#
Automated Theorem Proving with Extensions of First-Order Logic
Doctoral thesis, 2018

The work presented in the thesis addresses this challenge by developing an extension of first-order logic named FOOL. FOOL contains syntactical features of programming languages and more expressive logics, is friendly for translation of problems from various domains, and can be efficiently supported by existing theorem provers. We describe the syntax and semantics of FOOL and present a simple translation from FOOL to plain first-order logic. We describe an efficient clausal normal form transformation algorithm for FOOL and based on it implement a support for FOOL in the Vampire theorem prover. We illustrate the efficient use of FOOL for program verification by describing a concise encoding of next state relations of imperative programs in FOOL. We show a usage of features of FOOL in problems of static analysis of networks. We demonstrate the efficiency of automated theorem proving in FOOL with an extensive set of experiments. In these experiments we compare the performance of Vampire on a large collection of problems from various sources translated to FOOL and ordinary first-order logic. Finally, we fix the syntax for FOOL in TPTP, the standard language of first-order theorem provers.

clausal normal form

Program Verification

automated theorem proving

program analysis

TPTP

Vampire

first-order logic

## Author

### Evgenii Kotelnikov

Chalmers, Computer Science and Engineering (Chalmers), Formal methods

### A First Class Boolean Sort in First-Order Theorem Proving and TPTP

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),; Vol. 9150(2015)p. 71-86

**Paper in proceeding**

### A Clausal Normal Form Translation for FOOL

Proceedings of the 2nd Global Conference on Artificial Intelligence (GCAI),; Vol. EasyChair EPiC Series in Computing volume 41(2016)

**Paper in proceeding**

### A FOOLish Encoding of the Next State Relations of Imperative Programs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),; Vol. 10900 LNAI(2018)p. 405-421

**Paper in proceeding**

### TFX: The TPTP Extended Typed First-Order Form

Proceedings of the 6th Workshop on Practical Aspects of Automated Reasoning co-located with Federated Logic Conference 2018,; (2018)p. 72-87

**Paper in proceeding**

### Evgeny Kotelnikov, Pavle Subotic. Checking Network Reachability Properties by Automated Reasoning in First-Order Logic

### Subject Categories

Algebra and Logic

Software Engineering

Computer Science

### Areas of Advance

Information and Communication Technology

### ISBN

978-91-7597-770-6

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4451

### Publisher

Chalmers

Lecture hall ED, EDIT building

Opponent: Professor Dr. Stephan Schulz, DHBW Stuttgart, Fakultät Technik, Stuttgart, Germany