Consider the following premises. For all x_14, x_14 will work or x_14 is a poet. For all x_14, x_14 is fast or x_14 is not a taxi driver. For all x_14, if x_14 climbs a mountain, then x_14 is writing a letter. For all x_14, x_14 will climb a mountain. For all x_14, x_14 will not work or x_14 is a taxi driver. For all x_14, if x_14 were a poet, then x_14 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 will write a letter and x_14 is fast.
 From the fact that for all x_14, x_14 will work or x_14 is a poet, and that for all x_14, x_14 will not work or x_14 is a taxi driver we can infer that for all x_14, x_14 is a poet or x_14 is a taxi driver via universal resolution. From the fact that for all x_14, x_14 is fast or x_14 is not a taxi driver we can infer that for all x_14, if x_14 were a taxi driver, then x_14 is fast via universal rewriting. From the fact that for all x_14, if x_14 were a poet, then x_14 is fast, that for all x_14, if x_14 were a taxi driver, then x_14 is fast, and that for all x_14, x_14 is a poet or x_14 is a taxi driver we can infer that for all x_14, x_14 is fast via universal disjunction elimination. From the fact that for all x_14, if x_14 climbs a mountain, then x_14 is writing a letter, and that for all x_14, x_14 will climb a mountain we can infer that for all x_14, x_14 will write a letter via universal modus ponens. Finally, from the fact that for all x_14, x_14 will write a letter, and that for all x_14, x_14 is fast we can infer that for all x_14, x_14 will write a letter and x_14 is fast via universal conjunction. Therefore, the answer is yes.