Herbrands Theorem

Herbrand’s Theorem Automated theorem proving has two goals: (1) to prove theorems and (2) to do it automatically. Fully automated theorem provers for first-order logic have been developed, starting in the 1960’s, but as theorems get more complicated, the time that theorem provers spend tends to grow exponentially. As a result, no really interesting theorems of mathematics can be proved this way- the human life span is not long enough. Therefore a major problem is to …

…the early 1980s, however, they began successfully to be applied, not just to theorems whose proofs were known, but to the proof of open conjectures in several specialized fields of mathematics (conjectures that humans had formed but which they had been unable themselves to prove): see the articles by Winker and Wos in 1978,lxxxvi by Winker, Wos and Lusk in 1981,lxxxvii by Winker in 1982,lxxxviii by Wos in 1982,lxxxix and Wos and colleagues in 1983.xc