hello. Did you agree cooling off rights?
Does that mean you didn't discuss them?
Does the paper contract give you rights of cancellation?
Ok. Is there any online contract?
And you never made payment>?
In that case, I'm not sure that you are liable. You do not seem even to have verbally agreed to this contract unequivocally and you certainly have not signed anything or acted in a way that implies that you did agree. I'm not sure why they think you are liable.
Of course, they may not accept that you did not agree verbally and then it would come down to a dispute over fact that you may lose but the chances that they would sue are very low.
The only issue is that you seem to be saying above that you did sign paperwork and elsewhere that you did not.
If you sign a contract then you are bound by it. Whether you read it or not is a nonissue.
If you did not agree cancellation rights then none will exist automatically.
However if you try to cancel unlawfully then you will still only be liable for the loss that you have caused which will be nothing like the amount due under the contract.
Can I clarify anything for you?
Well, that is right basically. If you sign a contract then you are bound by it. Whether you read it or not is a nonissue.
No, not payment does not void the contract.
Payment would be evidence of a contract but that doesn't apply here.