Datasets:

saracandu
/

implications

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 formula
gold_formula: the overall truth value of the formula (True or False)

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

Downloads last month: 40

Size of downloaded dataset files:

1.23 MB

Size of the auto-converted Parquet files:

1.23 MB

Number of rows:

19,926

Collection including saracandu/implications

🧠 reasoning datasets

Collection

A collection of reasoning tasks to benchmark model abilities • 12 items • Updated 12 days ago

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

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