Quantified formulas with Uninterpreted Functions (UFs) over non-linear real arithmetic pose fundamental challenges for Satisfiability Modulo Theories (SMT) solving. Traditional quantifier instantiation methods struggle because they lack semantic understanding of UF constraints, forcing them to search through unbounded solution spaces with limited guidance. We present AquaForte, a framework that leverages Large Language Models to provide semantic guidance for UF instantiation by generating instantiated candidates for function definitions that satisfy the constraints, thereby significantly reducing the search space and complexity for solvers. Our approach preprocesses formulas through constraint separation, uses structured prompts to extract mathematical reasoning from LLMs, and integrates the results with traditional SMT algorithms through adaptive instantiation. AquaForte maintains soundness through systematic validation: LLM-guided instantiations yielding SAT solve the original problem, while UNSAT results generate exclusion clauses for iterative refinement. Completeness is preserved by fallback to traditional solvers augmented with learned constraints. Experimental evaluation on SMT-COMP benchmarks demonstrates that AquaForte solves numerous instances where state-of-the-art solvers like Z3 and CVC5 timeout, with particular effectiveness on satisfiable formulas. Our work shows that LLMs can provide valuable mathematical intuition for symbolic reasoning, establishing a new paradigm for SMT constraint solving.

The satisfiability problem modulo the nonlinear real arithmetic (NRA) theory serves as the foundation for a wide range of important applications, such as model checking, program analysis, and software testing. However, due to the high computational complexity, developing efficient solving algorithms for this problem has consistently presented a substantial challenge. We present a hybrid SMT(NRA) solver, called NRAgo, which combines the efficiency of gradient-based optimization method with the completeness of algebraic solving algorithm. With our approach, the practical performance on many satisfiable instances is substantially improved. The experimental evaluation shows that NRAgo achieves remarkable acceleration effects on a set of challenging SMT(NRA) benchmarks that are hard to solve for state-of-the-art SMT solvers.