What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all z, if z sleeps, then z is cooking. There is at least one z for which if z sleeps, then z is a police officer. For all z, z will not cook. For all z, if z cooks, then z is sleeping. For all z, z will sleep if and only if z is a police officer.
For all z, z will not sleep can be inferred via the universal modus tollens rule. There is at least one z for which if z cooks, then z is a police officer can be inferred via the existential transitivity rule. For all z, z will sleep if and only if z will cook can be inferred via the universal biconditional introduction rule. For all z, z will cook if and only if z will sleep can be inferred via the universal biconditional introduction rule. For all z, if z sleeps, then z is a police officer can be inferred via the universal biconditional elimination rule. For all z, if z were a police officer, then z is sleeping can be inferred via the universal biconditional elimination rule.