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Automated theorem proving (also known as ATP or automated deduction) 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 .
TPTP (Thousands of Problems for Theorem Provers) [1] is a freely available collection of problems for automated theorem proving. It is used to evaluate the efficacy of automated reasoning algorithms. [2] [3] [4] Problems are expressed in a simple text-based format for first order logic or higher-order logic. [5]
The Isabelle [a] automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala.As a Logic for Computable Functions (LCF) style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring, yet supporting, explicit proof objects.
In 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 human–machine collaboration. This involves some sort of interactive proof editor, or other interface , with which a human can guide the search for proofs, the details of which are ...
Automated reasoning has been most commonly used to build automated theorem provers. Oftentimes, however, theorem provers require some human guidance to be effective and so more generally qualify as proof assistants. In some cases such provers have come up with new approaches to proving a theorem. Logic Theorist is a good example of this.
OTTER (Organized Techniques for Theorem-proving and Effective Research [1]) is an automated theorem prover developed by William McCune at Argonne National Laboratory in Illinois. Otter was the first widely distributed, high-performance theorem prover for first-order logic, and it pioneered a number of important implementation techniques.
Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in early 1970s, based on the theoretical foundation of logic of computable functions previously proposed by Dana Scott.
Examples of automated theorem provers for first-order logic are: Prover9; ACL2; Vampire; Prover9 can be used in conjunction with the Mace4 model 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.