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Eight Mile first succeeded in establishing a breach of copyright after National was found to use a soundtrack infringing the musical work of Eminem's song Lose Yourself.
The National Party was ordered to pay damages of $600,000, but it appealed to the Court of Appeal on the cost of the damages, which was reduced to $225,000.
Following the decision, Eight Mile sought leave to appeal in the Supreme Court against the Court of Appeal's decision.
However, the court won't hear the case after declining to give leave this afternoon.
In 2017, the High Court deemed Eminem Esque, a song used in a National Party election ad in 2014, breached copyright of Eminem's hit Lose Yourself.
Justice Helen Cull instructed the party to pay $600,000 to Eminem and his representatives for using the alternative version.
The party lodged an appeal against the fee and in December last year, the Court of Appeal ruled the National Party would pay only $225,000 in damages.
Questioned about the case in 2014, National's campaign manager Steven Joyce said the National Party thought using the music was "pretty legal".
The National Party bought Eminem Esque from a company called Beatbox, which in turn bought the licence from California-based music library Labrador.