The Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) is a popular artificial intelligence (AI) benchmark comprising abstract reasoning tasks that test fluid intelligence in a generative, few-shot setting. Although humans solve ARC-AGI with ease, it remains extremely difficult for all but the most advanced AI systems. Inspired by methods for modelling biological intelligence spanning psychology to neuroscience, we present a general framework for automated solving of ARC-AGI tasks as well as two specific ARC-AGI solvers that implement our framework. Our cognitive inspiration draws on dual process theory (System 1 and System 2) and vector symbolic algebras (VSAs), and our solvers apply neurosymbolic, object-centric program synthesis. The first of our two ARC-AGI solvers, Solver 1, uses VSAs to represent objects. Solver 1 structures its solutions to ARC-AGI tasks as sets of conditional neurosymbolic rules implemented in a flexible domain-specific language (DSL), and synthesizes its solutions using System 1, VSA-enabled sample-efficient neural learning within System 2, VSA-powered heuristic search. Overall, Solver 1 scores 10.8 percent on ARC-AGI-1-Train and 3.0 percent on ARC-AGI-1-Eval. Additionally, Solver 1 scores 94.5 percent and 83.1 percent on the simpler Sort-of-ARC and 1D-ARC benchmarks—the latter of which outperforms GPT-4 without any computationally expensive pre-training. The second of our two ARC-AGI solvers, Solver 2, uses VSAs to represent programs. Solver 2 structures its solutions to ARC-AGI tasks as sequential compositions of primitives implemented in a bespoke DSL, and synthesizes its solutions using System 1, VSA-powered neural guidance for System 2, VSA-mediated procedural reasoning. Overall, Solver 2 scores 13.5 percent on ARC-AGI-1-Train and 3.5 percent on ARC-AGI-1-Eval. Additionally, our best version of Solver 2 is 7 times more efficient than a naive version of Solver 2, and 235 times more efficient than brute-force search. When combined into an ensemble, our two solvers score 21.0 percent on ARC-AGI-1-Train and 6.3 percent on ARC-AGI-1-Eval. Importantly, we believe that we are the first to apply VSAs to ARC-AGI and, in doing so, have developed two of the most efficient, interpretable, and cognitively plausible ARC-AGI solvers yet.