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_13, x_13 will listen to a song or x_13 is a nurse. For all x_13, if x_13 listens to a song, then x_13 is excited. For all x_13, x_13 will write a letter or x_13 will go running. For all x_13, if x_13 were a nurse, then x_13 is excited. There is at least one x_13 for which x_13 will not write a letter.
There is at least one x_13 for which x_13 will go running can be inferred via the existential disjunctive syllogism rule. For all x_13, x_13 is excited can be inferred via the universal disjunction elimination rule.