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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 .
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 ...
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.
In the early 1970s a theorem prover named AURA, for AUtomated Reasoning Assistant, developed by Overbeek replaced one that had been the standard in the field. [2]In 1983 he joined the Mathematics and Computer Science Division of Argonne National Laboratory, working on automated theorem proving, logic programming, and parallel computation.
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.
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.
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.
John Alan Robinson (9 March 1930 – 5 August 2016) was a philosopher, mathematician, and computer scientist.He was a professor emeritus at Syracuse University.. Alan Robinson's major contribution is to the foundations of automated theorem proving.