The state Supreme Court has not yet decided whether it will consider the university's appeal.
The case has "potentially exposed UT to years of defensive litigation in a case where the pleadings have failed the most minimal tests imposed by law," university lawyers wrote in their appeal. "If Kearney was in fact the victim of the discrimination she claims, it would not be difficult for her to identify similarly situated employees treated differently from her."
University lawyers argued Kearney hasn't shown how any of the alleged relationships raises in her lawsuit were "comparable in seriousness to Kearney's conduct."
Texas officials insist Kearney "crossed the line" of behavior for a coach and that it acted appropriately in forcing her out.
Kearney's lawyers, who declined immediate comment Wednesday, have said they will pursue witness statementsfrom some former and current Texas coaches and administrators who supervised Kearney or Applewhite, including Brown, former president Bill Powers, former men's athletic director DeLoss Dodds and current women's athletic director Chris Plonsky.
All evidence-gathering and witness interviews have been on hold since Texas pushed the case into the appeals courts in 2014.
Applewhite is the only witness deposed so far. His interview and documents previously released to Kearney's lawyers were sealed by a court order, requested by the university on the grounds that it was needed to protect private student information.