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_2, if z_2 climbs a mountain, then z_2 is a doctor. For all z_2, if z_2 were an artist, then z_2 is working. For all z_2, if z_2 were a doctor, then z_2 is an artist. There is at least one z_2 for which if z_2 works, then z_2 is climbing a mountain.
For all z_2, if z_2 climbs a mountain, then z_2 is an artist can be inferred via the universal transitivity rule. For all z_2, if z_2 were a doctor, then z_2 is working can be inferred via the universal transitivity rule. There is at least one z_2 for which if z_2 works, then z_2 is a doctor can be inferred via the existential transitivity rule. There is at least one z_2 for which if z_2 were an artist, then z_2 is climbing a mountain can be inferred via the existential transitivity rule.