Consider the following premises. For all x_5, if x_5 climbs a mountain, then x_5 is driving a car. There is at least one x_5 for which x_5 is excited. For all x_5, if x_5 reads a book, then x_5 is a police officer. For all x_5, x_5 will read a book or x_5 will climb a mountain. For all x_5, if x_5 were a police officer, then x_5 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, either x_5 will drive a car or x_5 is excited are not true.
 From the fact that for all x_5, if x_5 reads a book, then x_5 is a police officer, and that for all x_5, if x_5 were a police officer, then x_5 is driving a car we can infer that for all x_5, if x_5 reads a book, then x_5 is driving a car via universal transitivity. From the fact that for all x_5, if x_5 reads a book, then x_5 is driving a car, that for all x_5, if x_5 climbs a mountain, then x_5 is driving a car, and that for all x_5, x_5 will read a book or x_5 will climb a mountain we can infer that for all x_5, x_5 will drive a car via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 will drive a car, and that there is at least one x_5 for which x_5 is excited we can infer that there is at least one x_5 for which x_5 will drive a car and x_5 is excited via existential conjunction, which contradicts that For all x_5, either x_5 will drive a car or x_5 is excited are not true. Therefore, the answer is no.