Introduction to higher order categorical logic
Introduction to higher order categorical logic
Set theory in first-order logic: clauses for Go¨del's axioms
Journal of Automated Reasoning
A framework for defining logics
Journal of the ACM (JACM)
Handbook of logic in computer science
Theoretical Computer Science
Automated Development of Fundamental Mathematical Theories
Automated Development of Fundamental Mathematical Theories
Computer Proofs in Gödel’s Class Theory with Equational Definitions for Composite and Cross
Journal of Automated Reasoning
STMM: A Set Theory for Mechanized Mathematics
Journal of Automated Reasoning
Set Theory, Higher Order Logic or Both?
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
On Sets, Types, Fixed Points, and Checkerboards
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
System Description: TPS: A Theorem Proving System for Type Theory
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Vampire 1.1 (System Description)
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Mathematical Structures in Computer Science
A Tableau-Based Decision Procedure for a Fragment of Set Theory with Iterated Membership
Journal of Automated Reasoning
Connecting a logical framework to a first-order logic prover
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Encoding Functional Relations in Scunak
Electronic Notes in Theoretical Computer Science (ENTCS)
Formal Representation of Mathematics in a Dependently Typed Set Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Representing Model Theory in a Type-Theoretical Logical Framework
Electronic Notes in Theoretical Computer Science (ENTCS)
Representing model theory in a type-theoretical logical framework
Theoretical Computer Science
Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets
Journal of Automated Reasoning
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We describe a dependent type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated support for constructing proofs within this set theory. One of the novel aspects of the representation is that one is allowed to use any class (in the set theory) as a type (in the type theory). Such class types allow a natural way of representing partial functions (e.g., the first and second operators on the class of Kuratowski ordered pairs). We also discuss how automated search can be used to construct proofs. In particular, the first-order prover Vampire can be called to solve a challenge problem (the injective Cantor Theorem) which is notoriously difficult for higher-order automated provers.