Download PDFOpen PDF in browserEfficient Linear Model Building and Clause Evaluation17 pages•Published: October 24, 2026AbstractWe describe our implementation of the linear model building calculus first presented in "First-Order Automatic Literal Model Generation" at IJCAR 2024: Given a finite consistent set of ground literals, a so-called trail, we want to extend it to a complete Herbrand-style interpretation represented by linear literals. Moreover, we give an algorithm to evaluate arbitrary clauses in the resulting linear model. We provide concrete data structures for efficiently implementing model building and clause evaluation. The resulting model building procedure runs in time linear in the size of the trail for a fixed signature. Even though checking whether a clause is false in a linear model is worst-case NP-complete, we provide a lazy backtracking algorithm that avoids materializing intermediate substitutions and is efficient in practice.Our proposed algorithms are implemented as part of the SPASS(SCL) solver. Our experimental evaluation on all equality-free first-order TPTP problems shows that model building scales linearly in practice and, together with clause evaluation, accounts for less than one percent of the solver runtime on average on nontrivial runs. The generated models establish satisfiability for roughly a third of the satisfiable TPTP problems considered. If a generated interpretation is not a model of the input clauses, clause evaluation provides a concrete counterexample for extending the trail. Keyphrases: first order logic, model building, scl(fol), spass(scl) In: Stephan Schulz, Konstantin Korovin and Michael Rawson (editors). Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers), vol 23, pages 112-128.
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