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By Robert Nieuwenhuis

This publication constitutes the refereed lawsuits of the twentieth foreign convention on computerized Deduction, CADE-20, held in Tallinn, Estonia, in July 2005. The 25 revised complete papers and five approach descriptions awarded have been conscientiously reviewed and chosen from seventy eight submissions. All present features of automatic deduction are addressed, starting from theoretical and methodological concerns to presentation and assessment of theorem provers and logical reasoning platforms.

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Extra info for Automated deduction, CADE-20: 20th International Conference on Automated Deduction, Tallinn, Estonia, July 22-27, 2005 : proceedings

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P⊥ BOOL− [¬ ] = . ⊥ − ∨ . − ∨ . − ¬ . ¬ ¬ . LEAF0 ⊥ + − − ⊥+ + ¬ . + − . LEAF1− ¬ ¬ . − − Fig. 2. Expansion Tree and Extensional Expansion Dag Hιo [ H EQN0− = H⊥] = . H⊥ EQNGOAL0− Hιo [ H = H⊥] = . H⊥ DEC0− Hιo [ H = H⊥] = . H⊥ [Hιo BOOL0− = H⊥] = . ⊥ − ⊃ . EQN1+ Hιo = H⊥ [⊥ ⊃ . [Hιo ⊥ − . . = H⊥]] − [Hιo Hιo = . H[ H EUNIF0− = H⊥]] ∧ . H⊥] . [H⊥ = EQN2− = . H [H = H⊥] EQN4− Hιo ⊥ = . H⊥ DEC2− DEC4− − BOOL1 = . [Hιo = H⊥] − ⊃ . [[Hιo EQN3− + = H⊥] ⊃ . . ] − [⊥ = . ⊥] . . − EQNGOAL3− Hιo = .

The main point of this paper is to give a representation for α-equated lambdaterms that is based on names, is inductive and comes with a structural induction principle where the lambda-case needs to be proved for only fresh binders. In practice this will mean that we come quite close to the informal reasoning using Barendregt’s variable convention.

Automated proof construction in type theory using resolution. Journal of Automated Reasoning, 29(3):253–275, 2002. 4. E. Contejean, C. March´e, and X. Urbain. CiME3, 2004. fr/. 5. P. Corbineau. First-order reasoning in the Calculus of Inductive Constructions. In S. Berardi, M. Coppo, and F. Damiani, editors, TYPES 2003 : Types for Proofs and Programs, volume 3085 of LNCS, pages 162–177, Torino, Italy, Apr. 2004. Springer-Verlag. 6. P. Cr´egut. Une proc´edure de d´ecision r´eflexive pour l’arithm´etique de Presburger en Coq.

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