1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
|
/*
* 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/proof/proof_trace.h"
#include "atp/search/prover.h"
#include <gtest/gtest.h>
#include <string>
#include <utility>
#include <vector>
namespace atp {
namespace {
class ProofTraceTest : public ::testing::Test {
protected:
SymbolTable symbols_;
TermBank bank_{symbols_};
ClauseStore store_;
SymbolId sym_a_{}, sym_b_{};
SymbolId sym_p_{}, sym_q_{};
SymbolId sym_x_{};
TermId a_term_{}, b_term_{}, x_term_{};
void SetUp() override {
sym_a_ = symbols_.intern("a", SymbolKind::kConstant);
sym_b_ = symbols_.intern("b", SymbolKind::kConstant);
sym_p_ = symbols_.intern("P", SymbolKind::kPredicate, 1);
sym_q_ = symbols_.intern("Q", SymbolKind::kPredicate, 1);
sym_x_ = symbols_.intern("X", SymbolKind::kVariable);
a_term_ = bank_.makeTerm(sym_a_, {});
b_term_ = bank_.makeTerm(sym_b_, {});
x_term_ = bank_.makeVar(sym_x_);
}
TermId p(TermId arg) { return bank_.makeTerm(sym_p_, {{arg}}); }
TermId q(TermId arg) { return bank_.makeTerm(sym_q_, {{arg}}); }
static Literal pos(TermId atom) { return {.atom_ = atom, .is_positive_ = true}; }
static Literal neg(TermId atom) { return {.atom_ = atom, .is_positive_ = false}; }
static Clause makeClause(std::vector<Literal> lits) {
Clause cl;
cl.literals_ = std::move(lits);
return cl;
}
};
// ═══════════════════════════════════════════════════════════════════════════
// termToString Tests
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProofTraceTest, TermToStringConstant) {
EXPECT_EQ(termToString(a_term_, bank_), "a");
}
TEST_F(ProofTraceTest, TermToStringVariable) {
EXPECT_EQ(termToString(x_term_, bank_), "X");
}
TEST_F(ProofTraceTest, TermToStringCompound) {
TermId const pa = p(a_term_);
EXPECT_EQ(termToString(pa, bank_), "P(a)");
}
TEST_F(ProofTraceTest, TermToStringNested) {
SymbolId const sym_f = symbols_.intern("f", SymbolKind::kFunction, 1);
TermId const fa = bank_.makeTerm(sym_f, {{a_term_}});
TermId const pfa = p(fa);
EXPECT_EQ(termToString(pfa, bank_), "P(f(a))");
}
// ═══════════════════════════════════════════════════════════════════════════
// clauseToString Tests
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProofTraceTest, ClauseToStringEmpty) {
Clause const empty = makeClause({});
EXPECT_EQ(clauseToString(empty, bank_), "□");
}
TEST_F(ProofTraceTest, ClauseToStringSinglePositive) {
Clause const c = makeClause({pos(p(a_term_))});
EXPECT_EQ(clauseToString(c, bank_), "P(a)");
}
TEST_F(ProofTraceTest, ClauseToStringSingleNegative) {
Clause const c = makeClause({neg(p(a_term_))});
EXPECT_EQ(clauseToString(c, bank_), "¬P(a)");
}
TEST_F(ProofTraceTest, ClauseToStringMultipleLiterals) {
Clause const c = makeClause({neg(p(x_term_)), pos(q(x_term_))});
std::string const s = clauseToString(c, bank_);
EXPECT_EQ(s, "¬P(X) ∨ Q(X)");
}
// ═══════════════════════════════════════════════════════════════════════════
// extractProof Tests
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProofTraceTest, ExtractProofTrivial) {
// Run a trivial proof: {P(a)} + {¬P(a)} → □
Prover prover(bank_, store_);
prover.addClauses({makeClause({pos(p(a_term_))}), makeClause({neg(p(a_term_))})});
ProverResult const result = prover.prove();
ASSERT_EQ(result, ProverResult::kTheorem);
auto eid = prover.getEmptyClauseId();
ASSERT_TRUE(eid.has_value());
auto proof = extractProof(store_, *eid);
ASSERT_GE(proof.size(), 3U); // At least: 2 axioms + 1 empty clause
// First steps should be axioms (kInput)
EXPECT_EQ(proof.front().rule_, InferenceRule::kInput);
// Last step should be the empty clause
EXPECT_EQ(proof.back().clause_id_, *eid);
// Last step should be resolution
EXPECT_EQ(proof.back().rule_, InferenceRule::kResolution);
}
TEST_F(ProofTraceTest, ExtractProofTwoStep) {
// {P(a)}, {¬P(X), Q(X)}, {¬Q(a)} → □ in 2 resolution steps
Prover prover(bank_, store_);
prover.addClauses({makeClause({pos(p(a_term_))}), makeClause({neg(p(x_term_)), pos(q(x_term_))}),
makeClause({neg(q(a_term_))})});
ProverResult const result = prover.prove();
ASSERT_EQ(result, ProverResult::kTheorem);
auto eid = prover.getEmptyClauseId();
ASSERT_TRUE(eid.has_value());
auto proof = extractProof(store_, *eid);
// Should have axioms + intermediate + empty clause
ASSERT_GE(proof.size(), 4U); // 3 axioms + at least 1 intermediate + empty
// Last step is the empty clause
EXPECT_EQ(proof.back().clause_id_, *eid);
}
// ═══════════════════════════════════════════════════════════════════════════
// formatProof Tests
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(ProofTraceTest, FormatProofContainsExpectedElements) {
Prover prover(bank_, store_);
prover.addClauses({makeClause({pos(p(a_term_))}), makeClause({neg(p(a_term_))})});
prover.prove();
auto eid = prover.getEmptyClauseId();
ASSERT_TRUE(eid.has_value());
auto proof = extractProof(store_, *eid);
std::string const output = formatProof(proof, store_, bank_);
// Should contain key elements
EXPECT_NE(output.find("input"), std::string::npos) << output;
EXPECT_NE(output.find("resolution"), std::string::npos) << output;
EXPECT_NE(output.find("P(a)"), std::string::npos) << output;
// Empty clause should appear
std::string const empty_marker = "□";
EXPECT_NE(output.find(empty_marker), std::string::npos) << output;
}
TEST_F(ProofTraceTest, FormatProofNoParentsForAxioms) {
Prover prover(bank_, store_);
prover.addClauses({makeClause({pos(p(a_term_))}), makeClause({neg(p(a_term_))})});
prover.prove();
auto eid = prover.getEmptyClauseId();
auto proof = extractProof(store_, *eid);
std::string const output = formatProof(proof, store_, bank_);
// The first line (an axiom) should NOT have "[from ...]"
// Find the first newline
auto first_line = output.substr(0, output.find('\n'));
EXPECT_EQ(first_line.find("[from"), std::string::npos)
<< "Axiom should not have parent info: " << first_line;
}
} // namespace
} // namespace atp
|
