Consider the following premises. For all x_15, if x_15 cooks, then x_15 is running. For all x_15, x_15 will cook if and only if x_15 will go running. For all x_15, if x_15 were a musician, then x_15 is not climbing a mountain. For all x_15, x_15 will climb a mountain. There is at least one x_15 for which if x_15 cooks, then x_15 is a musician. Can we infer the following from them? For all x_15, if x_15 were a musician, then x_15 is not climbing a mountain.
That is one of the premises. Therefore, the answer is yes.