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Automated theorem proving

Definition

Automated theorem proving is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.

Related concepts

ACL2 ACM Transactions on Programming Languages and Systems AMD Abstract logic Ackermann set theory Ada (programming language)Alan Turing Aleph number Alfred North Whitehead Algebraic logic Allen Newell Alonzo Church Alphabet (formal languages)Alt-Ergo Andrei Voronkov (computer scientist)Andrei Voronkov (scientist)Argonne National Laboratory Argument Aristotelian logic Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated reasoning Automath Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras BSD Licenses Baden-Württemberg Cooperative State University Banach–Tarski paradox Begriffsschrift Benchmark (computing)Bertrand Russell Bijection Binary decision diagram Binary operation Boolean algebra Boolean algebras canonically defined Boolean function CADE ATP System Competition CARINE CVC (theorem prover)Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Cliff Shaw Co-NP-complete Codomain Compactness theorem Complement (set theory)Complete theory Completeness (logic)Computability Computability theory Computable function Computable set Computably enumerable Computably enumerable set Computer-aided proof Computer algebra system Computer program Computer science Concrete category Connect Four Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Countable set Curry–Howard correspondence DPLL algorithm David Luckham De Bruijn factor Decidability (logic)Decision problem Deductive system Defense Technical Information Center Diagram (mathematical logic)Discourse representation theory Disjunctive normal form Domain of a function Donald W. Loveland E theorem prover Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Elsevier Empty set Enumeration Equational prover Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Existential quantification Exponential time Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Finitary relation Finite-valued logic Finite model theory Finite set First-order logic First-order resolution First-order theory Fixed-point logic Floating point unit Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal semantics (natural language)Formal specification Formal system Formal verification Formation rule Foundations of geometry Foundations of mathematics Four color theorem FreeBSD license Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set GPL General Problem Solver General set theory Gottlob Frege Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Handbook of Automated Reasoning Herbert A. Simon Herbrand interpretation Herbrand universe Hereditary set Heuristic (computer science)Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Inference Inference rule Infinite-valued logic Infinite set Information theory Inhabited set Injective function Institute for Advanced Study Integer Integrated circuit design Intel Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)IsaPlanner Isabelle (proof assistant)Isomorphism JOHNNIAC Jacques Herbrand Jape (software)Jean Gallier John Alan Robinson Journal of Automated Reasoning KeY Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Kurt Gödel LCF (theorem prover)Lambda calculus Language (logic)Large cardinal Larry Wos Lemma (mathematics)Leopold Löwenheim Lindström's theorem List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logic Theorist Logic programming Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Löwenheim–Skolem theorem MIT License MIT Press Mace4 Many-valued logic Map (mathematics)Martin Davis (mathematician)Material conditional Mathematical induction Mathematical logic Mathematical object Mathematical proof Mathematical theorem Max Planck Institute for Computer Science McGraw–Hill Melvin Fitting Metalanguage Metamath Method of analytic tableaux Michael Kohlhase Minimal axioms for Boolean algebra Mizar system Model checking Model complete theory Model elimination Model theory Modus ponens Mojżesz Presburger Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory Mozilla Public License NP (complexity)Naive set theory Natural deduction Natural language processing Natural numbers Negation New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Non-surveyable proofs Notices of the American Mathematical Society NuPRL On Formally Undecidable Propositions of Principia Mathematica and Related Systems Open formula Operation (mathematics)Ordinal analysis Ordinal number Otter (theorem prover)P (complexity)P versus NP problem Paradox (theorem prover)Paradoxes of set theory Paramodulation Partition of a set Pascal (programming language)Peano axioms Pentium FDIV bug Philosophy of mathematics PhoX Power set Predicate (mathematical logic)Predicate logic Predicate variable Presburger arithmetic Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Program analysis (computer science)Program synthesis Program verification Proof assistant Proof checking Proof complexity Proof compression Proof of impossibility Proof theory Proof verification Proposition Propositional calculus Propositional formula Propositional logic Propositional variable Prototype Verification System Prover9 Quantifier (logic)Quantifier elimination Quantifier rank Ramanujan machine Recursion Recursive set Relation (mathematics)ResearchCyc Resolution (logic)Reverse mathematics Rewriting Robbins conjecture Robinson arithmetic Rule of inference Russell's paradox SETHEO SNARK theorem prover SPARK (programming language)SPASS Satisfiability Satisfiability modulo theories Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (logic)Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Stanford University Strength (mathematical logic)Strftime String (formal languages)Structure (mathematical logic)Stuttgart Substitution (logic)Substructure (mathematics)Superposition calculus Supertask Surjective function Syllogism Symbol (formal)Symbolic computation Syntax (logic)System on TPTP T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Technical University of Munich Term (logic)Term logic The Foundations of Arithmetic Theorem Theorem Proving System Theories of truth Theory (mathematical logic)Thoralf Skolem Thousands of Problems for Theorem Provers Three-valued logic Timeline of mathematical logic Transfer principle Transitive set True arithmetic Truth predicate Truth table Truth value Turing machine Twelf Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Unification (computing)Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)University of Manchester Urelement Vacuum-tube computer Validity (logic)Vampire theorem prover Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Wolfgang Bibel Wolfram Mathematica Z3 Theorem Prover Zermelo–Fraenkel set theory

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