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_4, x_4 will climb a mountain. There is at least one x_4 for which if x_4 were a scientist, then x_4 is not climbing a mountain. For all x_4, if x_4 were a scientist, then x_4 is a musician. For all x_4, if x_4 were a musician, then x_4 is a scientist.
There is at least one x_4 for which x_4 is not a scientist can be inferred via the existential modus tollens rule. For all x_4, x_4 is a scientist if and only if x_4 is a musician can be inferred via the universal biconditional introduction rule. For all x_4, x_4 is a musician if and only if x_4 is a scientist can be inferred via the universal biconditional introduction rule.