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 x_9, if x_9 were a doctor, then x_9 is writing a letter. For all x_9, if x_9 writes a letter, then x_9 is a doctor. For all x_9, if x_9 were an astronaut, then x_9 is a doctor. For all x_9, if x_9 goes running, then x_9 is an astronaut. There is at least one x_9 for which x_9 will write a letter or x_9 will go running.
For all x_9, if x_9 were an astronaut, then x_9 is writing a letter can be inferred via the universal transitivity rule. For all x_9, if x_9 goes running, then x_9 is a doctor can be inferred via the universal transitivity rule. For all x_9, x_9 is a doctor if and only if x_9 will write a letter can be inferred via the universal biconditional introduction rule. For all x_9, x_9 will write a letter if and only if x_9 is a doctor can be inferred via the universal biconditional introduction rule.