Consider the following premises. For all x_5, x_5 will climb a mountain or x_5 will sleep. For all x_5, x_5 is a taxi driver. For all x_5, if x_5 were a taxi driver, then x_5 is driving a car. For all x_5, x_5 will not climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which either x_5 will drive a car or x_5 will sleep are not true.
 From the fact that for all x_5, if x_5 were a taxi driver, then x_5 is driving a car, and that for all x_5, x_5 is a taxi driver we can infer that for all x_5, x_5 will drive a car via universal modus ponens. From the fact that for all x_5, x_5 will climb a mountain or x_5 will sleep, and that for all x_5, x_5 will not climb a mountain we can infer that for all x_5, x_5 will sleep via universal disjunctive syllogism. Finally, from the fact that for all x_5, x_5 will drive a car, and that for all x_5, x_5 will sleep we can infer that for all x_5, x_5 will drive a car and x_5 will sleep via universal conjunction, which contradicts that There is at least one x_5 for which either x_5 will drive a car or x_5 will sleep are not true. Therefore, the answer is no.