Automated theorem proving

Automated theorem proving uses computational methods to search for or verify formal proofs. Systems range from general-purpose proof search to specialized solvers for restricted logics.

Resolution (logic): A rule of inference that derives a clause by eliminating complementary literals from two clauses. Resolution underlies many automated searches for proofs by contradiction.
Formal logic: The study of formal systems of inference and the properties of valid reasoning. Automated provers implement formal reasoning within precisely specified logics.
Interactive theorem proving: The construction and checking of formal proofs with human guidance and software assistance. It contrasts with attempts to automate proof search with little or no guidance.
Logic Theorist: A 1950s computer program that proved theorems in propositional logic using heuristic search. It was an early demonstration that machines could discover formal proofs.
Unification: The process of finding substitutions that make two symbolic expressions identical. Unification lets a prover match inference rules to expressions in a goal.
First-order logic: A logical system with predicates, variables, quantifiers, and relations over a domain. Many theorem provers target its expressive language and inference rules.
Model checking: An automated method for checking whether a finite-state model satisfies a specified property. It often explores states directly rather than searching for a derivation in a proof calculus.
Davis–Putnam algorithm: An algorithm for deciding propositional satisfiability through variable elimination and related rules. It helped establish practical automated reasoning for propositional formulas.
Sequent calculus: A formal proof system that derives sequents using rules for logical connectives and quantifiers. Its structured inference rules provide a framework for proof search.
Formal system: A language, a set of axioms, and rules for deriving statements. A prover needs these components to define which conclusions count as proofs.

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