Consider the following premises. For all x_12, x_12 is not a lawyer. For all x_12, x_12 is a lawyer or x_12 will read a book. For all x_12, if x_12 were a taxi driver, then x_12 is an astronaut. For all x_12, x_12 will read a book if and only if x_12 will take a plane. For all x_12, if x_12 takes a plane, then x_12 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 is not an astronaut.
 From the fact that for all x_12, x_12 is a lawyer or x_12 will read a book, and that for all x_12, x_12 is not a lawyer we can infer that for all x_12, x_12 will read a book via universal disjunctive syllogism. From the fact that for all x_12, x_12 will read a book we can infer that for all x_12, x_12 will read a book or x_12 is a taxi driver via universal addition. From the fact that for all x_12, x_12 will read a book if and only if x_12 will take a plane we can infer that for all x_12, if x_12 reads a book, then x_12 is taking a plane via universal biconditional elimination. From the fact that for all x_12, if x_12 reads a book, then x_12 is taking a plane, and that for all x_12, if x_12 takes a plane, then x_12 is an astronaut we can infer that for all x_12, if x_12 reads a book, then x_12 is an astronaut via universal transitivity. Finally, from the fact that for all x_12, if x_12 reads a book, then x_12 is an astronaut, that for all x_12, if x_12 were a taxi driver, then x_12 is an astronaut, and that for all x_12, x_12 will read a book or x_12 is a taxi driver we can infer that for all x_12, x_12 is an astronaut via universal disjunction elimination, which contradicts that There is at least one x_12 for which x_12 is not an astronaut. Therefore, the answer is no.