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_8, x_8 will work if and only if x_8 will climb a mountain. For all x_8, x_8 will not work. For all x_8, x_8 will listen to a song if and only if x_8 will climb a mountain. For all x_8, if x_8 climbs a mountain, then x_8 is working.
For all x_8, x_8 will not climb a mountain can be inferred via the universal modus tollens rule. For all x_8, if x_8 works, then x_8 is climbing a mountain can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 listens to a song, then x_8 is climbing a mountain can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 climbs a mountain, then x_8 is working can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 climbs a mountain, then x_8 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_8, x_8 will not climb a mountain can be inferred via the universal biconditional elimination rule.