Consider the following premises. For all x_13, if x_13 drives a car, then x_13 is a carpenter. For all x_13, if x_13 were a cashier, then x_13 is a carpenter. For all x_13, x_13 will read a book. For all x_13, x_13 will drink water. For all x_13, x_13 will drive a car or x_13 is a cashier. For all x_13, if x_13 drinks water, then x_13 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which either x_13 is bored or x_13 is a carpenter are not true.
 From the fact that for all x_13, x_13 will drink water, and that for all x_13, x_13 will read a book we can infer that for all x_13, x_13 will drink water and x_13 will read a book via universal conjunction. From the fact that for all x_13, x_13 will drink water and x_13 will read a book we can infer that for all x_13, x_13 will drink water via universal simplification. From the fact that for all x_13, if x_13 drinks water, then x_13 is bored, and that for all x_13, x_13 will drink water we can infer that for all x_13, x_13 is bored via universal modus ponens. From the fact that for all x_13, if x_13 drives a car, then x_13 is a carpenter, that for all x_13, if x_13 were a cashier, then x_13 is a carpenter, and that for all x_13, x_13 will drive a car or x_13 is a cashier we can infer that for all x_13, x_13 is a carpenter via universal disjunction elimination. Finally, from the fact that for all x_13, x_13 is bored, and that for all x_13, x_13 is a carpenter we can infer that for all x_13, x_13 is bored and x_13 is a carpenter via universal conjunction, which contradicts that There is at least one x_13 for which either x_13 is bored or x_13 is a carpenter are not true. Therefore, the answer is no.