Consider the following premises. James is sleeping if and only if William is climbing a mountain. For all x_1, x_1 is not a scientist. For all x_1, x_1 will sleep if and only if x_1 is a scientist. Can we infer the following from them? William is not climbing a mountain or Barbara is running.
 From the fact that for all x_1, x_1 will sleep if and only if x_1 is a scientist, and that for all x_1, x_1 is not a scientist we can infer that for all x_1, x_1 will not sleep. From the fact that for all x_1, x_1 will not sleep we can infer that James is not sleeping. From the fact that James is sleeping if and only if William is climbing a mountain, and that James is not sleeping we can infer that William is not climbing a mountain. Finally, from the fact that William is not climbing a mountain we can infer that William is not climbing a mountain or Barbara is running. Therefore, the answer is yes.