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_12, if x_12 sleeps, then x_12 is working. For all x_12, if x_12 plays tennis, then x_12 is not working. For all x_12, x_12 will sleep or x_12 is an astronaut. For all x_12, x_12 will play tennis or x_12 is not a writer. For all x_12, if x_12 were an astronaut, then x_12 is working.
For all x_12, if x_12 were a writer, then x_12 is playing tennis can be inferred via the universal rewriting rule. For all x_12, x_12 will work can be inferred via the universal disjunction elimination rule.