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Let me see if I understand what you need:
1. You want to display the default time and date on your form now() - right?
2. I'm not sure what you mean by you don't want the field in the database -
Perhaps I don't have all the information - but I don't think you can use conditional logic because it works with fields -which submit values to your form's database.
A simpler method would be to use the date-time field:
Let us know if this helps