# Schematic Refutations of Formula Schemata

## TL;DR

This paper introduces a generalized resolution calculus for schematic proofs involving infinite proof sequences, enhancing previous methods and demonstrating its application through a schematic refutation of a weak pigeonhole principle.

## Contribution

It presents a new, more general framework for schematic proof calculus that improves upon earlier approaches and applies it to formalize a schematic refutation.

## Key findings

- The new calculus generalizes previous schematic deduction methods.
- It successfully formalizes a proof of a weak pigeonhole principle.
- The framework supports schematic refutations of complex formulas.

## Abstract

Proof schemata are infinite sequences of proofs which are defined inductively. In this paper we present a general framework for schemata of terms, formulas and unifiers and define a resolution calculus for schemata of quantifier-free formulas. The new calculus generalizes and improves former approaches to schematic deduction. As an application of the method we present a schematic refutation formalizing a proof of a weak form of the pigeon hole principle.