Kim Kardashian -- No Reconciliation ... Divorce On

Kim Kardashian is not reconciling with Kris Humphries, and the divorce is full steam ahead ... this according to sources with first-hand knowledge of the situation.

We're told even though Kim is somewhat conflicted, she knows divorce is the right thing to do, and the purpose of the trip to Minnesota last weekend was to create face-to-face closure.

Sources say Kris' Minnesota lawyer is handling the divorce for him.

And, we're told, there are "no conflicts" over the terms of the divorce.