Consider the following premises. For all x_5, x_5 will climb a mountain if and only if x_5 will drive a car. There is at least one x_5 for which x_5 will drive a car. For all x_5, if x_5 reads a book, then x_5 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not climb a mountain.
 From the fact that there is at least one x_5 for which x_5 will drive a car we can infer that there is at least one x_5 for which x_5 will drive a car or x_5 will read a book via existential addition. From the fact that for all x_5, x_5 will climb a mountain if and only if x_5 will drive a car we can infer that for all x_5, if x_5 drives a car, then x_5 is climbing a mountain via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 drives a car, then x_5 is climbing a mountain, that for all x_5, if x_5 reads a book, then x_5 is climbing a mountain, and that there is at least one x_5 for which x_5 will drive a car or x_5 will read a book we can infer that there is at least one x_5 for which x_5 will climb a mountain via existential disjunction elimination, which contradicts that For all x_5, x_5 will not climb a mountain. Therefore, the answer is no.