The phrase "automatically reply" is correct and usable in written English.
It can be used when referring to a system or software that responds to messages or inquiries without human intervention.
Example: "The email system is set to automatically reply to any messages received after business hours."
Alternatives: "auto-respond" or "send an automatic response".
They are set up to automatically reply whenever Donald Trump tweets; more often than not, they are the very first reply.
When asked, "Are you still Dreaming the Dream?" I would automatically reply, "Yes, but I'm also beginning to Feel the Fear".
The information processing of governments could almost automatically reply to be aware of the problem, to do the best they can within domestic boundaries etc.
The new driving mode silences notifications, turns the phone's display off, and can automatically reply to messages to warn friends that you are driving.
As a workaround, users who want to make the move to another account could switch on their vacation responder instead to automatically reply to emails with a note about their new address.
And they've also gone one step further…you can also set filters based on emails that contain certain keywords, or are from certain people, and automatically reply with a canned response.
"Girls can't marry girls," David automatically replied.
A student at the University of San Francisco, Mr. Abelson said, made a program that automatically replied to text messages, when he was driving.
When an e-mail message arrives from someone not on the recipient's approved list, the MailBlocks system automatically replies with a message of its own.
When asked by a friend's father, during the 1979 hostage crisis in Iran, what he thought of the situation, the author automatically replied (the caps are his): "I SUPPORT THE STRUGGLE OF THE IRANIAN WORKERS AND PEASANTS AGAINST U.S. IMPERIALISM".
That can be something as simple as automatically tweeting links to news articles – most of the Guardian's social media accounts are technically Twitter bots, for instance – to complex interactions like automatically generating Emoji-based art or automatically replying to climate change deniers with scientific evidence.
