Hearts insist they will continue to fight after their case with Partick Thistle against the SPFL will go to SFA arbitration.
Lord Clark made his ruling at Edinburgh's Court of Session at around 2pm this afternoon.
Hearts and Partick want relegations to be scrapped or a combined £10million in compensation, but their case will not be heard in court.
The Tynecastle club said in a joint statement with Thistle: "After three days of detailed and complex submissions, Heart of Midlothian and Partick Thistle today learned the outcome of our preliminary hearing in the Court of Session, presided over by Lord Clark.
"It is important to note that this was only to determine how to proceed.
"Lord Clark found in our favour in two motions while we were unsuccessful in one. While denied the opportunity for a public hearing in Court this simply means we now pursue the same outcome in a different forum.
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"Importantly, we were successful in the motion to get access to a number of documents that will be key to support our case in arbitration.
"Both clubs are also pleased to have received a fair hearing and 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.
"We promised our supporters that we would fight for them and we shall continue to do so.
"Neither club will be making any further comment today. "
