Consider the following premises. For all x_10, x_10 will not write a letter or x_10 is a sailor. For all x_10, x_10 is a writer if and only if x_10 will go running. For all x_10, x_10 will not go running. For all x_10, x_10 will write a letter or x_10 is a writer. Can we infer the following from them? If we can, name the inference rule being used: Mary is not a sailor.
 From the fact that for all x_10, x_10 is a writer if and only if x_10 will go running, and that for all x_10, x_10 will not go running we can infer that for all x_10, x_10 is not a writer via universal biconditional elimination. From the fact that for all x_10, x_10 will write a letter or x_10 is a writer, and that for all x_10, x_10 will not write a letter or x_10 is a sailor we can infer that for all x_10, x_10 is a writer or x_10 is a sailor via universal resolution. Finally, from the fact that for all x_10, x_10 is a writer or x_10 is a sailor, and that for all x_10, x_10 is not a writer we can infer that for all x_10, x_10 is a sailor via universal disjunctive syllogism, which contradicts that Mary is not a sailor. Therefore, the answer is no.