Which folks haven't mentioned yet, but z/OS is also a proprietary UNIX, albeit in a very strange way given that it is sorta like a subsystem/different way of looking at the same things, but is also in implemented in the base control program (kernel), so it isn't really a subsystem.
And it isn't the same as AIX. IBM has two alive commercial UNIXs, which is kinda wild.
The original tiny Version 1 through Version 6 system may have been more or less proprietary (although provided with source for comparatively little money) but the Unix ecosystem hasn't been proprietary for a very long time. Many of the commands people think of today came not from AT&T at all, but from Berkeley.
Even as the commercial Unix platforms split, flourished, and fell apart keeping their own source more or less private Ultrix, Solaris, Irix, AIX, SCO, SunOS, OSF/1, HP/UX, Digital Unix, and others were more or less "Unix" with a few caveats about compatibility. POSIX and the SUS were formed. Systems got certified.
Then the GNU tools were written and Linux became their kernel. Then, the Berkeley vs. AT&T lawsuit ended and we got the explosion of open source BSDs - NetBSD, OpenBSD, FreeBSD, Midnight BSD, DragonflyBSD...
So yes, technically the original AT&T Unix was proprietary. That's not all there is to Unix nor has it been for decades. There is no Single VMS Specification. There are no independent systems certified as VMS compliant. You run what DEC / Compaq / HP / VMS Systems supplies and you like it or you don't. There is no Single Windows Specification. You take what Microsoft gives you or not. Unix is an open standard.
It actually is Unix, depending on your definition. If you define it as meeting the standard, it is. If you define it as being the same changed code base, it's not.
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