Different researchers use "the philosophy of automated theorem proving " to cover different concepts, indeed, different levels of concepts. Some would count such issues as how to efficiently index databases as part of the philosophy of automated theorem proving. Others wonder about

David Stanovsk´y (Prague) ATP in algebra 1 / 18Automated theorem proving INPUT: A finite set of first order formulas OUTPUT: Satisfiable / Unsatisfiable / I don’t know (Timeout) What is it good for: proving theorems in mathematics David Stanovsk´y (Prague) ATP in algebra 2 / 18Automated theorem

The power and automation offered by modern satisfiability-modulo-theories (SMT) solvers is changing the landscape for mechanized formal theorem proving. For instance, the SMT-based program verifier Dafny supports a number of proof features traditionally found only in interactive proof assistants

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, support for testing and debugging, software reengineering, and software/hardware co-design (e.g., [16]). Wherever formal methods are applied, proof tasks of most different size and complexity arise in large quantities. Traditionally, interactive theorem provers (e.g., PVS, KIV, HOL, Isabelle) are being

In this paper we compare the performance of various automated theorem provers on nearly all of the theorems in loop theory known to have been obtained with the assistance of automated theorem provers. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop

Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or :A = 2 F. 2. If A 2 F and if B is the bh-normal form of A, then B F 2 Ñ S 2 . 3. If ::A 2 F, then A F 2 Ñ S . 4. If AB2F, then F A 2 Ñ S or F B 2 Ñ S . 5. If :(AB) 2 F, then F :A :B2 Ñ S . 6. If P a A 2 F, then F AB 2 Ñ S for each closed formula B 2 wff a (S). 7. If :P a A 2 F, then F :(Aw a ) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 8. If :(A = a!b B) 2 F, then F :(Aw a = Bw) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 9. If :(A = o B) 2 F, then F[fA;:Bg 2 Ñ S or F[f:A;Bg 2 Ñ S . Here, we treat equality as an abbreviation for Leibniz definition. We call an abstract consistency class saturated, iff for all F 2 Ñ S and all...

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this paper is to review the requirements for analogical reasoning in proof discovery and discuss some approaches. This paper is not intended as an objective survey of past approaches to this problem. Instead, it is a condensation of the important insights of others together with some of my own. However, in an area of research which is still in its early stages, there is no clear agreement of the "important insights," so the reader must accept my subjective bias. Furthermore, when I state the key ideas of some author's work, it should not be assumed that that author shares my assessment of what his contribution is. 2 Overview

The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, first order Automated Theorem Proving systems. CASC-20 was the tenth competition in the CASC series. Seventeen ATP systems and system variants competed in the various competition and demonstration divisions