Saturation-Driven Dataset Generation for LLM Mathematical Reasoning in
  the TPTP Ecosystem
The scarcity of high-quality, logically sound data is a critical bottleneck
for advancing the mathematical reasoning of Large Language Models (LLMs). Our
work confronts this challenge by turning decades of automated theorem proving
research into a scalable data engine. Rather than relying on error-prone LLMs
or complex proof-assistant syntax like Lean and Isabelle, our framework
leverages E-prover's saturation capabilities on the vast TPTP axiom library to
derive a massive, guaranteed-valid corpus of theorems. Our pipeline is
principled and simple: saturate axioms, filter for "interesting" theorems, and
generate tasks. With no LLMs in the loop, we eliminate factual errors by
construction. This purely symbolic data is then transformed into three
difficulty-controlled challenges: entailment verification, premise selection,
and proof reconstruction. Our zero-shot experiments on frontier models reveal a
clear weakness: performance collapses on tasks requiring deep, structural
reasoning. Our framework provides both the diagnostic tool to measure this gap
and a scalable source of symbolic training data to address it. We make the code
and data publicly available.
  https://github.com/sileod/reasoning_core
https://hf.co/datasets/reasoning-core/rc1
68bfdc49207285de11b07dd6
Valentin Quesnel
68bfdc49207285de11b07dd7
Damien Sileo
Saturation-Driven Dataset Generation for LLM Mathematical Reasoning in
  the TPTP Ecosystem
The scarcity of high-quality, logically sound data is a critical bottleneck
for advancing the mathematical reasoning of Large Language Models (LLMs). Our
work confronts this challenge by turning decades of automated theorem proving
research into a scalable data engine. Rather than relying on error-prone LLMs
or complex proof-assistant syntax like Lean and Isabelle, our framework
leverages E-prover's saturation capabilities on the vast TPTP axiom library to
derive a massive, guaranteed-valid corpus of theorems. Our pipeline is
principled and simple: saturate axioms, filter for "interesting" theorems, and
generate tasks. With no LLMs in the loop, we eliminate factual errors by
construction. This purely symbolic data is then transformed into three
difficulty-controlled challenges: entailment verification, premise selection,
and proof reconstruction. Our zero-shot experiments on frontier models reveal a
clear weakness: performance collapses on tasks requiring deep, structural
reasoning. Our framework provides both the diagnostic tool to measure this gap
and a scalable source of symbolic training data to address it. We make the code
and data publicly available.
  https://github.com/sileod/reasoning_core
https://hf.co/datasets/reasoning-core/rc1
A framework generates a large corpus of valid theorems using automated theorem proving to create symbolic training data for improving LLMs' mathematical reasoning.
Large Language Models automated theorem proving E-prover saturation capabilities TPTP axiom library entailment verification premise selection proof reconstruction zero-shot experiments