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