Consider the following premises. There is at least one x_14 for which x_14 will read a book or x_14 will work. For all x_14, if x_14 reads a book, then x_14 is making tea. For all x_14, x_14 will drink water if and only if x_14 will climb a mountain. For all x_14, if x_14 works, then x_14 is drinking water. For all x_14, if x_14 makes tea, then x_14 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 will not climb a mountain.
 From the fact that for all x_14, if x_14 reads a book, then x_14 is making tea, and that for all x_14, if x_14 makes tea, then x_14 is drinking water we can infer that for all x_14, if x_14 reads a book, then x_14 is drinking water via universal transitivity. From the fact that for all x_14, if x_14 reads a book, then x_14 is drinking water, that for all x_14, if x_14 works, then x_14 is drinking water, and that there is at least one x_14 for which x_14 will read a book or x_14 will work we can infer that there is at least one x_14 for which x_14 will drink water via existential disjunction elimination. From the fact that for all x_14, x_14 will drink water if and only if x_14 will climb a mountain we can infer that for all x_14, if x_14 drinks water, then x_14 is climbing a mountain via universal biconditional elimination. Finally, from the fact that for all x_14, if x_14 drinks water, then x_14 is climbing a mountain, and that there is at least one x_14 for which x_14 will drink water we can infer that there is at least one x_14 for which x_14 will climb a mountain via existential modus ponens, which contradicts that For all x_14, x_14 will not climb a mountain. Therefore, the answer is no.