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, x_12 will play a game or x_12 will write a letter. For all x_12, x_12 will work if and only if x_12 is a janitor. For all x_12, if x_12 writes a letter, then x_12 is working. For all x_12, if x_12 works, then x_12 is writing a letter. There is at least one x_12 for which x_12 will not play a game or x_12 is a janitor.
There is at least one x_12 for which x_12 will write a letter or x_12 is a janitor can be inferred via the existential resolution rule. For all x_12, x_12 will write a letter if and only if x_12 will work can be inferred via the universal biconditional introduction rule. For all x_12, x_12 will work if and only if x_12 will write a letter can be inferred via the universal biconditional introduction rule. For all x_12, if x_12 works, then x_12 is a janitor can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were a janitor, then x_12 is working can be inferred via the universal biconditional elimination rule.