The social contract is different from a legal contract that you must sign in order to be bound by it - as different as is a contract in the card game of Bridge.
A other beautiful way of saying that it is bullshit - and not a contract at all.
Another way of saying that you don't get to define what is and is not a contract. That has already been done. Social contract is its own thing just as a legal contract is also its own thing but something very different from social contract.
Yes, the social contract is "its own thing." It's a myth. It's not a contract in any sense of the word.
It's a justification for nut cases - particularly the government, to do whatever they want. It fails as a justification, because it doesn't exist!
Social contract has nothing to do with government though it can result in various forms of government. I wish there was some way to teach the concept to people who are determined to deny that it exists.