On June 16th, my ZAP log mentions some:
OSFW,2008/06/15,11:04:32 -7:00 GMT,UNKNOWN(0),Microsoft Windows Malicious Software Removal Tool,C:\WINDOWS\system32\MRT.exe,PROCESS,OPENPROCE SS,DST,\SystemRoot\System32\smss.exe
I realise it now, looking into my ZAP logs file.

Later in the summer this line multiplied dozens of times in the log and I realize that too now, but before I started having ZAP alerts, the violet ones saying
Generic Host Program for win32 services is trying to act as a server
and red alerts saying
LSA Shell Export Version is trying to communicate with C:\Windows\system32\Zonelabs\UpdClient.exe by opening its process, application Isass.exe.
among other things.
I always denied them but did not find the time to check this problem.
I have lots of problems in my p/c's function (for instance, help & support of Windows does not function when online) and today I tried to restore before this date (June 16th) basically in order to avoid those alerts and eventual trojan provoking them but I cannot restore before August (when I press the left arrow of restore system calendar being in August it does not function to lead me to July). It seems that restore system functions only for 3 months back maximum and I'm afraid that if it's about a trojan here I'll do nothing going only back to the 1st of August since the problem appears having occurred earlier.
Please advise.

Operating System:Windows XP Home Edition
Software Version:8.0
Product Name:ZoneAlarm Pro