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In-Depth Information
Table 2.1
The currently existing 45 negations
¬
x
,
b
,
a
1
¬
x
,
sg
(
a
),
sg
(
a
)
2
x
,
b
,
a
.
b
+
a
2
¬
3
¬
x
,
b
,
1
−
b
4
¬
x
,
sg
(
1
−
b
),
sg
(
1
−
b
)
5
¬
6
x
,
(
−
b
),
(
a
)
sg
1
sg
¬
x
,
sg
(
1
−
b
),
a
7
¬
x
,
1
−
a
,
a
8
¬
9
x
,
sg
(
a
),
a
¬
x
,
sg
(
1
−
b
),
1
−
b
10
¬
11
x
,
sg
(
b
),
sg
(
b
)
b
2
¬
12
x
,
b
.(
b
+
a
),
min
(
1
,
a
.(
+
a
+
b
.
a
))
¬
x
,
sg
(
1
−
a
),
sg
(
1
−
a
)
13
¬
14
x
,
sg
(
b
),
sg
(
1
−
a
)
¬
x
,
sg
(
1
−
b
),
sg
(
1
−
a
)
15
¬
x
,
sg
(
a
),
sg
(
1
−
a
)
16
¬
17
x
,
sg
(
1
−
b
),
sg
(
b
)
¬
x
,
b
.
sg
(
a
),
a
.
sg
(
b
)
18
¬
x
,
b
.
sg
(
a
),
0
19
¬
20
x
,
b
,
0
¬
x
,
min
(
1
−
a
,
sg
(
a
)),
min
(
a
,
sg
(
1
−
a
))
21
¬
x
,
min
(
1
−
a
,
sg
(
a
)),
0
22
¬
23
x
,
1
−
a
,
0
¬
x
,
min
(
b
,
sg
(
1
−
b
)),
min
(
1
−
b
,
sg
(
b
))
24
¬
x
,
min
(
b
,
sg
(
1
−
b
)),
0
25
¬
26
x
,
b
,
a
.
b
+
sg
(
1
−
a
)
¬
x
,
1
−
a
,
a
.(
1
−
a
)
+
sg
(
1
−
a
)
27
¬
x
,
b
,(
1
−
b
).
b
+
sg
(
b
)
28
¬
29
x
,
(
,
b
.
a
+
(
−
b
)),
(
,
a
.(
b
.
a
+
(
−
b
))
+
(
−
a
))
max
0
sg
1
m
in
1
sg
1
sg
1
¬
x
,
a
.
b
,
a
.(
a
.
b
+
sg
(
1
−
b
))
+
sg
(
1
−
a
)
30
¬
x
,
max
(
0
,(
1
−
a
).
a
+
sg
(
a
)),
min
(
1
,
a
.((
1
−
a
).
a
+
sg
(
a
))
+
sg
(
1
−
a
))
31
¬
32
x
,(
1
−
a
).
a
,
a
.((
1
−
a
).
a
+
sg
(
a
))
+
sg
(
1
−
a
)
¬
x
,
b
.(
1
−
b
)
+
sg
(
1
−
b
), (
1
−
b
).(
b
.(
1
−
b
)
+
sg
(
1
−
b
))
+
sg
(
b
))
33
¬
34
x
,
b
.(
1
−
b
), (
1
−
b
).(
b
.(
1
−
b
)
+
sg
(
1
−
b
))
+
sg
(
b
)
b
2
1
+
a
¬
,
35
2
b
3
2
+
a
¬
36
,
3
2
b
3
2
a
+
1
¬
,
37
3
1
−
a
2
+
a
¬
,
38
3
3
b
3
3
−
b
¬
39
,
3
2
−
2
a
3
1
+
2
a
3
¬
,
40
(continued)
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