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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/>.
*/
#include "atp/core/clause.h"
#include "atp/core/clause_store.h"
#include "atp/core/literal.h"
#include "atp/core/symbol_table.h"
#include "atp/core/term_bank.h"
#include "atp/core/types.h"
#include "atp/search/prover.h"
#include <gtest/gtest.h>
namespace atp {
namespace {
class ProverTest : public ::testing::Test {
protected:
SymbolTable symbols;
TermBank bank{symbols};
ClauseStore store;
SymbolId sym_a{}, sym_b{};
SymbolId sym_f{};
SymbolId sym_P{}, sym_Q{}, sym_R{};
SymbolId sym_X{}, sym_Y{};
TermId a{}, b{}, X{}, Y{};
void SetUp() override {
sym_a = symbols.intern("a", SymbolKind::kConstant);
sym_b = symbols.intern("b", SymbolKind::kConstant);
sym_f = symbols.intern("f", SymbolKind::kFunction, 1);
sym_P = symbols.intern("P", SymbolKind::kPredicate, 1);
sym_Q = symbols.intern("Q", SymbolKind::kPredicate, 1);
sym_R = symbols.intern("R", SymbolKind::kPredicate, 2);
sym_X = symbols.intern("X", SymbolKind::kVariable);
sym_Y = symbols.intern("Y", SymbolKind::kVariable);
a = bank.makeTerm(sym_a, {});
b = bank.makeTerm(sym_b, {});
X = bank.makeVar(sym_X);
Y = bank.makeVar(sym_Y);
}
TermId P(TermId arg) { return bank.makeTerm(sym_P, {{arg}}); }
TermId Q(TermId arg) { return bank.makeTerm(sym_Q, {{arg}}); }
TermId R(TermId a1, TermId a2) { return bank.makeTerm(sym_R, {{a1, a2}}); }
TermId f(TermId arg) { return bank.makeTerm(sym_f, {{arg}}); }
Literal pos(TermId atom) { return {.atom = atom, .is_positive = true}; }
Literal neg(TermId atom) { return {.atom = atom, .is_positive = false}; }
Clause makeClause(std::vector<Literal> lits) {
Clause cl;
cl.literals = std::move(lits);
return cl;
}
};
// ═══════════════════════════════════════════════════════════════════════════
// Trivial refutation: {P(a)} and {¬P(a)} → empty clause
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, TrivialRefutation) {
Prover prover(bank, store);
prover.addClauses({makeClause({pos(P(a))}), makeClause({neg(P(a))})});
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kTheorem);
EXPECT_TRUE(prover.getEmptyClauseId().has_value());
}
// ═══════════════════════════════════════════════════════════════════════════
// Unification required: {P(X)} and {¬P(a)} → empty clause
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, RefutationWithUnification) {
Prover prover(bank, store);
prover.addClauses({makeClause({pos(P(X))}), makeClause({neg(P(a))})});
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kTheorem);
}
// ═══════════════════════════════════════════════════════════════════════════
// Multi-step: {P(a)}, {¬P(X), Q(X)}, {¬Q(a)}
// Step 1: resolve P(a) with ¬P(X)∨Q(X) → Q(a)
// Step 2: resolve Q(a) with ¬Q(a) → empty
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, TwoStepRefutation) {
Prover prover(bank, store);
prover.addClauses(
{makeClause({pos(P(a))}), makeClause({neg(P(X)), pos(Q(X))}), makeClause({neg(Q(a))})});
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kTheorem);
}
// ═══════════════════════════════════════════════════════════════════════════
// Saturation: {P(a)}, {Q(b)} — no complementary literals
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, Saturation) {
Prover prover(bank, store);
prover.addClauses({makeClause({pos(P(a))}), makeClause({pos(Q(b))})});
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kSaturation);
}
// ═══════════════════════════════════════════════════════════════════════════
// Timeout: set very low limits
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, Timeout) {
ProverConfig config;
config.max_iterations = 1;
// Need enough clauses to not saturate in 1 iteration
Prover prover(bank, store, config);
prover.addClauses({makeClause({pos(P(X)), pos(Q(X))}), makeClause({neg(P(a)), pos(Q(a))}),
makeClause({neg(Q(X)), pos(P(f(X)))}), makeClause({neg(P(X)), neg(Q(X))})});
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kTimeout);
}
// ═══════════════════════════════════════════════════════════════════════════
// Chain reasoning: P(a), ¬P(X)∨Q(X), ¬Q(X)∨R(X), ¬R(a)
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, ThreeStepChain) {
SymbolId sym_S = symbols.intern("S", SymbolKind::kPredicate, 1);
auto S = [&](TermId arg) { return bank.makeTerm(sym_S, {{arg}}); };
Prover prover(bank, store);
prover.addClauses({
makeClause({pos(P(a))}), // P(a)
makeClause({neg(P(X)), pos(Q(X))}), // ¬P(X) ∨ Q(X)
makeClause({neg(Q(X)), pos(S(X))}), // ¬Q(X) ∨ S(X)
makeClause({neg(S(a))}) // ¬S(a)
});
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kTheorem);
}
// ═══════════════════════════════════════════════════════════════════════════
// Empty clause in input directly
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProverTest, EmptyClauseInInput) {
Prover prover(bank, store);
prover.addClauses({makeClause({}), // empty clause directly
makeClause({pos(P(a))})});
// Empty clause should be detected immediately when selected from queue
ProverResult result = prover.prove();
EXPECT_EQ(result, ProverResult::kTheorem);
}
} // namespace
} // namespace atp
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