Consider the following premises. For all x_6, x_6 will climb a mountain if and only if x_6 is a writer. For all x_6, x_6 is a writer or x_6 is not a taxi driver. 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 were a taxi driver does not imply that x_6 is climbing a mountain.
 From the fact that for all x_6, x_6 is a writer or x_6 is not a taxi driver we can infer that for all x_6, if x_6 were a taxi driver, then x_6 is a writer via universal rewriting. From the fact that for all x_6, x_6 will climb a mountain if and only if x_6 is a writer we can infer that for all x_6, if x_6 were a writer, 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 taxi driver, then x_6 is a writer, and that for all x_6, if x_6 were a writer, then x_6 is climbing a mountain we can infer that for all x_6, if x_6 were a taxi driver, then x_6 is climbing a mountain via universal transitivity, which contradicts that There is at least one x_6 for which the fact that x_6 were a taxi driver does not imply that x_6 is climbing a mountain. Therefore, the answer is no.