Here is the decision by the High Court where they determined that the the Marriage Equality (Same Sex) Act 2013 (ACT) is inconsistent with the Marriage Act 1961 (Cth) within the meaning of s 28(1) of the Australian Capital Territory (Self-Government) Act 1988 (Cth):

Click here to view the judgement.

The judgment was relatively short and almost a forgone conclusion. Power to legislate with respect to marriage clearly falls to the Commonwealth pursuant to the Constitution.