if you want find out the computers that doesnt have particualr software installed in,you may write query where applications!=adobe which will not return the correct result as you would expect.
you will have to use not in condition to get the correct result. here is you go:
Select Distinct
sys.Netbios_Name0,
sys.User_Domain0,
sys.User_Name0
FROM
v_R_System sys
JOIN v_Add_Remove_Programs arp ON sys.ResourceID = arp.ResourceID
WHERE
sys.ResourceID not in (select sys.ResourceID
from
v_R_System sys
JOIN v_Add_Remove_Programs arp ON sys.ResourceID = arp.ResourceID
where
DisplayName0 = @displayname)
Prompt for Displayname:
select DisplayName0 from v_Add_Remove_Programs