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