Partick Thistle admitted defeat in their joint legal battle against relegation with Hearts as the Scottish Professional Football League claimed vindication following an arbitration result.

The two clubs failed to overturn their demotions and were denied any compensation after claiming a combined £10million.

The pair's Court of Session action had been referred to a tribunal panel consisting of three people from the Scottish Football Association's arbitration pool of lawyers and retired members of the judiciary.

The outcome removed any uncertainty about this weekend's Scottish Premiership kick-off, with Championship winners Dundee United due to host St Johnstone while Hearts will prepare for their league season to start on October 17.

Details of the ruling following the private hearing are scarce but the panel were unanimous in rejecting Hearts and Thistle's challenge. The pair and Stranraer were consigned to the drop when clubs voted in April to curtail the season on a points-per-game average amid the coronavirus pandemic.

A statement from the tribunal said the SPFL had been entitled to pass the resolution and give effect "all that flowed from it" with the arbitration continuing only to decide on who should pay legal expenses.

A joint statement from the defeated clubs read: "As all parties have been requested not to comment on the tribunal's decision or reveal details of the hearings on the grounds of confidentiality, all we can only say is how disappointed and surprised we are at the outcome.

"We don't regret taking this action as it was the right thing for us to do. There were better ways to deal with ending the season, fairer ways other than putting the burden of a pandemic on to three clubs."

Thistle later confirmed they had drawn a line and "taken the fight to its conclusion".

"Our sole focus and our energy is now on the season ahead," the Jags said. "Our key word for the year ahead is 'success' not 'survival'. The board has already approved a financially responsible and balanced budget for season 2020/21 that gives the manager what he asked for to achieve everyone's desire for an immediate return to the Championship. The fightback has started.

"But I ask everyone associated with Thistle to never forget today. To never forget how it feels to be relegated unfairly. To never forget that there are many good decent people and clubs in Scotland who stood with us, publicly and privately – but there are some whose fear and self-interest got in the way of doing the right thing."

SPFL chief executive Neil Doncaster claimed the "clear, comprehensive and unanimous decision" exonerated the league.

"I am absolutely delighted that our approach has been vindicated throughout, following an intense period of legal scrutiny and review," he said.

"It has been a very demanding process, but I had complete confidence in the actions and decisions of the SPFL board and the SPFL executive team."

League chairman Murdoch MacLennan added: "It is regrettable that the league had to be concluded in the way that it was. However, despite calls to the contrary from some parties, subsequent events, including the virtual shutdown of our entire country for months, confirm that there was no viable alternative. With contact training only being allowed to resume on 29 June, it was simply impossible for games to be played or for season 2019/20 to continue.

"I want to make clear that it is unfortunate the early curtailment of the season relegated Hearts, Partick Thistle and Stranraer. However, in circumstances where reconstruction was comprehensively rejected by SPFL member clubs, there was no viable alternative."

Promoted Dundee United, Raith Rovers and Cove Rangers were drawn into the case after being issued with a petition by Hearts and Thistle.

United and Cove outlined why they had become so involved, stating they had been specifically named as respondents and given seven days to reply; were not prepared to stand by and watch their title achievements being undermined and that the SPFL was not in a position to fully address why clubs had voted the way they did.

The statement added: "To be clear, we had absolutely no desire to enter into costly legal proceedings raised by the petitioners. Like any responsible organisation or business served with notice of legal proceedings, we sought and obtained specialist legal advice.

"On considering that advice, we concluded that we had to enter the proceedings to protect our position. Any suggestion that we entered proceedings without justification or to stoke division is both unjustified and insulting."

Raith described the process as a "costly distraction" and thanked fans and other clubs for their support.

Hearts and Thistle will not be able to fully move on – both face SFA disciplinary hearings on August 6 after being accused of breaching rules by initially taking their case to a court of law rather than arbitration.