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