Vampire 5.0.1

Márton Hajdu
TU Wien, Austria

Vampire 5.0.1 remains similar in spirit to all previous versions, but a bumper crop of changes have been merged this competition cycle. Various non-competition improvements to Vampire landed, but for the competition we mention:

Clause-selection guidance based on Graph and Recursive Neural Networks [Suda25]
Higher-order support has been mostly merged with mainline Vampire, therefore our HOL support enjoys all competition-winning improvements over the last years, while remaining efficient on non-higher-order problems.
Detailed propositional proof output via the CaDiCaL SAT solver [BFF+24].
More detailed output, including proofs that are (more) TSTP-compliant.
Portability: Vampire is much more standards-compliant and portable than previously, with much-reduced dependence on platform-specific APIs and hardware architectures, aided by C++20.

Architecture

Vampire [Vampire25] is an automatic theorem prover for first-order logic with extensions to theory reasoning and higher-order logic. Vampire implements several extensions of a core superposition calculus. It also implements a MACE-style finite model builder for finding finite counter-examples [RSV16]. Splitting in saturation-based proof search is controlled by the AVATAR architecture which uses a SAT or SMT solver to make splitting decisions [Vor14, RB+16]. A number of standard redundancy criteria and simplification techniques are used for pruning the search space: subsumption, tautology deletion, subsumption resolution and rewriting by ordered unit equalities. Substitution tree and code tree indices are used to implement all major operations on sets of terms, literals and clauses. Internally, Vampire works only with clausal normal form: problems not already in CNF are clausified during preprocessing [RSV16]. Vampire implements many preprocessing transformations, including the SInE axiom selection algorithm for large theories and blocked clause elimination.

Strategies

Vampire 5.0.1 provides a very large number of options for strategy selection. The most important ones are:

Choices of saturation algorithm:
- Limited Resource Strategy [RV03]
- DISCOUNT loop
- Otter loop
- MACE-style finite model building with sort inference
Splitting via AVATAR [Vor14]
A variety of optional simplifications.
Parameterized reduction orderings KBO and LPO.
A number of built-in literal selection functions and different modes of comparing literals [HR+16].
Age-weight ratio that specifies how strongly lighter clauses are preferred for inference selection. This has been extended with a layered clause selection approach [GS20].
- Optionally, instead of age-weight alternation, clause selection can be fully delegated to a guiding neural network [Suda25].
The set-of-support strategy with extensions for theory reasoning.
For theory reasoning:
- Specialised calculi such as ALASCA.
- Addition of theory axioms and evaluation of interpreted functions [RSV21].
- Use of Z3 with AVATAR to restrict search to ground-theory-consistent splitting branches [RB+16].
- Specialised theory instantiation and unification [RSV18].
- Extensionality resolution with detection of extensionality axioms

For CASC, we prepared several clause-selection guiding networks trained on the TPTP library. As described in [Suda25], we were independently checking test performance on randomly held-out fraction of the library during the training. The test performance, although lower than the train performance, is greater than that of the baseline, which means that generalization to problems similar to those used in training is achieved.

Implementation

Vampire 5.0.1 is implemented in C++. It makes use of fixed versions of Minisat, CaDiCaL, GMP, VIRAS, and Z3. See the GitHub repository and associated wiki for more information.

The neural clause-selection guidance relies on the LibTorch library (v2.10), which is statically linked into the competition submission so that it can run on StarExec without requiring the library to be installed there.

Expected Competition Performance

Vampire 5.0.1 should be an improvement on the previous version. A reasonably strong performance across all divisions is therefore expected.

References

Suda25: Martin Suda (2025), Efficient Neural Clause-Selection Reinforcement, CADE pp. 403-422, Springer.
Vampire25: Filip Bártek, Ahmed Bhayat, Robin Coutelier, Márton Hajdu, Matthias Hetzenberger, Petra Hozzová, Laura Kovács, Jakob Rath, Michael Rawson, Giles Reger, Martin Suda, Johannes Schoisswohl and Andrei Voronkov (2025), The Vampire Diary, CAV, to appear.
HAHK+24: Petra Hozzová, Daneshvar Amrollahi, Márton Hajdu, Laura Kovács, Andrei Voronkov, and Eva Maria Wagner (2024), Synthesis of Recursive Programs in Saturation, IJCAR, pp. 154-171, Springer.
KKRS23: Konstatin Korovin, Laura Kovács, Giles Reger, and Johannes Schoisswohl (2023), ALASCA: Reasoning in Quantified Linear Arithmetic, TACAS, pp. 647-665, Springer.
SKK24: Johannes Schoisswohl, Laura Kovács, and Konstantin Korovin (2024), VIRAS: Conflict-Driven Quantifier Elimination for Integer-Real Arithmetic, LPAR, pp. 147-164, EasyChair.
HKV25: Márton Hajdu, Laura Kovács and Andrei Voronkov (2025), Partial Redundancy in Saturation, CADE, to appear.
HCKV25: Márton Hajdu, Robin Coutelier, Laura Kovács and Andrei Voronkov (2025), Term Ordering Diagrams, CADE, to appear.
BFF+24: Armin Biere, Tobias Faller, Katalin Fazekas, Mathias Fleury, Nils Froleyks, and Florian Pollitt (2024), CaDiCaL 2.0, CAV, pp. 133-152, Springer.