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_4 for which if x_4 goes running, then x_4 is a carpenter. For all x_4, if x_4 were a soldier, then x_4 is running. For all x_4, x_4 will cook or x_4 is a soldier. For all x_4, if x_4 cooks, then x_4 is running.
There is at least one x_4 for which if x_4 were a soldier, then x_4 is a carpenter can be inferred via the existential transitivity rule. There is at least one x_4 for which if x_4 cooks, then x_4 is a carpenter can be inferred via the existential transitivity rule. For all x_4, x_4 will go running can be inferred via the universal disjunction elimination rule.