Consider the following premises. For all x_6, x_6 will read a book if and only if x_6 will climb a mountain. For all x_6, if x_6 takes a plane, then x_6 is a poet. There is at least one x_6 for which if x_6 were a poet, then x_6 is reading a book. For all x_6, x_6 will climb a mountain or x_6 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not read a book.
 From the fact that for all x_6, if x_6 takes a plane, then x_6 is a poet, and that there is at least one x_6 for which if x_6 were a poet, then x_6 is reading a book we can infer that there is at least one x_6 for which if x_6 takes a plane, then x_6 is reading a book via existential transitivity. From the fact that for all x_6, x_6 will read a book if and only if x_6 will climb a mountain we can infer that for all x_6, if x_6 climbs a mountain, then x_6 is reading a book via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 climbs a mountain, then x_6 is reading a book, that there is at least one x_6 for which if x_6 takes a plane, then x_6 is reading a book, and that for all x_6, x_6 will climb a mountain or x_6 will take a plane we can infer that there is at least one x_6 for which x_6 will read a book via existential disjunction elimination, which contradicts that For all x_6, x_6 will not read a book. Therefore, the answer is no.