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 cooks, then z is playing tennis. There is at least one z for which if z were a politician, then z is cooking. For all z, if z plays tennis, then z is a politician.
For all z, if z cooks, then z is a politician can be inferred via the universal transitivity rule. There is at least one z for which if z were a politician, then z is playing tennis can be inferred via the existential transitivity rule. There is at least one z for which if z plays tennis, then z is cooking can be inferred via the existential transitivity rule.