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