Consider the following premises. For all x_12, x_12 will climb a mountain if and only if x_12 will work. Jessica is not bored. Michael is working if and only if Jessica is bored. Can we infer the following from them? Michael is not climbing a mountain.
 From the fact that for all x_12, x_12 will climb a mountain if and only if x_12 will work we can infer that Michael is climbing a mountain if and only if Michael is working. From the fact that Michael is working if and only if Jessica is bored we can infer that if Michael works, then Jessica is bored. From the fact that if Michael works, then Jessica is bored, and that Jessica is not bored we can infer that Michael is not working. Finally, from the fact that Michael is climbing a mountain if and only if Michael is working, and that Michael is not working we can infer that Michael is not climbing a mountain. Therefore, the answer is yes.