Consider the following premises. For all x_5, if x_5 drives a car, then x_5 is an office clerk. For all x_5, if x_5 climbs a mountain, then x_5 is a lawyer. For all x_5, x_5 will climb a mountain or x_5 will drive a car. For all x_5, if x_5 were an office clerk, then x_5 is a lawyer. For all x_5, x_5 will drink water. 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 is a lawyer or x_5 will drink water are not true.
 From the fact that for all x_5, if x_5 drives a car, then x_5 is an office clerk, and that for all x_5, if x_5 were an office clerk, then x_5 is a lawyer we can infer that for all x_5, if x_5 drives a car, then x_5 is a lawyer via universal transitivity. From the fact that for all x_5, if x_5 climbs a mountain, then x_5 is a lawyer, that for all x_5, if x_5 drives a car, then x_5 is a lawyer, and that for all x_5, x_5 will climb a mountain or x_5 will drive a car we can infer that for all x_5, x_5 is a lawyer via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 is a lawyer, and that for all x_5, x_5 will drink water we can infer that for all x_5, x_5 is a lawyer and x_5 will drink water via universal conjunction, which contradicts that There is at least one x_5 for which either x_5 is a lawyer or x_5 will drink water are not true. Therefore, the answer is no.