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_6, x_6 is a carpenter. For all x_6, if x_6 climbs a mountain, then x_6 is not a carpenter. There is at least one x_6 for which x_6 will play tennis if and only if x_6 is a writer. For all x_6, if x_6 were a writer, then x_6 is climbing a mountain.
For all x_6, x_6 will not climb a mountain can be inferred via the universal modus tollens rule. There is at least one x_6 for which if x_6 plays tennis, then x_6 is a writer can be inferred via the existential biconditional elimination rule. There is at least one x_6 for which if x_6 were a writer, then x_6 is playing tennis can be inferred via the existential biconditional elimination rule.