Proceedings of the Fifth Workshop on Proof eXchange for Theorem Proving

This volume of EPTCS contains the proceedings of the Fifth Workshop on Proof Exchange for Theorem Proving (PxTP 2017), held on September 23-24, 2017 as part of the Tableaux, FroCoS and ITP conferences in Brasilia, Brazil. The PxTP workshop series brings together researchers working on various aspects of communication, integration, and cooperation between reasoning systems and formalisms, with a special focus on proofs. The progress in computer-aided reasoning, both automated and interactive, during the past decades, made it possible to build deduction tools that are increasingly more applicable to a wider range of problems and are able to tackle larger problems progressively faster. In recent years, cooperation between such tools in larger systems has demonstrated the potential to reduce the amount of manual intervention. Cooperation between reasoning systems relies on availability of theoretical formalisms and practical tools to exchange problems, proofs, and models. The PxTP workshop series strives to encourage such cooperation by inviting contributions on all aspects of cooperation between reasoning tools, whether automatic or interactive.

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.

An Expressive Probabilistic Temporal Logic

This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic for reasoning about actions with uncertain outcomes. The logic is modal and higher-order: modalities annotated by actions are used to express possibility and necessity of propositions in the next states resulting from the actions, and a higher-order function is needed to express the probability operator. The proposed logic is shown to be an adequate extension of classical mathematical probability theory, and its expressiveness is illustrated through the formalization of the Monty Hall problem.

Formalization, Mechanization and Automation of Gödel's Proof of God's Existence

G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction proof. A formalization of the axioms, definitions and theorems in the TPTP THF syntax. Automatic verification of the consistency of the axioms and definitions with Nitpick. Automatic demonstration of the theorems with the provers LEO-II and Satallax. A step-by-step formalization using the Coq proof assistant. A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.