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The Philosophy of Automated Theorem Proving
 In Proceedings of the 12. International Joint Conference on Artificial Intelligence (IJCAI91
, 1991
"... 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 whether ..."
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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
Automated theorem proving in algebra
, 2009
"... 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 prov ..."
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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
Automated theorem proving in loop theory
 proceedings of the ESARM workshop
, 2008
"... 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 theor ..."
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Cited by 5 (3 self)
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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
Automating Theorem Proving with SMT
, 2013
"... The power and automation offered by modern satisfiabilitymodulotheories (SMT) solvers is changing the landscape for mechanized formal theorem proving. For instance, the SMTbased program verifier Dafny supports a number of proof features traditionally found only in interactive proof assistants, ..."
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Cited by 4 (2 self)
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The power and automation offered by modern satisfiabilitymodulotheories (SMT) solvers is changing the landscape for mechanized formal theorem proving. For instance, the SMTbased program verifier Dafny supports a number of proof features traditionally found only in interactive proof assistants
Automated Theorem Proving in Software Engineering
"... Introduction. The quickly rising amount and complexity of developed and used software require more and more a rigorous application of formal methods during the entire software life cycle. Points of particular interest include: specification and its refinements, program synthesis, software reuse, sup ..."
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, support for testing and debugging, software reengineering, and software/hardware codesign (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
Using Automated Theorem Provers in Nonassociative Algebra
"... We present a case study on how mathematicians use automated theorem provers to solve open problems in (nonassociative) algebra. 1 ..."
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We present a case study on how mathematicians use automated theorem provers to solve open problems in (nonassociative) algebra. 1
Automated Theorem Discovery: Future Direction for Theorem Provers
"... One obvious and important aspect of automated theorem proving is that the users know in advance which theorem they wish to prove. A possible future direction for theorem provers is to enable users to discover theorems which they were not necessarily aware of. We survey previous attempts at this ..."
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One obvious and important aspect of automated theorem proving is that the users know in advance which theorem they wish to prove. A possible future direction for theorem provers is to enable users to discover theorems which they were not necessarily aware of. We survey previous attempts
Semantic Selection of Premisses for Automated Theorem Proving
 PROC. THE CADE21 WORKSHOP ON EMPIRICALLY SUCCESSFUL AUTOMATED REASONING IN LARGE THEORIES (ESARLT2007)
, 2007
"... We develop and implement a novel algorithm for discovering the optimal sets of premisses for proving and disproving conjectures in firstorder logic. The algorithm uses interpretations to semantically analyze the conjectures and the set of premisses of the given theory to find the optimal subsets of ..."
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Cited by 9 (0 self)
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of the premisses. For each given conjecture the algorithm repeatedly constructs interpretations using an automated model finder, uses the interpretations to compute the optimal subset of premisses (based on the knowledge it has at the point) and tries to prove the conjecture using an automated theorem prover. 1
HigherOrder Automated Theorem Proving
, 1998
"... 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 ..."
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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 bhnormal 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...
Results 1  10
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