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Subfield of automated reasoning and mathematical logic
is allowed to be infinite enumerable. It follows that an automated theorem prover will fail to terminate while searching for a proof precisely when the
Automated_theorem_proving
Topics referred to by the same term
Theorem prover may refer to: Automated theorem prover Proof assistant, an interactive theorem prover This disambiguation page lists articles associated
Theorem_prover
Software for solving satisfiability problems
Z3, also known as the Z3 Theorem Prover, is a satisfiability modulo theories (SMT) solver developed by Microsoft. Z3 was developed in the Research in Software
Z3_Theorem_Prover
Interactive theorem prover software
computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by
Proof_assistant
E is a high-performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely
E_(theorem_prover)
Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester
Vampire_(theorem_prover)
1970s automated theorem prover
Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in
Logic for Computable Functions
Logic_for_Computable_Functions
Interactive theorem proving systems
Heidelberg: Springer-Verlag. ISBN 978-3-540-45949-1. "HOL Interactive Theorem Prover". "HOL Light". See LICENSE file in the tarball Archived 2012-03-03 at
HOL_(proof_assistant)
Programming language and theorem prover
language, an extensible theory in a first-order logic, and an automated theorem prover. ACL2 is designed to support automated reasoning in inductive logical
ACL2
Proof assistant
The Rocq Prover (formerly named Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical
Rocq
Proof assistant and programming language
2021, Lean 4 was released, which was a reimplementation of the Lean theorem prover capable of producing C code which is then compiled, enabling the development
Lean_(proof_assistant)
Higher-order logic (HOL) automated theorem prover
The Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As a Logic for Computable Functions
Isabelle_(proof_assistant)
Reasoning for mathematical statements
The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic
Mathematical_proof
Automated theorem prover
OTTER (Organized Techniques for Theorem-proving and Effective Research) is an automated theorem prover developed by William McCune at Argonne National
Otter_(theorem_prover)
Functional programming language
Vreeswijk, which is about a hen named Agda. This alludes to the name of the theorem prover Rocq, which was originally named Coq after Thierry Coquand. The main
Agda_(programming_language)
SNARK, (SRI's New Automated Reasoning Kit), is a theorem prover for multi-sorted first-order logic intended for applications in artificial intelligence
SNARK_(theorem_prover)
Software used in mathematical applications
ETPS F* HOL theorem prover HOL Light HOL4 Isabelle Jape Lean LEGO Matita Metamath MINLOG Mizar Nqthm NuPRL PhoX PVS Rocq Theorem Proving System Twelf
Mathematical_software
Software system
Nqthm is a theorem prover sometimes referred to as the Boyer–Moore theorem prover. It was a precursor to ACL2. The system was developed by Robert S. Boyer
Nqthm
theorem proving ACL2 theorem prover E equational theorem prover Gandalf theorem prover HOL theorem prover Isabelle theorem prover LCF theorem prover Otter
List of mathematical logic topics
List_of_mathematical_logic_topics
Logical problem studied in computer science
solvers, and the CVC format[citation needed] used by the CVC automated theorem prover. The SMT-LIB format also comes with a number of standardized benchmarks
Satisfiability modulo theories
Satisfiability_modulo_theories
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Fundamental theorem in mathematical logic
using the Isabelle theorem prover. Other proofs are also known. Original proof of Gödel's completeness theorem Trakhtenbrot's theorem Batzoglou, Serafim
Gödel's_completeness_theorem
Establishment of a theorem using inference from the axioms
help of computers in interactive theorem proving (e.g., through the use of proof checker and automated theorem prover). Significantly, these proofs can
Formal_proof
Software projects developed at universities
analyzer (MIT) Boyer–Moore theorem prover – automated theorem prover (Texas) FDR – CSP refinement checker (Oxford) HOL – theorem proving system (Cambridge) ISP
List of software developed at universities
List_of_software_developed_at_universities
Component of artificial intelligence systems
engines, artificial intelligence researchers focused on more powerful theorem prover environments that offered much fuller implementations of first-order
Inference_engine
Computer scientist
Leonardo de Moura is a computer scientist, and creator of the Z3 Theorem Prover and the Lean proof assistant during his time at Microsoft Research. He
Leonardo_de_Moura
Type of logical system
W. J., PVS Prover Guide 7.1 (Menlo Park: SRI International, August 2020). Fitting, M., First-Order Logic and Automated Theorem Proving (Berlin/Heidelberg:
First-order_logic
System of formal mathematical logic
higher-order logic and closely related to the logics of the HOL theorem prover family. The theorem proving systems TPS and ETPS Archived 2011-04-11 at the Wayback
Q0_(mathematical_logic)
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Theorem in topology
and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology. The theorem is also used for proving deep results about
Brouwer_fixed-point_theorem
General purpose functional programming language
(Meta Language) is the metalanguage developed for the Edinburgh LCF theorem prover in the 1970s. It is an early statically typed, functional language with
ML_(programming_language)
SMTLIB2-compliant, such as the Z3 Theorem Prover. Formal verification Vazou, Niki (2016). Liquid Haskell: Haskell as a theorem prover (Thesis). University of California
Liquid_Haskell
SMT solver
problem of constructing a formula B that can be conjoined with a formula A to prove a goal formula C. cvc5 has been subject to several independent test campaigns
Cooperating_Validity_Checker
Proof assistant program
assistant for classical higher-order logic. It is a member of the HOL theorem prover family. Compared with other HOL systems, HOL Light is intended to have
HOL_Light
In mathematics, a statement that has been proven
deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms
Theorem
Statement in mathematical combinatorics
errors. The formal proof was carried out using the HOL4 interactive theorem prover, limiting the potential for errors to the HOL4 kernel. Rather than directly
Ramsey's_theorem
Formal languages for expressing mathematical theories
the time, however, and so never achieved widespread use; nonetheless, it proved very influential in the later development of logical frameworks and proof
Automath
Method of deriving conclusions
inferences and solve problems. These frameworks often include an automated theorem prover, a program that uses rules of inference to generate or verify proofs
Rule_of_inference
American computer scientist
Strother Moore, for his work on the Boyer-Moore Theorem Prover. Matt Kaufman: The Boyer-Moore Theorem Prover (2005) Archived 2009-08-27 at the Wayback Machine
Matt_Kaufmann
counterexample. In 1996, William McCune proved the conjecture using the automated theorem prover EQP (equational prover). EQP was developed by McCune while
Robbins_algebra
Mathematical logician and computer scientist
Paris-Saclay University, best known for developing the interactive theorem prover Rocq. Paulin-Mohring received her PhD in 1989, under the supervision
Christine_Paulin-Mohring
Programming language that uses first order logic
the use of a resolution theorem prover with Horn clauses of the form: H :- B1, ..., Bn. The application of the theorem-prover treats such clauses as procedures:
Prolog
1995 publication in mathematics
theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Automated theorem proofer
automated theorem prover for first-order and equational logic developed by William McCune. Prover9 is the successor of the Otter theorem prover also developed
Prover9
Topics referred to by the same term
language Coq, the French word for "rooster" or "cock" Coq, an interactive theorem prover, renamed to Rocq in 2025 CoQ, common term for Coenzyme Q10, a naturally
Coq
Planar maps require at most four colors
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Characterization of how many integers are prime
Pillai–Selberg theorem and Erdős–Delange theorem. In 2005, Avigad et al. employed the Isabelle theorem prover to devise a computer-verified variant of
Prime_number_theorem
Finite-domain model finder for pure first-order logic with equality
University of Technology. It can a participate as part of an automated theorem proving system. The software is written mostly in the programming language
Paradox_(theorem_prover)
Collection of problems for Automated Theorem Proving
TPTP (Thousands of Problems for Theorem Provers) is a freely available collection of problems for automated theorem proving. It is used to evaluate the efficacy
Thousands of Problems for Theorem Provers
Thousands_of_Problems_for_Theorem_Provers
American computer scientist
the Working Programmer. His research is based around the interactive theorem prover Isabelle, which he introduced in 1986. He has worked on the verification
Lawrence_Paulson
Methods in artificial intelligence research
checker. ACL2 is a theorem prover that can handle proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also known as Nqthm. Knowledge-based
Symbolic artificial intelligence
Symbolic_artificial_intelligence
Graph data structure
produce proof certificates. E-graphs are also used in the Simplify theorem prover of ESC/Java. Equality saturation is used in specialized optimizing compilers
E-graph
American mathematician, computer scientist and philosopher
Boyer–Moore automated theorem prover, Nqthm, in 1992. Following this, he worked with Moore and Matt Kaufmann on another theorem prover called ACL2. He was
Robert_S._Boyer
methodology originates in the field of automated theorem proving and, more specifically, in the Vampire theorem prover project. The idea is inspired by the use
Run-time algorithm specialization
Run-time_algorithm_specialization
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Subfield of computer science and logic
argumentation system that is more specific than being just an automated theorem prover. Tools and techniques of automated reasoning include the classical logics
Automated_reasoning
American mathematician (1937–2025)
bandage completely. His research group designed the TPS, an automated theorem proving system for first-order and higher-order logic. A subsystem ETPS of
Peter_B._Andrews
Mathematical program specifications
validation (using theorem proving, BDDs, and symbolic evaluation), optimization for Intel IA-64 architecture using HOL light theorem prover, and verification
Formal_methods
Relates rational elliptic curves to modular forms
and Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's Last Theorem (FLT). Later, a series
Modularity_theorem
Theorem constraining types of hidden-variable theories
quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–KS theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B
Kochen–Specker_theorem
Every set is smaller than its power set
simplicity of the above proof, it is rather difficult for an automated theorem prover to produce it. The main difficulty lies in an automated discovery of
Cantor's_theorem
British computer scientist
Gordon led the development of the HOL theorem prover. The HOL system is an environment for interactive theorem proving in a higher-order logic. Its most outstanding
Michael_J._C._Gordon
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Inference rule in logic, proof theory, and automated theorem proving
mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation-complete theorem-proving technique for sentences in
Resolution_(logic)
Used to compare mixed characteristic situations with purely finite characteristic ones
Foundations of Perfectoid Spaces by Matthew Morrow Lean perfectoid spaces. The definition of perfectoid spaces formalized in the Lean theorem prover
Perfectoid_space
Process of achieving a goal by overcoming obstacles
using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering
Problem_solving
Decomposition of periodic functions
case. An alternative extension to compact groups is the Peter–Weyl theorem, which proves results about representations of compact groups analogous to those
Fourier_series
Heuristic search algorithm for evaluating game trees
Johann Schumann; Christian Suttner (1989). "Learning Heuristics for a Theorem Prover using Back Propagation.". In J. Retti; K. Leidlmair (eds.). 5. Österreichische
Monte_Carlo_tree_search
Proof assistant
introduction to the main functionalities of the Matita interactive theorem prover, offering a guided tour through a set of non-trivial examples in the
Matita
Theorem that arithmetical truth cannot be defined in arithmetic
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of
Tarski's undefinability theorem
Tarski's_undefinability_theorem
Structure editor for monomorphic Martin-Löf type theory
ALF ("Another logical framework") is a structure editor for monomorphic Martin-Löf type theory developed at Chalmers University. It is a predecessor of
ALF_(proof_assistant)
Subfield of artificial intelligence
net by generating it from symbolic rules. Examples include the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated
Neuro-symbolic_AI
Topics referred to by the same term
central line Chronic venous congestion Citrus variegated chlorosis CVC theorem prover Current–voltage characteristic Conserved vector current Contractile
CVC
Uniqueness of countable dense linear orders
formalized as a computer-verified proof using Rocq, an interactive theorem prover. This formalization process led to a strengthened result that when two
Cantor's_isomorphism_theorem
Decidable first-order theory of the natural numbers with addition
describe an automatic theorem prover that uses the simplex algorithm on an extended Presburger arithmetic without nested quantifiers to prove some of the instances
Presburger_arithmetic
The name originally stood for Synergetic Prover Augmenting Superposition with Sorts. The theorem-proving system is released under the FreeBSD license
SPASS
Family of computer programming languages
logic. Given a theorem, it can find a proof, making it a theorem-prover. Given a proof, it can find the theorem, making it a theorem-checker. Given part
MiniKanren
Many (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement
Superposition_calculus
Argument that leads to a logical absurdity
show that a given statement is entailed by given hypotheses, the automated prover assumes the hypotheses and the negation of the statement, and attempts to
Reductio_ad_absurdum
Impossible task in computing
Church in 1935–36 (Church's theorem) and independently shortly thereafter by Alan Turing in 1936 (Turing's proof). Church proved that there is no computable
Entscheidungsproblem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Argument for the existence of God
Attempts have also been made to validate Anselm's proof using an automated theorem prover. Other arguments have been categorised as ontological, including those
Ontological_argument
Classification theorem in group theory
mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s by Walter
Feit–Thompson_theorem
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Programming language
programming with formal specification. ATS has support for combining theorem proving with practical programming through the use of advanced type systems
ATS_(programming_language)
Theorem in quantum mechanics
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion)
Spin–statistics_theorem
Computer programming language
being developed. The Abella theorem prover has been designed to provide an interactive environment for proving theorems about the declarative core of
ΛProlog
Finiteness of sets of forbidden graph minors
In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph
Robertson–Seymour_theorem
American computer scientist (1945–2020)
research group developed the first parallel resolution theorem prover (Parthenon) and a theorem prover based on a symbolic computation system (Analytica)
Edmund_M._Clarke
Study of discrete mathematical structures
computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are
Discrete_mathematics
logic program, deductive database, or automated theorem prover. Many operations in automatic theorem provers require search in huge collections of terms and
Term_indexing
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
American computer scientist and author
Kaustuv Chaudhuri, Miller helped design the Abella interactive theorem prover. Since this prover directly supports λ-tree syntax, it is possible to use it
Dale_Miller_(academic)
Experimental programming language
indices of type Nat (natural numbers). Dependent ML employs a constraint theorem prover to decide a strong equational theory over the index expressions. DML's
Dependent_ML
CLIPS Expect LaTeXML Lemon (parser generator) MPICH MUMPS Netlib Otter (theorem prover) PForth SLIME SQLite Steel Bank Common Lisp Citadel (software) Climm
List of public domain projects
List_of_public_domain_projects
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_theorem
On triangles inscribed in a circle with a diameter as an edge
∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in
Thales's_theorem
Theorem for proving more complex theorems
proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma
Lemma_(mathematics)
Gives conditions that guarantee the max–min inequality holds with equality
mathematical area of game theory and of convex optimization, a minimax theorem is a theorem that claims that max x ∈ X min y ∈ Y f ( x , y ) = min y ∈ Y max
Minimax_theorem
Topics referred to by the same term
Metis (American musician) (fl. 21st century), American rapper Metis (theorem prover) Metis (Japanese musician) (born 1984), reggae singer Metis (moon),
Metis
THEOREM PROVER
THEOREM PROVER
Girl/Female
Greek
God's name.
Girl/Female
Egyptian
Great.
Girl/Female
Australian, Danish, Greek, Netherlands
Name of God
Girl/Female
Hindu
One who is deft in all theories
Girl/Female
Biblical
An offering dedicated to God.
Girl/Female
Biblical
There they are, their riches.
Girl/Female
Arabic
Happines
Girl/Female
Muslim/Islamic
Surah Tehrem in Quran
Biblical
Jehovah is there,the Lord is there
Boy/Male
Indian
There have been notable men
Boy/Male
Muslim
There have been notable men
Biblical
an offering dedicated to God
Biblical
there is God;
Boy/Male
Biblical
The Lord is there.
Girl/Female
Australian, Greek
Watcher
Biblical
there is God;
Surname or Lastname
English and Scandinavian
English and Scandinavian : variant of Thor.French (Thoré) : nickname for a strong or violent individual, from Old French t(h)or(el) ‘bull’. Compare Spanish Toro.French (Thoré) : from a reduced pet form of the personal name Maturin.
Girl/Female
German, Greek, Swedish
Harvester
Girl/Female
Greek
Watcher.
Girl/Female
Tamil
Sarvashaastramayi | ஸரà¯à®µà®·à®¾à®¸à¯à®¤à¯à®°à®®à®¯à¯€
One who is deft in all theories
Sarvashaastramayi | ஸரà¯à®µà®·à®¾à®¸à¯à®¤à¯à®°à®®à®¯à¯€
THEOREM PROVER
THEOREM PROVER
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Latin
Crowned with Laurels; Form of Lawrence; Laurel-crowned; From Laurentium
Boy/Male
Muslim
Prettiest face on the Moon, Bright star
Girl/Female
Indian, Tamil
Loveable; Cute; Life is Beautiful
Boy/Male
Indian
A wish, Desire
Female
French
French form of Latin Regina, RÉGINE means "queen."
Boy/Male
Hindu
Having principal place on arjunas flag
Biblical
bound; limit
Boy/Male
Bengali, Hindu, Indian
Lord Krishna
Surname or Lastname
English
English : variant of Wild, with the addition of Middle English man ‘man’.German (Wildmann) : from a short form of the Germanic personal name Wilto + Middle High German man ‘man’.
Girl/Female
Irish
Meaning “thirst†as in “thirst for goodness or knowledge.†St. Ide and St. Brigid are considered the most influential woman saints of early Irish Christianity. Associated with education, Ide founded a monastery in Killeedy in County Limerick where a holy well is dedicated to her. In an earlier legend she was the foster-mother of the infant Jesus.
THEOREM PROVER
THEOREM PROVER
THEOREM PROVER
THEOREM PROVER
THEOREM PROVER
n.
The science, as distinguished from the art; as, the theory and practice of medicine.
v. t.
To formulate into a theorem.
v. i.
To form a theory or theories; to form opinions solely by theory; to speculate.
n.
The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments.
pron.
In that matter, relation, etc.; at that point, stage, etc., regarded as a distinct place; as, he did not stop there, but continued his speech.
n.
That which is considered and established as a principle; hence, sometimes, a rule.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
The act or product of theorizing; the formation of a theory or theories; speculation.
n.
Speculation; theory.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
pl.
of Theory
n.
One who constructs theorems.
n.
One who forms theories; one given to theory and speculation; a speculatist.
n.
An instrument made like large lute, but having two necks, with two sets of pegs, the lower set holding the strings governed by frets, while to the upper set were attached the long bass strings used as open notes.
a.
Theorematic.
a.
Of or pertaining to the theorica.
n.
An exposition of the general or abstract principles of any science; as, the theory of music.
n.
A doctrine, or scheme of things, which terminates in speculation or contemplation, without a view to practice; hypothesis; speculation.
a.
Relating to, or skilled in, theory; theoretically skilled.
n.
A statement of a principle to be demonstrated.