VIP 2026

VIP development team
University of Montpellier / LIRMM, France

Architecture

VIP 2026 is an automatic theorem prover for first-order logic in TPTP FOF syntax. It was developed under a short time constraint as a standalone prover, with extensive LLM-assisted implementation. The submitted system does not call another ATP system as a backend.

The core is a given-clause saturation loop. Problems are parsed from TPTP files, include directives are expanded, formulae are clausified, and clauses are processed by resolution-style and superposition-style rules. The main inferences are binary resolution, factoring, equality resolution, equality factoring, and equality-oriented paramodulation/superposition steps.

Standard simplifications include tautology deletion, demodulation, forward simplification, subsumption, subsumption resolution, condensation, and contextual literal cutting. VIP contains a simple legacy engine and a more recent engine with stronger equality handling, indexing, and clause selection; the competition portfolio combines both.

The system also includes SInE-style axiom selection, layered clause selection, and limited deduction-modulo-inspired preprocessing for selected definitional equivalences. Experimental splitting code is not enabled in the submitted configuration.

Strategies

VIP uses a sequential portfolio. The main CASC-oriented portfolio is named casc-150. Each stage receives a fixed fraction of the available time and runs with fixed options for the FOF division. The submitted StarExec script uses the same command line for every FOF problem.

Strategy scheduling is based only on general syntactic characteristics of the input, such as equality density, clause shape, unit-clause ratio, polarity patterns, and symbol occurrence information. It is not based on problem names, file paths, comments, TPTP headers, or stored information about individual problems or their solutions.

The portfolio includes FEQ-oriented equality stages, FNE recovery stages using the legacy engine, SInE axiom-selection stages with different widths, legacy-guided modern stages, layered age/weight passive selection, and several fixed age/weight schedules. The submitted StarExec script does not hardcode the CASC time limit; it accepts the announced wall-clock budget as a wrapper argument or environment value. The default generated-clause limit is 75000.

Implementation

VIP is implemented in OCaml and is built with Dune. The executable installed in the StarExec package is vip; ip is kept as a compatibility alias in the source tree. The delivered binary is statically linked.

TPTP include files are resolved according to the standard TPTP convention: first relative to the problem file, and otherwise relative to the TPTP root supplied by the TPTP environment variable. Internal data structures include feature-vector style indices for subsumption candidates, discrimination-style indices for rewriting candidates, and KBO-style term ordering for equality reasoning.

In competition mode, VIP writes all result information to standard output, emits an SZS status line, and, when a refutation is found, prints a TPTP/TSTP-style proof delimited by SZS output markers. The required FOF sample problem SEU140+2 has been tested locally with TPTP4X and GDV.

The StarExec package provides bin/starexec_run_FOF and bin/starexec_run_default. The run script expects the problem file as its first argument and relies on the StarExec/TPTP environment for include-file resolution and resource enforcement.

Expected Competition Performance

VIP is expected to solve a useful subset of FOF theorem problems, with better performance on unsatisfiable problems where axiom selection, equality simplification, and staged saturation interact well. It is not expected to match mature ATP systems such as Vampire, E, or Zipperposition.

Development used CASC-style FOF benchmarks to tune general portfolio parameters. The submitted configuration includes additional soundness guards and is intended to use the wall-clock limit announced by the CASC organizers and the CASC memory environment.

References

No system paper is available for this first VIP release. The implementation follows standard saturation-based ATP techniques used in systems such as E, Vampire, Zipperposition, and Drodi: given-clause saturation, resolution, superposition-style equality reasoning, demodulation, subsumption, SInE-style axiom selection, layered clause selection, and age/weight scheduling.