How long does it take to get out of the ARMY DEP?

I sent my letter to the station commander to tell him i no longer wish to be part of DEP and i wish to pursue higher education. He and my recruiter brought me in to discuss my letter and then gave me a "random drug test". Of course i came out negative but they said on my discharge papers they are going to put they are discharging me for drug use-even tho this is not true-unless i say im going to continue to b in DEP. i said how can they even do that? then they said all they have to do i say i admitted it. they need no proof. is this true?