Corrected entry: A conservative estimate of the acid-filled vault's weight is about 4 tons, most likely much more (a previous corrector suggested it was a special light-weight safe that Two-face installed. You can tell from Batman's difficulty in lifting the door that it is solid metal). The strongest industrial cable would need to be at least 1/2 inch thick to hold the weight, even more considering it would have to withstand the additional force as the vault makes its downward arc. The 1/8 inch thick cable that Batman uses would have snapped like a thread under the weight, no matter what it was composed of.
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Correction: Batman uses a lot of high-tech stuff. Within the context of the movie, he could have a cable made of stronger material than is generally used elsewhere.
pross79