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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 paramodulation.h
/// @brief Paramodulation inference rule for equality reasoning.
///
/// Paramodulation replaces a subterm in one clause with an equal term
/// from an equation in another clause. Combined with term orderings,
/// this gives a complete calculus for first-order logic with equality
/// (the Superposition calculus).
#include "atp/core/clause.h"
#include "atp/core/term_bank.h"
#include "atp/rewrite/ordering.h"
#include <vector>
namespace atp {
/// Generate all paramodulants between two clauses.
/// Uses the term ordering to restrict to ordered paramodulation (superposition).
std::vector<Clause> paramodulate(const TermBank& bank, const Clause& c1, const Clause& c2,
const TermOrdering& ordering);
/// Simplify a clause by demodulation (rewriting with unit equalities).
/// Returns true if the clause was modified.
bool demodulate(TermBank& bank, Clause& clause, const Clause& unit_eq,
const TermOrdering& ordering);
} // namespace atp
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