facts
stringlengths
9
219
formula
stringlengths
6
173
num_operators
int64
1
20
gold_formula
bool
2 classes
j is false, q is true, s is true, p is false, b is true, f is true, c is true, o is false, i is false, y is false, l is false, h is true, n is true, v is false
l and o implies v or y implies f or n implies s or b implies j or c implies q or i and y implies j or h and s implies p
16
false
m is false, s is true, b is false, c is true, o is true, d is true, y is false, l is false, u is false, g is false, v is true
m and u and s and o implies v and d or b or o and g implies y or s implies l or c
12
true
e is false, w is true, x is true, a is false, u is false, n is true, c is true
a or e or w or u implies a and n implies x or c or a
8
true
e is false, r is true, m is false, q is false, p is false, b is false, d is false, g is true, k is true, l is true, a is false, y is true, u is true, n is false, v is true
m implies a and n implies r implies e or e implies p or u implies v implies b and d and q implies v and l and g implies d and p implies k and y
18
true
r is false, m is true, t is false, d is true
m and d and r implies t
3
true
e is true, m is false, j is false, s is false, b is true, t is true, y is true, l is true, a is true, u is true, n is true, f is true
e and m and s or t and t and f and n and y or u implies l or a or t or n or j implies b
14
true
e is false, r is true, b is false, x is false, i is true, o is false, a is true, c is true
i implies o or b and c or e and a implies c and x and r and x and o
10
true
b is true, x is false, o is true, y is false, k is false, l is false, g is true, c is false
y and c implies x and y and o and b and k or l implies g
8
true
e is true, r is false, q is false, j is false, w is false, x is true, o is true, t is false, y is false, g is false, n is false
r implies y implies w or q implies t implies n implies j or o implies g or x and e
10
true
q is false, j is true, x is true, c is false, o is true, t is false, y is false, d is false, a is true, g is false, v is true
x and o implies c or v and y or a and q implies g and y and j and g implies t and d
12
false
r is false, j is true, p is true, b is true, x is true, i is true, t is false, d is true, k is true, a is true, f is true
f or t or b and r implies a implies p and i or d and t implies k implies j implies x
11
true
j is true, m is false, q is true, w is false, b is false, x is false, p is true, f is false, c is false, o is false, d is false, a is false, u is false, g is true, v is true
x or w or c implies j implies v implies u implies m and o and q or b and d or d implies a implies p and g or u or f or q
17
true
x is false, h is true, n is true
n implies x implies h
2
true
j is true, m is false, f is true, v is false, o is true, i is true, y is false, u is false, c is false
f implies o implies i and u and c and o and o or y implies j implies v implies j implies m
11
false
e is false, j is false, b is false, z is false, d is true, g is true, n is false
z and b implies z or j implies n or j or e implies g implies d
8
true
j is true, m is true, s is false, p is false, b is false, x is false, z is true, v is true, o is false, t is true, k is false, l is false, a is true, h is true, c is true
b implies o and s and c and x or t or h implies j implies z and l implies p implies h implies m and k or v implies a
15
true
e is false, r is false, j is true, s is false, w is false, x is true, z is false, v is false, o is true, i is false, k is true, l is false, h is false, g is false, f is false
z and j and h or o implies e or f implies f or i implies l implies w and z and s implies g and v and x and e implies r implies k implies j or o implies z
20
false
b is false, t is false, y is false, a is true, g is true, n is false
n implies g implies a and b and y or t
5
false
m is false, j is false, s is true, w is true, z is false, u is true, v is false, t is false, y is false, g is true, l is false, k is true, h is false, n is false, f is false
n or n or m and z implies h implies y implies u implies w implies g or l or k and f implies s or y and f and y and w or v or j implies v and t
20
false
r is true, j is true, m is false, w is false, b is true, v is false, i is true, t is true, d is true, l is false, u is true, g is false, c is true
c implies j and b implies i and l implies b implies u and g implies t and l implies v implies v or d implies w and r and j or m
16
false
q is true, s is true, p is false, b is false, x is false, i is true, d is false, k is false, y is false, l is false, u is true, f is true
u implies q and y and b and k or f implies i and d and s implies l or p or x or p
12
true
e is true, j is false, s is true, w is true, p is false, x is false, h is true, u is false, o is true, k is false, g is true, n is false, c is true
x or s or w or k and s or p or g implies c and n implies s or o and u or j implies h and g and e and g or g implies n or h or k
20
true
r is true, q is false, b is true, x is true, k is false, y is true, l is true, a is true, u is true, n is false, v is true
a and r or x implies k implies v or y or l implies k implies u implies q or q or n implies b
12
true
d is false, k is false
d or k
1
false
e is false, r is true, m is true, q is true, w is false, p is false, z is false, f is false, i is true, l is true, h is true, n is false, v is true
w implies p implies e implies f or v and m or i and q or z and h or i implies r and l implies n implies v implies i implies p
16
false
e is false, r is true, j is false, p is false, b is true, z is false, i is false, d is false, t is false, a is false, u is true, n is false, v is true
n and p implies u and i and b implies d implies p and a or z and v implies j or r and z or e and z and i or t implies t
17
true
e is true, m is true, q is true, h is true, b is true, x is true, w is true, z is false, p is true, o is false, u is false, f is true
z and b and x implies m implies e implies e implies q implies f implies u or h and o and w implies p
12
true
e is false, z is true, o is false, d is false, k is true, l is false, v is true
z implies o or e or e and k implies e or l or k or d implies z implies k implies v
11
true
r is false, p is true, z is false, d is false, o is false, h is false, n is false
r implies d and h and p or d implies o or n or z
7
false
e is true, q is true, m is false, s is true, p is false, d is false, g is true, k is true, l is true, a is true, u is false, n is false, c is false
e implies n and n implies p and u or l implies d or q implies c implies g or q and p implies u implies k implies l or k implies s implies q or a implies m
19
false
e is true, s is false, x is true, k is false, y is false
s and e or y and k and s implies x
5
true
q is true, s is false, p is false, x is true, u is true, i is false, l is true, a is false, g is true, v is true
s and x or a or v or g or p implies l and s implies u or i and q
10
true
j is true, p is false, z is true, f is true, v is true, t is true, y is false, k is true, l is false, h is false, g is true, c is false
l and y or z and c and p and h or y implies t and t or g and v and f and h or k or j
14
true
e is false, m is false, s is true, p is false, z is true, d is true, t is false, y is false, k is false, a is false, c is false
y implies c or d and s implies d or p implies k and k and y and z and e and z and d or c implies s implies a or t and s implies t or p implies m
20
false
e is true, s is true, p is false, x is false, z is false, t is true, l is true, a is true
e or a implies p implies s or x implies z or t implies s implies l or t
9
true
s is true, w is true, b is false, h is false, f is true, c is true, d is false, i is false, t is true, o is false, u is false, g is true, v is false
d or u and w or b or i or s implies v and t and h and o and i and u or w implies g implies f implies i implies c
16
true
j is true, m is false, z is true, t is false, l is true, a is true, g is true, n is false, f is true
g implies z or a implies l implies l and t and j or n and f and m implies j and z
11
true
e is true, j is false, m is true, s is false, b is true, d is true, t is false, y is false, k is true, l is false, n is false, c is true
d or b or y and n or l and e and n implies y and c or c or j or b implies c and t or e and m and j or k implies d and s
19
false
r is false, m is true, q is true, w is false, h is true, z is false, v is false, o is false, t is false, y is true, g is true, n is true, c is true
n implies z and c implies o and m implies t or n implies q or v or g and r or w or n and h or y
14
true
r is true, s is false, p is true, h is false, z is false, t is true, k is true, l is true, g is true, n is true
l and z implies n and g implies g and r and l implies t implies l or k and s implies p implies h and p implies l or k
15
true
e is true, r is true, s is true, p is false, z is true, c is true, d is false, y is false, g is false, k is false, u is true, n is false, f is true
r implies c and f or u and z and y and p and s or n and d and s implies y or r and g and k or r implies e or z
17
true
q is false, p is false, b is true, d is true, i is false, y is true, h is false, f is false
q implies b implies d or b or h or f and b and y or b or p or i
10
true
e is true, r is false, m is true, s is false, x is false, z is false, o is true, d is false, k is false, y is true, n is false, c is true
d and m or c or r implies m implies o and e and z or k or x implies k or s implies d or n or d implies y and y or c
17
true
c is false, j is true, s is false
s implies j and c
2
true
r is true, q is true, m is false, s is false, x is true, u is false, c is false, i is true, h is true, f is true
h or f or x or r and h implies q or s or f and m implies c and u and f implies f or i implies f
14
true
q is true, s is true, b is false, z is false, c is false, d is true, t is true, y is true, a is true, u is false, f is false
u or s implies q and z or t or t implies s implies a and f and c implies y and a or d or b or f implies q
15
true
m is false, p is false, g is true, u is false, n is false
p or u implies m and n or g
4
true
x is true, f is false
f and x
1
false
j is false, w is true, b is false, x is false, u is true, c is false, o is true, i is true, k is true, t is false, l is false, g is false, f is false
g and l implies w or k implies l and o implies f implies u and o or g and j or i or t and f implies c or c or b implies f or x or x
19
true
e is false, r is true, m is false, j is true, h is false, p is true, w is true, b is false, z is false, i is true, t is false, k is true, o is true, l is true, a is false, u is true, g is true, c is true
z or u or r implies k implies l and h and i or i and c or g and t or m and g and a or e implies p or o implies j implies w implies b implies z
20
true
r is true, q is false, j is true, s is true, w is false, p is true, x is true, h is false, z is true, i is true, o is false, y is false, t is true, u is true, g is true, c is false
u implies q or w and x implies y or c or i or p or s implies r or o or q and c or t implies i implies z implies r and g or h or j
19
true
q is true, s is true, z is true, i is false, t is false, k is true, a is false, u is false, n is true, f is false
t implies n implies z implies f or n and s or q and i or q and a or i and u implies k or q implies q
14
true
e is false, r is false, m is false, z is false, d is true, o is false, y is true, k is true, f is false
m implies e and y and z and d or f implies o or k or o implies r or f
10
false
r is false, m is true, x is true, c is false, o is true, i is true, k is true, t is true, l is true, a is false, g is true, v is false
r implies k or a and a and v and g and c implies c or l or o implies i and x or t implies m
13
true
r is true, q is true, v is false, y is true, a is false, f is false
r or q or a and f implies y implies v
5
false
e is true, r is true, m is true, b is false, x is true, c is false, d is false, t is false, k is true, a is false, n is false, f is false
x implies r or k and e or f or k or m and r implies c and a and n or d implies b or t or d and a
15
true
e is true, r is false, s is true, w is false, b is true, z is true, v is false, i is false, g is false, l is false, h is true, n is false, c is true
s implies c implies h or r implies i and n and z implies h and b implies v implies e and g or z and w or v or l
15
true
m is false, s is false, p is false, k is false, y is true, l is false, a is false, u is false, c is true
c implies u or l or p and a or k implies y or c implies s and y implies m
10
true
q is true, s is true, c is false, d is false, t is true, y is false, g is true, u is true, n is false, f is true
y or n implies q implies u or u implies f or g and t implies d and y implies c or s implies g
12
true
r is true, j is false, q is false, p is false, x is true, z is true, y is false
x and p implies j and y and z and q and q or r or p and r
9
true
q is true, b is true, f is false, h is true, v is true
f implies v and h or h implies b or q
5
true
e is false, m is false, s is false, z is false, i is true, t is true, u is false, n is true, v is true
s implies n and u and t or z implies e and i implies m or v
8
true
q is true, j is true, b is true, x is false, v is false, o is false, t is false, d is true, k is true, l is false, g is true, n is false, c is true
l or c implies x implies t and o implies d and o or n implies q implies x implies v and b or j and n implies j implies k or g implies k implies v
18
false
r is true, m is false, s is true, f is true, c is true, d is true, o is false, k is false, y is true, l is true, h is false, v is true
d implies o implies s or v implies k implies f implies y and d or c implies s implies h and l implies m implies f implies r implies y or c
16
true
e is false, s is false, w is false, b is false, f is false, c is true, g is false, a is false, u is true, n is false, v is true
b and v implies w and u or e implies f and a and n or s implies g and c
10
true
h is false, n is true
h implies h and n
2
true
j is true, q is true, p is true, b is false, x is true, f is false, v is true, i is false, t is false, y is false, a is false, g is true, c is false
c and i or x and j or t and v and b or i or g implies q implies q and f or f or p implies t and i and a or y
17
false
e is true, c is false
e or c
1
true
e is false, r is false, s is true, w is true, x is true, u is true, n is false, f is true
u or x or w implies e or s implies f or n or r or n implies e
9
false
e is true, q is false, s is false, p is true, x is true, z is false, d is true, t is false, k is true, n is true, v is true
p or s implies q implies n implies z implies p implies e implies v or z implies t or q or x and k and k and t or d and s
16
false
m is true, w is false, p is true, u is true, o is true, t is false, k is true, d is true, l is false, g is true
g implies w implies k implies k implies t implies m and o or l or u or d or p
10
true
e is false, r is false, j is true, p is false, w is true, x is false, d is true, l is false, u is false, c is true
c and l or p or e and d implies x and r implies u implies w or j implies x or l
11
false
a is false, r is true, x is true
r and a implies x
2
true
q is false, b is true, x is false, c is false, d is false, i is false, a is true, h is true, f is false
a and b or x and q and d and f or c or h or q implies i
9
false
r is true, q is true, m is false, s is true, x is true, c is true, d is true, i is true, y is true, l is true, a is false, n is true, f is true
d implies s implies q implies a and r implies y implies l and n implies m or f and q and r or q or x or x and i and m implies c and y and m
19
false
e is true, j is true, w is false, p is false, x is true, v is false, d is true, i is false, y is false, k is false, a is true, f is true
f implies w implies y or j or p and k implies e implies j implies v or x and d implies i implies a and w
13
true
q is false, x is true, l is false
l and q or x
2
true
q is false, j is false, s is true, b is true, v is false, o is false, t is false, k is false, y is true, l is false, i is false, n is true, c is true
j and b or k and q implies n implies n implies c and v or q or k or s or j and l or j or y implies k implies t implies j and v implies o and i
20
true
e is true, m is false, w is true, b is true, u is false, d is true, k is true, g is false, h is false, n is true, f is true
h implies e implies d or n implies h or n and b or m implies k or d or g implies g implies f and k or w or u
15
true
e is true, q is true, z is false, t is false, y is true, l is true, a is true, u is true, v is false
e or l and t or u and z implies z or y implies q or a implies v
9
false
r is false, m is false, d is false, i is false, k is false, y is false, a is true, h is true
d or r implies k implies a and i implies h implies y or y implies m
8
true
z is false, f is false, o is true, k is false, l is true, v is false
l or k and v or k or v and f and o and z
7
true
e is false, j is false, q is false, s is true, x is false, z is false, i is false, d is false, a is false, h is true, n is false
i implies h implies x implies s and j and h implies s and d or z implies a and e implies n implies s or n and q
14
true
r is true, j is false, q is false, p is true, x is true, y is false, n is false, v is false
j implies y and p and x implies v and q implies r and n
7
true
m is true, w is true, z is true, k is false, y is true, a is false, u is true
y implies u or z or k implies m or w implies a
6
false
w is false, z is true, o is true, g is false, u is false, n is false, f is true
u and f implies z or n or g or w or o
6
true
j is true, m is false, f is true, d is true, o is true, k is false, y is false, l is true, g is false, n is true, c is false
c or n implies d or g implies k or y and l or j or o and m and d implies f
11
true
a is true, t is false
t and a
1
false
e is true, w is false, x is true, f is false, c is false, k is true, l is true, a is false, v is false
w and c implies e implies v and a implies f and c and l and x implies k
9
true
m is true, c is true
m and c
1
true
e is false, w is true, p is true, h is false, o is true, t is true, k is false, y is false, d is true, u is false, v is true
v and k and t and u or e and y and w implies w implies p implies y or o or o and d and h
13
true
r is false, j is true, q is true, m is true, s is true, b is false, f is true, i is true, k is false, a is true, g is true, n is true, c is false
c or q and i and b implies j and k or r and m implies a implies g and n implies i or s and f and n implies r and a
16
false
r is true, b is false, x is true, l is false, v is false
l implies r implies v implies v and b implies x
5
true
m is false, q is false, j is true, s is true, w is true, b is false, z is true, o is true, i is true, d is true, a is false, g is false, n is false
q implies m and o and n or w or j implies g implies s and z or j or q implies i implies a or d or b
14
true
j is false, m is false, h is false, b is false, x is false, p is false, z is false, u is false, w is true, d is true, o is false, k is false, i is true, a is false, g is true
m or k implies j implies d or x and g and d and z implies b or h and j or u or o and i or a and j implies p and a or w
18
true
r is false, p is false, b is false, x is true, w is true, z is false, o is false, t is true, i is false, g is false, y is true, a is false, h is false, n is true, f is true
x and h or o or n and p and f implies a or t and i implies b implies w and z or b and z or g implies y and r and g and a
18
false
r is false, b is false, x is false, z is false, t is false, y is true, h is false, v is true
b implies y or x implies z and h or v or r implies t and v implies v or b implies x
11
false
r is true, q is true, j is true, s is false, p is true, b is true, x is false, w is true, z is false, o is false, t is true, l is false, h is false, n is false, v is true
o and b and n implies q implies b and v implies j or x implies p or r or w or s implies l implies l implies h implies z or t and q or j
18
true
q is true, m is true, p is false, x is false, f is false, d is true, k is true, g is true, v is true
q or v and p or d and k or g implies f implies m and x
8
true
e is true, r is true, j is true, s is false, p is false, u is true, o is false, t is false, y is false, d is true, l is true, a is true, h is true, v is false
p or a implies l or y and o or e or j and t implies a and s and o implies j implies l or t or o and h implies r and u or v and d or a
20
true