Justice Chelameswar, who represented the four judges in an unprecedented press conference, said they had approached the CJI with a letter but failed to convince him.
However, Justice Chelameswar asked Sibal and Prashant Bhushan to come back tomorrow (Tuesday).
Naidu had said that his decision conformed with provisions in the Constitution and the Judges Inquiry Act.
"It is submitted that it is not the Chairman's prerogative to adjudicate whether there has been any abuse by the Hon'ble CJI of his power as the Master of the Roster".
"That merits of the charges are for the inquiry committee to investigate and present a report on".
"The order cites judicial authorities and goes into an impermissible arena of quasi-judicial determination of Charge No.5 which is impermissible and illegal", it said. "All facts as stated in motion don't make out a case which can lead any reasonable mind to conclude that CJI on these facts can be ever held guilty of misbehavior", said Naidu further.
It is contended that this provision pertains to the genuineness and authenticity of the signatures to the Notice of Motion, and can not extend to going into the merits of the motion.
"It is odd that when the motion related to the impeachment of the Chief Justice, the chairman deemed it fit to consult legal luminaries, constitutional experts, former secretary generals, former law officers, Law Commission members and eminent jurists but had not thought it appropriate and fit to consult the judges of the Supreme Court of India".
They have also petitioned that the order passed by Naidu be set aside.
Naidu then held discussions with a number of constitutional and legal experts, including Attorney General KK Venugopal, and former top law officer K Parasaran.
The petition said, "That Chief Justice Dipak Misra acquired land when he was an advocate, by giving an affidavit that was found to be false and despite the orders of the ADM cancelling the allotment in 1985, surrendered the said land only in 2012 after he was elevated to the Supreme Court". It has also been prayed that Section 3 (1) of the Judges Inquiry Act be read down, and that the Court issued an order directing the Chairman to expeditiously refer the charges highlighted in the motion to an Inquiry Committee.
Facing the possibility of an impeachment motion against him, Justice Pardiwala expunged the remarks he had made against reservation in the Hardik Patel case order on an application by the state government seeking removal of the controversial portion.