In a joint statement, the “extremely unhappy” trio say that could “potentially have catastrophic financial implications” not just for them, but for each of the SPFL’s 42 clubs.
They also confirm they have instructed lawyers to act for them.
“We have undertaken extensive and costly preparations for a new season in new leagues, including obtaining major financial commitments from our supporters, business partners and stakeholders,” the statement read. “Our removal from those leagues would be ruinous on and off the field.
“Our status as champions is not being contested, and nor should the promotion which has always, and should always, come with it. We must and will robustly defend our position.”
After filing the petition in Edinburgh on Wednesday, Hearts and Thistle said they “have no wish to disrupt” Scottish football, but “reserve the right” to try to delay the Scottish Premiership season.
The SPFL had seven days from then to respond to the petition, and a spokesman for the league said its solicitors are “studying this carefully”.
Hearts, Thistle and Stranraer had their demotions confirmed on Monday when clubs failed to support league reconstruction to extend the top flight from 12 teams to 14.
That followed a vote in April to curtail the campaign, with Hearts bottom of the Premiership and Thistle last in the Championship.