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 climbs a mountain, then z is a police officer. There is at least one z for which if z were a police officer, then z is climbing a mountain. For all z, z will not listen to a song. For all z, z will play squash if and only if z will listen to a song. For all z, z will play squash if and only if z is a police officer.
There is at least one z for which z is a police officer if and only if z will climb a mountain can be inferred via the existential biconditional introduction rule. There is at least one z for which z will climb a mountain if and only if z is a police officer can be inferred via the existential biconditional introduction rule. For all z, if z plays squash, then z is listening to a song can be inferred via the universal biconditional elimination rule. For all z, if z plays squash, then z is a police officer can be inferred via the universal biconditional elimination rule. For all z, if z listens to a song, then z is playing squash can be inferred via the universal biconditional elimination rule. For all z, if z were a police officer, then z is playing squash can be inferred via the universal biconditional elimination rule. For all z, z will not play squash can be inferred via the universal biconditional elimination rule.