User Profile: delete default property

Hi,

Im trying to delete a default User Property in UserProfileManager, I'm using the following PS

$site = Get-SPSite http://url
$serviceContext = Get-SPServiceContext $site 

$upcm = New-Object Microsoft.Office.Server.UserProfiles.UserProfileConfigManager($serviceContext)
$pdtc = $upcm.GetPropertyDataTypes()
$ppm = $upcm.ProfilePropertyManager
$cpm = $ppm.GetCoreProperties()

$property = $cpm.GetPropertyByName("SPS-School")
$propertyName=$property.Name
if($propertyName -ne $null)
{
$cpm.RemovePropertyByName($propertyName)
write-host -f yellow property is deleted successfully
}
else {
write-host -f red property does not exist
}

But when I executed this script I receive an error message like:

Exception calling "RemovePropertyByName" with "1" argument(s): "Property
update's Stored Procedure call returned an error. Error Code: 4. Errors
removing properties: 1. Errors updating or creating properties: 0."
At line:3 char:1
+ $cpm.RemovePropertyByName($propertyName)
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (:) [], MethodInvocationException
    + FullyQualifiedErrorId : CommitFailedException

Is not possible to delete the default properties? Only is it possible to hide them?

Thanks