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
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International Class 009
Goods and Services COMPUTER PROGRAMS;
DATE OF FIRST USE: 1972.12.14;
DATE OF FIRST USE IN COMMERCE: 1972.12.14
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This would appear to imply that the trademark was first registered by
AT&T, and is now in the hands of
UNIX System Laboratories.