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: There is at least one x_5 for which if x_5 were a doctor, then x_5 is a politician. For all x_5, if x_5 were a politician, then x_5 is playing tennis. For all x_5, if x_5 were a sailor, then x_5 is a doctor. For all x_5, x_5 is a sailor or x_5 is a server. For all x_5, if x_5 were a server, then x_5 is a doctor.
There is at least one x_5 for which if x_5 were a doctor, then x_5 is playing tennis can be inferred via the existential transitivity rule. There is at least one x_5 for which if x_5 were a sailor, then x_5 is a politician can be inferred via the existential transitivity rule. There is at least one x_5 for which if x_5 were a server, then x_5 is a politician can be inferred via the existential transitivity rule. For all x_5, x_5 is a doctor can be inferred via the universal disjunction elimination rule.