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_9, if x_9 writes a letter, then x_9 is a musician. There is at least one x_9 for which if x_9 were a musician, then x_9 is a carpenter. For all x_9, x_9 will work if and only if x_9 is a musician. For all x_9, x_9 will write a letter.
For all x_9, x_9 is a musician can be inferred via the universal modus ponens rule. There is at least one x_9 for which if x_9 writes a letter, then x_9 is a carpenter can be inferred via the existential transitivity rule. For all x_9, if x_9 works, then x_9 is a musician can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 were a musician, then x_9 is working can be inferred via the universal biconditional elimination rule.