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_9 for which x_9 will write a letter if and only if x_9 is bored. For all x_9, x_9 is a scientist if and only if x_9 will write a letter. For all x_9, if x_9 were bored, then x_9 is making tea. For all x_9, x_9 will not make tea.
For all x_9, x_9 is not bored can be inferred via the universal modus tollens rule. For all x_9, if x_9 were a scientist, then x_9 is writing a letter can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 writes a letter, then x_9 is bored can be inferred via the existential biconditional elimination rule. For all x_9, if x_9 writes a letter, then x_9 is a scientist can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 were bored, then x_9 is writing a letter can be inferred via the existential biconditional elimination rule.