Free Cell

You may have played it. I know that I have. Recently, I've been ill, and I've rediscovered it.

To describe to you just how numbingly involving this game can be, I'd have to crawl into your head, sever all of your ties to reality, and then massage your brain with a scrub brush.
I've spent perhaps 10 hours in the last week playing this game.
It tracks my percentage of wins/losses, though I never manage to keep it higher than 85%-90%.

The "Help" section of the program states that: "It is believed (although not proven) that every game is winnable."

I felt that I was getting really good at the game, and was starting to wonder just how good I could get. If I was careful enough, and only played the game when I wasn't tired, could I eliminate enough of my own errors to win every time? Is that even possible?

That bothered me, so I decided to find out. The day I decided to do so, I didn't have internet access, so I had to figure this out without research.

Hypothesis: All possible initial arrangements of the deck can lead to a win.

Ok. From that, I set out to prove how one could win every game, but that soon became a formulation of tactics, which I already know that I don't have enough of a mastery of to be able to win every time. It began to seem impossible to prove that every game could be won.
Then I remembered that there are very few situations in which I lose, and realized that it would be much simpler to imagine a game which could not be won, if that were possible.

Challenge: Find an initial arrangement of the deck in which no win is possible.

The picture at the top of this post is what I came up with.

1. If the aces cannot be freed, the game cannot be won.
2. Picking up any four cards will not free an ace.
3. Every card is at least four cards away from its top or bottom mate (the number before or after it of opposite color).
4. No more than three cards can be brought to a top mate before a no-win situation is reached.
5. The only movements that allow three cards to move to their top mates, do not free any aces.
6. The aces in this initial arrangement of cards cannot be freed, so this is an arrangement that cannot be solved.
7. If this arrangement is included as a possible game in Free Cell, then there is at least one game of Free Cell that cannot be won, therefore:

It is not possible to win every game of Free Cell.