Results of searching the USPTO database:

1. 2096022 -- UNIX  
2. 2039887 -- UNIX DIAPERS BY PANNOLINI  
3. 1988510 -- UNIXTRACS  
4. 1845474 -- UNIXWARE  
5. 1780785 -- UNIX SYSTEM LABORATORIES  
6. 1392203 -- UNIX  
7. 1390593 -- UNIX
Number 6 seems to be the relevant one:
Word Mark UNIX  
Owner Name (REGISTRANT) AMERICAN TELEPHONE AND 
           TELEGRAPH COMPANY  
Owner Address 550 MADISON AVENUE 
              NEW YORK NEW YORK 10022
              CORPORATION NEW YORK  
Owner Name (LAST LISTED OWNER) UNIX SYSTEM LABORATORIES, INC.  
Owner Address 295 NORTH MAPLE AVENUE 
              BASKING RIDGE NEW JERSEY 07920 
              CORPORATION DELAWARE  
Attorney of Record FRANK L. POLITANO  
Serial Number 73-544900  
Registration Number 1392203  
Filing Date 06/24/1985  
Registration Date 05/06/1986  
Mark Drawing Code (1) TYPED DRAWING  
Register PRINCIPAL  
Published for Opposition 10/29/1985  
Affidavits SECT 15.; SECT 8 (6-YR)  
Type of Mark TRADEMARK  
--------------------
International Class 009  
Goods and Services COMPUTER PROGRAMS;
  DATE OF FIRST USE: 1972.12.14; 
  DATE OF FIRST USE IN COMMERCE: 1972.12.14  
--------------------
This would appear to imply that the trademark was first registered by AT&T, and is now in the hands of UNIX System Laboratories.