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_10, if x_10 were bored, then x_10 is working. There is at least one x_10 for which if x_10 works, then x_10 is bored. For all x_10, x_10 will work or x_10 will listen to a song. For all x_10, x_10 is not bored.
There is at least one x_10 for which x_10 will not work can be inferred via the existential modus tollens rule. There is at least one x_10 for which x_10 will work if and only if x_10 is bored can be inferred via the existential biconditional introduction rule. There is at least one x_10 for which x_10 is bored if and only if x_10 will work can be inferred via the existential biconditional introduction rule.