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: There is at least one x_7 for which if x_7 were happy, then x_7 is running. For all x_7, if x_7 climbs a mountain, then x_7 is running. For all x_7, if x_7 goes running, then x_7 is climbing a mountain. For all x_7, if x_7 goes running, then x_7 is happy. For all x_7, x_7 will not climb a mountain.
For all x_7, x_7 will not go running can be inferred via the universal modus tollens rule. For all x_7, if x_7 climbs a mountain, then x_7 is happy can be inferred via the universal transitivity rule. There is at least one x_7 for which if x_7 were happy, then x_7 is climbing a mountain can be inferred via the existential transitivity rule. For all x_7, x_7 will climb a mountain if and only if x_7 will go running can be inferred via the universal biconditional introduction rule. For all x_7, x_7 will go running if and only if x_7 will climb a mountain can be inferred via the universal biconditional introduction rule. There is at least one x_7 for which x_7 is happy if and only if x_7 will go running can be inferred via the existential biconditional introduction rule. There is at least one x_7 for which x_7 will go running if and only if x_7 is happy can be inferred via the existential biconditional introduction rule.