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, x_13 is a scientist if and only if x_13 is sad. For all x_13, if x_13 were a scientist, then x_13 is an office clerk. For all x_13, x_13 is not an office clerk. There is at least one x_13 for which x_13 is sad if and only if x_13 will work.
For all x_13, x_13 is not a scientist can be inferred via the universal modus tollens rule. For all x_13, if x_13 were a scientist, then x_13 is sad can be inferred via the universal biconditional elimination rule. There is at least one x_13 for which if x_13 were sad, then x_13 is working can be inferred via the existential biconditional elimination rule. For all x_13, if x_13 were sad, then x_13 is a scientist can be inferred via the universal biconditional elimination rule. There is at least one x_13 for which if x_13 works, then x_13 is sad can be inferred via the existential biconditional elimination rule.