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_13, if x_13 were a bartender, then x_13 is writing a letter. For all x_13, x_13 will cook or x_13 is happy. For all x_13, x_13 is a bartender if and only if x_13 is happy. There is at least one x_13 for which if x_13 cooks, then x_13 is a bartender.
There is at least one x_13 for which if x_13 cooks, then x_13 is writing a letter can be inferred via the existential transitivity rule. For all x_13, if x_13 were a bartender, then x_13 is happy can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were happy, then x_13 is a bartender can be inferred via the universal biconditional elimination rule.