What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? For all x_1, if x_1 were a nurse, then x_1 is cooking. For all x_1, x_1 will not cook. For all x_1, x_1 is a nurse if and only if x_1 is a police officer. There is at least one x_1 for which x_1 is a police officer if and only if x_1 is a nurse.
For all x_1, x_1 is not a nurse. For all x_1, if x_1 were a nurse, then x_1 is a police officer. There is at least one x_1 for which if x_1 were a police officer, then x_1 is a nurse. For all x_1, if x_1 were a police officer, then x_1 is a nurse. There is at least one x_1 for which if x_1 were a nurse, then x_1 is a police officer.