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_15, if x_15 were a musician, then x_15 is a cashier. There is at least one x_15 for which if x_15 were happy, then x_15 is a musician. For all x_15, x_15 will climb a mountain if and only if x_15 is a cashier. For all x_15, if x_15 climbs a mountain, then x_15 is happy.
There is at least one x_15 for which if x_15 were happy, then x_15 is a cashier can be inferred via the existential transitivity rule. There is at least one x_15 for which if x_15 climbs a mountain, then x_15 is a musician can be inferred via the existential transitivity rule. For all x_15, if x_15 climbs a mountain, then x_15 is a cashier can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 were a cashier, then x_15 is climbing a mountain can be inferred via the universal biconditional elimination rule.