This code should work for you: It is checking if the contents of Unique.txt are found ANYWHERE in CheckIp.
with open("Unique.txt") as firstFile:
checkIP = firstFile.read().strip()
with open("CheckIp.txt") as secondFile:
contents = secondFile.read().strip()
if checkIP in contents:
print ("{} IP is Already Present".format(checkIP))
else:
print ("Processing Ip: {}".format(checkIP))
However, if both files contain ONLY the IP that you are trying to compare, than you could do a more specific check:
if checkIP == contents:
print ("{} IP is Already Present".format(checkIP))
else:
print ("Processing Ip: {}".format(checkIP))