Consider the following premises. For all x_10, x_10 is a carpenter. For all x_1, if x_1 writes a letter, then x_1 is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will write a letter.
 From the fact that for all x_10, x_10 is a carpenter we can infer that Linda is a carpenter via universal instantiation. From the fact that Linda is a carpenter we can infer that there is at least one x_1 for which x_1 is a carpenter via existential generalization. Finally, from the fact that for all x_1, if x_1 writes a letter, then x_1 is not a carpenter, and that there is at least one x_1 for which x_1 is a carpenter we can infer that there is at least one x_1 for which x_1 will not write a letter via existential modus tollens, which contradicts that For all x_1, x_1 will write a letter. Therefore, the answer is no.