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