I understand the Adamantium is hard to break. I get the idea of normal metal not able to break it since they are not as hard as Adamantium, I also understand that perhaps when Adamantium hit Adamantium, it can possibly break since they are the same hardness.
In The Wolverine, the sword used to cut the claws was heated. When metal is heated, it becomes liquid if heated long enough, or at least the metal will become softer (molecules moving faster, in other words metal can be bend easier when heated). So my question is, if this is true and the heated metal is softer, why would it cut the claw which is harder since it is not heated?