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...Frank P. Ramsey]], is a fragment of [[first-order logic]] formulas where [[satisfiability]] is [[Decidability (logic)|decidable]]. The satisfiability problem for this class is [[NEXPTIME]]-complete.<ref>{{citation ...

...s to the variables of the formula. It is a generalization of the [[Boolean satisfiability problem]], which asks whether there exists a truth assignment that makes al ...problem), since its solution easily leads to the solution of the [[boolean satisfiability problem]], which is [[NP-complete]]. ...

|class=[[Boolean satisfiability problem]] ...formulae]] in [[conjunctive normal form]], i.e. for solving the [[Boolean satisfiability problem|CNF-SAT]] problem. ...

...ls that aim to solve the SMT problem for a practical subset of inputs. SMT solvers such as [[Z3 Theorem Prover|Z3]] and [[cvc5]] have been used as a building ...s. The resulting decision procedures are often implemented directly in SMT solvers; see, for instance, the decidability of [[Presburger arithmetic]]. SMT can ...

...s whether there exists an [[Interpretation (logic)|interpretation]] that [[Satisfiability|satisfies]] a given [[Boolean logic|Boolean]] [[Formula (mathematical logic ...ear = 2015 | doi = 10.1109/JPROC.2015.2455034|title=Boolean Satisfiability Solvers and Their Applications in Model Checking| s2cid = 10190144 }}</ref>{{additi ...

...rovers]], including in particular [[satisfiability modulo theories]] (SMT) solvers. This approach has the disadvantage that it may require the user to underst ...are employed, most notably using [[satisfiability modulo theories]] (SMT) solvers, and [[genetic programming]],<ref>{{cite journal |last1=Le Goues |first1=Cl ...

...type|Boolean]] domains, where only true/false constraints apply ([[Boolean satisfiability problem|SAT problem]]) % in other Prolog environments or using other constraint solvers. ...

...of a theorem) to be reduced to (potentially infinitely many) propositional satisfiability problems.<ref>{{cite thesis |first=J. |last=Herbrand |title=Recherches sur ...rogram used conversion to [[disjunctive normal form]], a form in which the satisfiability of a formula is obvious.<ref name=Davis2001/><ref>{{cite journal|last=Gilmo ...

...nment]] (IDE) for formal methods. In recent years, a substantial number of theories and system extensions have been collected in the Isabelle ''Archive of Form ...of-automation interface, external [[satisfiability modulo theories]] (SMT) solvers (including [[CVC4]]) and [[Resolution (logic)|resolution]]-based [[automate ...

Presburger arithmetic can be viewed as a [[First-order logic#First-order theories, models, and elementary classes|first-order theory]] with equality containi ...burger arithmetic formulas. More recent [[satisfiability modulo theories]] solvers use complete [[integer programming]] techniques to handle quantifier-free f ...

*solvers for [[differential equation]]s<ref>{{Cite web|title=dsolve - Maple Programm * [[Satisfiability modulo theories]] ...

...lly, the [[Boolean satisfiability problem]] (SAT), [[satisfiability modulo theories]] (SMT), [[mixed integer programming]] (MIP) and [[answer set programming]] ...with tutorials of [[Constraint programming|CP]], ASP, Boolean SAT and SMT solvers. In the general case, constraint problems can be much harder, and may not b ...

...ograms]] using a theorem-prover (like [[satisfiability modulo theories|SMT-solvers]] or [[Interactive theorem proving|proof assistants]]): see [[Frama-C]] or ...

...'' or ''equational unification'', or '''E-unification''', or ''unification modulo theory''. ...rard|last2=Huet|title=Complete Sets of Unifiers and Matchers in Equational Theories|journal=Theoretical Computer Science|volume=43|pages=189–200|year=1986|doi= ...

...=978-3-540-32247-4|s2cid=5223577 }}</ref> and even [[Satisfiability modulo theories|SMT]] formulas<ref>{{Cite book |last1=Hoder |first1=Kryštof |last2=Bjørner ...ref> Datalog has been integrated with [[Satisfiability modulo theories|SMT solvers]] to make it easier to write certain static analyses.<ref>{{Cite journal |l ...