Consider the following premises. There is at least one x for which x will climb a mountain if and only if x is a writer. For all x, x is a writer or x is an astronaut. For all x, if x were an astronaut, then x is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not climb a mountain.
 From the fact that there is at least one x for which x will climb a mountain if and only if x is a writer we can infer that there is at least one x for which if x were a writer, then x is climbing a mountain via existential biconditional elimination. Finally, from the fact that there is at least one x for which if x were a writer, then x is climbing a mountain, that for all x, if x were an astronaut, then x is climbing a mountain, and that for all x, x is a writer or x is an astronaut we can infer that there is at least one x for which x will climb a mountain via existential disjunction elimination, which contradicts that For all x, x will not climb a mountain. Therefore, the answer is no.