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Hearts and Partick Thistle have lost their fight to have their respective relegations overturned by the courts - but say they will "pursue the same outcome in a different forum".

Lord Clark said the rules of the football authorities mean the case must be heard by an independent tribunal set up through the Scottish FA rules.

However, the association will not adjudicate in the case, leading the two clubs to say they were "pleased to have received a fair hearing" and to say they will continue to fight demotion.

Hearts and Thistle have hailed the success of a motion to get access to documents that they say "will be key to support our case in arbitration".

QC's from both sides had been providing submissions via video link to the Court of Session for the past three days.

Hearts and Partick claimed unfair prejudice after clubs agreed to end the season early, resulting in their relegation, and wanted the case heard in open court.

A motion by the three clubs whose promotions could be scrapped - Dundee Utd, Raith Rovers and Cove Rangers - to have the case dropped was also dismissed by the judge.

That led to Hearts and Thistle saying Lord Clark had "found in our favour in two motions, while we were unsuccessful in one".

The petition from Hearts and Thistle came after SPFL clubs failed to support the league's proposal for reconstruction, which would have kept those two and League One's bottom side Stranraer up.

The two clubs added: "We feel it important to point to Lord Clark's words that: 'I do not blame the petitioners for not raising proceedings or seeking arbitration whilst that important and potentially crucial alternative [of reconstruction] was available and was actively being facilitated by the SPFL.'."

Dundee United, Raith and Cove said they remain "very disappointed and unhappy" at being drawn into proceedings, but will prepare for arbitration and "very much look forward to an early resolution".

In a statement of their own, the SPFL said the "welcome" the decision and that they will "now prepare for the Scottish FA arbitration".

So what happens now?

Lord Clark has ruled he had no other option other than to order independent arbitration and the process sounds simple.

Each party nominates an individual from the Tribunal Candidate List, and those two appoint someone who has been a judge, solicitor or advocate for at least ten years to act as chairman.

Gerry Moynihan QC, acting for the SPFL, intimated this could happen as early as Monday however, as yet, no formal dispute has been registered with the Scottish FA.

At the outset, the legal representative for Hearts and Thistle said it was unlikely an agreement could be reached through arbitration but that is now how their claims of "unfair prejudice" in being relegated will be adjudicated upon.