Consider the following premises. For all z_1, if z_1 were sad, then z_1 is working. For all z_1, z_1 will work if and only if z_1 is sad. There is at least one z_1 for which if z_1 works, then z_1 is sad. Can we infer the following from them? For all z_1, the fact that z_1 works does not imply that z_1 is sad.
That contradicts the premises. Therefore the answer is no.