:: GATE_3 semantic presentation
theorem Th1: :: GATE_3:1
for b
1, b
2, b
3, b
4, b
5, b
6, b
7, b
8, b
9, b
10, b
11, b
12 being
set holds
not ( not (
$ b
1 & not
$ AND2 (NOT1 b10),
(NOT1 b9) ) & not (
$ AND2 (NOT1 b10),
(NOT1 b9) & not
$ b
1 ) & not (
$ b
2 & not
$ AND2 (NOT1 b10),b
9 ) & not (
$ AND2 (NOT1 b10),b
9 & not
$ b
2 ) & not (
$ b
3 & not
$ AND2 b
10,
(NOT1 b9) ) & not (
$ AND2 b
10,
(NOT1 b9) & not
$ b
3 ) & not (
$ b
4 & not
$ AND2 b
10,b
9 ) & not (
$ AND2 b
10,b
9 & not
$ b
4 ) & not (
$ b
5 & not
$ AND2 (NOT1 b12),
(NOT1 b11) ) & not (
$ AND2 (NOT1 b12),
(NOT1 b11) & not
$ b
5 ) & not (
$ b
6 & not
$ AND2 (NOT1 b12),b
11 ) & not (
$ AND2 (NOT1 b12),b
11 & not
$ b
6 ) & not (
$ b
7 & not
$ AND2 b
12,
(NOT1 b11) ) & not (
$ AND2 b
12,
(NOT1 b11) & not
$ b
7 ) & not (
$ b
8 & not
$ AND2 b
12,b
11 ) & not (
$ AND2 b
12,b
11 & not
$ b
8 ) & not (
$ b
11 & not
$ NOT1 b
10 ) & not (
$ NOT1 b
10 & not
$ b
11 ) & not (
$ b
12 & not
$ b
9 ) & not (
$ b
9 & not
$ b
12 ) & not ( not (
$ b
6 & not
$ b
1 ) & not (
$ b
1 & not
$ b
6 ) & not (
$ b
8 & not
$ b
2 ) & not (
$ b
2 & not
$ b
8 ) & not (
$ b
7 & not
$ b
4 ) & not (
$ b
4 & not
$ b
7 ) & not (
$ b
5 & not
$ b
3 ) & not (
$ b
3 & not
$ b
5 ) ) )
theorem Th2: :: GATE_3:2
for b
1, b
2, b
3, b
4, b
5, b
6, b
7, b
8, b
9, b
10, b
11, b
12, b
13 being
set holds
not ( not (
$ b
1 & not
$ AND2 (NOT1 b10),
(NOT1 b9) ) & not (
$ AND2 (NOT1 b10),
(NOT1 b9) & not
$ b
1 ) & not (
$ b
2 & not
$ AND2 (NOT1 b10),b
9 ) & not (
$ AND2 (NOT1 b10),b
9 & not
$ b
2 ) & not (
$ b
3 & not
$ AND2 b
10,
(NOT1 b9) ) & not (
$ AND2 b
10,
(NOT1 b9) & not
$ b
3 ) & not (
$ b
4 & not
$ AND2 b
10,b
9 ) & not (
$ AND2 b
10,b
9 & not
$ b
4 ) & not (
$ b
5 & not
$ AND2 (NOT1 b12),
(NOT1 b11) ) & not (
$ AND2 (NOT1 b12),
(NOT1 b11) & not
$ b
5 ) & not (
$ b
6 & not
$ AND2 (NOT1 b12),b
11 ) & not (
$ AND2 (NOT1 b12),b
11 & not
$ b
6 ) & not (
$ b
7 & not
$ AND2 b
12,
(NOT1 b11) ) & not (
$ AND2 b
12,
(NOT1 b11) & not
$ b
7 ) & not (
$ b
8 & not
$ AND2 b
12,b
11 ) & not (
$ AND2 b
12,b
11 & not
$ b
8 ) & not (
$ b
11 & not
$ AND2 (NOT1 b10),b
13 ) & not (
$ AND2 (NOT1 b10),b
13 & not
$ b
11 ) & not (
$ b
12 & not
$ AND2 b
9,b
13 ) & not (
$ AND2 b
9,b
13 & not
$ b
12 ) & not ( not (
$ b
6 & not
$ AND2 b
1,b
13 ) & not (
$ AND2 b
1,b
13 & not
$ b
6 ) & not (
$ b
8 & not
$ AND2 b
2,b
13 ) & not (
$ AND2 b
2,b
13 & not
$ b
8 ) & not (
$ b
7 & not
$ AND2 b
4,b
13 ) & not (
$ AND2 b
4,b
13 & not
$ b
7 ) & not (
$ b
5 & not
$ OR2 (AND2 b3,b13),
(NOT1 b13) ) & not (
$ OR2 (AND2 b3,b13),
(NOT1 b13) & not
$ b
5 ) ) )
theorem Th3: :: GATE_3:3
for b
1, b
2, b
3, b
4, b
5, b
6, b
7, b
8, b
9, b
10, b
11, b
12, b
13, b
14, b
15, b
16, b
17, b
18, b
19, b
20, b
21, b
22 being
set holds
not ( not (
$ b
1 & not
$ AND3 (NOT1 b19),
(NOT1 b18),
(NOT1 b17) ) & not (
$ AND3 (NOT1 b19),
(NOT1 b18),
(NOT1 b17) & not
$ b
1 ) & not (
$ b
2 & not
$ AND3 (NOT1 b19),
(NOT1 b18),b
17 ) & not (
$ AND3 (NOT1 b19),
(NOT1 b18),b
17 & not
$ b
2 ) & not (
$ b
3 & not
$ AND3 (NOT1 b19),b
18,
(NOT1 b17) ) & not (
$ AND3 (NOT1 b19),b
18,
(NOT1 b17) & not
$ b
3 ) & not (
$ b
4 & not
$ AND3 (NOT1 b19),b
18,b
17 ) & not (
$ AND3 (NOT1 b19),b
18,b
17 & not
$ b
4 ) & not (
$ b
5 & not
$ AND3 b
19,
(NOT1 b18),
(NOT1 b17) ) & not (
$ AND3 b
19,
(NOT1 b18),
(NOT1 b17) & not
$ b
5 ) & not (
$ b
6 & not
$ AND3 b
19,
(NOT1 b18),b
17 ) & not (
$ AND3 b
19,
(NOT1 b18),b
17 & not
$ b
6 ) & not (
$ b
7 & not
$ AND3 b
19,b
18,
(NOT1 b17) ) & not (
$ AND3 b
19,b
18,
(NOT1 b17) & not
$ b
7 ) & not (
$ b
8 & not
$ AND3 b
19,b
18,b
17 ) & not (
$ AND3 b
19,b
18,b
17 & not
$ b
8 ) & not (
$ b
9 & not
$ AND3 (NOT1 b22),
(NOT1 b21),
(NOT1 b20) ) & not (
$ AND3 (NOT1 b22),
(NOT1 b21),
(NOT1 b20) & not
$ b
9 ) & not (
$ b
10 & not
$ AND3 (NOT1 b22),
(NOT1 b21),b
20 ) & not (
$ AND3 (NOT1 b22),
(NOT1 b21),b
20 & not
$ b
10 ) & not (
$ b
11 & not
$ AND3 (NOT1 b22),b
21,
(NOT1 b20) ) & not (
$ AND3 (NOT1 b22),b
21,
(NOT1 b20) & not
$ b
11 ) & not (
$ b
12 & not
$ AND3 (NOT1 b22),b
21,b
20 ) & not (
$ AND3 (NOT1 b22),b
21,b
20 & not
$ b
12 ) & not (
$ b
13 & not
$ AND3 b
22,
(NOT1 b21),
(NOT1 b20) ) & not (
$ AND3 b
22,
(NOT1 b21),
(NOT1 b20) & not
$ b
13 ) & not (
$ b
14 & not
$ AND3 b
22,
(NOT1 b21),b
20 ) & not (
$ AND3 b
22,
(NOT1 b21),b
20 & not
$ b
14 ) & not (
$ b
15 & not
$ AND3 b
22,b
21,
(NOT1 b20) ) & not (
$ AND3 b
22,b
21,
(NOT1 b20) & not
$ b
15 ) & not (
$ b
16 & not
$ AND3 b
22,b
21,b
20 ) & not (
$ AND3 b
22,b
21,b
20 & not
$ b
16 ) & not (
$ b
20 & not
$ NOT1 b
19 ) & not (
$ NOT1 b
19 & not
$ b
20 ) & not (
$ b
21 & not
$ b
17 ) & not (
$ b
17 & not
$ b
21 ) & not (
$ b
22 & not
$ b
18 ) & not (
$ b
18 & not
$ b
22 ) & not ( not (
$ b
10 & not
$ b
1 ) & not (
$ b
1 & not
$ b
10 ) & not (
$ b
12 & not
$ b
2 ) & not (
$ b
2 & not
$ b
12 ) & not (
$ b
16 & not
$ b
4 ) & not (
$ b
4 & not
$ b
16 ) & not (
$ b
15 & not
$ b
8 ) & not (
$ b
8 & not
$ b
15 ) & not (
$ b
13 & not
$ b
7 ) & not (
$ b
7 & not
$ b
13 ) & not (
$ b
9 & not
$ b
5 ) & not (
$ b
5 & not
$ b
9 ) & not (
$ b
11 & not
$ b
6 ) & not (
$ b
6 & not
$ b
11 ) & not (
$ b
14 & not
$ b
3 ) & not (
$ b
3 & not
$ b
14 ) ) )
theorem Th4: :: GATE_3:4
for b
1, b
2, b
3, b
4, b
5, b
6, b
7, b
8, b
9, b
10, b
11, b
12, b
13, b
14, b
15, b
16, b
17, b
18, b
19, b
20, b
21, b
22, b
23 being
set holds
not ( not (
$ b
1 & not
$ AND3 (NOT1 b19),
(NOT1 b18),
(NOT1 b17) ) & not (
$ AND3 (NOT1 b19),
(NOT1 b18),
(NOT1 b17) & not
$ b
1 ) & not (
$ b
2 & not
$ AND3 (NOT1 b19),
(NOT1 b18),b
17 ) & not (
$ AND3 (NOT1 b19),
(NOT1 b18),b
17 & not
$ b
2 ) & not (
$ b
3 & not
$ AND3 (NOT1 b19),b
18,
(NOT1 b17) ) & not (
$ AND3 (NOT1 b19),b
18,
(NOT1 b17) & not
$ b
3 ) & not (
$ b
4 & not
$ AND3 (NOT1 b19),b
18,b
17 ) & not (
$ AND3 (NOT1 b19),b
18,b
17 & not
$ b
4 ) & not (
$ b
5 & not
$ AND3 b
19,
(NOT1 b18),
(NOT1 b17) ) & not (
$ AND3 b
19,
(NOT1 b18),
(NOT1 b17) & not
$ b
5 ) & not (
$ b
6 & not
$ AND3 b
19,
(NOT1 b18),b
17 ) & not (
$ AND3 b
19,
(NOT1 b18),b
17 & not
$ b
6 ) & not (
$ b
7 & not
$ AND3 b
19,b
18,
(NOT1 b17) ) & not (
$ AND3 b
19,b
18,
(NOT1 b17) & not
$ b
7 ) & not (
$ b
8 & not
$ AND3 b
19,b
18,b
17 ) & not (
$ AND3 b
19,b
18,b
17 & not
$ b
8 ) & not (
$ b
9 & not
$ AND3 (NOT1 b22),
(NOT1 b21),
(NOT1 b20) ) & not (
$ AND3 (NOT1 b22),
(NOT1 b21),
(NOT1 b20) & not
$ b
9 ) & not (
$ b
10 & not
$ AND3 (NOT1 b22),
(NOT1 b21),b
20 ) & not (
$ AND3 (NOT1 b22),
(NOT1 b21),b
20 & not
$ b
10 ) & not (
$ b
11 & not
$ AND3 (NOT1 b22),b
21,
(NOT1 b20) ) & not (
$ AND3 (NOT1 b22),b
21,
(NOT1 b20) & not
$ b
11 ) & not (
$ b
12 & not
$ AND3 (NOT1 b22),b
21,b
20 ) & not (
$ AND3 (NOT1 b22),b
21,b
20 & not
$ b
12 ) & not (
$ b
13 & not
$ AND3 b
22,
(NOT1 b21),
(NOT1 b20) ) & not (
$ AND3 b
22,
(NOT1 b21),
(NOT1 b20) & not
$ b
13 ) & not (
$ b
14 & not
$ AND3 b
22,
(NOT1 b21),b
20 ) & not (
$ AND3 b
22,
(NOT1 b21),b
20 & not
$ b
14 ) & not (
$ b
15 & not
$ AND3 b
22,b
21,
(NOT1 b20) ) & not (
$ AND3 b
22,b
21,
(NOT1 b20) & not
$ b
15 ) & not (
$ b
16 & not
$ AND3 b
22,b
21,b
20 ) & not (
$ AND3 b
22,b
21,b
20 & not
$ b
16 ) & not (
$ b
20 & not
$ AND2 (NOT1 b19),b
23 ) & not (
$ AND2 (NOT1 b19),b
23 & not
$ b
20 ) & not (
$ b
21 & not
$ AND2 b
17,b
23 ) & not (
$ AND2 b
17,b
23 & not
$ b
21 ) & not (
$ b
22 & not
$ AND2 b
18,b
23 ) & not (
$ AND2 b
18,b
23 & not
$ b
22 ) & not ( not (
$ b
10 & not
$ AND2 b
1,b
23 ) & not (
$ AND2 b
1,b
23 & not
$ b
10 ) & not (
$ b
12 & not
$ AND2 b
2,b
23 ) & not (
$ AND2 b
2,b
23 & not
$ b
12 ) & not (
$ b
16 & not
$ AND2 b
4,b
23 ) & not (
$ AND2 b
4,b
23 & not
$ b
16 ) & not (
$ b
15 & not
$ AND2 b
8,b
23 ) & not (
$ AND2 b
8,b
23 & not
$ b
15 ) & not (
$ b
13 & not
$ AND2 b
7,b
23 ) & not (
$ AND2 b
7,b
23 & not
$ b
13 ) & not (
$ b
9 & not
$ OR2 (AND2 b5,b23),
(NOT1 b23) ) & not (
$ OR2 (AND2 b5,b23),
(NOT1 b23) & not
$ b
9 ) & not (
$ b
11 & not
$ AND2 b
6,b
23 ) & not (
$ AND2 b
6,b
23 & not
$ b
11 ) & not (
$ b
14 & not
$ AND2 b
3,b
23 ) & not (
$ AND2 b
3,b
23 & not
$ b
14 ) ) )
theorem Th5: :: GATE_3:5
for b
1, b
2, b
3, b
4, b
5, b
6, b
7, b
8, b
9, b
10, b
11, b
12, b
13, b
14, b
15, b
16, b
17, b
18, b
19, b
20, b
21, b
22, b
23, b
24, b
25, b
26, b
27, b
28, b
29, b
30, b
31, b
32, b
33, b
34, b
35, b
36, b
37, b
38, b
39, b
40 being
set holds
not ( not (
$ b
1 & not
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) & not
$ b
1 ) & not (
$ b
2 & not
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),b
33 ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),b
33 & not
$ b
2 ) & not (
$ b
3 & not
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,
(NOT1 b33) & not
$ b
3 ) & not (
$ b
4 & not
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,b
33 ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,b
33 & not
$ b
4 ) & not (
$ b
5 & not
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),
(NOT1 b33) & not
$ b
5 ) & not (
$ b
6 & not
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),b
33 ) & not (
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),b
33 & not
$ b
6 ) & not (
$ b
7 & not
$ AND4 (NOT1 b36),b
35,b
34,
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),b
35,b
34,
(NOT1 b33) & not
$ b
7 ) & not (
$ b
8 & not
$ AND4 (NOT1 b36),b
35,b
34,b
33 ) & not (
$ AND4 (NOT1 b36),b
35,b
34,b
33 & not
$ b
8 ) & not (
$ b
9 & not
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) & not
$ b
9 ) & not (
$ b
10 & not
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),b
33 ) & not (
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),b
33 & not
$ b
10 ) & not (
$ b
11 & not
$ AND4 b
36,
(NOT1 b35),b
34,
(NOT1 b33) ) & not (
$ AND4 b
36,
(NOT1 b35),b
34,
(NOT1 b33) & not
$ b
11 ) & not (
$ b
12 & not
$ AND4 b
36,
(NOT1 b35),b
34,b
33 ) & not (
$ AND4 b
36,
(NOT1 b35),b
34,b
33 & not
$ b
12 ) & not (
$ b
13 & not
$ AND4 b
36,b
35,
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 b
36,b
35,
(NOT1 b34),
(NOT1 b33) & not
$ b
13 ) & not (
$ b
14 & not
$ AND4 b
36,b
35,
(NOT1 b34),b
33 ) & not (
$ AND4 b
36,b
35,
(NOT1 b34),b
33 & not
$ b
14 ) & not (
$ b
15 & not
$ AND4 b
36,b
35,b
34,
(NOT1 b33) ) & not (
$ AND4 b
36,b
35,b
34,
(NOT1 b33) & not
$ b
15 ) & not (
$ b
16 & not
$ AND4 b
36,b
35,b
34,b
33 ) & not (
$ AND4 b
36,b
35,b
34,b
33 & not
$ b
16 ) & not (
$ b
17 & not
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) & not
$ b
17 ) & not (
$ b
18 & not
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),b
37 ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),b
37 & not
$ b
18 ) & not (
$ b
19 & not
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,
(NOT1 b37) & not
$ b
19 ) & not (
$ b
20 & not
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,b
37 ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,b
37 & not
$ b
20 ) & not (
$ b
21 & not
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),
(NOT1 b37) & not
$ b
21 ) & not (
$ b
22 & not
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),b
37 ) & not (
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),b
37 & not
$ b
22 ) & not (
$ b
23 & not
$ AND4 (NOT1 b40),b
39,b
38,
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),b
39,b
38,
(NOT1 b37) & not
$ b
23 ) & not (
$ b
24 & not
$ AND4 (NOT1 b40),b
39,b
38,b
37 ) & not (
$ AND4 (NOT1 b40),b
39,b
38,b
37 & not
$ b
24 ) & not (
$ b
25 & not
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) & not
$ b
25 ) & not (
$ b
26 & not
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),b
37 ) & not (
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),b
37 & not
$ b
26 ) & not (
$ b
27 & not
$ AND4 b
40,
(NOT1 b39),b
38,
(NOT1 b37) ) & not (
$ AND4 b
40,
(NOT1 b39),b
38,
(NOT1 b37) & not
$ b
27 ) & not (
$ b
28 & not
$ AND4 b
40,
(NOT1 b39),b
38,b
37 ) & not (
$ AND4 b
40,
(NOT1 b39),b
38,b
37 & not
$ b
28 ) & not (
$ b
29 & not
$ AND4 b
40,b
39,
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 b
40,b
39,
(NOT1 b38),
(NOT1 b37) & not
$ b
29 ) & not (
$ b
30 & not
$ AND4 b
40,b
39,
(NOT1 b38),b
37 ) & not (
$ AND4 b
40,b
39,
(NOT1 b38),b
37 & not
$ b
30 ) & not (
$ b
31 & not
$ AND4 b
40,b
39,b
38,
(NOT1 b37) ) & not (
$ AND4 b
40,b
39,b
38,
(NOT1 b37) & not
$ b
31 ) & not (
$ b
32 & not
$ AND4 b
40,b
39,b
38,b
37 ) & not (
$ AND4 b
40,b
39,b
38,b
37 & not
$ b
32 ) & not (
$ b
37 & not
$ NOT1 b
36 ) & not (
$ NOT1 b
36 & not
$ b
37 ) & not (
$ b
38 & not
$ b
33 ) & not (
$ b
33 & not
$ b
38 ) & not (
$ b
39 & not
$ b
34 ) & not (
$ b
34 & not
$ b
39 ) & not (
$ b
40 & not
$ b
35 ) & not (
$ b
35 & not
$ b
40 ) & not ( not (
$ b
18 & not
$ b
1 ) & not (
$ b
1 & not
$ b
18 ) & not (
$ b
20 & not
$ b
2 ) & not (
$ b
2 & not
$ b
20 ) & not (
$ b
24 & not
$ b
4 ) & not (
$ b
4 & not
$ b
24 ) & not (
$ b
32 & not
$ b
8 ) & not (
$ b
8 & not
$ b
32 ) & not (
$ b
31 & not
$ b
16 ) & not (
$ b
16 & not
$ b
31 ) & not (
$ b
29 & not
$ b
15 ) & not (
$ b
15 & not
$ b
29 ) & not (
$ b
25 & not
$ b
13 ) & not (
$ b
13 & not
$ b
25 ) & not (
$ b
17 & not
$ b
9 ) & not (
$ b
9 & not
$ b
17 ) & not (
$ b
22 & not
$ b
3 ) & not (
$ b
3 & not
$ b
22 ) & not (
$ b
28 & not
$ b
6 ) & not (
$ b
6 & not
$ b
28 ) & not (
$ b
23 & not
$ b
12 ) & not (
$ b
12 & not
$ b
23 ) & not (
$ b
30 & not
$ b
7 ) & not (
$ b
7 & not
$ b
30 ) & not (
$ b
27 & not
$ b
14 ) & not (
$ b
14 & not
$ b
27 ) & not (
$ b
21 & not
$ b
11 ) & not (
$ b
11 & not
$ b
21 ) & not (
$ b
26 & not
$ b
5 ) & not (
$ b
5 & not
$ b
26 ) & not (
$ b
19 & not
$ b
10 ) & not (
$ b
10 & not
$ b
19 ) ) )
theorem Th6: :: GATE_3:6
for b
1, b
2, b
3, b
4, b
5, b
6, b
7, b
8, b
9, b
10, b
11, b
12, b
13, b
14, b
15, b
16, b
17, b
18, b
19, b
20, b
21, b
22, b
23, b
24, b
25, b
26, b
27, b
28, b
29, b
30, b
31, b
32, b
33, b
34, b
35, b
36, b
37, b
38, b
39, b
40, b
41 being
set holds
not ( not (
$ b
1 & not
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) & not
$ b
1 ) & not (
$ b
2 & not
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),b
33 ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),
(NOT1 b34),b
33 & not
$ b
2 ) & not (
$ b
3 & not
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,
(NOT1 b33) & not
$ b
3 ) & not (
$ b
4 & not
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,b
33 ) & not (
$ AND4 (NOT1 b36),
(NOT1 b35),b
34,b
33 & not
$ b
4 ) & not (
$ b
5 & not
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),
(NOT1 b33) & not
$ b
5 ) & not (
$ b
6 & not
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),b
33 ) & not (
$ AND4 (NOT1 b36),b
35,
(NOT1 b34),b
33 & not
$ b
6 ) & not (
$ b
7 & not
$ AND4 (NOT1 b36),b
35,b
34,
(NOT1 b33) ) & not (
$ AND4 (NOT1 b36),b
35,b
34,
(NOT1 b33) & not
$ b
7 ) & not (
$ b
8 & not
$ AND4 (NOT1 b36),b
35,b
34,b
33 ) & not (
$ AND4 (NOT1 b36),b
35,b
34,b
33 & not
$ b
8 ) & not (
$ b
9 & not
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),
(NOT1 b33) & not
$ b
9 ) & not (
$ b
10 & not
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),b
33 ) & not (
$ AND4 b
36,
(NOT1 b35),
(NOT1 b34),b
33 & not
$ b
10 ) & not (
$ b
11 & not
$ AND4 b
36,
(NOT1 b35),b
34,
(NOT1 b33) ) & not (
$ AND4 b
36,
(NOT1 b35),b
34,
(NOT1 b33) & not
$ b
11 ) & not (
$ b
12 & not
$ AND4 b
36,
(NOT1 b35),b
34,b
33 ) & not (
$ AND4 b
36,
(NOT1 b35),b
34,b
33 & not
$ b
12 ) & not (
$ b
13 & not
$ AND4 b
36,b
35,
(NOT1 b34),
(NOT1 b33) ) & not (
$ AND4 b
36,b
35,
(NOT1 b34),
(NOT1 b33) & not
$ b
13 ) & not (
$ b
14 & not
$ AND4 b
36,b
35,
(NOT1 b34),b
33 ) & not (
$ AND4 b
36,b
35,
(NOT1 b34),b
33 & not
$ b
14 ) & not (
$ b
15 & not
$ AND4 b
36,b
35,b
34,
(NOT1 b33) ) & not (
$ AND4 b
36,b
35,b
34,
(NOT1 b33) & not
$ b
15 ) & not (
$ b
16 & not
$ AND4 b
36,b
35,b
34,b
33 ) & not (
$ AND4 b
36,b
35,b
34,b
33 & not
$ b
16 ) & not (
$ b
17 & not
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) & not
$ b
17 ) & not (
$ b
18 & not
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),b
37 ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),
(NOT1 b38),b
37 & not
$ b
18 ) & not (
$ b
19 & not
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,
(NOT1 b37) & not
$ b
19 ) & not (
$ b
20 & not
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,b
37 ) & not (
$ AND4 (NOT1 b40),
(NOT1 b39),b
38,b
37 & not
$ b
20 ) & not (
$ b
21 & not
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),
(NOT1 b37) & not
$ b
21 ) & not (
$ b
22 & not
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),b
37 ) & not (
$ AND4 (NOT1 b40),b
39,
(NOT1 b38),b
37 & not
$ b
22 ) & not (
$ b
23 & not
$ AND4 (NOT1 b40),b
39,b
38,
(NOT1 b37) ) & not (
$ AND4 (NOT1 b40),b
39,b
38,
(NOT1 b37) & not
$ b
23 ) & not (
$ b
24 & not
$ AND4 (NOT1 b40),b
39,b
38,b
37 ) & not (
$ AND4 (NOT1 b40),b
39,b
38,b
37 & not
$ b
24 ) & not (
$ b
25 & not
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),
(NOT1 b37) & not
$ b
25 ) & not (
$ b
26 & not
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),b
37 ) & not (
$ AND4 b
40,
(NOT1 b39),
(NOT1 b38),b
37 & not
$ b
26 ) & not (
$ b
27 & not
$ AND4 b
40,
(NOT1 b39),b
38,
(NOT1 b37) ) & not (
$ AND4 b
40,
(NOT1 b39),b
38,
(NOT1 b37) & not
$ b
27 ) & not (
$ b
28 & not
$ AND4 b
40,
(NOT1 b39),b
38,b
37 ) & not (
$ AND4 b
40,
(NOT1 b39),b
38,b
37 & not
$ b
28 ) & not (
$ b
29 & not
$ AND4 b
40,b
39,
(NOT1 b38),
(NOT1 b37) ) & not (
$ AND4 b
40,b
39,
(NOT1 b38),
(NOT1 b37) & not
$ b
29 ) & not (
$ b
30 & not
$ AND4 b
40,b
39,
(NOT1 b38),b
37 ) & not (
$ AND4 b
40,b
39,
(NOT1 b38),b
37 & not
$ b
30 ) & not (
$ b
31 & not
$ AND4 b
40,b
39,b
38,
(NOT1 b37) ) & not (
$ AND4 b
40,b
39,b
38,
(NOT1 b37) & not
$ b
31 ) & not (
$ b
32 & not
$ AND4 b
40,b
39,b
38,b
37 ) & not (
$ AND4 b
40,b
39,b
38,b
37 & not
$ b
32 ) & not (
$ b
37 & not
$ AND2 (NOT1 b36),b
41 ) & not (
$ AND2 (NOT1 b36),b
41 & not
$ b
37 ) & not (
$ b
38 & not
$ AND2 b
33,b
41 ) & not (
$ AND2 b
33,b
41 & not
$ b
38 ) & not (
$ b
39 & not
$ AND2 b
34,b
41 ) & not (
$ AND2 b
34,b
41 & not
$ b
39 ) & not (
$ b
40 & not
$ AND2 b
35,b
41 ) & not (
$ AND2 b
35,b
41 & not
$ b
40 ) & not ( not (
$ b
18 & not
$ AND2 b
1,b
41 ) & not (
$ AND2 b
1,b
41 & not
$ b
18 ) & not (
$ b
20 & not
$ AND2 b
2,b
41 ) & not (
$ AND2 b
2,b
41 & not
$ b
20 ) & not (
$ b
24 & not
$ AND2 b
4,b
41 ) & not (
$ AND2 b
4,b
41 & not
$ b
24 ) & not (
$ b
32 & not
$ AND2 b
8,b
41 ) & not (
$ AND2 b
8,b
41 & not
$ b
32 ) & not (
$ b
31 & not
$ AND2 b
16,b
41 ) & not (
$ AND2 b
16,b
41 & not
$ b
31 ) & not (
$ b
29 & not
$ AND2 b
15,b
41 ) & not (
$ AND2 b
15,b
41 & not
$ b
29 ) & not (
$ b
25 & not
$ AND2 b
13,b
41 ) & not (
$ AND2 b
13,b
41 & not
$ b
25 ) & not (
$ b
17 & not
$ OR2 (AND2 b9,b41),
(NOT1 b41) ) & not (
$ OR2 (AND2 b9,b41),
(NOT1 b41) & not
$ b
17 ) & not (
$ b
22 & not
$ AND2 b
3,b
41 ) & not (
$ AND2 b
3,b
41 & not
$ b
22 ) & not (
$ b
28 & not
$ AND2 b
6,b
41 ) & not (
$ AND2 b
6,b
41 & not
$ b
28 ) & not (
$ b
23 & not
$ AND2 b
12,b
41 ) & not (
$ AND2 b
12,b
41 & not
$ b
23 ) & not (
$ b
30 & not
$ AND2 b
7,b
41 ) & not (
$ AND2 b
7,b
41 & not
$ b
30 ) & not (
$ b
27 & not
$ AND2 b
14,b
41 ) & not (
$ AND2 b
14,b
41 & not
$ b
27 ) & not (
$ b
21 & not
$ AND2 b
11,b
41 ) & not (
$ AND2 b
11,b
41 & not
$ b
21 ) & not (
$ b
26 & not
$ AND2 b
5,b
41 ) & not (
$ AND2 b
5,b
41 & not
$ b
26 ) & not (
$ b
19 & not
$ AND2 b
10,b
41 ) & not (
$ AND2 b
10,b
41 & not
$ b
19 ) ) )