  Hilbert called the validity problem for first-order logic, the entscheidungsproblem. In a textbook, Principles of Mathematical Logic by Hilbert and Ackermann, the authors wrote, “The Entscheidungsproblem is solved when we know a procedure that allows for any given logical expression to decide by finitely many operations its validity or satisfiability.… The entscheidungsproblem must be considered the main problem of mathematical logic.” (Böerger, Grädel, &amp; Gurevich 1997).