Consider the following premises. For all z, z will cook if and only if z will go running. For all z, z will not go running. For all z, if z plays squash, then z is playing tennis. There is at least one z for which if z plays tennis, then z is cooking. For all z, if z goes running, then z is cooking. Can we infer the following from them? For all z, z will cook if and only if z will go running.
That is one of the premises. Therefore, the answer is yes.