A formal process of debate dating from the time of Surak, in which a claim is tested before a quorum, invoked by Michael Burnham on Ni'Var to seek the SB-19 data.
The T'Kal-in-ket is an ancient Vulcan procedure for uncovering deep truths. A petitioner argues a case before a quorum, with an advocate to speak for them, and the challenge cannot be refused once a graduate of the Vulcan Science Academy invokes it.
It appears in the Discovery episode Unification III, set in 3189. Denied access to the data from the SB-19 experiment, Michael Burnham invokes the rite before President T'Rina. The quorum of three reflects the Vulcan, Romulan and mixed strands of Ni'Var society, and her advocate, drawn from the Qowat Milat, proves to be her mother Gabrielle.
Gabrielle's absolute candour forces Burnham to face her own doubts about Starfleet. Seeing the divisions the hearing is opening, Burnham withdraws her request, and T'Rina later hands her the data privately.