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 resolution.h
+/// @brief Binary resolution and factoring inference rules.
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+
+#include <optional>
+#include <vector>
+
+namespace atp {
+
+/// Attempt binary resolution between two clauses on the specified literal indices.
+/// @return The resolvent clause if resolution succeeds, std::nullopt otherwise.
+std::optional<Clause> resolve(const TermBank& bank, const Clause& c1, size_t lit_idx1,
+                              const Clause& c2, size_t lit_idx2);
+
+/// Generate all possible resolvents between two clauses.
+std::vector<Clause> allResolvents(const TermBank& bank, const Clause& c1, const Clause& c2);
+
+/// Attempt factoring on a single clause (merge two unifiable literals).
+std::vector<Clause> factor(const TermBank& bank, const Clause& c);
+
+}  // namespace atp