Inference is not a fact. It is an action performed in thinking about what you know.
There are no fact about inference. It is something that is implied but not stated directly.
A observation
The difference between an inference and a fact is that an inference is generally something which is worked out or deduced from other factual information (but can also relate to something being suggested, although in this case I think the original definition applies), whereas a fact is something which is known to be a true piece of information, without necessarily relying on other information to support this.
inference
iNFeReNCe is hyPoThEsES disEaSe