Which system applies to the soldiers who are not amenable do correction by non-punitive or non-judicial methods of Correction or discipline?

The system that applies to soldiers who are not amenable to correction by non-punitive or non-judicial methods is the Uniform Code of Military Justice (UCMJ). Under the UCMJ, disciplinary actions can include courts-martial, which are formal legal proceedings that can lead to various penalties, including confinement, reduction in rank, or discharge. This system is designed to maintain military order and discipline when less severe measures are ineffective.