To forgive and to forget?

The saying goes "To forgive and to forget"...

Personally, I think it is not enough just to forgive and to forget. If you say that you forgive but you cannot forget, then I feel that you have not truly forgiven because you still remember what the other party has done to you.

To truly forgive is to forget completely the wrong that the other party has done to you. Once you have forgotten, it means that it does not matter anymore. It does not mean anything to you anymore, so there is no need to remember about it. So you forget about it.

Makes sense?

It is easy to say that you forgive but being humans, it is more difficult to forget. So when you have truly forgiven but you have not forgotten, does it mean that you have not truly forgiven?