. References, . Baader, . Nipkow, F. Baader, and T. Nipkow, Term Rewriting and all That, 1998.

D. Bonacina, M. P. Bonacina, and N. Dershowitz, Abstract canonical inference, ACM Transactions on Computational Logic, vol.8, issue.1, 2007.
DOI : 10.1145/1182613.1182619

. Brauner, Principles of Superdeduction, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), 2007.
DOI : 10.1109/LICS.2007.37
URL : https://hal.archives-ouvertes.fr/inria-00133557

K. Brünnler, Deep Inference and Symmetry in Classical Proofs, 2003.

S. R. Buss, Abstract, The Journal of Symbolic Logic, vol.22, issue.04, pp.916-927, 1987.
DOI : 10.1016/0304-3975(85)90144-6

S. R. Buss, Abstract, The Journal of Symbolic Logic, vol.77, issue.03, pp.737-756, 1994.
DOI : 10.2307/2275906

. Cook, . Reckhow, S. A. Cook, and R. A. Reckhow, The relative efficiency of propositional proof systems, The Journal of Symbolic Logic, vol.87, issue.01, pp.36-50, 1979.
DOI : 10.1007/BF01475439

D. Cousineau, D. Cousineau, and G. Dowek, Embedding pure type systems in the lambdapi-calculus modulo, 2007.

. Curry, Combinatory Logic, 1958.

K. Dershowitz, N. Dershowitz, and C. Kirchner, Abstract canonical presentations, Theoretical Computer Science, vol.357, issue.1-3, pp.53-69, 2006.
DOI : 10.1016/j.tcs.2006.03.012
URL : https://hal.archives-ouvertes.fr/inria-00121760

. Dowek, HOL-?? an intentional first-order expression of higher-order logic, Mathematical Structures in Computer Science, vol.11, issue.1, pp.1-25, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00098847

. Dowek, 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

G. Dowek and B. Werner, Abstract, The Journal of Symbolic Logic, vol.87, issue.04, pp.1289-1316, 2003.
DOI : 10.1007/BFb0037116

W. Dowek, G. Dowek, and B. Werner, Arithmetic as a Theory Modulo, Lecture Notes in Computer Science, vol.3467, pp.423-437, 2005.
DOI : 10.1007/978-3-540-32033-3_31

J. H. Gallier, Logic for Computer Science: Foundations of Automatic Theorem Proving Revised On-Line Version, Computer Science and Technology Series, vol.5, 1986.

K. Gödel, The Collected Papers of Gerhard Gentzen as Investigations into Logical Deduction ¨ Uber die Länge von Beweisen, Mathematische Zeitschrift Ergebnisse eines Mathematischen Kolloquiums, vol.39, issue.7, pp.176-210, 1936.

K. Gödel, On the length of proofs, Kurt Gödel: Collected Works, pp.396-399, 1986.

A. Guglielmi, Polynomial size deep-inference proofs instead of exponential size shallowinference proofs, 2004.

F. Kirchner, A Finite First-Order Theory of Classes, 2006.
DOI : 10.1007/978-3-540-74464-1_13

. Mostowski, Undecidable Theories, Studies in Logic and the Foundations of Mathematics, 1953.

. Nipkow, Isabelle/HOL ? A Proof Assistant for Higher-Order Logic, LNCS, vol.2283, 2002.

R. J. Parikh, Some results on the length of proofs, Transactions of the American Mathematical Society, vol.177, pp.29-36, 1973.
DOI : 10.1090/S0002-9947-1973-0432416-X