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 happy, then x_13 is taking a plane. There is at least one x_13 for which x_13 will take a plane if and only if x_13 is a carpenter. For all x_13, if x_13 were a carpenter, then x_13 is sad. For all x_13, if x_13 were sad, then x_13 is happy.
For all x_13, if x_13 were a carpenter, then x_13 is happy can be inferred via the universal transitivity rule. For all x_13, if x_13 were sad, then x_13 is taking a plane can be inferred via the universal transitivity rule. There is at least one x_13 for which if x_13 takes a plane, then x_13 is a carpenter can be inferred via the existential biconditional elimination rule. There is at least one x_13 for which if x_13 were a carpenter, then x_13 is taking a plane can be inferred via the existential biconditional elimination rule.