🧠 reasoning datasets
Collection
A collection of reasoning tasks to benchmark model abilities • 12 items • Updated
Datasets:
facts stringlengths 9 219 | formula stringlengths 6 173 | num_operators int64 1 20 | gold_formula bool 2 classes |
|---|---|---|---|
g is true, s is false, v is false | v or s and s or g | 3 | true |
e is false, u is false, g is false | u and g and e | 2 | false |
q is false, s is true, w is false, z is false, d is false, k is true, l is true, u is false, g is true, v is false | d implies l or z and w or v and u implies k implies q implies g implies s implies q and q | 11 | false |
q is false, v is true | q implies v | 1 | true |
m is true, s is false, p is false, b is false, x is true, z is false, f is false, d is true, y is true, l is false, n is true, v is true | l and b or z implies y implies s and z or x implies d and y and v implies d or f implies v and m implies n and n or p | 16 | true |
m is false, h is true, b is true, i is true, t is true, k is true, l is false, g is false, n is false | l and m or i and b and g or n and h and g implies k and t | 9 | true |
e is false, r is false, j is true, m is true, p is false, b is true, h is false, w is false, z is false, c is true, k is false, l is true, a is true, g is true, f is true | k and l implies g implies j implies k and p implies f and a implies b and h implies w and c or z implies g and m and r and e | 16 | false |
e is true, j is false, q is true, s is false, p is false, v is true, o is false, t is true, a is true, h is false, f is false | v and t implies f or j and p and s or q or e and q or a implies o or o implies h implies p and p | 14 | false |
q is false, j is false, w is true, z is false, c is true, i is false, d is false, y is false, o is true, a is false, n is false, h is true, g is false, f is false | i or y or y or f and a and d or h or o or q or i and c implies h implies z implies g implies y or z or w implies a implies j and i and n | 20 | true |
r is true, m is false, j is true, q is true, s is false, p is false, b is false, y is false, l is false, a is true, u is false, g is true | u implies p or j or m and y and g and r implies s implies g implies q and l or b implies a | 12 | true |
e is true, r is true, j is false, s is true, b is true, z is true, v is true, i is false, t is true, l is false, h is true, g is true, f is true | s or l and s implies h or j or s and z implies g implies f and t or t or e and r and b and i and v | 15 | true |
e is false, j is false, d is false, o is false, k is true, l is true | e and k or d and o implies l and j | 5 | true |
q is true, s is false, w is false, p is false, o is true, k is true, h is true, v is true | w and h or k or v implies p or q and v implies s or p and h implies o | 10 | true |
j is false, x is true, i is false, t is true, n is true | t or x implies i or n and i implies j | 5 | true |
e is true, j is false, m is false, q is true, w is false, p is false, b is true, o is true, d is true, y is false, h is false, c is true | p or e implies h implies w or o or j or c implies y implies b or y and y or m and d implies q and h and h | 15 | false |
q is true, m is false, p is true, x is true, z is false, d is true, t is true, k is true, l is false, h is false, v is false | k or q or v implies l and x implies d and m and h and t or z or k implies p | 11 | true |
m is false, s is false, w is false, k is true, l is false, g is false, n is true | g or m or s implies l implies w implies k or n implies l | 7 | false |
e is false, r is true, j is false, s is false, i is true, k is true, l is true, n is true | e implies s implies j implies r implies i and l implies k or n | 7 | true |
m is true, b is true, n is false, a is false | b and n or m and n implies b implies a | 5 | false |
r is false, q is false, s is false, h is true, p is true, x is true, c is true, d is true, t is false, y is true, a is true, u is false, v is false | x or r or y implies v or y implies u implies h and h or a and c and d and q and a or t or s and a or r or h or p or h | 19 | true |
p is true, z is true, t is true, k is false, l is true, h is false, g is false, v is true | k or h and p and t and g or l and v or l and z | 8 | true |
q is true, p is true, w is false, z is false, i is false, a is true, u is false, n is true, f is false | u or p implies u implies i and n and q and f and a and z implies z and w or i or q or u and n | 14 | true |
b is true, u is false, f is false, a is false, h is false, c is false | a implies h and c or b or u or f | 5 | true |
m is true, p is true, x is false, h is true, c is false | p and m and x and h implies c implies p | 5 | true |
j is true, b is true, x is true, y is true, k is false, n is false | k or j or y implies x or x and b or n | 6 | true |
e is true, r is true, s is false, w is true, p is true, x is true, z is false, d is true, i is false, o is true, t is true, l is false, a is true, g is true, n is false | r implies x implies x or d implies s implies x implies e or l implies w and p implies l or z implies i and d and n or o and g implies t implies x implies a | 19 | true |
j is false, s is true, i is false, d is false, k is false, a is false, h is true, n is false, c is true | j implies n implies c and a or i implies n or s or h or c or d or k or k | 11 | true |
m is true, q is false, j is false, s is false, w is false, x is false, z is true, u is true, i is true, l is true, a is false, h is true, n is true, v is true | u or h or n and x implies m and z implies q implies a and l and v or w and q or j and x and i and w or s | 16 | true |
s is true, b is true, x is false, u is false, d is true, o is true, i is false, h is false, v is false | s and x and h implies d and b or u implies o or v and i | 8 | true |
p is true, b is false, n is true, h is false | n and p and b and h and n | 4 | false |
e is false, n is true, x is false | e or n implies x | 2 | false |
e is true, j is false, i is true, t is true, o is true, g is true, n is true | e implies n or g or j and t and i or o implies e | 7 | true |
e is true, w is true, b is true, t is true, g is false | b and e and g implies t implies w | 4 | true |
h is true, b is false, t is false | b implies t implies h | 2 | true |
j is true, m is true, p is true, b is false, w is false, z is true, c is true, i is false, t is true, d is false, k is true, o is true, v is false | c and i and j and v or t or d and p or k and t implies k or t implies z implies o or d implies b implies m or w or m or m implies d | 19 | false |
q is true, b is false, z is false | b or z or q | 2 | true |
r is false, q is true, j is false, m is false, b is true, u is true, o is true, t is true, k is false, a is false, g is true, n is false, f is false | g implies n implies a or q and j or b and m and u implies r and k or t and f and o | 12 | false |
m is true, b is false, z is false, v is true, d is true, i is false, g is true, f is true | g or v and m or b implies f and z and z or d implies i | 8 | false |
q is false, s is false, w is false, b is false, v is false, t is true, f is false | b or w implies q and f and t or v implies s | 6 | false |
e is false, j is true, k is true, c is false | j implies k or c implies e | 3 | false |
e is false, r is true, q is true, m is true, x is true, d is true, o is false, k is false, a is false, h is true, n is false, v is true | q implies q or q or k or k or h implies e or n or d implies o and m and v or x implies q and a or h implies r | 16 | true |
q is true, j is false, s is true, p is false, z is true, c is true, d is false, i is true, y is false, k is false, t is true, o is true, f is true | f implies d and q implies i or j and p and y implies z or s implies c or k or d or q and f and t and o implies j or k and j | 18 | false |
j is false, s is true, w is true, z is true, c is true, o is false, t is false, k is false, a is false, u is false, f is false | k or w implies a and j or f implies z and t implies u implies z or z or s implies f implies o implies c and k | 14 | false |
b is true, x is true, u is true, d is false, t is false, k is true, y is false, l is false, h is true, f is true | f and d implies f and l and k and x and h and h implies b or u implies y implies t | 11 | true |
r is true, j is false, q is true, p is true, b is false, y is true, g is true | q and p and b implies g or j and r or y implies q | 7 | true |
r is false, m is true, q is true, w is true, b is false, x is true, y is true, c is true | b implies m or x or r or y and q and w and c | 7 | true |
m is true, o is true, z is false | z and o implies m | 2 | true |
r is true, m is false, j is false, s is false, w is false, p is false, x is false, z is true, v is false, c is false, i is false, d is false, t is false, f is false | w or i implies x or m and f and z and s and w and d and t or s implies c implies r or t or s and c implies p or v implies j | 18 | true |
t is true, u is false, x is false, v is false | x and v or t and u | 3 | false |
j is false, w is false, h is false, x is false, b is false, z is true, c is false, o is false, i is false, y is false, k is true, a is true, u is true, v is false | c implies u implies y implies z implies z or v implies w implies h or j or o and k or x implies k or a implies b implies i or k | 16 | true |
j is true, i is false, t is true, l is false, h is true, n is false, v is true | l implies i implies j or n and t or v implies h or l | 7 | true |
b is false, k is true, s is true | k and s or s or b | 3 | true |
e is false, r is true, z is false, v is true, t is true, k is true, y is false, u is false, n is true, c is true | u or y or c implies k and r implies v or n and e or z or t | 9 | true |
m is true, j is false, q is true, b is true, x is false, d is true, i is true, y is true, t is false, g is false | d and x and j or m and i or y implies i implies t and g and t and b implies g implies b or i and q and b | 15 | true |
o is false, j is false | o or j | 1 | false |
i is false, s is true | i implies s | 1 | true |
a is true, t is false, v is false | a or v and t | 2 | true |
d is true, y is false, u is false | d or u and y and d | 3 | true |
q is false, s is true, b is false, t is false, l is false, a is false, c is false | a implies t or q and l implies c and s implies b | 6 | true |
m is false, j is false, p is true, i is false, h is false, g is false, v is false | g implies m and m or v and j implies h or p and i | 7 | false |
e is false, q is true, s is true, w is false, b is true, p is true, u is true, v is false, d is false, t is true, i is false, k is false, l is true, o is false, g is false, c is false | e or g and w and t implies s or d implies b implies l implies i or k or c and o or v and w implies q or u and e or p or q and u | 19 | true |
r is true, j is false, p is false, h is true, x is true, z is true, f is false, c is false, o is true, d is false, u is false, n is true, v is true | z and v or u and z and p implies x implies f or o and n and h implies d implies o and o implies j implies c or n or r | 16 | true |
q is false, b is false, z is true, f is true, d is false, i is false, y is false, o is false, a is true, n is true, c is true | f implies n and d or c and b implies i implies d implies a and y or o and z and q or d | 12 | true |
r is false, j is false, m is true, h is false, x is true, z is true, v is true, i is false, o is true, y is false, k is false, l is false, a is true, u is true, g is true, c is true | v or r or x implies i and c and u implies j and y implies z or a and m and j or i and c and k implies g implies o and l implies h | 18 | true |
p is true, d is true, k is true, n is true, c is false | k or d and c or n and p | 4 | true |
r is true, x is false, z is true, u is false, t is false, l is false, g is true, v is true | r or t and g and u implies l implies x and v implies z | 7 | true |
x is true, z is false, v is true | z and x and v | 2 | false |
i is true, s is true | i and s | 1 | true |
r is true, j is true, h is true, b is false, z is false, f is true, v is true, i is false, t is true, y is false, k is true, g is true, n is true, c is true | i implies n and r implies c and t and y or k or t or g implies y or b and n implies v and i or k implies c and f and j or z and h | 19 | true |
q is false, m is true, j is false, s is true, p is true, x is true, z is true, d is true, f is true | s or z or m and j implies z and s or q and x implies f or d and p | 10 | true |
e is false, r is true, q is true, s is false, b is true, z is false, v is false, d is true, o is true, k is false, c is false | b or k or q or c implies z and v or v or d and d or r implies o implies e and r and s | 13 | false |
j is false, s is false, w is false, p is true, x is false, b is false, i is false, t is false, d is false, h is true | x implies w or j implies i or s implies i or p or t or w implies d or b or h | 11 | true |
e is false, j is false, p is false, x is true, i is true, k is true, y is true | x implies j or x and k or y implies p or i or e | 7 | true |
r is true, q is false, b is true, u is false, c is false, d is false, t is true, a is true, n is false, h is false, g is false, f is true | d implies c implies q implies a or f and t or r or h and g or n implies g and u or b | 12 | true |
r is false, j is false, x is false, t is false, g is true | r and x and t or j and r and g | 5 | false |
e is true, h is false, l is false | l implies e implies h | 2 | false |
m is false, s is false, l is false, g is true, f is false | f implies g and s and g and l and m | 5 | true |
m is false, q is false, s is false, z is true, f is false, d is false, i is true, k is true, a is true, g is true, c is true | g or z and m or c and q and s or d and k and i implies a and s or f | 11 | false |
m is false, q is false, i is false, y is false, a is true, n is true | y or q and i or m implies a implies y implies n or a | 7 | true |
s is true, w is false, p is true, x is true, z is false, h is true, g is false, v is true | v implies x or v implies s implies h or z implies g implies w or w and x and p implies v | 11 | true |
w is true, d is false, o is false, i is false, c is false | c implies i implies o implies w implies d | 4 | false |
r is true, q is false, h is false, x is false, f is false, d is false, o is true, k is false, l is true, a is true, u is true, g is true, c is false | d implies k or c implies l and q and r implies u and f or x or g implies l and c or a or h or r or o | 15 | true |
m is false, q is true, s is false, p is false, b is true, x is true, o is true, t is true, y is true, l is true, u is false | l and b implies u or u implies m and x or o implies y and s or l or t implies y and p or q | 13 | true |
b is true, u is false, d is false, h is false, g is false | u implies h and g implies b or g and d | 5 | true |
e is false, m is false, b is true, x is false, d is true, i is true, k is true, y is false, l is true, a is true, u is false | k implies e implies u implies e and d and x implies l or a or l and l and i implies b and l and m or y | 14 | false |
r is true, m is true, j is false, w is false, b is true, v is true, t is false, k is true, a is false, h is true, n is true, f is true | j implies b and m or j or n or w and t or m or t and f or a or r or h or k implies v implies w | 15 | false |
e is true, r is false, j is true, s is true, w is true, p is true, x is true, c is true, i is false, t is true, y is false, a is true, h is true, n is true, v is false | v or i implies r implies s and w and c implies y or c or p and j and h implies s and e implies x or t or a implies h implies n implies p and i implies v | 20 | true |
s is false, b is false, x is false, o is false, i is true, u is false, v is false | i and u or o implies x implies v and s or b | 6 | false |
e is false, r is false, b is true, x is false, o is true, t is true, y is false, d is true, l is false, a is true, h is false, n is false, v is true | h and h and y or r or l and y or t or n and y or a implies v and e or x or o and b or b implies e implies o or d | 18 | true |
b is false, f is false, l is false, s is true | s implies f implies f or l and b implies s | 5 | true |
q is false, j is true, s is false, x is false, u is true, o is false, d is true, k is false, h is true | s and q implies j implies h and k implies o implies u or x or d | 8 | true |
u is false, v is true, i is true, k is true, g is true, c is true | k or g implies u implies c or i implies v | 5 | true |
a is true, p is false | a and p | 1 | false |
w is true, x is true, c is true, d is true, k is false, u is false, f is true | c and f or d and u and x or w and k and f | 7 | true |
e is false, p is false, w is true, o is true, t is false, l is true, a is true, u is false, n is false | a and u implies t or p or o and e implies p and w or n or u or n implies l | 11 | true |
m is false, w is true, b is true, u is false, f is false, g is false, a is true, h is true, n is false, c is false | h or u implies c or a and m or u or a implies n or b and f or w and g | 11 | false |
q is true, x is false, o is true, t is true, l is true, h is false, f is true | q or l or x and l implies q or o implies h and f implies t | 8 | true |
e is true, q is false, s is false, z is false, o is false | q and e or o implies z and s | 4 | true |
m is false, j is true, s is false, w is false, h is false, c is true, o is true, i is false, l is true, a is false, u is true, v is false | w or w and j or v implies w and u implies m or l implies a or o or s and i implies h or a or c or s | 15 | true |
e is false, s is true, w is true, b is true, x is false, o is false, d is false, l is true, n is true, h is false, g is true | e implies h and x or o implies s or b implies g or e or w implies d and n or l | 11 | true |
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Implications
Dataset Description
Implications is a synthetic dataset of logical formulas with Boolean variables and logical operators (and, or, implies).
Each example contains:
facts: truth values assigned to variables (e.g.,a is true, b is false, ...)formula: a linear formula without parentheses (e.g.,a and b implies c or d)num_operators: the number of logical operators in the formulagold_formula: the overall truth value of the formula (TrueorFalse)
All duplicate (facts, formula) pairs have been removed to ensure that each combination is unique.
The dataset is designed for training models on logical reasoning, linear probing, or LLMs to predict the truth value of formulas.
Data Fields
| Column | Type | Description |
|---|---|---|
| facts | string | Boolean values assigned to variables |
| formula | string | Linear formula without parentheses |
| num_operators | int | Number of logical operators in the formula |
| gold_formula | bool | Truth value of the full formula |
num_operators counts (both in train and in test)
| num_operators | train_count | test_count |
|---|---|---|
| 1 | 730 | 196 |
| 2 | 775 | 225 |
| 3 | 811 | 189 |
| 4 | 814 | 186 |
| 5 | 788 | 212 |
| 6 | 799 | 201 |
| 7 | 788 | 212 |
| 8 | 800 | 200 |
| 9 | 808 | 192 |
| 10 | 795 | 205 |
| 11 | 806 | 194 |
| 12 | 787 | 213 |
| 13 | 817 | 183 |
| 14 | 806 | 194 |
| 15 | 817 | 183 |
| 16 | 819 | 181 |
| 17 | 815 | 185 |
| 18 | 793 | 207 |
| 19 | 778 | 222 |
| 20 | 795 | 205 |
Note: All duplicate (facts, formula) pairs have been removed to ensure each example is unique.
Example
facts,formula,num_operators,gold_formula
"a is true, b is false, c is true","a and b or c implies d",5,True
"p is false, q is true","p or q implies r",2,False
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Size of downloaded dataset files:
1.23 MB
Size of the auto-converted Parquet files:
1.23 MB
Number of rows:
19,926