McCharen, J., Overbeek, R., and Wos, L., Problems and experiments for and with automated theoremproving programs, IEEE Transactions on Computers, C-25 (8), (1976).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....cl time 37.51 forsub time 56.03 renumber time 69.31 keep cl time 9.72 printcl time 0.00 conflict time 1. 43 postprocess time 65.32 back demod time 53.96 backsub time 10.91 lexrpo time 76.22 The job finished Thu Jun 4 18:15:07 1992 7 Conclusion Years of experimentation with theorem proving systems [4, 9, 3, 5, 6] have enabled us to accumulate a wide variety of variations and parameters to control our basic theorem proving algorithm. The typical user need know about only a few of them. This contest forced us to consider how we would set them if there were to be a parameterless version of OTTER. Most of the ....

J. McCharen, R. Overbeek, and L. Wos. Problems and experiments for and with automated theorem-proving programs. IEEE Transactions on Computers, C-25(8):773--782, August 1976.

....all the solution paths explored. However, choosing a higher bound and allowing a few violations can provide a much more effective restriction of the search space. 5.2. 3 Experimental Results Training data from 21 rather simple theorems (well known benchmark problems from group and ring theory [MOW76]) were collected, and a 2 layer back propagation network was used to learn a heuristic, called 21 mixed in the following. Then two more difficult problems from the same problem set (namely wos15 and wos22) were chosen to test the heuristic. Figure 3 shows for both test problems the time required ....

J. McCharen, R. Overbeek, and L. Wos. Problems and Experiments for and with Automated Theorem Proving Programs. IEEE Transactions on Computers, C-25, 1976.

....to get al..l the solution paths explored. However, choosing a higher bound and allowing a few violations can provide a much more effective restriction of the search space. 4 Experimental Results Training data from 21 rather simple theorems (well known benchmark problems from group and ring theory [McCharen et al. 1976]) were collected, and a 3 layer backpropagation network was used to learn a heuristic, called 21 mixed in the following. Then two more difficult problems from the same problem set (namely wos15 and wos22) were chosen to test the heuristic. 3 The availability of unfailing guidance would imply ....

J. McCharen, R. Overbeek, and L. Wos (1976). Problems and Experiments for and with Automated Theorem Proving Programs. !IEEE Transactions on Computers?, C-25:773--782.

....on researchers collected problems in order to obtain a basis for experimentation. Problems in FOF, published by mathematicians and logicians prior to the mechanization of reasoning, e.g. Chu56] provided the first source for ATP researchers. The first major publication 1 in this regard was [MOW76] which provides an explicit listing of clauses for 63 CNF problems, many of which are still relevant today. In the same year [WM76] documented 86 CNF problems which have since commonly been used for ATP testing. The problem clauses are not supplied in [WM76] however. A second major thrust was ....

....0 0 285 309 2 PLA 23 30 0 0 0 0 23 30 0 PRV 9 9 0 0 0 0 9 9 0 PUZ 36 57 4 2 2 0 36 55 4 RNG 40 100 0 0 0 0 40 100 0 ROB 27 36 0 0 0 0 27 36 0 SET 562 700 0 5 5 0 562 695 0 SYN 403 500 28 149 150 1 340 350 27 TOP 19 24 0 0 0 0 19 24 0 Table 8: TPTP Domain Sizes. References : General [Mac71] ATP [MOW76] CID Circuit Design. Circuits are formed by inter connecting logic gates. Circuit design is used to form a circuit that will transform given input patterns to required output patterns. Indices : DDC 621.395; MSC 94CXX. References : General [Hay93] ATP [WW83] CIV Circuit Verification. Circuit ....

[Article contains additional citation context not shown here]

J.D. McCharen, R.A. Overbeek, and L.A. Wos. Problems and Experiments for and with Automated Theorem-Proving Programs. IEEE Transactions on Computers, C-25(8):773--782, 1976.

....problems that were proposed as challenges to ATP systems by Woody Bledsoe [Ble90] They include the Intermediate Value Theorem and the problem to prove that the sum of two continuous functions is continuous. The domain contains two standard axiomatizations. Both are in relational form, taken from [MOW76] and [Ble90] This domain contains a mix of problems that are Horn, non Horn, with equality, and without equality. Indices : DDC 515; MSC 26XX. References : General [Ros90] ATP [Ble90] 3.3 Boolean Algebra A Boolean algebra is a set of elements with two binary operations which are idempotent, ....

....commutative, and associative. These operations are mutually distributive, there exist universal bounds 0; 1, and there is a unary operation of complementation. Most of the abstract problems in the Boolean Algebra domain were first brought to the attention of ATP research by McCharen, et al. MOW76] Bob Veroff later reformulated the problems using a pure equality axiomatization, and added some new problems [Ver94] The problems prove identities in Boolean Algebra. The domain contains four standard axiomatizations. The first is an equality axiomatization distributed with the Otter ATP ....

[Article contains additional citation context not shown here]

J.D. McCharen, R.A. Overbeek, and L.A. Wos. Problems and Experiments for and with Automated Theorem-Proving Programs. IEEE Transactions on Computers, C-25(8):773--782, 1976.

....of interesting problems have accumulated over the years in the ATP community. Besides publishing particularly interesting individual problems, from early on researchers have collected problems in order to obtain a basis for experimentation. The first major publication 3 in this regard was [MOW76] 3 The first circulation of problems for testing theorem provers to our knowledge is due to L. Wos in the late sixties. which provides an explicit listing of clauses for 63 problems, many of which are still relevant today. In the same year Wilson and Minker [WM76] tested six resolution ....

J. McCharen, A. Overbeek, and L. Wos. Problems and Experiments for and with Automated Theorem-Proving Programs. IEEE Transactions on Computers, C-25(8):773 -- 782, August 1976.

....early on researchers collected problems in order to obtain a basis for experimentation. Problems in FOF, published by mathematicians and logicians prior to the mechanization of reasoning (e.g. Chu56] provided the first source for ATP researchers. The first major publication in this regard was [MOW76] which provides an explicit listing of clauses for 63 CNF problems, many of which are still relevant today 1 . In the same year [WM76] documented 86 CNF problems which have commonly been used for ATP testing. The problem clauses are not supplied in [WM76] however. A second major thrust was ....

....FOF problems. Indices : DDC 511.324, 512.89; MSC 06EXX. References : General [Whi61, BM65, BB70] ATP . CAT Category Theory. A category is a mathematical structure together with the morphisms that preserve this structure. Indices : DDC 512.55; MSC 18XX. References : General [Mac71] ATP [MOW76] CID Circuit Design. Circuits are formed by inter connecting logic gates. Circuit design is used to form a circuit that will transform given input patterns to required output patterns. Indices : DDC 621.395; MSC 94CXX. References : General [Hay93] ATP [WW83] CIV Circuit Verification. Circuit ....

[Article contains additional citation context not shown here]

J.D. McCharen, R.A. Overbeek, and L.A. Wos. Problems and Experiments for and with Automated Theorem-Proving Programs. IEEE Transactions on Computers, C-25(8):773--782, 1976.

....we were able to show speedups for the proof search of one order of magnitude with the hybrid system compared to the purely symbolic system. Figure 1 gives an impression of these results. Training data from 21 rather simple theorems (well known benchmark problems from group and ring theory [ McCharen et al. 1976 ] were collected, and a 3 layer backpropagation network was used to learn a heuristic, called 21 mixed in the following. Two more difficult problems from the same problem set (namely wos15 and wos22) were chosen to test the heuristic. The input for the heuristic evaluation function (neural ....

J. McCharen, R. Overbeek, and L. Wos. Problems and Experiments for and with Automated Theorem Proving Programs. IEEE Transactions on Computers, C-25:773--782, 1976.

....number of interesting problems have accumulated over the years in the ATP community. Besides publishing particularly interesting individual problems, from early on researchers collected problems in order to obtain a basis for experimentation. The first major publication 1 in this regard was [61], which provides an explicit listing of clauses for 63 problems, many of which are still relevant today. In the same year [125] documented 86 problems which have since commonly been used for ATP testing. The problem clauses are not supplied in [125] however. A second major thrust was provided by ....

....operation of complementation. Indices : DDC 511.324, 512.89; MSC 06EXX. References : General [122, 11, 10] ATP . CAT Category Theory. A category is a mathematical structure together with the morphisms that preserve this structure. Indices : DDC 512.55; MSC 18XX. References : General [59] ATP [61]. CID Circuit Design. Circuits are formed by inter connecting logic gates. Circuit design is used to form a circuit that will transform given input patterns to required output patterns. Indices : DDC 621.395; MSC 94CXX. References : General [36] ATP [128] CIV Circuit Verification. Circuit ....

[Article contains additional citation context not shown here]

\Phi J.D. McCharen, R.A. Overbeek, and L.A. Wos. Problems and Experiments for and with Automated Theorem-Proving Programs. IEEE Transactions on Computers, C-25(8):773--782, 1976.

....representation of a b = c. Equality is still required and is indeed quite useful for demodulation. Although not explicitly stated in the contest rules, we believe that demodulation is permitted, but that paramodulation is not. This has been the traditional approach when using the P formulation [5, 4], and we have followed it. Theorem 1. x 2 = e groups are commutative, stated in the P formulation. Theorem 2. The commutator theorem: if a group has the property x 3 = e, then [ x; y] y] e, where [x; y] xyx Gamma1 y Gamma1 . The theorem is stated in the P formulation. Theorem 3. ....

J. McCharen, R. Overbeek, and L. Wos. Problems and experiments for and with automated theorem-proving programs. IEEE Transactions on Computers, C-25(8):773--782, August 1976.

....early on researchers collected problems in order to obtain a basis for experimentation. Problems in FOF, published by mathematicians and logicians prior to the mechanization of reasoning (e.g. Chu56] provided the first source for ATP researchers. The first major publication in this regard was [MOW76] which provides an explicit listing of clauses for 63 CNF problems, many of which are still relevant today 1 . In the same year [WM76] documented 86 CNF problems which have commonly been used for ATP testing. The problem clauses are not supplied in [WM76] however. A second major thrust was ....

....of complementation. Indices : DDC 511.324, 512.89; MSC 06EXX. References : General [Whi61, BM65, BB70] ATP . CAT Category Theory. A category is a mathematical structure together with the morphisms that preserve this structure. Indices : DDC 512.55; MSC 18XX. References : General [Mac71] ATP [MOW76] CID Circuit Design. Circuits are formed by inter connecting logic gates. Circuit design is used to form a circuit that will transform given input patterns to required output patterns. Indices : DDC 621.395; MSC 94CXX. References : General [Hay93] ATP [WW83] Logic Combinatory logic COL ....

[Article contains additional citation context not shown here]

J.D. McCharen, R.A. Overbeek, and L.A. Wos. Problems and Experiments for and with Automated Theorem-Proving Programs. IEEE Transactions on Computers, C-25(8):773--782, 1976.

....of one of the parallel provers and a proposal for integrating the heuristics into its control can be found in [5] Results. So far experimental results only exist for the sequential prover. Training data from 21 rather simple theorems (well known benchmark problems from group and ring theory [6]) were collected, and a 3 layer backpropagation network was used to learn a heuristic, called 21 mixed in the following. Then two more difficult problems from the same problem set (namely wos15 and wos22) were chosen to test the heuristic. Figure 2 shows for both test problems the time required ....

J. McCharen, R. Overbeek, and L. Wos, "Problems and Experiments for and with Automated Theorem Proving Programs," IEEE Transactions on Computers, vol. C-25, pp. 773--782, 1976.

....The program RG1 [38] designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodulation, demodulation, and the set of support strategy. The second generation, started by Ross Overbeek in 1970, was based on the NIUTP (Northern Illinois University Theorem Prover) series [10, 11], Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W 31 109 Eng 38. 2 WILLIAM McCUNE and LARRY WOS which evolved into AURA (AUtomated Reasoning Assistant) ....

J. McCharen, R. Overbeek, and L. Wos. Problems and experiments for and with automated theorem-proving programs. IEEE Trans. on Computers, C-25(8):773-- 782, August 1976.

....for equality) designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodulation, demodulation, and the set of support strategy. The second generation, started by Ross Overbeek in 1970 [28] was based on the NIUTP (Northern Illinois University Theorem Prover) series [12, 13], which Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W 31 109 Eng 38. 2 WILLIAM McCUNE and LARRY WOS evolved into AURA (AUtomated Reasoning ....

J. McCharen, R. Overbeek, and L. Wos. Problems and experiments for and with automated theorem-proving programs. IEEE Transactions on Computers, C-25(8):773--782, August 1976.

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McCharen, J., Overbeek, R., and Wos, L., Problems and experiments for and with automated theoremproving programs, IEEE Transactions on Computers, C-25 (8), (1976).

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John D. McCharen, Ross A. Overbeek, and Lawrence A. Wos. Problems and experiments for and with automated theorem-proving programs. IEEE Trans. Comput., C-25(8):773--782, August 1976.

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