, x_6 is a server if and only if x_6 will climb a mountain we can infer that for all x_6, if x_6 were a server, then x_6 is climbing a mountain via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 were a server, then x_6 is climbing a mountain, and that for all x_6, if x_6 climbs a mountain, then x_6 is a server we can infer that for all x_6, x_6 is a server if and only if x_6 will climb a mountain via universal biconditional introduction, which contradicts that There is at least one x_6 for which if is not true that x_6 is a server if and only if x_6 will climb a mountain. Therefore, the answer is no.