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_14, x_14 will listen to a song if and only if x_14 will work. For all x_14, if x_14 works, then x_14 is not writing a letter. For all x_14, x_14 will not read a book or x_14 is excited. For all x_14, x_14 will read a book or x_14 will listen to a song. There is at least one x_14 for which x_14 will write a letter.
There is at least one x_14 for which x_14 will not work can be inferred via the existential modus tollens rule. For all x_14, x_14 will listen to a song or x_14 is excited can be inferred via the universal resolution rule. For all x_14, if x_14 listens to a song, then x_14 is working can be inferred via the universal biconditional elimination rule. For all x_14, if x_14 works, then x_14 is listening to a song can be inferred via the universal biconditional elimination rule.