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_12, x_12 will cook if and only if x_12 is a carpenter. For all x_12, x_12 is a carpenter and x_12 will play tennis. There is at least one x_12 for which x_12 is an office clerk.
For all x_12, x_12 is a carpenter can be inferred via the universal simplification rule. For all x_12, x_12 will play tennis can be inferred via the universal simplification rule. For all x_12, if x_12 cooks, then x_12 is a carpenter can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were a carpenter, then x_12 is cooking can be inferred via the universal biconditional elimination rule.