Le problème est formellement exprimé comme suit : ?x, y, z (distinct_points(x, y) ? incident_point_and_line(x, z) ? incident_point_and_line(y, z) ? equal_lines(z, line_connecting ,
sont des feuilles de l'arbre de preuve. En suivant cette preuve, il est possible de construire la preuve suivante : ? Étant donnés les points T4, T6 (étape 3), et la droite T8 (étape 4) tels que H10: distinct_points(T4,T6) ,
T6) (étapes 8 à 11), nous devons montrer le but précédent (H14 niée) dans les cas suivants : 1, nous avons aussi H10: distinct_points(T4,T6), ce qui est absurde ,
T6)), c'est exactement le 6.5. TRACES DE SUPER ZENON fof(geometry_conjecture, conjecture, => equal_lines (Z, line_connecting(X, Y))))) ,
The B-Book, Assigning Programs to Meanings, pp.24-47, 1996. ,
Modeling in Event-B -System and Software Engineering, 2010. ,
Click???n Prove: Interactive Proofs within Set Theory, Lecture Notes in Computer Science, vol.2758, pp.1-24, 2003. ,
DOI : 10.1007/10930755_1
URL : https://hal.archives-ouvertes.fr/inria-00099836
On Using Conditional Definitions in Formal Theories, pp.242-269 ,
DOI : 10.1007/3-540-45648-1_13
A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses, Lecture Notes in Computer Science, vol.53, issue.6, pp.135-150, 2011. ,
DOI : 10.1145/1217856.1217859
URL : https://hal.archives-ouvertes.fr/hal-00639130
A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses, Certified Programs and Proofs 2011 of Lecture notes in computer science -LNCS, pp.135-150, 2011. ,
DOI : 10.1145/1217856.1217859
URL : https://hal.archives-ouvertes.fr/hal-00639130
Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants, Journal of Symbolic Computation, vol.32, issue.1-2, pp.3-22, 2001. ,
DOI : 10.1006/jsco.2001.0455
CVC3, Proceedings of the 19 th International Conference on Computer Aided Verification (CAV '07), pp.298-302, 2007. ,
DOI : 10.1007/978-3-540-73368-3_34
Validation des r??gles de base de l'Atelier B, Techniques et sciences informatiques, vol.23, issue.7, pp.855-878, 2004. ,
DOI : 10.3166/tsi.23.855-878
Formal Specification and Development in Z and, 2nd International Conference of B and Z Users Proceedings, volume 2272 of Lecture Notes in Computer Science, p.176, 2002. ,
A Flexible Proof Format for SMT : a Proposal ,
URL : https://hal.archives-ouvertes.fr/hal-00642544
Semantic Entailment and Formal Derivability, Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen, vol.18, issue.13 101, pp.309-342, 1955. ,
Implementing polymorphism in SMT solvers, Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning, SMT '08/BPR '08, p.32, 2008. ,
DOI : 10.1145/1512464.1512466
Type Synthesis in B and the Translation of B to PVS, pp.350-369 ,
DOI : 10.1007/3-540-45648-1_18
Sledgehammer: Judgement Day, Lecture Notes in Computer Science, vol.6173, pp.107-121 ,
DOI : 10.1007/978-3-642-14203-1_9
TaMeD: A Tableau Method for Deduction Modulo, Lecture Notes in Computer Science, vol.3097, pp.445-459, 2004. ,
DOI : 10.1007/978-3-540-25984-8_33
Zenon: An Extensible Automated Theorem Prover Producing Checkable Proofs, Dershowitz and Voronkov [35], pp.151-165 ,
DOI : 10.1007/978-3-540-75560-9_13
URL : https://hal.archives-ouvertes.fr/inria-00315920
A Semantic Completeness Proof for TaMeD, LNCS, vol.19, issue.4246, pp.141-167, 2006. ,
DOI : 10.1007/11916277_12
URL : https://hal.archives-ouvertes.fr/hal-01337086
Experience with Embedding Hardware Description Languages in HOL, TPCD, volume A-10 of IFIP Transactions, pp.129-156, 1992. ,
Principles of Superdeduction, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), pp.41-50, 2007. ,
DOI : 10.1109/LICS.2007.37
URL : https://hal.archives-ouvertes.fr/inria-00133557
Traitement des expressions dépourvues de sens de la théorie des ensembles : Application à la méthode B, p.96, 2000. ,
Unbounded Proof-Length Speed-Up in Deduction Modulo, Computer Science Logic, pp.496-511, 2007. ,
DOI : 10.1007/978-3-540-74915-8_37
URL : https://hal.archives-ouvertes.fr/inria-00138195
Formalisation of B in Isabelle/HOL, LNCS, vol.1393, pp.66-82, 1998. ,
DOI : 10.1007/BFb0053356
From Axioms to Analytic Rules in Nonclassical Logics, 2008 23rd Annual IEEE Symposium on Logic in Computer Science, pp.229-240, 2008. ,
DOI : 10.1109/LICS.2008.39
Using Rewriting and Strategies for Describing the B Predicate Prover, Strategies in Automated Deduction, pp.25-36, 1998. ,
URL : https://hal.archives-ouvertes.fr/inria-00098748
Guide de rédaction de règles mathématiques, p.40 ,
Atelier B 4.0, Feb, p.37, 2009. ,
RODIN (Rigorous Open Development Environment for Complex Systems), EDCC-5, pp.23-26, 2005. ,
Coq, l'alpha et l'omega de la preuve pour B ?, p.31, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00361302
Z3: An Efficient SMT Solver, TACAS, pp.337-340, 2008. ,
DOI : 10.1007/978-3-540-78800-3_24
SMT Solvers for Rodin, pp.194-207 ,
DOI : 10.1007/978-3-642-30885-7_14
A Tactic Language for the System Coq, Logic for Programming and Automated Reasoning (LPAR), pp.85-95, 2000. ,
DOI : 10.1007/3-540-44404-1_7
URL : https://hal.archives-ouvertes.fr/hal-01125070
Recovering Intuition from Automated Formal Proofs using Tableaux with Superdeduction, Electronic Journal of Mathematics & Technology, pp.2013-2034 ,
URL : https://hal.archives-ouvertes.fr/hal-01099371
Theorem Proving Modulo, Journal of Automated Reasoning, vol.31, issue.1, pp.33-72, 2003. ,
DOI : 10.1023/A:1027357912519
URL : https://hal.archives-ouvertes.fr/hal-01199506
Expressiveness + Automation + Soundness: Towards Combining SMT Solvers and Interactive Proof Assistants, Lecture Notes in Computer Science, vol.29, issue.3-4, pp.167-181, 2006. ,
DOI : 10.1007/3-540-45620-1_26
URL : https://hal.archives-ouvertes.fr/inria-00001088
Form and Content in Quantification Theory, IFIP TCS, pp.33-40, 1955. ,
Représentation et interaction des preuves en superdéduction modulo, 0118. ,
Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving, SEFM, pp.253-268, 2011. ,
DOI : 10.1007/3-540-45648-1_8
URL : https://hal.archives-ouvertes.fr/hal-00722373
Tableaux Modulo Theories Using Superdeduction, Lecture Notes in Computer Science, vol.7364, issue.21, pp.332-338, 2012. ,
DOI : 10.1007/978-3-642-31365-3_26
URL : https://hal.archives-ouvertes.fr/hal-01099338
Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving, Software and Systems Modeling (SoSyM), 2013. À paraître, p.101 ,
DOI : 10.1007/3-540-45648-1_8
URL : https://hal.archives-ouvertes.fr/hal-00722373
Why Would You Trust B ? In Dershowitz and Voronkov, pp.288-302 ,
iProver ??? An Instantiation-Based Theorem Prover for First-Order Logic (System Description), IJ- CAR, pp.292-298, 2008. ,
DOI : 10.1007/978-3-540-71070-7_24
Automatiser la validation des règles, INSA (Rennes), vol.59, p.64, 2008. ,
ProB: an automated analysis toolset for the B method, International Journal on Software Tools for Technology Transfer, vol.49, issue.3, pp.185-203, 2008. ,
DOI : 10.1007/s10009-007-0063-9
On an Extensible Rule-Based Prover for Event-B, Lecture Notes in Computer Science, vol.5977, issue.38, pp.407-454, 2010. ,
DOI : 10.1007/978-3-642-11811-1_40
Discharging Proof Obligations from Atelier??B Using Multiple Automated Provers, Derrick et al. [34], pp.238-251 ,
DOI : 10.1007/978-3-642-30885-7_17
Automatic Verification of TLA???+??? Proof Obligations with SMT Solvers, Lecture Notes in Computer Science, vol.7180, issue.32, pp.289-303, 2012. ,
DOI : 10.1007/978-3-642-28717-6_23
URL : https://hal.archives-ouvertes.fr/hal-00760570
Abstract, Bulletin of Symbolic Logic, vol.4, issue.04, pp.418-435, 1998. ,
DOI : 10.2307/420956
Strong and weak points of the MUSCADET theorem prover -examples from CASC-JC, Journal of AI Communications, vol.15, issue.2-3, pp.147-160, 2002. ,
Natural Deduction. A Proof-Theoretical Study, Stockholm Studies in Philosophy, vol.3, p.116, 1965. ,
The design and implementation of Vampire, Journal of AI Communications, vol.15, issue.32, pp.91-110, 2002. ,
First-Order Logic, p.101, 1968. ,
DOI : 10.1201/b10689-23
Guide méthodologique de validation de la base de règles de l, Atelier B, p.46, 1996. ,
The TPTP Problem Library and Associated Infrastructure, Journal of Automated Reasoning, vol.13, issue.2, pp.337-362, 2009. ,
DOI : 10.1007/s10817-009-9143-8
SPASS Version 3.5, Lecture Notes in Computer Science, vol.18, issue.2-4, pp.140-145, 2009. ,
DOI : 10.1007/978-3-540-73595-3_38
An automated prover for Zermelo???Fraenkel set theory in Theorema, Journal of Symbolic Computation, vol.41, issue.3-4 ,
DOI : 10.1016/j.jsc.2005.04.013