Consider the following premises. For all z_1, z_1 will not play squash. For all z_1, if z_1 were fast, then z_1 is a cashier. For all z_1, if z_1 were a cashier, then z_1 is fast. There is at least one z_1 for which z_1 is a cashier if and only if z_1 will play squash. Can we infer the following from them? For all z_1, z_1 will not play squash.
That is one of the premises. Therefore, the answer is yes.