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"The paper formulates formal problem-solving as a deterministic Markov decision process and implements FPS inside formal theorem proving environments (Section 3.1).",
"Deductive Formal Problem-Solving decouples forward answer construction from optional backward proof validation for find-all problems (Figure 2).",
"FPS soundness is proved: any direct answer produced by FPS satisfies the formal problem predicate (Theorem 3.6).",
"D-FPS completeness and soundness for find-all problems are stated as formal theorems under the paper's conditions (Theorems 3.8 and 3.9).",
"The benchmark suite consists of FormalMath500, MiniF2F-Solving, and PutnamBench-Solving, constructed from informal and theorem-proving math benchmarks (Section 4.2).",
"The strongest evaluated baselines solve at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving (Table 1)."
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