Equational methods in first order predicate calculus
Journal of Symbolic Computation
Journal of Automated Reasoning
Partial evaluation and &ohgr;-completeness of algebraic specifications
Theoretical Computer Science
A strong restriction of the inductive completion procedure
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Proof by induction using test sets
Proc. of the 8th international conference on Automated deduction
Artificial Intelligence
Journal of Automated Reasoning
On the use of conditional rewrite rules in inductive theorem proving
1st international workshop on Conditional Term Rewriting Systems
Automatic proofs by induction in theories without constructors
Information and Computation
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
Term rewriting and beyond - theorem proving in Isabelle
Formal Aspects of Computing
Tools for proving inductive equalities, relative completeness, and &ohgr;-completeness
Information and Computation
Journal of Automated Reasoning
Automating inductionless induction using test sets
Journal of Symbolic Computation
Experiments with proof plans for induction
Journal of Automated Reasoning
Adapting a resolution calculus for inductive proofs
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Testing for the ground (co-)reducibility property in term-rewriting systems
CAAP '90 Selected papers of the conference on Fifteenth colloquium on trees in algebra and programming
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Complete axiomatizations of some quotient term algebras
Theoretical Computer Science
Middle-out reasoning for logic program synthesis
ICLP'93 Proceedings of the tenth international conference on logic programming on Logic programming
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
An extension of the Boyer-Moore theorem prover to support first-order quantification
Journal of Automated Reasoning
Which data types have &ohgr;-complete initial algebra specifications?
Theoretical Computer Science
A constructor-based approach to positive/negative-conditional equational specifications
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Handbook of logic in artificial intelligence and logic programming
An automated tool for analyzing completeness of equational specifications
ISSTA '94 Proceedings of the 1994 ACM SIGSOFT international symposium on Software testing and analysis
An overview of the Tecton proof system
Theoretical Computer Science - Special issue on formal methods in databases and software engineering
On proving the termination of algorithms by machine
Artificial Intelligence
Recursive data types in algebraically &ohgr;-complete categories
Information and Computation
Using induction and rewriting to verify and complete parameterized specifications
Theoretical Computer Science
An Industrial Strength Theorem Prover for a Logic Based on Common Lisp
IEEE Transactions on Software Engineering
Automated theorem proving by test set induction
Journal of Symbolic Computation
The use of proof planning for co-operative theorem proving
Journal of Symbolic Computation - Special issue graphical user interfaces and protocols
Proving Theorems about LISP Functions
Journal of the ACM (JACM)
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Artificial Intelligence
Induction = I-axiomatization + first-order consistency
Information and Computation - Special issue on RTA-98
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
On terminating lemma speculations
Information and Computation
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of Automated Reasoning: Volume 1
Handbook of Automated Reasoning: Volume 1
Planning Proofs of Equations in CCS
Automated Software Engineering
Coloring Terms to Control Equational Reasoning
Journal of Automated Reasoning
Journal of Automated Reasoning
Abstract Proof Checking: An Example Motivated by an Incompleteness Theorem
Journal of Automated Reasoning
Recursive Program Optimization through Inductive Synthesis Proof Transformation
Journal of Automated Reasoning
The CADE-15 ATP System Competition
Journal of Automated Reasoning
Managing Structural Information by Higher-Order Colored Unification
Journal of Automated Reasoning
Structured Theory Development for a Mechanized Logic
Journal of Automated Reasoning
A General Setting for Flexibly Combining and Augmenting Decision Procedures
Journal of Automated Reasoning
The IJCAR ATP System Competition
Journal of Automated Reasoning
Automata-driven automated induction
Information and Computation
Incorporating decision procedures in implicit induction
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Patching Proofs for Reuse (Extended Abstract)
ECML '95 Proceedings of the 8th European Conference on Machine Learning
SPIKE, an Automatic Theorem Prover
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
On the Use of the Constructive Omega-Rule within Automated Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
The Use of Planning Critics in Mechanizing Inductive Proofs
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Incresing the Versatility of Heuristic Based Theorem Provers
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
Proof Plans for the Correction of False Conjectures
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
SPIKE: A System for Automatic Inductive Proofs
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
Automating Induction over Mutually Recursive Functions
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
Context Induction: a Proof Principle for Behavioural Abstractions
DISCO '90 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Experiments in Automating Hardware Verification Using Inductive Proof Planning
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Proceedings of the Workshop on Formal Methods in Databases and Software Engineering
Rewriting, Decision Procedures and Lemma Speculation for Automated Hardware Verification
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A New Strategy for Proving omega-Completeness applied to Process Algebra
CONCUR '90 Proceedings of the Theories of Concurrency: Unification and Extension
Termination of Constraint Contextual Rewriting
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Generalization Discovery for Proofs by Induction in Conditional Theories
Proceedings of the Twelfth International Florida Artificial Intelligence Research Society Conference
Formal Software Development in the Verification Support Environment (VSE)
Proceedings of the Thirteenth International Florida Artificial Intelligence Research Society Conference
Using Linear Arithmetic Procedure for Generating Induction Schemes
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
General Framework for Mechanizing Induction using Test Set
PRICAI '96 Proceedings of the 4th Pacific Rim International Conference on Artificial Intelligence: Topics in Artificial Intelligence
Structured Contextual Rewriting
RTA '87 Proceedings of the 2nd International Conference on Rewriting Techniques and Applications
An Overview of Rewrite Rule Laboratory (RRL)
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Inductive Proofs by Specification Transformation
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Using the Rippling Heuristic in Set Membership Proofs
ZUM '97 Proceedings of the 10th International Conference of Z Users on The Z Formal Specification Notation
Deduction in the Verification Support Environment (VSE)
FME '96 Proceedings of the Third International Symposium of Formal Methods Europe on Industrial Benefit and Advances in Formal Methods
Using Rippling for Equational Reasoning
KI '96 Proceedings of the 20th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Mechanical Verification of an Ideal Incremental ABR Conformance
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Proving Inductive Theorems Based on Term Rewriting Systems
Proceedings of the International Workshop on Algebraic and Logic Programming
PVS: Combining Specification, Proof Checking, and Model Checking
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
The AFFIRM Theorem Prover: Proof Forests and Management of Large Proofs
Proceedings of the 5th Conference on Automated Deduction
The Karlsruhe Induction Theorem Proving System
Proceedings of the 8th International Conference on Automated Deduction
A Proof Environment for Arithmetic with the Omega Rule
AISMC-2 Selected Papers from the Second International Conference on Integrating Symbolic Mathematical Computation and Artificial Intelligence
Instantiation of Existentially Quantified Variables in Inductive Specification Proofs
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
Overview of a Theorem-Prover for A Computational Logic
Proceedings of the 8th International Conference on Automated Deduction
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
Isabelle: The Next Seven Hundred Theorem Provers
Proceedings of the 9th International Conference on Automated Deduction
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
An Interactive Enhancement to the Boyer-Moore Theorem Prover
Proceedings of the 9th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
UNICOM: A Refined Completion Based Inductive Theorem Prover
Proceedings of the 10th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
Extensions to the Rippling-Out Tactic for Guiding Inductive Proofs
Proceedings of the 10th International Conference on Automated Deduction
A Theorem Prover for a Computational Logic
Proceedings of the 10th International Conference on Automated Deduction
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Proving the Chinese Remainder Theorem by the Cover Set Induction
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Synthesis of Induction Orderings for Existence Proofs
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Mechanizable Inductive Proofs for a Class of Forall Exists Formulas
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
On Notions of Inductive Validity for First-Oder Equational Clauses
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Lazy Generation of Induction Hypotheses
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Termination of Theorem Proving by Reuse
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Lemma Discovery in Automated Induction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Extensions to a Generalization Critic for Inductive Proof
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
A Colored Version of the Lambda-Calculus
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
ACL2 Support for Verification Projects (Invited Talk)
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
System Description: Proof Planning in Higher-Order Logic with Lambda-Clam
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
System Description: SystemOn TPTP
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Extending Decision Procedures with Induction Schemes
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Inductive Theorem Proving by Consistency for First-Order Clauses
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Abstract Notions and Inference Systems for Proofs by Mathematical Induction
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
A Comparison of PVS and Isabelle/HOL
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Sufficient Completeness and Parameterized Proofs by Induction
ALP '94 Proceedings of the 4th International Conference on Algebraic and Logic Programming
Automated Verification by Induction with Associative-Commutative Operators
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Induction using Term Orderings
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Mechanical Verification of an Ideal Incremental ABR Conformance Algorithm
Journal of Automated Reasoning
Resolution decision procedures
Handbook of automated reasoning
Ground Reducibility is EXPTIME-complete
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Proving Properties of Security Protocols by Induction
CSFW '97 Proceedings of the 10th IEEE workshop on Computer Security Foundations
Model building with ordered resolution: extracting models from saturated clause sets
Journal of Symbolic Computation - Special issue: First order theorem proving
Constraint contextual rewriting
Journal of Symbolic Computation - Special issue: First order theorem proving
Journal of Automated Reasoning
Automatic verification of functions with accumulating parameters
Journal of Functional Programming
Sound generalizations in mathematical induction
Theoretical Computer Science
A rational reconstruction and extension of recursion analysis
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 1
Automatic case analysis in proof by induction
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Combining induction axioms by machine
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
A lemma driven automatic theorem prover for recursive function theory
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Analyzing mathematical proofs (or reading between the lines)
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
Proving theorems about LISP functions
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Relational rippling: a general approach
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
"Term partition" for mathematical induction
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Mechanizing inductive reasoning
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Contextual Rewriting In Automated Reasoning
Fundamenta Informaticae
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(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP.