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_12, x_12 will cook if and only if x_12 is a scientist. There is at least one x_12 for which x_12 will cook if and only if x_12 is a soldier. For all x_12, x_12 is not a soldier.
For all x_12, if x_12 cooks, then x_12 is a scientist can be inferred via the universal biconditional elimination rule. There is at least one x_12 for which if x_12 cooks, then x_12 is a soldier can be inferred via the existential biconditional elimination rule. For all x_12, if x_12 were a scientist, then x_12 is cooking can be inferred via the universal biconditional elimination rule. There is at least one x_12 for which if x_12 were a soldier, then x_12 is cooking can be inferred via the existential biconditional elimination rule. There is at least one x_12 for which x_12 will not cook can be inferred via the existential biconditional elimination rule.