:: GATE_4 semantic presentation
theorem Th1: :: GATE_4:1
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, 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 being
set holds
(
$ b
1 &
$ b
13 & not (
$ b
26 & not
$ XOR2 b
38,
(AND2 b1,b25) ) & not (
$ XOR2 b
38,
(AND2 b1,b25) & not
$ b
26 ) & not (
$ b
27 & not
$ XOR2 b
14,
(AND2 b2,b25) ) & not (
$ XOR2 b
14,
(AND2 b2,b25) & not
$ b
27 ) & not (
$ b
28 & not
$ XOR2 b
15,
(AND2 b3,b25) ) & not (
$ XOR2 b
15,
(AND2 b3,b25) & not
$ b
28 ) & not (
$ b
29 & not
$ XOR2 b
16,
(AND2 b4,b25) ) & not (
$ XOR2 b
16,
(AND2 b4,b25) & not
$ b
29 ) & not (
$ b
30 & not
$ XOR2 b
17,
(AND2 b5,b25) ) & not (
$ XOR2 b
17,
(AND2 b5,b25) & not
$ b
30 ) & not (
$ b
31 & not
$ XOR2 b
18,
(AND2 b6,b25) ) & not (
$ XOR2 b
18,
(AND2 b6,b25) & not
$ b
31 ) & not (
$ b
32 & not
$ XOR2 b
19,
(AND2 b7,b25) ) & not (
$ XOR2 b
19,
(AND2 b7,b25) & not
$ b
32 ) & not (
$ b
33 & not
$ XOR2 b
20,
(AND2 b8,b25) ) & not (
$ XOR2 b
20,
(AND2 b8,b25) & not
$ b
33 ) & not (
$ b
34 & not
$ XOR2 b
21,
(AND2 b9,b25) ) & not (
$ XOR2 b
21,
(AND2 b9,b25) & not
$ b
34 ) & not (
$ b
35 & not
$ XOR2 b
22,
(AND2 b10,b25) ) & not (
$ XOR2 b
22,
(AND2 b10,b25) & not
$ b
35 ) & not (
$ b
36 & not
$ XOR2 b
23,
(AND2 b11,b25) ) & not (
$ XOR2 b
23,
(AND2 b11,b25) & not
$ b
36 ) & not (
$ b
37 & not
$ XOR2 b
24,
(AND2 b12,b25) ) & not (
$ XOR2 b
24,
(AND2 b12,b25) & not
$ b
37 ) implies ( not (
$ b
25 & not
$ AND2 b
13,b
25 ) & not (
$ AND2 b
13,b
25 & not
$ b
25 ) & not (
$ b
24 & not
$ XOR2 b
37,
(AND2 b12,b25) ) & not (
$ XOR2 b
37,
(AND2 b12,b25) & not
$ b
24 ) & not (
$ b
23 & not
$ XOR2 b
36,
(AND2 b11,b25) ) & not (
$ XOR2 b
36,
(AND2 b11,b25) & not
$ b
23 ) & not (
$ b
22 & not
$ XOR2 b
35,
(AND2 b10,b25) ) & not (
$ XOR2 b
35,
(AND2 b10,b25) & not
$ b
22 ) & not (
$ b
21 & not
$ XOR2 b
34,
(AND2 b9,b25) ) & not (
$ XOR2 b
34,
(AND2 b9,b25) & not
$ b
21 ) & not (
$ b
20 & not
$ XOR2 b
33,
(AND2 b8,b25) ) & not (
$ XOR2 b
33,
(AND2 b8,b25) & not
$ b
20 ) & not (
$ b
19 & not
$ XOR2 b
32,
(AND2 b7,b25) ) & not (
$ XOR2 b
32,
(AND2 b7,b25) & not
$ b
19 ) & not (
$ b
18 & not
$ XOR2 b
31,
(AND2 b6,b25) ) & not (
$ XOR2 b
31,
(AND2 b6,b25) & not
$ b
18 ) & not (
$ b
17 & not
$ XOR2 b
30,
(AND2 b5,b25) ) & not (
$ XOR2 b
30,
(AND2 b5,b25) & not
$ b
17 ) & not (
$ b
16 & not
$ XOR2 b
29,
(AND2 b4,b25) ) & not (
$ XOR2 b
29,
(AND2 b4,b25) & not
$ b
16 ) & not (
$ b
15 & not
$ XOR2 b
28,
(AND2 b3,b25) ) & not (
$ XOR2 b
28,
(AND2 b3,b25) & not
$ b
15 ) & not (
$ b
14 & not
$ XOR2 b
27,
(AND2 b2,b25) ) & not (
$ XOR2 b
27,
(AND2 b2,b25) & not
$ b
14 ) & not (
$ b
38 & not
$ XOR2 b
26,
(AND2 b1,b25) ) & not (
$ XOR2 b
26,
(AND2 b1,b25) & not
$ b
38 ) ) )
theorem Th2: :: GATE_4:2
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, 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, b
42, b
43, b
44, b
45, b
46, b
47, b
48, b
49, b
50 being
set holds
(
$ b
1 &
$ b
17 & not (
$ b
34 & not
$ XOR2 b
50,
(AND2 b1,b33) ) & not (
$ XOR2 b
50,
(AND2 b1,b33) & not
$ b
34 ) & not (
$ b
35 & not
$ XOR2 b
18,
(AND2 b2,b33) ) & not (
$ XOR2 b
18,
(AND2 b2,b33) & not
$ b
35 ) & not (
$ b
36 & not
$ XOR2 b
19,
(AND2 b3,b33) ) & not (
$ XOR2 b
19,
(AND2 b3,b33) & not
$ b
36 ) & not (
$ b
37 & not
$ XOR2 b
20,
(AND2 b4,b33) ) & not (
$ XOR2 b
20,
(AND2 b4,b33) & not
$ b
37 ) & not (
$ b
38 & not
$ XOR2 b
21,
(AND2 b5,b33) ) & not (
$ XOR2 b
21,
(AND2 b5,b33) & not
$ b
38 ) & not (
$ b
39 & not
$ XOR2 b
22,
(AND2 b6,b33) ) & not (
$ XOR2 b
22,
(AND2 b6,b33) & not
$ b
39 ) & not (
$ b
40 & not
$ XOR2 b
23,
(AND2 b7,b33) ) & not (
$ XOR2 b
23,
(AND2 b7,b33) & not
$ b
40 ) & not (
$ b
41 & not
$ XOR2 b
24,
(AND2 b8,b33) ) & not (
$ XOR2 b
24,
(AND2 b8,b33) & not
$ b
41 ) & not (
$ b
42 & not
$ XOR2 b
25,
(AND2 b9,b33) ) & not (
$ XOR2 b
25,
(AND2 b9,b33) & not
$ b
42 ) & not (
$ b
43 & not
$ XOR2 b
26,
(AND2 b10,b33) ) & not (
$ XOR2 b
26,
(AND2 b10,b33) & not
$ b
43 ) & not (
$ b
44 & not
$ XOR2 b
27,
(AND2 b11,b33) ) & not (
$ XOR2 b
27,
(AND2 b11,b33) & not
$ b
44 ) & not (
$ b
45 & not
$ XOR2 b
28,
(AND2 b12,b33) ) & not (
$ XOR2 b
28,
(AND2 b12,b33) & not
$ b
45 ) & not (
$ b
46 & not
$ XOR2 b
29,
(AND2 b13,b33) ) & not (
$ XOR2 b
29,
(AND2 b13,b33) & not
$ b
46 ) & not (
$ b
47 & not
$ XOR2 b
30,
(AND2 b14,b33) ) & not (
$ XOR2 b
30,
(AND2 b14,b33) & not
$ b
47 ) & not (
$ b
48 & not
$ XOR2 b
31,
(AND2 b15,b33) ) & not (
$ XOR2 b
31,
(AND2 b15,b33) & not
$ b
48 ) & not (
$ b
49 & not
$ XOR2 b
32,
(AND2 b16,b33) ) & not (
$ XOR2 b
32,
(AND2 b16,b33) & not
$ b
49 ) implies ( not (
$ b
33 & not
$ AND2 b
17,b
33 ) & not (
$ AND2 b
17,b
33 & not
$ b
33 ) & not (
$ b
32 & not
$ XOR2 b
49,
(AND2 b16,b33) ) & not (
$ XOR2 b
49,
(AND2 b16,b33) & not
$ b
32 ) & not (
$ b
31 & not
$ XOR2 b
48,
(AND2 b15,b33) ) & not (
$ XOR2 b
48,
(AND2 b15,b33) & not
$ b
31 ) & not (
$ b
30 & not
$ XOR2 b
47,
(AND2 b14,b33) ) & not (
$ XOR2 b
47,
(AND2 b14,b33) & not
$ b
30 ) & not (
$ b
29 & not
$ XOR2 b
46,
(AND2 b13,b33) ) & not (
$ XOR2 b
46,
(AND2 b13,b33) & not
$ b
29 ) & not (
$ b
28 & not
$ XOR2 b
45,
(AND2 b12,b33) ) & not (
$ XOR2 b
45,
(AND2 b12,b33) & not
$ b
28 ) & not (
$ b
27 & not
$ XOR2 b
44,
(AND2 b11,b33) ) & not (
$ XOR2 b
44,
(AND2 b11,b33) & not
$ b
27 ) & not (
$ b
26 & not
$ XOR2 b
43,
(AND2 b10,b33) ) & not (
$ XOR2 b
43,
(AND2 b10,b33) & not
$ b
26 ) & not (
$ b
25 & not
$ XOR2 b
42,
(AND2 b9,b33) ) & not (
$ XOR2 b
42,
(AND2 b9,b33) & not
$ b
25 ) & not (
$ b
24 & not
$ XOR2 b
41,
(AND2 b8,b33) ) & not (
$ XOR2 b
41,
(AND2 b8,b33) & not
$ b
24 ) & not (
$ b
23 & not
$ XOR2 b
40,
(AND2 b7,b33) ) & not (
$ XOR2 b
40,
(AND2 b7,b33) & not
$ b
23 ) & not (
$ b
22 & not
$ XOR2 b
39,
(AND2 b6,b33) ) & not (
$ XOR2 b
39,
(AND2 b6,b33) & not
$ b
22 ) & not (
$ b
21 & not
$ XOR2 b
38,
(AND2 b5,b33) ) & not (
$ XOR2 b
38,
(AND2 b5,b33) & not
$ b
21 ) & not (
$ b
20 & not
$ XOR2 b
37,
(AND2 b4,b33) ) & not (
$ XOR2 b
37,
(AND2 b4,b33) & not
$ b
20 ) & not (
$ b
19 & not
$ XOR2 b
36,
(AND2 b3,b33) ) & not (
$ XOR2 b
36,
(AND2 b3,b33) & not
$ b
19 ) & not (
$ b
18 & not
$ XOR2 b
35,
(AND2 b2,b33) ) & not (
$ XOR2 b
35,
(AND2 b2,b33) & not
$ b
18 ) & not (
$ b
50 & not
$ XOR2 b
34,
(AND2 b1,b33) ) & not (
$ XOR2 b
34,
(AND2 b1,b33) & not
$ b
50 ) ) )
theorem Th3: :: GATE_4:3
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, 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 being
set holds
(
$ b
1 &
$ b
13 & not
$ b
38 & not (
$ b
26 & not
$ XOR2 b
39,b
25 ) & not (
$ XOR2 b
39,b
25 & not
$ b
26 ) & not (
$ b
27 & not
$ XOR2 b
14,
(AND2 b2,b26) ) & not (
$ XOR2 b
14,
(AND2 b2,b26) & not
$ b
27 ) & not (
$ b
28 & not
$ XOR2 b
15,
(AND2 b3,b26) ) & not (
$ XOR2 b
15,
(AND2 b3,b26) & not
$ b
28 ) & not (
$ b
29 & not
$ XOR2 b
16,
(AND2 b4,b26) ) & not (
$ XOR2 b
16,
(AND2 b4,b26) & not
$ b
29 ) & not (
$ b
30 & not
$ XOR2 b
17,
(AND2 b5,b26) ) & not (
$ XOR2 b
17,
(AND2 b5,b26) & not
$ b
30 ) & not (
$ b
31 & not
$ XOR2 b
18,
(AND2 b6,b26) ) & not (
$ XOR2 b
18,
(AND2 b6,b26) & not
$ b
31 ) & not (
$ b
32 & not
$ XOR2 b
19,
(AND2 b7,b26) ) & not (
$ XOR2 b
19,
(AND2 b7,b26) & not
$ b
32 ) & not (
$ b
33 & not
$ XOR2 b
20,
(AND2 b8,b26) ) & not (
$ XOR2 b
20,
(AND2 b8,b26) & not
$ b
33 ) & not (
$ b
34 & not
$ XOR2 b
21,
(AND2 b9,b26) ) & not (
$ XOR2 b
21,
(AND2 b9,b26) & not
$ b
34 ) & not (
$ b
35 & not
$ XOR2 b
22,
(AND2 b10,b26) ) & not (
$ XOR2 b
22,
(AND2 b10,b26) & not
$ b
35 ) & not (
$ b
36 & not
$ XOR2 b
23,
(AND2 b11,b26) ) & not (
$ XOR2 b
23,
(AND2 b11,b26) & not
$ b
36 ) & not (
$ b
37 & not
$ XOR2 b
24,
(AND2 b12,b26) ) & not (
$ XOR2 b
24,
(AND2 b12,b26) & not
$ b
37 ) implies ( not (
$ b
37 & not
$ XOR2 (XOR2 b24,(AND2 b12,b25)),
(XOR2 b38,(AND2 b12,b39)) ) & not (
$ XOR2 (XOR2 b24,(AND2 b12,b25)),
(XOR2 b38,(AND2 b12,b39)) & not
$ b
37 ) & not (
$ b
36 & not
$ XOR2 (XOR2 b23,(AND2 b11,b25)),
(XOR2 b38,(AND2 b11,b39)) ) & not (
$ XOR2 (XOR2 b23,(AND2 b11,b25)),
(XOR2 b38,(AND2 b11,b39)) & not
$ b
36 ) & not (
$ b
35 & not
$ XOR2 (XOR2 b22,(AND2 b10,b25)),
(XOR2 b38,(AND2 b10,b39)) ) & not (
$ XOR2 (XOR2 b22,(AND2 b10,b25)),
(XOR2 b38,(AND2 b10,b39)) & not
$ b
35 ) & not (
$ b
34 & not
$ XOR2 (XOR2 b21,(AND2 b9,b25)),
(XOR2 b38,(AND2 b9,b39)) ) & not (
$ XOR2 (XOR2 b21,(AND2 b9,b25)),
(XOR2 b38,(AND2 b9,b39)) & not
$ b
34 ) & not (
$ b
33 & not
$ XOR2 (XOR2 b20,(AND2 b8,b25)),
(XOR2 b38,(AND2 b8,b39)) ) & not (
$ XOR2 (XOR2 b20,(AND2 b8,b25)),
(XOR2 b38,(AND2 b8,b39)) & not
$ b
33 ) & not (
$ b
32 & not
$ XOR2 (XOR2 b19,(AND2 b7,b25)),
(XOR2 b38,(AND2 b7,b39)) ) & not (
$ XOR2 (XOR2 b19,(AND2 b7,b25)),
(XOR2 b38,(AND2 b7,b39)) & not
$ b
32 ) & not (
$ b
31 & not
$ XOR2 (XOR2 b18,(AND2 b6,b25)),
(XOR2 b38,(AND2 b6,b39)) ) & not (
$ XOR2 (XOR2 b18,(AND2 b6,b25)),
(XOR2 b38,(AND2 b6,b39)) & not
$ b
31 ) & not (
$ b
30 & not
$ XOR2 (XOR2 b17,(AND2 b5,b25)),
(XOR2 b38,(AND2 b5,b39)) ) & not (
$ XOR2 (XOR2 b17,(AND2 b5,b25)),
(XOR2 b38,(AND2 b5,b39)) & not
$ b
30 ) & not (
$ b
29 & not
$ XOR2 (XOR2 b16,(AND2 b4,b25)),
(XOR2 b38,(AND2 b4,b39)) ) & not (
$ XOR2 (XOR2 b16,(AND2 b4,b25)),
(XOR2 b38,(AND2 b4,b39)) & not
$ b
29 ) & not (
$ b
28 & not
$ XOR2 (XOR2 b15,(AND2 b3,b25)),
(XOR2 b38,(AND2 b3,b39)) ) & not (
$ XOR2 (XOR2 b15,(AND2 b3,b25)),
(XOR2 b38,(AND2 b3,b39)) & not
$ b
28 ) & not (
$ b
27 & not
$ XOR2 (XOR2 b14,(AND2 b2,b25)),
(XOR2 b38,(AND2 b2,b39)) ) & not (
$ XOR2 (XOR2 b14,(AND2 b2,b25)),
(XOR2 b38,(AND2 b2,b39)) & not
$ b
27 ) & not (
$ b
26 & not
$ XOR2 (XOR2 b38,(AND2 b1,b25)),
(XOR2 b38,(AND2 b1,b39)) ) & not (
$ XOR2 (XOR2 b38,(AND2 b1,b25)),
(XOR2 b38,(AND2 b1,b39)) & not
$ b
26 ) ) )
theorem Th4: :: GATE_4:4
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, 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, b
42, b
43, b
44, b
45, b
46, b
47, b
48, b
49, b
50, b
51 being
set holds
(
$ b
1 &
$ b
17 & not
$ b
50 & not (
$ b
34 & not
$ XOR2 b
51,b
33 ) & not (
$ XOR2 b
51,b
33 & not
$ b
34 ) & not (
$ b
35 & not
$ XOR2 b
18,
(AND2 b2,b34) ) & not (
$ XOR2 b
18,
(AND2 b2,b34) & not
$ b
35 ) & not (
$ b
36 & not
$ XOR2 b
19,
(AND2 b3,b34) ) & not (
$ XOR2 b
19,
(AND2 b3,b34) & not
$ b
36 ) & not (
$ b
37 & not
$ XOR2 b
20,
(AND2 b4,b34) ) & not (
$ XOR2 b
20,
(AND2 b4,b34) & not
$ b
37 ) & not (
$ b
38 & not
$ XOR2 b
21,
(AND2 b5,b34) ) & not (
$ XOR2 b
21,
(AND2 b5,b34) & not
$ b
38 ) & not (
$ b
39 & not
$ XOR2 b
22,
(AND2 b6,b34) ) & not (
$ XOR2 b
22,
(AND2 b6,b34) & not
$ b
39 ) & not (
$ b
40 & not
$ XOR2 b
23,
(AND2 b7,b34) ) & not (
$ XOR2 b
23,
(AND2 b7,b34) & not
$ b
40 ) & not (
$ b
41 & not
$ XOR2 b
24,
(AND2 b8,b34) ) & not (
$ XOR2 b
24,
(AND2 b8,b34) & not
$ b
41 ) & not (
$ b
42 & not
$ XOR2 b
25,
(AND2 b9,b34) ) & not (
$ XOR2 b
25,
(AND2 b9,b34) & not
$ b
42 ) & not (
$ b
43 & not
$ XOR2 b
26,
(AND2 b10,b34) ) & not (
$ XOR2 b
26,
(AND2 b10,b34) & not
$ b
43 ) & not (
$ b
44 & not
$ XOR2 b
27,
(AND2 b11,b34) ) & not (
$ XOR2 b
27,
(AND2 b11,b34) & not
$ b
44 ) & not (
$ b
45 & not
$ XOR2 b
28,
(AND2 b12,b34) ) & not (
$ XOR2 b
28,
(AND2 b12,b34) & not
$ b
45 ) & not (
$ b
46 & not
$ XOR2 b
29,
(AND2 b13,b34) ) & not (
$ XOR2 b
29,
(AND2 b13,b34) & not
$ b
46 ) & not (
$ b
47 & not
$ XOR2 b
30,
(AND2 b14,b34) ) & not (
$ XOR2 b
30,
(AND2 b14,b34) & not
$ b
47 ) & not (
$ b
48 & not
$ XOR2 b
31,
(AND2 b15,b34) ) & not (
$ XOR2 b
31,
(AND2 b15,b34) & not
$ b
48 ) & not (
$ b
49 & not
$ XOR2 b
32,
(AND2 b16,b34) ) & not (
$ XOR2 b
32,
(AND2 b16,b34) & not
$ b
49 ) implies ( not (
$ b
49 & not
$ XOR2 (XOR2 b32,(AND2 b16,b33)),
(XOR2 b50,(AND2 b16,b51)) ) & not (
$ XOR2 (XOR2 b32,(AND2 b16,b33)),
(XOR2 b50,(AND2 b16,b51)) & not
$ b
49 ) & not (
$ b
48 & not
$ XOR2 (XOR2 b31,(AND2 b15,b33)),
(XOR2 b50,(AND2 b15,b51)) ) & not (
$ XOR2 (XOR2 b31,(AND2 b15,b33)),
(XOR2 b50,(AND2 b15,b51)) & not
$ b
48 ) & not (
$ b
47 & not
$ XOR2 (XOR2 b30,(AND2 b14,b33)),
(XOR2 b50,(AND2 b14,b51)) ) & not (
$ XOR2 (XOR2 b30,(AND2 b14,b33)),
(XOR2 b50,(AND2 b14,b51)) & not
$ b
47 ) & not (
$ b
46 & not
$ XOR2 (XOR2 b29,(AND2 b13,b33)),
(XOR2 b50,(AND2 b13,b51)) ) & not (
$ XOR2 (XOR2 b29,(AND2 b13,b33)),
(XOR2 b50,(AND2 b13,b51)) & not
$ b
46 ) & not (
$ b
45 & not
$ XOR2 (XOR2 b28,(AND2 b12,b33)),
(XOR2 b50,(AND2 b12,b51)) ) & not (
$ XOR2 (XOR2 b28,(AND2 b12,b33)),
(XOR2 b50,(AND2 b12,b51)) & not
$ b
45 ) & not (
$ b
44 & not
$ XOR2 (XOR2 b27,(AND2 b11,b33)),
(XOR2 b50,(AND2 b11,b51)) ) & not (
$ XOR2 (XOR2 b27,(AND2 b11,b33)),
(XOR2 b50,(AND2 b11,b51)) & not
$ b
44 ) & not (
$ b
43 & not
$ XOR2 (XOR2 b26,(AND2 b10,b33)),
(XOR2 b50,(AND2 b10,b51)) ) & not (
$ XOR2 (XOR2 b26,(AND2 b10,b33)),
(XOR2 b50,(AND2 b10,b51)) & not
$ b
43 ) & not (
$ b
42 & not
$ XOR2 (XOR2 b25,(AND2 b9,b33)),
(XOR2 b50,(AND2 b9,b51)) ) & not (
$ XOR2 (XOR2 b25,(AND2 b9,b33)),
(XOR2 b50,(AND2 b9,b51)) & not
$ b
42 ) & not (
$ b
41 & not
$ XOR2 (XOR2 b24,(AND2 b8,b33)),
(XOR2 b50,(AND2 b8,b51)) ) & not (
$ XOR2 (XOR2 b24,(AND2 b8,b33)),
(XOR2 b50,(AND2 b8,b51)) & not
$ b
41 ) & not (
$ b
40 & not
$ XOR2 (XOR2 b23,(AND2 b7,b33)),
(XOR2 b50,(AND2 b7,b51)) ) & not (
$ XOR2 (XOR2 b23,(AND2 b7,b33)),
(XOR2 b50,(AND2 b7,b51)) & not
$ b
40 ) & not (
$ b
39 & not
$ XOR2 (XOR2 b22,(AND2 b6,b33)),
(XOR2 b50,(AND2 b6,b51)) ) & not (
$ XOR2 (XOR2 b22,(AND2 b6,b33)),
(XOR2 b50,(AND2 b6,b51)) & not
$ b
39 ) & not (
$ b
38 & not
$ XOR2 (XOR2 b21,(AND2 b5,b33)),
(XOR2 b50,(AND2 b5,b51)) ) & not (
$ XOR2 (XOR2 b21,(AND2 b5,b33)),
(XOR2 b50,(AND2 b5,b51)) & not
$ b
38 ) & not (
$ b
37 & not
$ XOR2 (XOR2 b20,(AND2 b4,b33)),
(XOR2 b50,(AND2 b4,b51)) ) & not (
$ XOR2 (XOR2 b20,(AND2 b4,b33)),
(XOR2 b50,(AND2 b4,b51)) & not
$ b
37 ) & not (
$ b
36 & not
$ XOR2 (XOR2 b19,(AND2 b3,b33)),
(XOR2 b50,(AND2 b3,b51)) ) & not (
$ XOR2 (XOR2 b19,(AND2 b3,b33)),
(XOR2 b50,(AND2 b3,b51)) & not
$ b
36 ) & not (
$ b
35 & not
$ XOR2 (XOR2 b18,(AND2 b2,b33)),
(XOR2 b50,(AND2 b2,b51)) ) & not (
$ XOR2 (XOR2 b18,(AND2 b2,b33)),
(XOR2 b50,(AND2 b2,b51)) & not
$ b
35 ) & not (
$ b
34 & not
$ XOR2 (XOR2 b50,(AND2 b1,b33)),
(XOR2 b50,(AND2 b1,b51)) ) & not (
$ XOR2 (XOR2 b50,(AND2 b1,b33)),
(XOR2 b50,(AND2 b1,b51)) & not
$ b
34 ) ) )