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
|
/*
* 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/literal.h"
#include "atp/core/symbol_table.h"
#include "atp/core/term_bank.h"
#include "atp/core/types.h"
#include "atp/simplify/subsumption.h"
#include "atp/simplify/tautology.h"
#include <gtest/gtest.h>
namespace atp {
namespace {
class SimplifyTest : public ::testing::Test {
protected:
SymbolTable symbols;
TermBank bank{symbols};
SymbolId sym_a{}, sym_b{}, sym_c{};
SymbolId sym_P{}, sym_Q{}, sym_R{};
SymbolId sym_X{};
TermId a{}, b{}, c{}, X{};
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_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);
a = bank.makeTerm(sym_a, {});
b = bank.makeTerm(sym_b, {});
c = bank.makeTerm(sym_c, {});
X = bank.makeVar(sym_X);
}
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}}); }
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;
}
};
// ═══════════════════════════════════════════════════════════════════════════
// Tautology Tests
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(SimplifyTest, TautologyComplementaryLiterals) {
// {P(a), ¬P(a)} → tautology
Clause cl = makeClause({pos(P(a)), neg(P(a))});
EXPECT_TRUE(isTautology(cl));
}
TEST_F(SimplifyTest, TautologyWithExtraLiterals) {
// {Q(b), P(a), ¬P(a)} → tautology
Clause cl = makeClause({pos(Q(b)), pos(P(a)), neg(P(a))});
EXPECT_TRUE(isTautology(cl));
}
TEST_F(SimplifyTest, NotTautologySamePolarity) {
// {P(a), P(a)} → NOT tautology (same polarity)
Clause cl = makeClause({pos(P(a)), pos(P(a))});
EXPECT_FALSE(isTautology(cl));
}
TEST_F(SimplifyTest, NotTautologyDifferentAtoms) {
// {P(a), ¬P(b)} → NOT tautology (different atoms)
Clause cl = makeClause({pos(P(a)), neg(P(b))});
EXPECT_FALSE(isTautology(cl));
}
TEST_F(SimplifyTest, NotTautologyDifferentPredicates) {
// {P(a), ¬Q(a)} → NOT tautology (different predicates)
Clause cl = makeClause({pos(P(a)), neg(Q(a))});
EXPECT_FALSE(isTautology(cl));
}
TEST_F(SimplifyTest, NotTautologyEmptyClause) {
Clause cl = makeClause({});
EXPECT_FALSE(isTautology(cl));
}
TEST_F(SimplifyTest, NotTautologySingleLiteral) {
Clause cl = makeClause({pos(P(a))});
EXPECT_FALSE(isTautology(cl));
}
TEST_F(SimplifyTest, TautologyVariableAtom) {
// {P(X), ¬P(X)} → tautology (same variable term)
Clause cl = makeClause({pos(P(X)), neg(P(X))});
EXPECT_TRUE(isTautology(cl));
}
TEST_F(SimplifyTest, NotTautologyVarVsConst) {
// {P(X), ¬P(a)} → NOT tautology (syntactically different)
Clause cl = makeClause({pos(P(X)), neg(P(a))});
EXPECT_FALSE(isTautology(cl));
}
// ═══════════════════════════════════════════════════════════════════════════
// Subsumption Tests
// ═══════════════════════════════════════════════════════════════════════════
TEST_F(SimplifyTest, SubsumesSubset) {
// {P(a)} subsumes {P(a), Q(b)}
Clause gen = makeClause({pos(P(a))});
Clause spec = makeClause({pos(P(a)), pos(Q(b))});
EXPECT_TRUE(subsumes(gen, spec));
}
TEST_F(SimplifyTest, SubsumesIdentical) {
// {P(a), Q(b)} subsumes {P(a), Q(b)}
Clause c1 = makeClause({pos(P(a)), pos(Q(b))});
Clause c2 = makeClause({pos(P(a)), pos(Q(b))});
EXPECT_TRUE(subsumes(c1, c2));
}
TEST_F(SimplifyTest, SubsumesEmptyClause) {
// {} subsumes everything
Clause empty = makeClause({});
Clause cl = makeClause({pos(P(a)), neg(Q(b))});
EXPECT_TRUE(subsumes(empty, cl));
}
TEST_F(SimplifyTest, SubsumesNotLarger) {
// {P(a), Q(b)} does NOT subsume {P(a)}
Clause gen = makeClause({pos(P(a)), pos(Q(b))});
Clause spec = makeClause({pos(P(a))});
EXPECT_FALSE(subsumes(gen, spec));
}
TEST_F(SimplifyTest, SubsumesRequiresSamePolarity) {
// {P(a)} does NOT subsume {¬P(a)}
Clause gen = makeClause({pos(P(a))});
Clause spec = makeClause({neg(P(a))});
EXPECT_FALSE(subsumes(gen, spec));
}
TEST_F(SimplifyTest, SubsumesRequiresSameAtom) {
// {P(a)} does NOT subsume {P(b)}
Clause gen = makeClause({pos(P(a))});
Clause spec = makeClause({pos(P(b))});
EXPECT_FALSE(subsumes(gen, spec));
}
TEST_F(SimplifyTest, SubsumesNegativeLiterals) {
// {¬P(a)} subsumes {¬P(a), Q(b)}
Clause gen = makeClause({neg(P(a))});
Clause spec = makeClause({neg(P(a)), pos(Q(b))});
EXPECT_TRUE(subsumes(gen, spec));
}
TEST_F(SimplifyTest, SubsumesOrderIndependent) {
// {Q(b), P(a)} subsumes {P(a), Q(b), R(a,b)} regardless of order
Clause gen = makeClause({pos(Q(b)), pos(P(a))});
Clause spec = makeClause({pos(P(a)), pos(Q(b)), pos(R(a, b))});
EXPECT_TRUE(subsumes(gen, spec));
}
} // namespace
} // namespace atp
|
