Datasets:
tasksource
/
logical-entailment

Dataset card Data Studio Files
xet
Community
A
stringlengths
4
41
B
stringlengths
4
41
E
int64
0
1
H1
int64
0
1
H2
int64
0
1
H3
int64
0
1
label
stringclasses
2 values
(((x|(i>((x&i)>r)))|q)>r)
((i|i)>((i|x)&x))
0
1
1
0
not entailment
(((i&i)|r)&((r|(~(q)&r))&i))
(r|(x|((x|q)&r)))
1
1
0
0
entailment
(~((r|(q>x)))&(i|r))
~((i&r))
1
1
1
0
entailment
(((i&i)|r)&((r|(~(q)&r))&i))
~((i&r))
0
1
1
0
not entailment
(~((r|(q>x)))&(i|r))
(r|(x|((x|q)&r)))
0
1
1
0
not entailment
(i|(((r>x)&i)&q))
((x|q)|i)
1
1
1
1
entailment
(r&~((~(((~(r)>i)&(r&r)))&(q|x))))
(r|(q|(x>r)))
1
1
1
0
entailment
(i|(((r>x)&i)&q))
(r|(q|(x>r)))
0
1
1
0
not entailment
(r&~((~(((~(r)>i)&(r&r)))&(q|x))))
((x|q)|i)
0
1
1
0
not entailment
~((~((i|~(~((x>q)))))>r))
((x>((r|x)>(x&i)))>((q|r)>i))
1
1
1
0
entailment
((q&(x|r))&r)
(((x>~(q))>~((i>q)))|q)
1
0
0
0
entailment
~((~((i|~(~((x>q)))))>r))
(((x>~(q))>~((i>q)))|q)
0
1
1
0
not entailment
((q&(x|r))&r)
((x>((r|x)>(x&i)))>((q|r)>i))
0
0
0
0
not entailment
((r|r)|((~(~(~(r)))|(r|r))&(i|r)))
(((x|i)|(q>(r|r)))|(((i>r)>~(~(r)))|x))
1
0
0
0
entailment
(q|q)
((q|r)|(r&(~(x)&x)))
1
0
0
0
entailment
((r|r)|((~(~(~(r)))|(r|r))&(i|r)))
((q|r)|(r&(~(x)&x)))
0
1
0
0
not entailment
(q|q)
(((x|i)|(q>(r|r)))|(((i>r)>~(~(r)))|x))
0
0
0
0
not entailment
((((x>q)>(i|q))|(r&i))>(q|i))
((x>(r|q))|(r|(i&x)))
1
1
1
0
entailment
~((((r>i)|r)&r))
(r>((i|~((x>r)))&(x|q)))
1
0
0
0
entailment
((((x>q)>(i|q))|(r&i))>(q|i))
(r>((i|~((x>r)))&(x|q)))
0
1
1
0
not entailment
~((((r>i)|r)&r))
((x>(r|q))|(r|(i&x)))
0
0
0
0
not entailment
((i&x)&~(~((i&x))))
((~((x|~(((r&i)&(q&i)))))|i)|r)
1
0
0
0
entailment
~((i&(q|i)))
(((i>q)|~(r))|(~(x)&((r|r)&(r|q))))
1
0
0
0
entailment
((i&x)&~(~((i&x))))
(((i>q)|~(r))|(~(x)&((r|r)&(r|q))))
0
0
0
0
not entailment
~((i&(q|i)))
((~((x|~(((r&i)&(q&i)))))|i)|r)
0
0
0
0
not entailment
((q|i)&i)
~(((~((x>(i>r)))>(i>q))&~((~(x)|i))))
1
0
0
0
entailment
~((x>q))
(((q&(q>i))&r)>x)
1
0
0
0
entailment
((q|i)&i)
(((q&(q>i))&r)>x)
0
0
0
0
not entailment
~((x>q))
~(((~((x>(i>r)))>(i>q))&~((~(x)|i))))
0
0
0
0
not entailment
((q&x)&i)
(q|q)
1
1
1
1
entailment
~((((q&i)|i)>((x|((x&q)>r))&((x&i)&x))))
(~(x)&(i&(i|x)))
1
1
1
1
entailment
((q&x)&i)
(~(x)&(i&(i|x)))
0
0
1
0
not entailment
~((((q&i)|i)>((x|((x&q)>r))&((x&i)&x))))
(q|q)
0
1
1
1
not entailment
~(((c|y)|(y&z)))
(y>(h|(c&c)))
1
1
0
0
entailment
((((z|h)|((z&h)&h))&~((h&(y>(h|y)))))>h)
(z>h)
1
1
1
1
entailment
~(((c|y)|(y&z)))
(z>h)
0
1
0
0
not entailment
((((z|h)|((z&h)&h))&~((h&(y>(h|y)))))>h)
(y>(h|(c&c)))
0
1
0
0
not entailment
(c&~(~(~((h>((c>~(y))&z))))))
(~((h>(z&((y&~((c>y)))&(z>c)))))>c)
1
0
1
0
entailment
((~(c)|y)&(c|~(~(h))))
(~((h|((h&h)&(z>c))))|(c>(y&((h|c)&h))))
1
0
0
0
entailment
(c&~(~(~((h>((c>~(y))&z))))))
(~((h|((h&h)&(z>c))))|(c>(y&((h|c)&h))))
0
0
1
0
not entailment
((~(c)|y)&(c|~(~(h))))
(~((h>(z&((y&~((c>y)))&(z>c)))))>c)
0
0
0
0
not entailment
((~(z)|h)&((h|((y>z)|(c&h)))>c))
(z>c)
1
1
1
1
entailment
(y|y)
~(~((y&y)))
1
0
1
1
entailment
((~(z)|h)&((h|((y>z)|(c&h)))>c))
~(~((y&y)))
0
1
1
1
not entailment
(y|y)
(z>c)
0
1
0
0
not entailment
~((y>(z|h)))
(z>(c&z))
1
1
0
0
entailment
(z|~(((c&~(y))>((z>(c>c))>y))))
(((h&z)|(y|(y&~(~((z>c))))))>z)
1
1
0
0
entailment
~((y>(z|h)))
(((h&z)|(y|(y&~(~((z>c))))))>z)
0
0
0
0
not entailment
(z|~(((c&~(y))>((z>(c>c))>y))))
(z>(c&z))
0
1
1
1
not entailment
(~((c>(z>h)))&y)
((~(~(((((z|c)|z)|z)|(y>z))))|~(h))|c)
1
0
1
0
entailment
((y|(y>(h&c)))>h)
(h|h)
1
1
1
1
entailment
(~((c>(z>h)))&y)
(h|h)
0
1
1
0
not entailment
((y|(y>(h&c)))>h)
((~(~(((((z|c)|z)|z)|(y>z))))|~(h))|c)
0
0
0
0
not entailment
~((c>(h>(((y>y)&~(c))&((h|(h>h))|h)))))
(~((~(~(((c>h)>(c>c))))&(c&c)))|(c>h))
1
1
1
0
entailment
~((~(((h&z)&c))>(z|~((h|(h>z))))))
~(z)
1
1
1
1
entailment
~((c>(h>(((y>y)&~(c))&((h|(h>h))|h)))))
~(z)
0
1
0
0
not entailment
~((~(((h&z)&c))>(z|~((h|(h>z))))))
(~((~(~(((c>h)>(c>c))))&(c&c)))|(c>h))
0
0
1
0
not entailment
~(((~(y)&h)|(y>(y>z))))
((h|((y|c)&(y>y)))|(h|(z|(y&h))))
1
0
0
0
entailment
~((y&((z&h)|(z>(y|(c>c))))))
((c|~(c))&((h|y)>~(y)))
1
1
1
1
entailment
~(((~(y)&h)|(y>(y>z))))
((c|~(c))&((h|y)>~(y)))
0
1
0
0
not entailment
~((y&((z&h)|(z>(y|(c>c))))))
((h|((y|c)&(y>y)))|(h|(z|(y&h))))
0
0
1
0
not entailment
(~((c&c))|~(~((y&h))))
(~(((h>~(z))>(c&h)))>(~((c&z))|h))
1
0
0
0
entailment
(c&~(~(y)))
(c|(h&z))
1
1
0
0
entailment
(~((c&c))|~(~((y&h))))
(c|(h&z))
0
1
0
0
not entailment
(c&~(~(y)))
(~(((h>~(z))>(c&h)))>(~((c&z))|h))
0
0
0
0
not entailment
(h&(h&h))
(~(z)>(h|~(c)))
1
0
0
0
entailment
~(((z|((c|y)&h))|~((c&y))))
~((((c>c)&(y|y))&(z&z)))
1
1
1
1
entailment
(h&(h&h))
~((((c>c)&(y|y))&(z&z)))
0
0
0
0
not entailment
~(((z|((c|y)&h))|~((c&y))))
(~(z)>(h|~(c)))
0
1
1
0
not entailment
(h&(z|h))
(((c|z)>h)|~(z))
1
0
0
0
entailment
~(~(((((h>c)>(h>~(y)))&(c|y))|(z&c))))
(((y&c)|h)>((y>y)>(((z&h)>c)|y)))
1
1
1
0
entailment
(h&(z|h))
(((y&c)|h)>((y>y)>(((z&h)>c)|y)))
0
0
0
0
not entailment
~(~(((((h>c)>(h>~(y)))&(c|y))|(z&c))))
(((c|z)>h)|~(z))
0
1
1
0
not entailment
((y>c)&z)
(~((((y|(~(c)>y))&h)|c))>~(y))
1
0
0
0
entailment
((~(z)&(y&y))&(c>y))
((~((z>z))>y)>(z>c))
1
1
1
0
entailment
((y>c)&z)
((~((z>z))>y)>(z>c))
0
0
1
0
not entailment
((~(z)&(y&y))&(c>y))
(~((((y|(~(c)>y))&h)|c))>~(y))
0
0
0
0
not entailment
~((c>(z&c)))
~(((((c>z)>y)|y)&((c|y)>(h&~(c)))))
1
0
0
0
entailment
~(~(((z&y)&(y|c))))
(y&~(~(((y>z)>((~(z)&y)>h)))))
1
0
0
0
entailment
~((c>(z&c)))
(y&~(~(((y>z)>((~(z)&y)>h)))))
0
0
0
0
not entailment
~(~(((z&y)&(y|c))))
~(((((c>z)>y)|y)&((c|y)>(h&~(c)))))
0
0
0
0
not entailment
(((h&(z>(z|c)))>~(((y&z)>y)))&~(z))
(~(((c&z)|~((z|(((z>h)|c)|c)))))&(z>y))
1
0
1
0
entailment
((z&h)&((h>~(h))>(~((~((h|h))&h))>h)))
(c|(((~(~((c>h)))&y)>((h>c)&z))|(h|c)))
1
1
0
0
entailment
(((h&(z>(z|c)))>~(((y&z)>y)))&~(z))
(c|(((~(~((c>h)))&y)>((h>c)&z))|(h|c)))
0
0
1
0
not entailment
((z&h)&((h>~(h))>(~((~((h|h))&h))>h)))
(~(((c&z)|~((z|(((z>h)|c)|c)))))&(z>y))
0
1
0
0
not entailment
~((h&(~(h)>(z|(c|z)))))
~((((y>z)&h)&(z&((y>~(z))>(z&c)))))
1
0
0
0
entailment
((h&(y&c))&(c&c))
(((h>y)&h)&y)
1
1
1
0
entailment
~((h&(~(h)>(z|(c|z)))))
(((h>y)&h)&y)
0
1
0
0
not entailment
((h&(y&c))&(c&c))
~((((y>z)&h)&(z&((y>~(z))>(z&c)))))
0
0
0
0
not entailment
~(((z|c)|((h>y)>c)))
((h|(z>~((y>(h|z)))))|(y&(y&y)))
1
0
1
0
entailment
((h>y)&~((z>((~(y)|h)>y))))
(z|(c&z))
1
1
0
0
entailment
~(((z|c)|((h>y)>c)))
(z|(c&z))
0
1
1
0
not entailment
((h>y)&~((z>((~(y)|h)>y))))
((h|(z>~((y>(h|z)))))|(y&(y&y)))
0
0
1
0
not entailment
~(((y|z)|~((y>y))))
((y&z)>~((~(((h&(h|c))&y))|((h|h)>z))))
1
0
0
0
entailment
~((~(~(((z>c)&y)))>h))
((((y|y)|(h&h))&(z>~(h)))&((h&y)|y))
1
0
1
0
entailment
~(((y|z)|~((y>y))))
((((y|y)|(h&h))&(z>~(h)))&((h&y)|y))
0
0
0
0
not entailment
~((~(~(((z>c)&y)))>h))
((y&z)>~((~(((h&(h|c))&y))|((h|h)>z))))
0
0
1
0
not entailment
~(((l|(q|z))>((l>(l&(l>~(q))))|(z|e))))
((l&q)|(q&~((l&e))))
1
1
1
1
entailment
((z&~(l))&(z|(~(q)&l)))
~(((l|l)&~(e)))
1
1
0
0
entailment
~(((l|(q|z))>((l>(l&(l>~(q))))|(z|e))))
~(((l|l)&~(e)))
0
1
1
0
not entailment