Consider the following premises. For all x_11, x_11 will work and x_11 will play a game. For all x_11, x_11 will drive a car or x_11 will read a book. For all x_11, if x_11 reads a book, then x_11 is climbing a mountain. For all x_11, x_11 will drive a car if and only if x_11 will climb a mountain. Can we infer the following from them? There is at least one x_11 for which either x_11 will work or x_11 will climb a mountain are not true.
 From the fact that for all x_11, x_11 will drive a car if and only if x_11 will climb a mountain we can infer that for all x_11, if x_11 drives a car, then x_11 is climbing a mountain. From the fact that for all x_11, if x_11 drives a car, then x_11 is climbing a mountain, that for all x_11, if x_11 reads a book, then x_11 is climbing a mountain, and that for all x_11, x_11 will drive a car or x_11 will read a book we can infer that for all x_11, x_11 will climb a mountain. From the fact that for all x_11, x_11 will work and x_11 will play a game we can infer that for all x_11, x_11 will work. Finally, from the fact that for all x_11, x_11 will work, and that for all x_11, x_11 will climb a mountain we can infer that for all x_11, x_11 will work and x_11 will climb a mountain, which contradicts that There is at least one x_11 for which either x_11 will work or x_11 will climb a mountain are not true. Therefore, the answer is no.