First-Order Schemata and Inductive Proof Analysis

David Cerna is a computational logician who has held positions at several research institutions including Czech Academy of Sciences, Dynatrace Research, and the Research Institute for Symbolic Computation. In 2015, he earned his PhD from the Technical University of Vienna in the field of computational proof theory. He has expertise in the areas of Inductive Synthesis, Unification Theory, and automated reasoning.Alexander Leitsch is retired professor of Mathematics and Theoretical Computer Science at the Technische Universität Wien. His main research areas are Computational Logic, Proof Theory and Automated Deduction. He is author of the book The Resolution calculus (Springer 1997) and of the book Methods of Cut-Elimination with coauthor Matthias Baaz (Springer 2011). He was the head of the Theory and Logic group in the Institute of Logic and Computation and the leader of seven research projects in various areas of Computational Logic supported by the Austrian Science Fund.Anela Lolić is a logician at the Institute of Logic and Computation, TU Wien, specializing in structural proof theory. She earned her PhD in Computer Science from TU Wien in 2020, with a thesis focused on the CERES method for automated proof analysis. As principal investigator and researcher, she leads projects such as PANDAFOREST ("Proof analysis and automated deduction for recursive structures") and on Skolemization and Interpolation, supported by the Austrian Science Fund FWF and the Austrian Academy of Sciences.

• 1. Introduction.- 2. Schemata and Point Transition Systems.- 3. Term schemata and formula schemata.- 4. Term Schemata and Unification.- 5. Proof schemata.- 6. Proof schemata and arithmetic.- 7. Cut-Elimination and the Method CERES.- 8. Schematic CERES (completely new - improves former publications).- 9. An Application of Schematic CERES.- 10. Schematic Reasoning in GAPT.- 11. Conclusion.