about limited to running your Pro license on up to two machines

Quotation:

As a single developer you are limited to running your Pro license on up to two machines.

i uninstall "unity3d pro" on ONE of the two machines,

and then Can I install it on ANOTHER machine?

As a result, "unity3d pro" is installed on two computer.

Hi guys, lets clear this up.

Each serial number entitles you to install Unity on two machines that you have exclusive use of. i.e each license cannot be shared between two people.

If you wish to migrate your license from one machine to another (i.e you upgrade your machine) simply contact us at support@unity3d.com requesting to migrate your license stating the name of the machine you wish to migrate from and include your serial number or the email address you purchased Unity with.

We will then migrate the license across on our activation servers and once you uninstall Unity from the old machine you can then go ahead and install on your new setup.

Joe Robins Support Team Unity Technologies support@unity3d.com

No, I don't think you can do that. I am not 100% how this works, but as I know that means that you can only install Unity Pro twice, once on a machine and once on a different machine. The Unity Pro license code than is somehow bound by these two machines. So, the only thing you can do is uninstall Unity Pro on a machine and doing a reinstall on the same machine. That works! But just uninstalling from a machine and installing on a third machine, I don't think it will work. Even if in the end you will still have it installed on two machines.

But, you can write to Unity support any time and ask them to activate your license for a third machine (maybe offering a short explanation about why you need to do that and stating that you will still have it installed on two machines). They will help you out with this. I know someone else who did that!

If so,

if I reinstall OS on the computer that "Unity3D Pro" is installed,

The computer's "Unity3D Pro license" is valid?

That's where the fun begins. Theoretically it should be valid, yes. But sometimes it isn't. If it doesn't work, than your only solution is to write or talk to the Unity Support guys.