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...r in [[mathematical logic]], [[computer algebra]], and [[automated theorem proving]], a '''fresh variable''' is a variable that did not occur in the context c | title = Theorem Proving in Higher Order Logics, 9th International Conference, TPHOLs'96, Turku, Fin ...

| name = Z3 Theorem Prover | logo = Z3 Theorem Prover Logo 329x329.jpg ...

...ringer.com/chapter/10.1007/978-3-319-24312-2_13 |conference=TABLEAUX 2015: Automated Reasoning with Analytic Tableaux and Related Methods, Wrocław, Poland |seri Such a normal form is commonly used for [[automated theorem proving]] using [[tableau calculi]] and [[resolution calculi]] techniques due to it ...

...tion Proofs via Partial Regularization''. 23rd International Conference on Automated Deduction, 2011.</ref> '''Theorem:''' Let <math>\varphi</math> be a potentially [[redundant proof]], and <mat ...

| journal = [[Journal of Automated Reasoning]] ...first=William |title=Solution of the Robbins Problem |journal=[[Journal of Automated Reasoning]] |volume=19 |year=1997 |issue=3 |pages=263–276 |doi=10.1023/A:10 ...

...] tools such as [[SAT solver]]s, [[SMT solver|SMT-solvers]], [[first-order theorem provers]] and [[proof assistant]]s. ...onal Resolution Proofs via Partial Regularization]''. 23rd [[Conference on Automated Deduction]], 2011.</ref> ...

==Theorem== {{harvtxt|Dyckhoff|Negri|2015}} list eight consequences of the above theorem that explain its significance (omitting footnotes and most references):{{sf ...

...ty can be [[formal proof|derived]] using that system, i.e. is one of its [[theorem]]s; otherwise the system is said to be '''incomplete'''. ...emantically complete" when all its [[tautology (logic)|tautologies]] are [[theorem]]s, whereas a formal system is "sound" when all theorems are tautologies (t ...

...so called a '''Cook–Reckhow propositional proof system''', is a system for proving [[classical logic|classical]] [[propositional logic|propositional]] tautolo ...on-deterministic algorithm for solving membership in TAUT. This means that proving a superpolynomial proof size lower-bound for pps would rule out existence o ...

...in Computer Science |volume=12842 |pages=74–91 |location=Cham |conference=Automated Reasoning with Analytic Tableaux and Related Methods: 30th International Co ...tle=Efficient Strategies for CEGAR-Based Model Checking|journal=Journal of Automated Reasoning|volume=64|issue=4|pages=1051–1091|date=11 November 2019|doi=10.10 ...

...>[[Melvin Fitting|Fitting, M.]], ''First-Order Logic and Automated Theorem Proving'' (Berlin/Heidelberg: Springer, 1990), [https://books.google.com/books?id=e ...>[[Melvin Fitting|Fitting, M.]], ''First-Order Logic and Automated Theorem Proving'' (Berlin/Heidelberg: Springer, 1990), [https://books.google.com/books?id=e ...

[[Theorem-prover|Theorem provers]] based on the [[Resolution (logic)|resolution]] or [[Superposition ...Comprehensive Framework for Saturation Theorem Proving |journal=Journal of Automated Reasoning |language=en |volume=66 |issue=4 |pages=499–539 |doi=10.1007/s108 ...

...onsistency for first-order logic, a result known as [[Gödel's completeness theorem]]. The negation of satisfiability is unsatisfiability, and the negation of ...In [[universal algebra]], [[equational theory]], and [[automated theorem proving]], the methods of [[term rewriting]], [[congruence closure]] and [[unificat ...

...t=Geoff |chapter=The Lean 4 Theorem Prover and Programming Language |title=Automated Deduction – CADE 28 |series=Lecture Notes in Computer Science |volume=12699 ...|editor1-first=Andr'e |editor2-last=Sutcliffe |editor2-first=Geoff |title=Automated Deduction -- CADE 28 |date=2021 |publisher=Springer International Publishin ...

'''Theorem.''' For an ARS the following three conditions are equivalent: (i) it has th '''Theorem''' ([[Newman's Lemma]]): A terminating ARS is confluent if and only if it i ...

...ing only the three operations, but cannot prove with the axioms. However, proving seemingly innocuous statements can require long proofs using only the above ...>Jian Zhang, ''Computer search for counterexamples to Wilkie's identity'', Automated Deduction – CADE-20, [[Springer Science+Business Media|Springer]] (2005), p ...

...first2=Greg |last3=Saxe |first3=James B. |date=May 2005 |title=Simplify: a theorem prover for program checking |journal=Journal of the ACM |volume=52 |issue=3 ...ite book|last1=de Moura|first1=Leonardo|last2=Bjørner|first2=Nikolaj|title=Automated Deduction – CADE-21 |chapter=Efficient E-Matching for SMT Solvers |date=200 ...

...y]] and [[model theory]], branches of mathematics, '''Cantor's isomorphism theorem''' states that every two countable [[dense order|dense]] unbounded [[Total ...forth" half of this method. In terms of [[model theory]], the isomorphism theorem can be expressed by saying that the [[first-order theory]] of unbounded den ...

== Theorem provers == {{excerpt|Automated theorem proving|Free software}} ...

...ms and 'Anti-Unification'|book-title=Proc. 8th International Conference on Automated Deduction|publisher=Springer|series=LNCS|volume=230|pages=128–140|year=1986 ...et|title=Anti-Unification for Unranked Terms and Hedges|journal=Journal of Automated Reasoning|volume=52|number=2|pages=155–190|url=https://link.springer.com/co ...