Disable social signup and avoid welcome email

Hi everyone,
hope that you all are able to help me to cover this scenario.

Basically I want that:

  • user can’t register with social connection, only login (I used disable social signup rule to avoid signup and linking account rule to merge accounts)
  • user don’t receive the welcome email if the login didn’t go well because the access has been denied from disable social signup rule

Right now after denied the access the user receives the welcome email because he has been written in the database but he will not able to login.