A lawyer representing promoted clubs has argued that Hearts and Partick Thistle have no right to take their case against relegation to the Court of Session.
The first hearing of the legal battle took place via video link on Wednesday under the authority of the Edinburgh court.
Hearts and Thistle launched legal action after several attempts at Scottish Professional Football League reconstruction failed to halt them slipping down a division, along with Stranraer, following a vote by clubs in April to curtail the season in the wake of the coronavirus pandemic.
Lord Clark heard a number of arguments from Garry Borland QC, acting for promoted clubs Dundee United, Raith Rovers and Cove Rangers, that the case should not have been brought to court.
He pointed out that clubs were "contractually obliged" to comply with SPFL rules and Scottish Football Association articles, and that the row was a "football dispute" which required to be settled by arbitration under the latter.
He added: "SFA members may not take a football dispute to a court of law except with prior approval of the Scottish Football Asccociation board."
Lord Clark pointed out that there was a potential timing issue with taking the case to arbitration given the Premiership season was due to start in early August and questioned whether it would be feasible for arbitration to decide the matter beforehand.
Borland argued it was feasible and blamed the petitioners for the timing issue given they had waited two months to launch legal action.
He added that it was "inconceivable" that the league could be halted if it started and Hearts subsequently won their argument, with the petitioners recognising that reality because they had sought damages if their attempts to avert relegation failed.
Borland argued against the five points made in the petition that declared both clubs had the right to pursue the matter in the courts, including that the case was not technically a "football dispute" as stated in SFA article 99.
"It is obvious that the present dispute arises out of and relates to association football," he said. "The contention of the petitioners to the contrary is fanciful.
"What they are attempting to do is stop relegation and promotion, which has been decided. Promotion and relegation are fundamental parts of football. They are the meat and drink of football."
Lawyers for the SPFL and the two clubs will speak after a break for lunch and the hearing could be extended until later in the week.
Lord Clark recognised the benefits of dealing with the matter "as swiftly as possible" but accepted the complexity of the matter might take time to consider.
The Premiership season is due to start on August 1 with the fixtures expected to be released in the next seven days.
