The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic, Automated Theorem Proving (ATP) systems – the world championship for such systems. CASC-29 was the twenty-eighth competition in the CASC series. Twenty-four ATP systems competed in the various divisions. This paper presents an outline of the competition design and a commentated summary of the results.
A.Bhayat, M.Rawson and J.Schoisswohl, Superposition with delayed unification, in: Proceedings of the 29th International Conference on Automated Deduction, B.Pientka and C.Tinelli, eds, Lecture Notes in Computer Science, Springer-Verlag, 2023, pp. 23–40.
2.
A.Bhayat and G.Reger, A combinator-based superposition calculus for higher-order logic, in: Proceedings of the 10th International Joint Conference on Automated Reasoning, N.Peltier and V.Sofronie-Stokkermans, eds, Lecture Notes in Artificial Intelligence, 2020, pp. 278–296. doi:10.1007/978-3-030-51074-9_16.
3.
J.Blanchette, M.Haslbeck, D.Matichuk and T.Nipkow, Mining the archive of formal proofs, in: Proceedings of the 8th Conference on Intelligent Computer Mathematics, M.Kerber, J.Carette, C.Kaliszyk, F.Rabe and V.Sorge, eds, Lecture Notes in Computer Science, 2015, pp. 3–17. doi:10.1007/978-3-319-20615-8_1.
4.
J.Blanchette and T.Nipkow, Nitpick: A counterexample generator for higher-order logic based on a relational model finder, in: Proceedings of the 1st International Conference on Interactive Theorem Proving, M.Kaufmann and L.Paulson, eds, Lecture Notes in Computer Science, Springer-Verlag, 2010, pp. 131–146. doi:10.1007/978-3-642-14052-5_11.
5.
F.Bobot, M.Bromberger and J.Hoenicke, 18th International Satisfiability Modulo Theories Competition (SMT-COMP 2023): Rules and Procedures, 2023, https://smt-comp.github.io/2023/rules.pdf.
6.
F.Bobot, J.-C.Filliâtre, C.Marché and A.Paskevich, Let’s verify this with Why3, International Journal on Software Tools for Technology Transfer17(6) (2015), 709–727. doi:10.1007/s10009-014-0314-5.
7.
K.Claessen and N.Sörensson, New techniques that improve MACE-style finite model finding, in: Proceedings of the CADE-19 Workshop: Model Computation – Principles, Algorithms, Applications, P.Baumgartner and C.Fermueller, eds, 2003.
8.
L.de Moura and S.Ullrich, The Lean 4 theorem prover and programming language, in: Proceedings of the 28th International Conference on Automated Deduction, A.Platzer and G.Sutcliffe, eds, Lecture Notes in Computer Science, Springer-Verlag, 2015, pp. 625–635.
9.
M.Desharnais, P.Vukmirović, J.Blanchette and M.Wnezel, Seventeen provers under the Hammer, in: Proceedings of the 13th International Conference on Interactive Theorem Proving, J.Andronick and L.de Moura, eds, Leibniz International Proceedings in Informatics, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2022, pp. 8:1–8:18.
10.
H.Ganzinger, C.Meyer and C.Weidenbach, Soft typing for ordered resolution, in: Proceedings of the 14th International Conference on Automated Deduction, W.W.McCune, ed., Lecture Notes in Artificial Intelligence, Springer-Verlag, 1997, pp. 321–335.
11.
B.Gleiss and M.Suda, Layered clause selection for theory reasoning, in: Proceedings of the 10th International Joint Conference on Automated Reasoning, N.Peltier and V.Sofronie-Stokkermans, eds, Lecture Notes in Computer Science, 2020, pp. 402–409. doi:10.1007/978-3-030-51074-9_23.
12.
K.Hoder, G.Reger, M.Suda and A.Voronkov, Selecting the selection, in: Proceedings of the 8th International Joint Conference on Automated Reasoning, N.Olivetti and A.Tiwari, eds, Lecture Notes in Artificial Intelligence, 2016, pp. 313–329. doi:10.1007/978-3-319-40229-1_22.
13.
J.Jakubuv and J.Urban, ENIGMA: Efficient learning-based inference guiding machine, in: Proceedings of the 10th International Conference on Intelligent Computer Mathematics, H.Geuvers, M.England, O.Hasan, F.Rabe and O.Teschke, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2017, pp. 292–302.
14.
K.Korovin, L.Kovac, G.Reger, J.Schoisswohl and A.Voronkov, ALASCA: Reasoning in quantified linear arithmetic (extended version), EasyChair preprints, 2023, https://easychair.org/publications/preprint/KJX2.
15.
L.Kovacs and A.Voronkov, First-order theorem proving and vampire, in: Proceedings of the 25th International Conference on Computer Aided Verification, N.Sharygina and H.Veith, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2013, pp. 1–35.
16.
U.Martin and T.Nipkow, Ordered rewriting and confluence, in: Proceedings of the 10th International Conference on Automated Deduction, M.E.Stickel, ed., Lecture Notes in Artificial Intelligence, Springer-Verlag, 1990, pp. 366–380. doi:10.1007/3-540-52885-7_100.
17.
J.McKeown and G.Sutcliffe, An interactive interpretation viewer for typed first-order logic, in: Proceedings of the 36th International FLAIRS Conference, A.Ae Chun and M.Franklin, eds, 2023. doi:10.32473/flairs.36.133073.
18.
J.Parsert, C.Brown, M.Janota and C.Kaliszyk, Experiments on infinite model finding in SMT solving, in: Proceedings of 24th International Conference on Logic for Programming Artificial Intelligence and Reasoning, R.Piskac and A.Voronkov, eds, EPiC Series in Computing, EasyChair Publications, 2023, pp. 317–328.
19.
L.Paulson and J.Blanchette, Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers, in: Proceedings of the 8th International Workshop on the Implementation of Logics, G.Sutcliffe, E.Ternovska and S.Schulz, eds, EPiC Series in Computing, EasyChair Publications, 2010, pp. 1–11.
20.
F.J.Pelletier, G.Sutcliffe and C.B.Suttner, The development of CASC, AI Communications15(2–3) (2002), 79–90.
21.
A.Riazanov and A.Voronkov, Limited resource strategy in resolution theorem proving, Journal of Symbolic Computation36(1–2) (2003), 101–115. doi:10.1016/S0747-7171(03)00040-3.
22.
A.Robinson and A.Voronkov, Handbook of Automated Reasoning, Elsevier Science, 2001.
23.
O.Roussel, Controlling a solver execution with the runsolver tool, Journal of Satisfiability, Boolean Modeling and Computation7(4) (2011), 139–144. doi:10.3233/SAT190083.
24.
P.Rümmer, A constraint sequent calculus for first-order logic with linear integer arithmetic, in: Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, I.Cervesato, H.Veith and A.Voronkov, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2008, pp. 274–289.
25.
A.Steen, G.Sutcliffe, P.Fontaine and J.McKeown, Representation, verification, and visualization of tarskian interpretations for typed first-order logic, in: Proceedings of 24th International Conference on Logic for Programming Artificial Intelligence and Reasoning, R.Piskac and A.Voronkov, eds, EPiC Series in Computing, EasyChair Publications, 2023, pp. 369–385.
26.
C.Sticksel and K.Korovin, A note on model representation and proof extraction in the first-order instantiation-based calculus inst-gen, in: Proceedings of the 19th Automated Reasoning Workshop, R.Schmidt and F.Papacchini, eds, 2012, pp. 11–12.
27.
A.Stump, G.Sutcliffe and C.Tinelli, StarExec: A cross-community infrastructure for logic solving, in: Proceedings of the 7th International Joint Conference on Automated Reasoning, S.Demri, D.Kapur and C.Weidenbach, eds, Lecture Notes in Artificial Intelligence, 2014, pp. 367–373. doi:10.1007/978-3-319-08587-6_28.
28.
M.Suda, Vampire getting noisy: Will random bits help conquer chaos? (system description), in: Proceedings of the 11th International Joint Conference on Automated Reasoning, J.Blanchette, L.Kovacs and D.Pattinson, eds, Lecture Notes in Artificial Intelligence, 2022, pp. 659–667. doi:10.1007/978-3-031-10769-6_38.
29.
G.Sutcliffe, The CADE-16 ATP system competition, Journal of Automated Reasoning24(3) (2000), 371–396. doi:10.1023/A:1006393501098.
30.
G.Sutcliffe, The CADE ATP system competition – CASC, AI Magazine37(2) (2016), 99–101. doi:10.1609/aimag.v37i2.2620.
31.
G.Sutcliffe, The TPTP problem library and associated infrastructure. From CNF to TH0, TPTP v6.4.0, Journal of Automated Reasoning59(4) (2017), 483–502. doi:10.1007/s10817-017-9407-7.
32.
G.Sutcliffe, The CADE-26 Automated Theorem Proving system competition – CASC-26, AI Communications30(6) (2017), 419–432.
33.
G.Sutcliffe, The logic languages of the TPTP world, Logic Journal of the IGPL (2022). doi:10.1093/jigpal/jzac068.
34.
G.Sutcliffe, Proceedings of the CADE-29 ATP system competition, online, 2023, http://tptp.org/CASC/29/Proceedings.pdf.
35.
G.Sutcliffe and M.Desharnais, The 11th IJCAR Automated Theorem Proving system competition – CASC-J11, AI Communications36(2) (2023), 73–91. doi:10.3233/AIC-220244.
36.
G.Sutcliffe, S.Schulz, K.Claessen and A.Van Gelder, Using the TPTP language for writing derivations and finite interpretations, in: Proceedings of the 3rd International Joint Conference on Automated Reasoning, U.Furbach and N.Shankar, eds, Lecture Notes in Artificial Intelligence, Springer, 2006, pp. 67–81. doi:10.1007/11814771_7.
37.
G.Sutcliffe and C.B.Suttner, Evaluating general purpose Automated Theorem Proving systems, Artificial Intelligence131(1–2) (2001), 39–54.
38.
A.Voronkov, AVATAR: The new architecture for first-order theorem provers, in: Proceedings of the 26th International Conference on Computer Aided Verification, A.Biere and R.Bloem, eds, Lecture Notes in Computer Science, 2014, pp. 696–710. doi:10.1007/978-3-319-08867-9_46.
39.
A.Voronkov, Spider: Learning in the Sea of Options, 2023, https://easychair.org/smart-program/Vampire23/2023-07-05.html.
40.
P.Vukmirović, A.Bentkamp and V.Nummelin, Efficient full higher-order unification, in: Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction, Z.M.Ariola, ed., Leibniz International Proceedings in Informatics, Dagstuhl Publishing, 2020, pp. 5:1–5:20.
41.
S.Winkler and G.Moser, MaedMax: A maximal ordered completion tool, in: Proceedings of the 9th International Joint Conference on Automated Reasoning, D.Galmiche, S.Schulz and R.Sebastiani, eds, Lecture Notes in Computer Science, 2018, pp. 388–404.