sample_id
int64
1
200k
sequent
stringlengths
6
112
rule
stringclasses
11 values
rule_idx
int64
0
10
pivot
int64
0
8
target_value
float64
1
1
root_sequent
stringlengths
6
112
trace_step
int64
1
1
total_trace_steps
int64
1
1
input_ids
listlengths
6
109
token_length
int64
6
109
1
(S => (P & Q)), S |- P
L_IMP
2
0
1
(S => (P & Q)), S |- P
1
1
[ 84, 67, 22, 6, 22, 84, 64, 22, 7, 22, 65, 85, 85, 86, 22, 67, 22, 8, 92, 22, 64 ]
21
2
S |- S
AXIOM
0
0
1
S |- S
1
1
[ 67, 22, 8, 92, 22, 67 ]
6
3
(P & Q), S |- P
L_AND
4
0
1
(P & Q), S |- P
1
1
[ 84, 64, 22, 7, 22, 65, 85, 86, 22, 67, 22, 8, 92, 22, 64 ]
15
4
P, Q, S |- P
AXIOM
0
0
1
P, Q, S |- P
1
1
[ 64, 86, 22, 65, 86, 22, 67, 22, 8, 92, 22, 64 ]
12
5
((P & Q) => R) |- (P => (Q => R))
R_IMP
1
0
1
((P & Q) => R) |- (P => (Q => R))
1
1
[ 84, 84, 64, 22, 7, 22, 65, 85, 22, 6, 22, 66, 85, 22, 8, 92, 22, 84, 64, 22, 6, 22, 84, 65, 22, 6, 22, 66, 85, 85 ]
30
6
P, ((P & Q) => R) |- (Q => R)
R_IMP
1
0
1
P, ((P & Q) => R) |- (Q => R)
1
1
[ 64, 86, 22, 84, 84, 64, 22, 7, 22, 65, 85, 22, 6, 22, 66, 85, 22, 8, 92, 22, 84, 65, 22, 6, 22, 66, 85 ]
27
7
Q, P, ((P & Q) => R) |- R
L_IMP
2
2
1
Q, P, ((P & Q) => R) |- R
1
1
[ 65, 86, 22, 64, 86, 22, 84, 84, 64, 22, 7, 22, 65, 85, 22, 6, 22, 66, 85, 22, 8, 92, 22, 66 ]
24
8
Q, P |- (P & Q)
R_AND
3
0
1
Q, P |- (P & Q)
1
1
[ 65, 86, 22, 64, 22, 8, 92, 22, 84, 64, 22, 7, 22, 65, 85 ]
15
9
Q, P |- P
AXIOM
0
0
1
Q, P |- P
1
1
[ 65, 86, 22, 64, 22, 8, 92, 22, 64 ]
9
10
Q, P |- Q
AXIOM
0
0
1
Q, P |- Q
1
1
[ 65, 86, 22, 64, 22, 8, 92, 22, 65 ]
9
11
R, Q, P |- R
AXIOM
0
0
1
R, Q, P |- R
1
1
[ 66, 86, 22, 65, 86, 22, 64, 22, 8, 92, 22, 66 ]
12
12
Q, S, ~Q, ~T |- T
L_NOT
9
2
1
Q, S, ~Q, ~T |- T
1
1
[ 65, 86, 22, 67, 86, 22, 9, 65, 86, 22, 9, 68, 22, 8, 92, 22, 68 ]
17
13
Q, S, ~T |- Q
AXIOM
0
0
1
Q, S, ~T |- Q
1
1
[ 65, 86, 22, 67, 86, 22, 9, 68, 22, 8, 92, 22, 65 ]
13
14
((T & S) => P) |- (T => (S => P))
R_IMP
1
0
1
((T & S) => P) |- (T => (S => P))
1
1
[ 84, 84, 68, 22, 7, 22, 67, 85, 22, 6, 22, 64, 85, 22, 8, 92, 22, 84, 68, 22, 6, 22, 84, 67, 22, 6, 22, 64, 85, 85 ]
30
15
T, ((T & S) => P) |- (S => P)
R_IMP
1
0
1
T, ((T & S) => P) |- (S => P)
1
1
[ 68, 86, 22, 84, 84, 68, 22, 7, 22, 67, 85, 22, 6, 22, 64, 85, 22, 8, 92, 22, 84, 67, 22, 6, 22, 64, 85 ]
27
16
S, T, ((T & S) => P) |- P
L_IMP
2
2
1
S, T, ((T & S) => P) |- P
1
1
[ 67, 86, 22, 68, 86, 22, 84, 84, 68, 22, 7, 22, 67, 85, 22, 6, 22, 64, 85, 22, 8, 92, 22, 64 ]
24
17
S, T |- (T & S)
R_AND
3
0
1
S, T |- (T & S)
1
1
[ 67, 86, 22, 68, 22, 8, 92, 22, 84, 68, 22, 7, 22, 67, 85 ]
15
18
S, T |- T
AXIOM
0
0
1
S, T |- T
1
1
[ 67, 86, 22, 68, 22, 8, 92, 22, 68 ]
9
19
S, T |- S
AXIOM
0
0
1
S, T |- S
1
1
[ 67, 86, 22, 68, 22, 8, 92, 22, 67 ]
9
20
P, S, T |- P
AXIOM
0
0
1
P, S, T |- P
1
1
[ 64, 86, 22, 67, 86, 22, 68, 22, 8, 92, 22, 64 ]
12
21
(~T & (S & T)), R |- T
L_AND
4
0
1
(~T & (S & T)), R |- T
1
1
[ 84, 9, 68, 22, 7, 22, 84, 67, 22, 7, 22, 68, 85, 85, 86, 22, 66, 22, 8, 92, 22, 68 ]
22
22
~T, (S & T), R |- T
L_NOT
9
0
1
~T, (S & T), R |- T
1
1
[ 9, 68, 86, 22, 84, 67, 22, 7, 22, 68, 85, 86, 22, 66, 22, 8, 92, 22, 68 ]
19
23
(S & T), R |- T
L_AND
4
0
1
(S & T), R |- T
1
1
[ 84, 67, 22, 7, 22, 68, 85, 86, 22, 66, 22, 8, 92, 22, 68 ]
15
24
S, T, R |- T
AXIOM
0
0
1
S, T, R |- T
1
1
[ 67, 86, 22, 68, 86, 22, 66, 22, 8, 92, 22, 68 ]
12
25
~P, P |- (Q => T)
R_IMP
1
0
1
~P, P |- (Q => T)
1
1
[ 9, 64, 86, 22, 64, 22, 8, 92, 22, 84, 65, 22, 6, 22, 68, 85 ]
16
26
Q, ~P, P |- T
L_NOT
9
1
1
Q, ~P, P |- T
1
1
[ 65, 86, 22, 9, 64, 86, 22, 64, 22, 8, 92, 22, 68 ]
13
27
Q, P |- P
AXIOM
0
0
1
Q, P |- P
1
1
[ 65, 86, 22, 64, 22, 8, 92, 22, 64 ]
9
28
(S & (Q | P)) |- ((S & Q) | (S & P))
L_AND
4
0
1
(S & (Q | P)) |- ((S & Q) | (S & P))
1
1
[ 84, 67, 22, 7, 22, 84, 65, 22, 8, 22, 64, 85, 85, 22, 8, 92, 22, 84, 84, 67, 22, 7, 22, 65, 85, 22, 8, 22, 84, 67, 22, 7, 22, 64, 85, 85 ]
36
29
S, (Q | P) |- ((S & Q) | (S & P))
L_OR
7
1
1
S, (Q | P) |- ((S & Q) | (S & P))
1
1
[ 67, 86, 22, 84, 65, 22, 8, 22, 64, 85, 22, 8, 92, 22, 84, 84, 67, 22, 7, 22, 65, 85, 22, 8, 22, 84, 67, 22, 7, 22, 64, 85, 85 ]
33
30
Q, S |- ((S & Q) | (S & P))
R_OR_1
5
0
1
Q, S |- ((S & Q) | (S & P))
1
1
[ 65, 86, 22, 67, 22, 8, 92, 22, 84, 84, 67, 22, 7, 22, 65, 85, 22, 8, 22, 84, 67, 22, 7, 22, 64, 85, 85 ]
27
31
Q, S |- (S & Q)
R_AND
3
0
1
Q, S |- (S & Q)
1
1
[ 65, 86, 22, 67, 22, 8, 92, 22, 84, 67, 22, 7, 22, 65, 85 ]
15
32
Q, S |- S
AXIOM
0
0
1
Q, S |- S
1
1
[ 65, 86, 22, 67, 22, 8, 92, 22, 67 ]
9
33
Q, S |- Q
AXIOM
0
0
1
Q, S |- Q
1
1
[ 65, 86, 22, 67, 22, 8, 92, 22, 65 ]
9
34
P, S |- ((S & Q) | (S & P))
R_OR_2
6
0
1
P, S |- ((S & Q) | (S & P))
1
1
[ 64, 86, 22, 67, 22, 8, 92, 22, 84, 84, 67, 22, 7, 22, 65, 85, 22, 8, 22, 84, 67, 22, 7, 22, 64, 85, 85 ]
27
35
P, S |- (S & P)
R_AND
3
0
1
P, S |- (S & P)
1
1
[ 64, 86, 22, 67, 22, 8, 92, 22, 84, 67, 22, 7, 22, 64, 85 ]
15
36
P, S |- S
AXIOM
0
0
1
P, S |- S
1
1
[ 64, 86, 22, 67, 22, 8, 92, 22, 67 ]
9
37
P, S |- P
AXIOM
0
0
1
P, S |- P
1
1
[ 64, 86, 22, 67, 22, 8, 92, 22, 64 ]
9
38
~(T | R) |- (~T & ~R)
R_AND
3
0
1
~(T | R) |- (~T & ~R)
1
1
[ 9, 84, 68, 22, 8, 22, 66, 85, 22, 8, 92, 22, 84, 9, 68, 22, 7, 22, 9, 66, 85 ]
21
39
~(T | R) |- ~T
R_NOT
8
0
1
~(T | R) |- ~T
1
1
[ 9, 84, 68, 22, 8, 22, 66, 85, 22, 8, 92, 22, 9, 68 ]
14
40
T, ~(T | R) |- 0
L_NOT
9
1
1
T, ~(T | R) |- 0
1
1
[ 68, 86, 22, 9, 84, 68, 22, 8, 22, 66, 85, 22, 8, 92, 22, 10 ]
16
41
T |- (T | R)
R_OR_1
5
0
1
T |- (T | R)
1
1
[ 68, 22, 8, 92, 22, 84, 68, 22, 8, 22, 66, 85 ]
12
42
T |- T
AXIOM
0
0
1
T |- T
1
1
[ 68, 22, 8, 92, 22, 68 ]
6
43
~(T | R) |- ~R
R_NOT
8
0
1
~(T | R) |- ~R
1
1
[ 9, 84, 68, 22, 8, 22, 66, 85, 22, 8, 92, 22, 9, 66 ]
14
44
R, ~(T | R) |- 0
L_NOT
9
1
1
R, ~(T | R) |- 0
1
1
[ 66, 86, 22, 9, 84, 68, 22, 8, 22, 66, 85, 22, 8, 92, 22, 10 ]
16
45
R |- (T | R)
R_OR_2
6
0
1
R |- (T | R)
1
1
[ 66, 22, 8, 92, 22, 84, 68, 22, 8, 22, 66, 85 ]
12
46
R |- R
AXIOM
0
0
1
R |- R
1
1
[ 66, 22, 8, 92, 22, 66 ]
6
47
Q, P, S, Q |- (R => R)
R_IMP
1
0
1
Q, P, S, Q |- (R => R)
1
1
[ 65, 86, 22, 64, 86, 22, 67, 86, 22, 65, 22, 8, 92, 22, 84, 66, 22, 6, 22, 66, 85 ]
21
48
R, Q, P, S, Q |- R
AXIOM
0
0
1
R, Q, P, S, Q |- R
1
1
[ 66, 86, 22, 65, 86, 22, 64, 86, 22, 67, 86, 22, 65, 22, 8, 92, 22, 66 ]
18
49
S, ~S |- (P & P)
R_AND
3
0
1
S, ~S |- (P & P)
1
1
[ 67, 86, 22, 9, 67, 22, 8, 92, 22, 84, 64, 22, 7, 22, 64, 85 ]
16
50
S, ~S |- P
L_NOT
9
1
1
S, ~S |- P
1
1
[ 67, 86, 22, 9, 67, 22, 8, 92, 22, 64 ]
10
51
S |- S
AXIOM
0
0
1
S |- S
1
1
[ 67, 22, 8, 92, 22, 67 ]
6
52
S, ~S |- P
L_NOT
9
1
1
S, ~S |- P
1
1
[ 67, 86, 22, 9, 67, 22, 8, 92, 22, 64 ]
10
53
S |- S
AXIOM
0
0
1
S |- S
1
1
[ 67, 22, 8, 92, 22, 67 ]
6
54
~(S | P) |- (~S & ~P)
R_AND
3
0
1
~(S | P) |- (~S & ~P)
1
1
[ 9, 84, 67, 22, 8, 22, 64, 85, 22, 8, 92, 22, 84, 9, 67, 22, 7, 22, 9, 64, 85 ]
21
55
~(S | P) |- ~S
R_NOT
8
0
1
~(S | P) |- ~S
1
1
[ 9, 84, 67, 22, 8, 22, 64, 85, 22, 8, 92, 22, 9, 67 ]
14
56
S, ~(S | P) |- 0
L_NOT
9
1
1
S, ~(S | P) |- 0
1
1
[ 67, 86, 22, 9, 84, 67, 22, 8, 22, 64, 85, 22, 8, 92, 22, 10 ]
16
57
S |- (S | P)
R_OR_1
5
0
1
S |- (S | P)
1
1
[ 67, 22, 8, 92, 22, 84, 67, 22, 8, 22, 64, 85 ]
12
58
S |- S
AXIOM
0
0
1
S |- S
1
1
[ 67, 22, 8, 92, 22, 67 ]
6
59
~(S | P) |- ~P
R_NOT
8
0
1
~(S | P) |- ~P
1
1
[ 9, 84, 67, 22, 8, 22, 64, 85, 22, 8, 92, 22, 9, 64 ]
14
60
P, ~(S | P) |- 0
L_NOT
9
1
1
P, ~(S | P) |- 0
1
1
[ 64, 86, 22, 9, 84, 67, 22, 8, 22, 64, 85, 22, 8, 92, 22, 10 ]
16
61
P |- (S | P)
R_OR_2
6
0
1
P |- (S | P)
1
1
[ 64, 22, 8, 92, 22, 84, 67, 22, 8, 22, 64, 85 ]
12
62
P |- P
AXIOM
0
0
1
P |- P
1
1
[ 64, 22, 8, 92, 22, 64 ]
6
63
T, Q, ~T |- P
L_NOT
9
2
1
T, Q, ~T |- P
1
1
[ 68, 86, 22, 65, 86, 22, 9, 68, 22, 8, 92, 22, 64 ]
13
64
T, Q |- T
AXIOM
0
0
1
T, Q |- T
1
1
[ 68, 86, 22, 65, 22, 8, 92, 22, 68 ]
9
65
0 |- ~~(~~T => T)
R_NOT
8
0
1
0 |- ~~(~~T => T)
1
1
[ 10, 22, 8, 92, 22, 9, 9, 84, 9, 9, 68, 22, 6, 22, 68, 85 ]
16
66
~(~~T => T) |- 0
L_CONTR
10
0
1
~(~~T => T) |- 0
1
1
[ 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 22, 8, 92, 22, 10 ]
15
67
~(~~T => T), ~(~~T => T) |- 0
L_NOT
9
0
1
~(~~T => T), ~(~~T => T) |- 0
1
1
[ 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 86, 22, 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 22, 8, 92, 22, 10 ]
27
68
~(~~T => T) |- (~~T => T)
R_IMP
1
0
1
~(~~T => T) |- (~~T => T)
1
1
[ 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 22, 8, 92, 22, 84, 9, 9, 68, 22, 6, 22, 68, 85 ]
23
69
~~T, ~(~~T => T) |- T
L_NOT
9
0
1
~~T, ~(~~T => T) |- T
1
1
[ 9, 9, 68, 86, 22, 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 22, 8, 92, 22, 68 ]
20
70
~(~~T => T) |- ~T
R_NOT
8
0
1
~(~~T => T) |- ~T
1
1
[ 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 22, 8, 92, 22, 9, 68 ]
16
71
T, ~(~~T => T) |- 0
L_NOT
9
1
1
T, ~(~~T => T) |- 0
1
1
[ 68, 86, 22, 9, 84, 9, 9, 68, 22, 6, 22, 68, 85, 22, 8, 92, 22, 10 ]
18
72
T |- (~~T => T)
R_IMP
1
0
1
T |- (~~T => T)
1
1
[ 68, 22, 8, 92, 22, 84, 9, 9, 68, 22, 6, 22, 68, 85 ]
14
73
~~T, T |- T
AXIOM
0
0
1
~~T, T |- T
1
1
[ 9, 9, 68, 86, 22, 68, 22, 8, 92, 22, 68 ]
11
74
(S => (T & Q)), S |- T
L_IMP
2
0
1
(S => (T & Q)), S |- T
1
1
[ 84, 67, 22, 6, 22, 84, 68, 22, 7, 22, 65, 85, 85, 86, 22, 67, 22, 8, 92, 22, 68 ]
21
75
S |- S
AXIOM
0
0
1
S |- S
1
1
[ 67, 22, 8, 92, 22, 67 ]
6
76
(T & Q), S |- T
L_AND
4
0
1
(T & Q), S |- T
1
1
[ 84, 68, 22, 7, 22, 65, 85, 86, 22, 67, 22, 8, 92, 22, 68 ]
15
77
T, Q, S |- T
AXIOM
0
0
1
T, Q, S |- T
1
1
[ 68, 86, 22, 65, 86, 22, 67, 22, 8, 92, 22, 68 ]
12
78
(T & Q), R |- (T => Q)
R_IMP
1
0
1
(T & Q), R |- (T => Q)
1
1
[ 84, 68, 22, 7, 22, 65, 85, 86, 22, 66, 22, 8, 92, 22, 84, 68, 22, 6, 22, 65, 85 ]
21
79
T, (T & Q), R |- Q
L_AND
4
1
1
T, (T & Q), R |- Q
1
1
[ 68, 86, 22, 84, 68, 22, 7, 22, 65, 85, 86, 22, 66, 22, 8, 92, 22, 65 ]
18
80
T, Q, T, R |- Q
AXIOM
0
0
1
T, Q, T, R |- Q
1
1
[ 68, 86, 22, 65, 86, 22, 68, 86, 22, 66, 22, 8, 92, 22, 65 ]
15
81
(T & (P | R)) |- ((T & P) | (T & R))
L_AND
4
0
1
(T & (P | R)) |- ((T & P) | (T & R))
1
1
[ 84, 68, 22, 7, 22, 84, 64, 22, 8, 22, 66, 85, 85, 22, 8, 92, 22, 84, 84, 68, 22, 7, 22, 64, 85, 22, 8, 22, 84, 68, 22, 7, 22, 66, 85, 85 ]
36
82
T, (P | R) |- ((T & P) | (T & R))
L_OR
7
1
1
T, (P | R) |- ((T & P) | (T & R))
1
1
[ 68, 86, 22, 84, 64, 22, 8, 22, 66, 85, 22, 8, 92, 22, 84, 84, 68, 22, 7, 22, 64, 85, 22, 8, 22, 84, 68, 22, 7, 22, 66, 85, 85 ]
33
83
P, T |- ((T & P) | (T & R))
R_OR_1
5
0
1
P, T |- ((T & P) | (T & R))
1
1
[ 64, 86, 22, 68, 22, 8, 92, 22, 84, 84, 68, 22, 7, 22, 64, 85, 22, 8, 22, 84, 68, 22, 7, 22, 66, 85, 85 ]
27
84
P, T |- (T & P)
R_AND
3
0
1
P, T |- (T & P)
1
1
[ 64, 86, 22, 68, 22, 8, 92, 22, 84, 68, 22, 7, 22, 64, 85 ]
15
85
P, T |- T
AXIOM
0
0
1
P, T |- T
1
1
[ 64, 86, 22, 68, 22, 8, 92, 22, 68 ]
9
86
P, T |- P
AXIOM
0
0
1
P, T |- P
1
1
[ 64, 86, 22, 68, 22, 8, 92, 22, 64 ]
9
87
R, T |- ((T & P) | (T & R))
R_OR_2
6
0
1
R, T |- ((T & P) | (T & R))
1
1
[ 66, 86, 22, 68, 22, 8, 92, 22, 84, 84, 68, 22, 7, 22, 64, 85, 22, 8, 22, 84, 68, 22, 7, 22, 66, 85, 85 ]
27
88
R, T |- (T & R)
R_AND
3
0
1
R, T |- (T & R)
1
1
[ 66, 86, 22, 68, 22, 8, 92, 22, 84, 68, 22, 7, 22, 66, 85 ]
15
89
R, T |- T
AXIOM
0
0
1
R, T |- T
1
1
[ 66, 86, 22, 68, 22, 8, 92, 22, 68 ]
9
90
R, T |- R
AXIOM
0
0
1
R, T |- R
1
1
[ 66, 86, 22, 68, 22, 8, 92, 22, 66 ]
9
91
Q, Q |- (P => P)
R_IMP
1
0
1
Q, Q |- (P => P)
1
1
[ 65, 86, 22, 65, 22, 8, 92, 22, 84, 64, 22, 6, 22, 64, 85 ]
15
92
P, Q, Q |- P
AXIOM
0
0
1
P, Q, Q |- P
1
1
[ 64, 86, 22, 65, 86, 22, 65, 22, 8, 92, 22, 64 ]
12
93
P, ~P, ((Q & Q) => ~T), (T & (R | P)) |- S
L_NOT
9
1
1
P, ~P, ((Q & Q) => ~T), (T & (R | P)) |- S
1
1
[ 64, 86, 22, 9, 64, 86, 22, 84, 84, 65, 22, 7, 22, 65, 85, 22, 6, 22, 9, 68, 85, 86, 22, 84, 68, 22, 7, 22, 84, 66, 22, 8, 22, 64, 85, 85, 22, 8, 92, 22, 67 ]
41
94
P, ((Q & Q) => ~T), (T & (R | P)) |- P
AXIOM
0
0
1
P, ((Q & Q) => ~T), (T & (R | P)) |- P
1
1
[ 64, 86, 22, 84, 84, 65, 22, 7, 22, 65, 85, 22, 6, 22, 9, 68, 85, 86, 22, 84, 68, 22, 7, 22, 84, 66, 22, 8, 22, 64, 85, 85, 22, 8, 92, 22, 64 ]
37
95
(Q & (T | P)) |- ((Q & T) | (Q & P))
L_AND
4
0
1
(Q & (T | P)) |- ((Q & T) | (Q & P))
1
1
[ 84, 65, 22, 7, 22, 84, 68, 22, 8, 22, 64, 85, 85, 22, 8, 92, 22, 84, 84, 65, 22, 7, 22, 68, 85, 22, 8, 22, 84, 65, 22, 7, 22, 64, 85, 85 ]
36
96
Q, (T | P) |- ((Q & T) | (Q & P))
L_OR
7
1
1
Q, (T | P) |- ((Q & T) | (Q & P))
1
1
[ 65, 86, 22, 84, 68, 22, 8, 22, 64, 85, 22, 8, 92, 22, 84, 84, 65, 22, 7, 22, 68, 85, 22, 8, 22, 84, 65, 22, 7, 22, 64, 85, 85 ]
33
97
T, Q |- ((Q & T) | (Q & P))
R_OR_1
5
0
1
T, Q |- ((Q & T) | (Q & P))
1
1
[ 68, 86, 22, 65, 22, 8, 92, 22, 84, 84, 65, 22, 7, 22, 68, 85, 22, 8, 22, 84, 65, 22, 7, 22, 64, 85, 85 ]
27
98
T, Q |- (Q & T)
R_AND
3
0
1
T, Q |- (Q & T)
1
1
[ 68, 86, 22, 65, 22, 8, 92, 22, 84, 65, 22, 7, 22, 68, 85 ]
15
99
T, Q |- Q
AXIOM
0
0
1
T, Q |- Q
1
1
[ 68, 86, 22, 65, 22, 8, 92, 22, 65 ]
9
100
T, Q |- T
AXIOM
0
0
1
T, Q |- T
1
1
[ 68, 86, 22, 65, 22, 8, 92, 22, 68 ]
9