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Secondorder matching modulo evaluation  A technique for reusing proofs
 Proceedings of IJCAI 95
, 1995
"... in our prototype of a learning prover, the PLAGlATORsystem [Brauburger, 1994], has proved successful for many examples, including those from Table 1. Hence we are able to verify these conjectures by automatically reusing the proofs of previously proved, similar conjectures. As a side effect useful ..."
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Cited by 18 (5 self)
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in our prototype of a learning prover, the PLAGlATORsystem [Brauburger, 1994], has proved successful for many examples, including those from Table 1. Hence we are able to verify these conjectures by automatically reusing the proofs of previously proved, similar conjectures. As a side effect useful lemmata are speculated by our method. Table 1 also suggests a recursive organization of the reuse procedure as the proof obligations returned by our solution algorithm may also be proved by reuse. The (heuristic) control of this recursion for avoiding nontermination by cyclic reuses is subject to future work. Another future topic is concerned with the management of learned schematic proofs for an efficient selection of the proof shell which is to be reused for a
Experiments in the Heuristic Use of Past Proof Experience
 Proc. CADE13
, 1996
"... Problems stemming from the study of logic calculi in connection with an inference rule called "condensed detachment" are widely acknowledged as prominent test sets for automated deduction systems and their search guiding heuristics. It is in the light of these problems that we demonstrate ..."
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Cited by 16 (4 self)
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Problems stemming from the study of logic calculi in connection with an inference rule called "condensed detachment" are widely acknowledged as prominent test sets for automated deduction systems and their search guiding heuristics. It is in the light of these problems that we demonstrate the power of heuristics that make use of past proof experience with numerous experiments. We present two such heuristics. The first heuristic attempts to reenact a proof of a proof problem found in the past in a flexible way in order to find a proof of a similar problem. The second heuristic employs "features" in connection with past proof experience to prune the search space. Both these heuristics not only allow for substantial speedups, but also make it possible to prove problems that were out of reach when using socalled basic heuristics. Moreover, a combination of these two heuristics can further increase performance. We compare our results with the results the creators of Otter obtained with t...
Proof Management and Retrieval
, 1995
"... Automated theorem provers might be improved if they reuse previously computed proofs. Our approach for reuse is based on socalled proof shells which are obtained from computed proofs by secondorder generalization. Each proof shell represents a schematic proof of a schematic conjecture and applie ..."
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Cited by 8 (4 self)
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Automated theorem provers might be improved if they reuse previously computed proofs. Our approach for reuse is based on socalled proof shells which are obtained from computed proofs by secondorder generalization. Each proof shell represents a schematic proof of a schematic conjecture and applies for each instance of the schematic conjecture yielding (firstorder) proof obligations justifying a successful proof reuse. But since there may be different proofs for different instances of a schematic conjecture, we have to select a reusable proof shell among the applicable proof shells for a new conjecture. For supporting such a retrieval efficiently, the set of computed proof shells is organized by socalled proof volumes and a proof dictionary. All applicable proof shells can be accessed by searching for the right proof volume in the proof dictionary, if the applicability of proof shells is determined by socalled simple secondorder matchers.
Flexible ProofReplay with Heuristics
 IN PROC. 8TH PORTUGUESE CONFERENCE ON ARTIFICIAL INTELLIGENCE (EPIA97), LNAI 1323
, 1997
"... We present a general framework for developing search heuristics for automated theorem provers. This framework allows for the construction of heuristics that are on the one hand able to replay (parts of) a given proof found in the past but are on the other hand flexible enough to deviate from the giv ..."
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Cited by 3 (3 self)
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We present a general framework for developing search heuristics for automated theorem provers. This framework allows for the construction of heuristics that are on the one hand able to replay (parts of) a given proof found in the past but are on the other hand flexible enough to deviate from the given proof path in order to solve similar proof problems. We substantiate the abstract framework by the presentation of three distinct techniques for learning appropriate search heuristics based on socalled features. We demonstrate the usefulness of these techniques in the area of equational deduction. Comparisons with the renowned theorem prover Otter validate the applicability and strength of our approach.
Termination of Theorem Proving by Reuse
 Proc. CADE13
, 1996
"... . We investigate the improvement of theorem provers by reusing previously computed proofs. We formulate our method for reusing proofs as an instance of the problem reduction paradigm and then develop a termination requirement for our reuse procedure. We prove the soundness of our proposal and show t ..."
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. We investigate the improvement of theorem provers by reusing previously computed proofs. We formulate our method for reusing proofs as an instance of the problem reduction paradigm and then develop a termination requirement for our reuse procedure. We prove the soundness of our proposal and show that reusability of proofs is not spoiled by the termination requirement imposed on the reuse procedure. We also give evidence for the general usefulness of our termination requirement for lemma speculation in induction theorem proving. 1 Introduction We investigate the improvement of theorem provers by reusing previously computed proofs, cf. [12, 13]. Our work has similarities with the methodologies of explanationbased learning [7], analogical reasoning [9], and abstraction [8], cf. [14] for a more detailed comparison. Consider the following general architecture: Some problem solver PS is augmented with a facility for storing and retrieving solutions of problems solved during the system's...
Adaptation of Proofs for Reuse
 WORKING NOTES OF THE 1995 AAAI FALL SYMPOSIUM ON ADAPTATION OF KNOWLEDGE FOR REUSE, 6167
, 1995
"... Automated theorem provers might be improved if they are enabled to reuse previously computed proofs. Our approach for reuse is based on generalizing computed proofs by replacing function symbols with function variables. This yields a schematic proof which is instantiated subsequently for obtainin ..."
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Automated theorem provers might be improved if they are enabled to reuse previously computed proofs. Our approach for reuse is based on generalizing computed proofs by replacing function symbols with function variables. This yields a schematic proof which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse method, which requires no human support, demands two steps of proof adaptation, viz. solution of socalled free function variables and patching of completely instantiated proofs. We develop algorithms for solving free function variables and for computing patched proofs and demonstrate their usefulness with several examples.
Theorem Proving by Analogy  A Compelling Example
, 1995
"... This paper shows how a new approach to theorem proving by analogy is applicable to real maths problems. This approach works at the level of proofplans and employs reformulation that goes beyond symbol mapping. The HeineBorel theorem is a widely known result in mathematics. It is usually stated in ..."
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This paper shows how a new approach to theorem proving by analogy is applicable to real maths problems. This approach works at the level of proofplans and employs reformulation that goes beyond symbol mapping. The HeineBorel theorem is a widely known result in mathematics. It is usually stated in R¹ and similar versions are also true in R², in topology, and metric spaces. Its analogical transfer was proposed as a challenge example and could not be solved by previous approaches to theorem proving by analogy. We use a proofplan of the HeineBorel theorem in R¹ as a guide in automatically producing a proofplan of the HeineBorel theorem in R² by analogydriven proofplan construction.
Proving Theorems by Mimicking a Human’s Skill
"... Abstract. x We investigate the improvement of theorem proven by reusing previously computed proofs. We have developed and implemented the PLAGIATOR system which proves theorems by mathematical induction with the aid ors human advisor: If a conjecture is submitted to the system, it tries to reuse a ..."
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Abstract. x We investigate the improvement of theorem proven by reusing previously computed proofs. We have developed and implemented the PLAGIATOR system which proves theorems by mathematical induction with the aid ors human advisor: If a conjecture is submitted to the system, it tries to reuse a proof of a previously verified conjecture. If successful, resources are saved, because the n,,mhex of required user interactions is decreased. The pexfonnance of the overall system is improved, because neceuory lernmata might be specu/ated. If the reuse fails, the human advisor is called for providing a hand cxafted proof for such a conjecture, which subsequently after some (automated) preparation steps m is stored in the system’s memory, to be in stock for future reasoning problems. The success of out approach is based on our te~h,,;que for preparing given proofs as well as by our techn/que for reusing proofs.