Consider the following premises. For all x_6, x_6 will read a book. There is at least one x_6 for which if x_6 were a lawyer, then x_6 is a carpenter. For all x_6, x_6 is a lawyer or x_6 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not a carpenter.
 From the fact that for all x_6, x_6 is a lawyer or x_6 will not read a book we can infer that for all x_6, if x_6 reads a book, then x_6 is a lawyer via universal rewriting. From the fact that for all x_6, if x_6 reads a book, then x_6 is a lawyer, and that for all x_6, x_6 will read a book we can infer that for all x_6, x_6 is a lawyer via universal modus ponens. Finally, from the fact that there is at least one x_6 for which if x_6 were a lawyer, then x_6 is a carpenter, and that for all x_6, x_6 is a lawyer we can infer that there is at least one x_6 for which x_6 is a carpenter via existential modus ponens, which contradicts that For all x_6, x_6 is not a carpenter. Therefore, the answer is no.