Consider the following premises. For all x_6, if x_6 were a server, then x_6 is taking a plane. For all x_6, if x_6 climbs a mountain, then x_6 is a server. For all x_6, x_6 will climb a mountain or x_6 will not take a plane. 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 the fact that x_6 climbs a mountain does not imply that x_6 is taking a plane.
 From the fact that for all x_6, if x_6 climbs a mountain, then x_6 is a server, and that for all x_6, if x_6 were a server, then x_6 is taking a plane we can infer that for all x_6, if x_6 climbs a mountain, then x_6 is taking a plane via universal transitivity. From the fact that for all x_6, x_6 will climb a mountain or x_6 will not take a plane we can infer that for all x_6, if x_6 takes a plane, then x_6 is climbing a mountain via universal rewriting. From the fact that for all x_6, if x_6 climbs a mountain, then x_6 is taking a plane, and that for all x_6, if x_6 takes a plane, then x_6 is climbing a mountain we can infer that for all x_6, x_6 will climb a mountain if and only if x_6 will take a plane via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 will climb a mountain if and only if x_6 will take a plane we can infer that for all x_6, if x_6 climbs a mountain, then x_6 is taking a plane via universal biconditional elimination, which contradicts that There is at least one x_6 for which the fact that x_6 climbs a mountain does not imply that x_6 is taking a plane. Therefore, the answer is no.