Consider the following premises. For all x_6, x_6 is sad. For all x_6, x_6 will read a book or x_6 will not take a plane. For all x_6, x_6 is a carpenter or x_6 will take a plane. For all x_6, if x_6 were a carpenter, then x_6 is reading 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 sad and x_6 will read a book.
 From the fact that for all x_6, x_6 will read a book or x_6 will not take a plane we can infer that for all x_6, if x_6 takes a plane, then x_6 is reading a book via universal rewriting. From the fact that for all x_6, if x_6 were a carpenter, then x_6 is reading a book, that for all x_6, if x_6 takes a plane, then x_6 is reading a book, and that for all x_6, x_6 is a carpenter or x_6 will take a plane we can infer that for all x_6, x_6 will read a book via universal disjunction elimination. Finally, from the fact that for all x_6, x_6 is sad, and that for all x_6, x_6 will read a book we can infer that for all x_6, x_6 is sad and x_6 will read a book via universal conjunction. Therefore, the answer is yes.