Large Language Models Imitate Logical Reasoning, but at what Cost?

We present a longitudinal study which evaluates the reasoning capability of frontier Large Language Models over an eighteen month period. We measured the accuracy of three leading models from December 2023, September 2024 and June 2025 on true or false questions from the PrOntoQA dataset and their faithfulness to reasoning strategies provided through in-context learning. The improvement in performance from 2023 to 2024 can be attributed to hidden Chain of Thought prompting. The introduction of thinking models allowed for significant improvement in model performance between 2024 and 2025. We then present a neuro-symbolic architecture which uses LLMs of less than 15 billion parameters to translate the problems into a standardised form. We then parse the standardised forms of the problems into a program to be solved by Z3, an SMT solver, to determine the satisfiability of the query. We report the number of prompt and completion tokens as well as the computational cost in FLOPs for open source models. The neuro-symbolic approach significantly reduces the computational cost while maintaining near perfect performance. The common approximation that the number of inference FLOPs is double the product of the active parameters and total tokens was accurate within 10% for all experiments.