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_14, x_14 is an astronaut if and only if x_14 is a musician. For all x_14, x_14 is not a musician. For all x_14, x_14 is an astronaut or x_14 is not rich. For all x_14, if x_14 were a carpenter, then x_14 is rich. There is at least one x_14 for which if x_14 were an astronaut, then x_14 is a carpenter.
There is at least one x_14 for which if x_14 were an astronaut, then x_14 is rich can be inferred via the existential transitivity rule. For all x_14, if x_14 were rich, then x_14 is an astronaut can be inferred via the universal rewriting rule. For all x_14, if x_14 were an astronaut, then x_14 is a musician can be inferred via the universal biconditional elimination rule. For all x_14, if x_14 were a musician, then x_14 is an astronaut can be inferred via the universal biconditional elimination rule. For all x_14, x_14 is not an astronaut can be inferred via the universal biconditional elimination rule.