For example: let's say a good friend of yours (Bob) is flying in today, and you agreed to pick them up at the airport, even though you dislike waiting there.
He said the plane would arrive sometime between 5:00 and 6:00. Now, you want to meet him as soon as Bob arrives, and not leave him waiting, more than you dislike waiting yourself (I don't care if your not like this in real life, but bear with me.)
Now, another friend of yours (Jill) tells you that she knows that Bob will arrive at between 5:15 and 5:30... because of a dream she had.
Do you believe Jill?
If yes, then you would arrive at 5:15 and wait for him to arrive (because you don't want to wait arround for the 15 minuts before hand.)
If you disbelieve Jill, would you leave at 5:15 and come back at 5:30, to avoid waiting at the airport for those 15 minuts?
By my interpretation of disbelief:
By disbelieving in Jill you would merely reject that "Bob will certainly arrive between 5:15 and 5:30", but you will not accept that "he will not arrive between 5:15 and 5:30."
Thus, by disbelieving Jill, you come to the airport at 5:00, but don't leave at 5:15.
Do you agree with my interpretation?