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: There is at least one x_1 for which if x_1 were a janitor, then x_1 is writing a letter. For all x_1, x_1 will not write a letter. For all x_1, if x_1 writes a letter, then x_1 is a janitor.
There is at least one x_1 for which x_1 is not a janitor can be inferred via the existential modus tollens rule. There is at least one x_1 for which x_1 is a janitor if and only if x_1 will write a letter can be inferred via the existential biconditional introduction rule. There is at least one x_1 for which x_1 will write a letter if and only if x_1 is a janitor can be inferred via the existential biconditional introduction rule.