Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The schematic CERES method [8] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction rule to the LK-calculus. In this work,  formalize a schematic version of the infinitary pigeonhole principle, which  call the Non-injectivity Assertion schema (NiA-schema), in the LKS-calculus [8], and analyse the clause set schema extracted from the NiA-schema using some of the structure provided by the schematic CERES method. To the best of our knowledge, this is the first appli- cation of the constructs built for proof analysis of proof schemata to a mathematical argument since its publication.  discuss the role of Automated Theorem Proving (ATP) in schematic proof analysis, as ll as the shortcomings of the schematic CERES method concerning the formalization of the NiA-schema, namely, the expressive por of the schematic resolution calculus.  conclude with a discussion concerning the usage of ATP in schematic proof analysis.
['David Cerna', 'Alexander Leitsch']
I am writing a research paper on a idea Analysis of Clause set Schema Aided by Automated Theorem Proving: A Case Study [Extended Paper]
[{"from": "human", "value": "I am writing a research paper on a idea Analysis of Clause set Schema Aided by Automated Theorem Proving: A Case Study [Extended Paper]"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The schematic CERES method [8] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction rule to the LK-calculus. In this work,  formalize a schematic version of the infinitary pigeonhole principle, which  call the Non-injectivity Assertion schema (NiA-schema), in the LKS-calculus [8], and analyse the clause set schema extracted from the NiA-schema using some of the structure provided by the schematic CERES method. To the best of our knowledge, this is the first appli- cation of the constructs built for proof analysis of proof schemata to a mathematical argument since its publication.  discuss the role of Automated Theorem Proving (ATP) in schematic proof analysis, as ll as the shortcomings of the schematic CERES method concerning the formalization of the NiA-schema, namely, the expressive por of the schematic resolution calculus.  conclude with a discussion concerning the usage of ATP in schematic proof analysis."}]