Seller, you should NOT refund.
1. No warranty period stated, and the buyer didn't bother to ask.
2. Seller sold item in a good condition, even the buyer tested it 24hrs before buying.
3. After sale, seller asked buyer THREE times about the item he bought, and buyer said YES (good) to that three times.

If he persists on asking for a refund, ask him to bring the warranty he "got".
If he say "u didn't give me" then he's answering his own problem.
Ask him back "so how?" so how.