/* * 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 . */ #include "atp/core/clause.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/infer/resolution.h" #include #include #include namespace atp { namespace { class ResolutionTest : public ::testing::Test { protected: SymbolTable symbols_; TermBank bank_{symbols_}; SymbolId sym_a_{}, sym_b_{}, sym_c_{}; SymbolId sym_f_{}; SymbolId sym_p_{}, sym_q_{}, sym_r_{}; SymbolId sym_x_{}, sym_y_{}, sym_z_{}; TermId a_{}, b_{}, c_{}; TermId x_{}, y_{}, z_{}; void SetUp() override { sym_a_ = symbols_.intern("a", SymbolKind::kConstant); sym_b_ = symbols_.intern("b", SymbolKind::kConstant); sym_c_ = symbols_.intern("c", 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); sym_z_ = symbols_.intern("Z", SymbolKind::kVariable); a_ = bank_.makeTerm(sym_a_, {}); b_ = bank_.makeTerm(sym_b_, {}); c_ = bank_.makeTerm(sym_c_, {}); x_ = bank_.makeVar(sym_x_); y_ = bank_.makeVar(sym_y_); z_ = bank_.makeVar(sym_z_); } 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}}); } // Helper: make a clause from literals static Clause makeClause(std::vector lits, ClauseId id = kInvalidId) { Clause c; c.id_ = id; c.literals_ = std::move(lits); return c; } static Literal pos(TermId atom) { return {.atom_ = atom, .is_positive_ = true}; } static Literal neg(TermId atom) { return {.atom_ = atom, .is_positive_ = false}; } }; // ═══════════════════════════════════════════════════════════════════════════ // Basic Resolution Tests // ═══════════════════════════════════════════════════════════════════════════ TEST_F(ResolutionTest, SimpleGroundResolution) { // {P(a)} and {¬P(a), Q(b)} → {Q(b)} Clause const c1 = makeClause({pos(p(a_))}, 0); Clause const c2 = makeClause({neg(p(a_)), pos(q(b_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_EQ(result->literals_.size(), 1); EXPECT_EQ(result->literals_[0].atom_, q(b_)); EXPECT_TRUE(result->literals_[0].is_positive_); } TEST_F(ResolutionTest, ResolutionWithUnification) { // {P(X)} and {¬P(a)} → {} (empty clause!) Clause const c1 = makeClause({pos(p(x_))}, 0); Clause const c2 = makeClause({neg(p(a_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_TRUE(result->isEmpty()) << "Should derive empty clause (contradiction)"; } TEST_F(ResolutionTest, ResolutionFailsSamePolarity) { // {P(a)} and {P(b)} → no resolution (both positive) Clause const c1 = makeClause({pos(p(a_))}, 0); Clause const c2 = makeClause({pos(p(b_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); EXPECT_FALSE(result.has_value()); } TEST_F(ResolutionTest, ResolutionFailsNoUnifier) { // {P(a)} and {¬P(b)} → can't unify a with b Clause const c1 = makeClause({pos(p(a_))}, 0); Clause const c2 = makeClause({neg(p(b_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); EXPECT_FALSE(result.has_value()); } TEST_F(ResolutionTest, ResolutionAppliesSubstToRemainingLiterals) { // {P(X), Q(X)} and {¬P(a)} → {Q(a)} Clause const c1 = makeClause({pos(p(x_)), pos(q(x_))}, 0); Clause const c2 = makeClause({neg(p(a_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_EQ(result->literals_.size(), 1); EXPECT_EQ(result->literals_[0].atom_, q(a_)); } TEST_F(ResolutionTest, ResolutionMultipleLiterals) { // {P(X), Q(b)} and {¬P(a), R(a, c)} → {Q(b), R(a, c)} Clause const c1 = makeClause({pos(p(x_)), pos(q(b_))}, 0); Clause const c2 = makeClause({neg(p(a_)), pos(r(a_, c_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_EQ(result->literals_.size(), 2); } TEST_F(ResolutionTest, VariableRenamingWorks) { // Both clauses use variable X // {P(X)} and {¬P(X), Q(X)} → {Q(a)} only if X is renamed in c2 Clause const c1 = makeClause({pos(p(a_))}, 0); Clause const c2 = makeClause({neg(p(x_)), pos(q(x_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_EQ(result->literals_.size(), 1); // Q(X) should become Q(a) after substitution {X→a} EXPECT_EQ(result->literals_[0].atom_, q(a_)); } TEST_F(ResolutionTest, VariableRenamingPreventsClash) { // {R(X, a)} and {¬R(b, X)} // Without renaming: X would clash between c1 and c2 // With renaming: c2's X → _R0, then unify R(X,a) with R(b,_R0) → {X→b, _R0→a} Clause const c1 = makeClause({pos(r(x_, a_))}, 0); Clause const c2 = makeClause({neg(r(b_, x_))}, 1); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_TRUE(result->isEmpty()); } // ═══════════════════════════════════════════════════════════════════════════ // AllResolvents Tests // ═══════════════════════════════════════════════════════════════════════════ TEST_F(ResolutionTest, AllResolventsFindsAll) { // {P(a), Q(a)} and {¬P(a), ¬Q(a)} // Can resolve on P or Q → 2 resolvents Clause const c1 = makeClause({pos(p(a_)), pos(q(a_))}, 0); Clause const c2 = makeClause({neg(p(a_)), neg(q(a_))}, 1); auto results = allResolvents(bank_, c1, c2); EXPECT_EQ(results.size(), 2); } TEST_F(ResolutionTest, AllResolventsEmpty) { // {P(a)} and {Q(b)} → no complementary pairs Clause const c1 = makeClause({pos(p(a_))}, 0); Clause const c2 = makeClause({pos(q(b_))}, 1); auto results = allResolvents(bank_, c1, c2); EXPECT_TRUE(results.empty()); } // ═══════════════════════════════════════════════════════════════════════════ // Factoring Tests // ═══════════════════════════════════════════════════════════════════════════ TEST_F(ResolutionTest, SimpleFactoring) { // {P(X), P(a), Q(X)} → factor P(X) with P(a): {P(a), Q(a)} Clause const c = makeClause({pos(p(x_)), pos(p(a_)), pos(q(x_))}, 0); auto results = factor(bank_, c); ASSERT_EQ(results.size(), 1); EXPECT_EQ(results[0].literals_.size(), 2); // After factoring: {P(a), Q(a)} EXPECT_EQ(results[0].literals_[0].atom_, p(a_)); EXPECT_EQ(results[0].literals_[1].atom_, q(a_)); } TEST_F(ResolutionTest, NoFactoring) { // {P(a), Q(b)} → different predicates, can't factor Clause const c = makeClause({pos(p(a_)), pos(q(b_))}, 0); auto results = factor(bank_, c); EXPECT_TRUE(results.empty()); } TEST_F(ResolutionTest, FactoringDifferentPolarity) { // {P(a), ¬P(a)} → different polarity, can't factor Clause const c = makeClause({pos(p(a_)), neg(p(a_))}, 0); auto results = factor(bank_, c); EXPECT_TRUE(results.empty()); } TEST_F(ResolutionTest, FactoringNonUnifiable) { // {P(a), P(b)} → can't unify a with b Clause const c = makeClause({pos(p(a_)), pos(p(b_))}, 0); auto results = factor(bank_, c); EXPECT_TRUE(results.empty()); } // ═══════════════════════════════════════════════════════════════════════════ // Provenance Tests // ═══════════════════════════════════════════════════════════════════════════ TEST_F(ResolutionTest, ResolventHasProvenance) { Clause const c1 = makeClause({pos(p(x_))}, 5); Clause const c2 = makeClause({neg(p(a_))}, 7); auto result = resolve(bank_, c1, 0, c2, 0); ASSERT_TRUE(result.has_value()); EXPECT_EQ(result->rule_, InferenceRule::kResolution); EXPECT_EQ(result->parent1_, 5); EXPECT_EQ(result->parent2_, 7); } TEST_F(ResolutionTest, FactoredHasProvenance) { Clause const c = makeClause({pos(p(x_)), pos(p(a_))}, 3); auto results = factor(bank_, c); ASSERT_FALSE(results.empty()); EXPECT_EQ(results[0].rule_, InferenceRule::kFactoring); EXPECT_EQ(results[0].parent1_, 3); } } // namespace } // namespace atp