Initial commit: Build project architecture, define interfaces, write documentation, with the help of Claude

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+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file problem_analyzer.h
+/// @brief Analyzes input clauses and selects the optimal Calculus.
+///
+/// Before the Prover starts its main loop, the ProblemAnalyzer inspects
+/// the input clause set to determine problem characteristics:
+///   - Contains equality?             → enable paramodulation
+///   - Pure Horn clauses?             → use SLD resolution
+///   - Contains arithmetic literals?  → enable theory solver
+///   - Problem size / clause density  → tune resource limits
+///
+/// This is the "auto mode" that mature ATPs use to avoid loading
+/// unnecessary inference rules that would explode the search space.
+
+#include "atp/core/clause.h"
+#include "atp/strategy/calculus.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Features detected in the input problem.
+struct ProblemFeatures {
+    bool has_equality = false;        ///< Contains '=' predicate
+    bool is_purely_propositional = false;  ///< No function symbols, no variables
+    bool is_horn = false;             ///< All clauses are Horn clauses
+    bool has_existential = false;     ///< Had existential quantifiers (Skolemized)
+    size_t num_clauses = 0;
+    size_t num_predicates = 0;
+    size_t num_functions = 0;
+    size_t max_clause_size = 0;
+    size_t max_term_depth = 0;
+};
+
+/// Analyze the input clauses and extract problem features.
+ProblemFeatures analyzeFeatures(const std::vector<Clause>& clauses, const TermBank& bank);
+
+/// Select the optimal calculus based on detected features.
+/// This is the core strategy dispatch logic.
+std::unique_ptr<Calculus> selectCalculus(const ProblemFeatures& features);
+
+}  // namespace atp