Consider the following premises. There is at least one x_4 for which if x_4 were a nurse, then x_4 is playing squash. For all x_4, x_4 will play squash or x_4 is not a nurse. For all x_4, if x_4 plays squash, then x_4 is a nurse. For all x_4, x_4 is not a nurse. Can we infer the following from them? For all x_4, x_4 will play squash.
 From the fact that for all x_4, x_4 will play squash or x_4 is not a nurse we can infer that for all x_4, if x_4 were a nurse, then x_4 is playing squash. From the fact that for all x_4, if x_4 were a nurse, then x_4 is playing squash, and that for all x_4, if x_4 plays squash, then x_4 is a nurse we can infer that for all x_4, x_4 is a nurse if and only if x_4 will play squash. From the fact that for all x_4, x_4 is a nurse if and only if x_4 will play squash we can infer that for all x_4, if x_4 plays squash, then x_4 is a nurse. From the fact that for all x_4, if x_4 plays squash, then x_4 is a nurse, and that there is at least one x_4 for which if x_4 were a nurse, then x_4 is playing squash we can infer that there is at least one x_4 for which x_4 will play squash if and only if x_4 is a nurse. Finally, from the fact that there is at least one x_4 for which x_4 will play squash if and only if x_4 is a nurse, and that for all x_4, x_4 is not a nurse we can infer that there is at least one x_4 for which x_4 will not play squash, which contradicts that For all x_4, x_4 will play squash. Therefore, the answer is no.