Hehe, it's a trick question. UNIX is not an acronym therefore does not short for anything. An early versions of UNIX was actually called UNICS and it was short for UNiplexed Information and Computing Service. Additional information about UNIX can be found on this page.

Here's a little history info. on UNIX
This information and more can be viewed

Year | Event

1957 - Bell Labs found they needed an operating system for their computer center which at the time was running various batch jobs. The BESYS operating system was created at Bell Labs to deal with these needs.

1965 - Bell Labs was adopting third generation computer equipment and decided to join forces with General Electric and MIT to create Multrics (Multiplexed Information and Computing Service).
1969- By April 1969, AT&T made a decision to withdraw Multrics and go with GECOS. When Multrics was withdrawn Ken Thompson and Dennis Ritchie needed to rewrite an operating system in order to play space travel on another smaller machine (a DEC PDP-7 [Programmed Data Processor 4K memory for user programs). The result was a system which a punning colleague caled UNICS (UNiplexed Information and Computing Service)--an 'emasculated Multrics'.
1969 - Summer 1969 UNIX was developed.

1971- First edition of UNIX released 11/03/1971. The first edition of the "UNIX PROGRAMMER'S MANUAL [by] K. Thompson [and] D. M. Ritchie" is also dated "November 3, 1971". It includes over 60 commands like: b (compile B program); boot (reboot system); cat (concatenate files); chdir (change working directory); chmod (change access mode); chown (change owner); cp (copy file); ls (list directory contents); mv (move or rename file); roff (run off text); wc (get word count); who (who is one the system). The main thing missing was pipes.
1972- Second edition of UNIX released 12/06/1972
1972- Ritchie rewrote B and called the new language C.
1973- UNIX had been installed on 16 sites (all within AT&T/Western Electric); it was publically unveiled at a conference in October.
1973- Third edition of UNIX released 02/xx/1973
1973- Forth edition of UNIX released 11/xx/1973
1974- Fifth edition of UNIX released 06/xx/1974
1974 -Thompson went to UC Berkeley to teach for a year, Bill Joy arrived as a new graduate student. Frustrated with ed, Joy developed a more featured editor em.
1975- Sixth edition of UNIX released 05/xx/1975
1977 -1BSD released late 1977
1978 -2BSD released mid 1978
1979 -Seventh edition of UNIX released 01/xx/1979
1979 -3BSD released late 1979
1979 -SCO founded by Doug and Larry Michels as UNIX porting and consulting company.

1980- 4.0BSD released 10/xx/1980
1982- SGI introduces IRIX.
1983- SCO delivers its first packaged UNIX system called SCO XENIX System V for Intel 8086 and 8088 processor-based PCs.
1984- Ultrix 1.0 was released.
1985- Eighth edition of UNIX released 02/xx/1985
1986- HP-UX 1.0 released.
1986- Ninth edition of UNIX released 09/xx/1986
1987- Sun and AT&T lay the groundwork for business computing in the next decade with an alliance to develop UNIX System V Release 4.
1988 -HP-UX 2.0 released.
1988- HP-UX 3.0 released.
1989- SCO ships SCO UNIX System V/386, the first volume commercial product licensed by AT&T to use the UNIX System trademark.
1989- HP-UX 7.0 released.
1989 -Tenth edition of UNIX released 10/xx/1989

1990- AIX short for Advanced Interactive eXecutive was first entered into the market by IBM February 1990.
1991- Sun unveils Solaris 2 operating environment, specially tuned for symetric multiprocessing.
1991 -Linux is introduced by Linus Torvald, a student in Finland. Who post to the comp.os.minix newsgroup with the words:
Hello everybody out there using minix -

I'm doing a (free) operating system (just a hobby, won't be big and professional like gnu) for 386(486) AT clones.

1991 HP-UX 8.0 released.
1991 BSD/386 ALPHA First code released to people outside BSDI 12/xx/1991
1992 HP-UX 9.0 released.
1993 NetBSD 0.8 released 04/20/1993
1993 FreeBSD 1.0 released December of 1993
1994 Red Hat Linux is introduced.
1994 Caldera, Inc was founded in 1994 by Ransom Love and Bryan Sparks.
1994 NetBSD 1.0 released 10/26/1994
1995 FreeBSD 2.0 released 01/xx/1995
1995 SCO acquires UNIX Systems source technology business from Novell Corporation (which had acquired it from AT&T's UNIX System Laboratories). SCO also acquires UnixWare 2 operating system from Novell.
1995 HP-UX 10.0 released.
1995 4.4 BSD Lite Release 2 the true final distribution from the CSRG 06/xx/1995
1997 HP-UX 11.0 released.
1997 Caldera ships OpenLinux Standard 1.1 May 5, 1997, the second offering in Caldera's OpenLinux product line
1998 IRIX 6.5 the fifth generation of SGI UNIX is released July 6, 1998.
1998 SCO delivers UnixWare 7 operating system.
1998 Sun Solaris 7 operating system released.
1998 FreeBSD 3.0 released 10/16/1998
2000 FreeBSD 4.0 released 03/13/2000
2000 Caldera Systems Inc. today announced that Caldera Systems has entered into agreement to acquire the SCO Server Software Division and the Professional Services Division

Just food for thought.