But the incorrectly predicted failure of the AE-35 was the only reason they considered shutting him down in the first place. So how did this happen? If this was an actual mistake by HAL, it makes his actions paranoid results of denial of his own fallibility. If (as I believe) the predicted failure was a ruse, it was a test by HAL to see if his infallibility would ever be questioned. In this case his decision to kill was based on the astronauts' reaction, and his actions are a logical, if heartless, attempt to protect the mission. Either way works.
When HAL says "I wonder if you might be having some second thoughts about the mission", I got the distinct impression that he was trying to drop some serious hints to Dave about the conflict in programming (i.e. HAL having full knowledge of the mission but also being forbidden to tell Dave and Frank about it). You'll notice that HAL goes out of his way to mention "rumors about something being dug up on the Moon" and also the "melodramatic touch" of Hunter, Kimball and Kaminsky being trained separately.
Meaning, HAL was trying as best he could to alert Dave that something was wrong, and was hoping that Dave would discover the truth on his own.
But when Dave doesn't seem to pick up on HAL's hints - all Dave says is "You're working up your crew psychology report" - HAL is obviously disappointed, and only then does he make the decision to eliminate the crew.
As for the failure of the AE-35: HAL only did that after his hints to Dave didn't work. I think the AE-35 thing was just an excuse to get Frank outside the ship where he could be killed. It was the beginning of HAL's plan to kill everyone.
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