  Gentzen wrote that he was unable to prove a normalization theorem for a classical system of ND. He therefore invented another logical  calculus that he called sequent calculus (Sequenzenkalkul,  literally “calculus of sequences”) and made it the  central topic of his thesis. The name of the calculus comes from the  representation of assumptions of a derivation as a list. The word  “sequent” used as a noun is a suggestion of Kleene's in  his Introduction to Metamathematics (1952: 441), taken up  in many languages in the form of purely invented words.