Model Elimination is the name attached to a pair of proof procedure

Proof procedure

In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of statements....

s invented by Donald W. Loveland, the first of which was published in 1968 in the Journal of the ACM. Their primary purpose is to carry out automated theorem proving

Automated theorem proving

Automated theorem proving or automated deduction, currently the most well-developed subfield of automated reasoning , is the proving of mathematical theorems by a computer program.- Decidability of the problem :...

, though they can readily be extended to logic programming

Logic programming

Logic programming is, in its broadest sense, the use of mathematical logic for computer programming. In this view of logic programming, which can be traced at least as far back as John McCarthy's [1958] advice-taker proposal, logic is used as a purely declarative representation language, and a...

, including the more general disjunctive logic programming.

Model Elimination is closely related to resolution

Resolution (logic)

In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic...

while also bearing characteristics of a Tableaux

Method of analytic tableaux

In proof theory, the semantic tableau is a decision procedure for sentential and related logics, and a proof procedure for formulas of first-order logic. The tableau method can also determine the satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure...

 method. It is a progenitor of the SLD resolution

SLD resolution

SLD resolution is the basic inference rule used in logic programming. It is a refinement of resolution, which is both sound and refutation complete for Horn clauses.-The SLD inference rule:...

 procedure used in the Prolog

Prolog

Prolog is a general purpose logic programming language associated with artificial intelligence and computational linguistics.Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is declarative: the program logic is expressed in terms of...

logic programming language.

While somewhat eclipsed by attention to and progress in Resolution
theorem provers, Model Elimination has continued to attract the
attention of researchers and software developers. Today there are several theorem provers under active development that are based on the Model Elimination procedure.