Consider the following premises. For all x_7, x_7 is not a sailor. For all x_7, x_7 will not read a book or x_7 will write a letter. For all x_7, x_7 is a taxi driver if and only if x_7 is a sailor. For all x_7, x_7 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will not write a letter.
 From the fact that for all x_7, x_7 will read a book we can infer that for all x_7, x_7 will read a book or x_7 is a taxi driver via universal addition. From the fact that for all x_7, x_7 is a taxi driver if and only if x_7 is a sailor, and that for all x_7, x_7 is not a sailor we can infer that for all x_7, x_7 is not a taxi driver via universal biconditional elimination. From the fact that for all x_7, x_7 will read a book or x_7 is a taxi driver, and that for all x_7, x_7 will not read a book or x_7 will write a letter we can infer that for all x_7, x_7 is a taxi driver or x_7 will write a letter via universal resolution. Finally, from the fact that for all x_7, x_7 is a taxi driver or x_7 will write a letter, and that for all x_7, x_7 is not a taxi driver we can infer that for all x_7, x_7 will write a letter via universal disjunctive syllogism, which contradicts that There is at least one x_7 for which x_7 will not write a letter. Therefore, the answer is no.