Consider the following premises. There is at least one x_11 for which if x_11 were a politician, then x_11 is reading a book. For all x_11, if x_11 reads a book, then x_11 is sleeping. For all x_11, if x_11 climbs a mountain, then x_11 is reading a book. For all x_11, if x_11 cooks, then x_11 is a politician. For all x_11, x_11 will climb a mountain or x_11 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which if x_11 were a politician, then x_11 is reading a book.
That is one of the premises. Therefore, the answer is yes.