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
(a&~(o))
(l|(y|a))
1
1
0
0
entailment
(~((k>y))|o)
(l|(y|a))
0
1
0
0
not entailment
(a&~(o))
(((~(~(~(o)))>a)&~(o))>~((~(k)&a)))
0
0
0
0
not entailment
(((k|a)&((k|y)>((l&a)&(a&a))))&y)
(~(~((((o&y)|(k|a))|y)))|o)
1
1
0
0
entailment
(((o|y)|a)>~((~(a)>((k>o)&o))))
(a>(~(a)|o))
1
1
1
0
entailment
(((k|a)&((k|y)>((l&a)&(a&a))))&y)
(a>(~(a)|o))
0
1
0
0
not entailment
(((o|y)|a)>~((~(a)>((k>o)&o))))
(~(~((((o&y)|(k|a))|y)))|o)
0
1
1
0
not entailment
(~(~((~((l&l))>(a>y))))&(a&((l|l)>l)))
(y>~(~(((o&~(~((y|(y&k)))))>a))))
1
1
0
0
entailment
((o|o)&k)
((k|y)&(a|(y>y)))
1
0
0
0
entailment
(~(~((~((l&l))>(a>y))))&(a&((l|l)>l)))
((k|y)&(a|(y>y)))
0
1
0
0
not entailment
((o|o)&k)
(y>~(~(((o&~(~((y|(y&k)))))>a))))
0
0
0
0
not entailment
(k&((y&y)>(l>y)))
((((~((l>y))>a)|o)>k)>((l>(l>k))&k))
1
0
0
0
entailment
(((k&~((a>l)))>((a>o)&o))&~((y|~(l))))
((y|(o|y))>(l|((o>((l|~(y))>(l&a)))|l)))
1
1
1
0
entailment
(k&((y&y)>(l>y)))
((y|(o|y))>(l|((o>((l|~(y))>(l&a)))|l)))
0
0
0
0
not entailment
(((k&~((a>l)))>((a>o)&o))&~((y|~(l))))
((((~((l>y))>a)|o)>k)>((l>(l>k))&k))
0
1
1
0
not entailment
(((y>o)&(a>(l>l)))>((a|l)&y))
(o|y)
1
1
1
0
entailment
(~((k|(y|((k|y)&l))))&l)
(k>o)
1
1
0
0
entailment
(((y>o)&(a>(l>l)))>((a|l)&y))
(k>o)
0
1
0
0
not entailment
(~((k|(y|((k|y)&l))))&l)
(o|y)
0
1
0
0
not entailment
((~(~(((y&(k|l))>l)))&(k&o))&(l>a))
(y|(((a|(l>o))>(~(a)>((l&y)&l)))>(l>o)))
1
0
1
0
entailment
~((~(((l>k)|o))>~(((a&k)|(a>o)))))
(l&((k&(o|o))>(l>o)))
1
1
1
0
entailment
((~(~(((y&(k|l))>l)))&(k&o))&(l>a))
(l&((k&(o|o))>(l>o)))
0
1
1
0
not entailment
~((~(((l>k)|o))>~(((a&k)|(a>o)))))
(y|(((a|(l>o))>(~(a)>((l&y)&l)))>(l>o)))
0
0
0
0
not entailment
(a&((k|o)|~((a&(y|(l>a))))))
((o&y)>(l|((k|a)>a)))
1
1
1
0
entailment
((~((k&a))&(k>(y|~(y))))>(y&k))
(y>k)
1
1
1
1
entailment
(a&((k|o)|~((a&(y|(l>a))))))
(y>k)
0
1
1
1
not entailment
((~((k&a))&(k>(y|~(y))))>(y&k))
((o&y)>(l|((k|a)>a)))
0
1
0
0
not entailment
((o&o)|k)
(y|~(~(((k|(y|~(~(l))))|o))))
1
0
0
0
entailment
~(((o>y)>(l|a)))
((~(o)>o)|(a>~(a)))
1
0
1
0
entailment
((o&o)|k)
((~(o)>o)|(a>~(a)))
0
0
0
0
not entailment
~(((o>y)>(l|a)))
(y|~(~(((k|(y|~(~(l))))|o))))
0
0
0
0
not entailment
(a&y)
(k>a)
1
1
0
0
entailment
((a>(l>k))&(y&o))
(l|o)
1
1
1
0
entailment
(a&y)
(l|o)
0
1
0
0
not entailment
((a>(l>k))&(y&o))
(k>a)
0
1
1
0
not entailment
(((k&a)&(~(y)&l))&~(~(o)))
(o&a)
1
1
1
1
entailment
~((k|((a|~((k|~(k))))&~(l))))
~(~(~((k|k))))
1
1
1
1
entailment
(((k&a)&(~(y)&l))&~(~(o)))
~(~(~((k|k))))
0
1
1
0
not entailment
~((k|((a|~((k|~(k))))&~(l))))
(o&a)
0
1
0
0
not entailment
(o&k)
(((o|(o>a))>((k|o)|(l>y)))>k)
1
0
0
0
entailment
~((l|~(y)))
(a>y)
1
1
0
0
entailment
(o&k)
(a>y)
0
1
0
0
not entailment
~((l|~(y)))
(((o|(o>a))>((k|o)|(l>y)))>k)
0
0
0
0
not entailment
((o>a)&(((a&k)|l)&k))
((a>((o>l)>a))>(y|k))
1
1
0
0
entailment
(a&((l|~(o))&(~(a)|(k>~(a)))))
~(~((k>a)))
1
1
1
1
entailment
((o>a)&(((a&k)|l)&k))
~(~((k>a)))
0
1
1
0
not entailment
(a&((l|~(o))&(~(a)|(k>~(a)))))
((a>((o>l)>a))>(y|k))
0
1
0
0
not entailment
~(((l&l)>((o>y)&o)))
(~((((((y|y)|o)&(a|o))&l)>a))|(o|l))
1
0
0
0
entailment
(~(l)&~(~((~((k|(y&o)))|~(a)))))
(((~(a)&l)&l)>a)
1
1
1
0
entailment
~(((l&l)>((o>y)&o)))
(((~(a)&l)&l)>a)
0
1
0
0
not entailment
(~(l)&~(~((~((k|(y&o)))|~(a)))))
(~((((((y|y)|o)&(a|o))&l)>a))|(o|l))
0
1
1
0
not entailment
(((a|a)|a)&(y>k))
(l|a)
1
1
0
0
entailment
~(~(((((k>k)|(k&o))|l)>o)))
(k>~(~((o|o))))
1
1
1
1
entailment
(((a|a)|a)&(y>k))
(k>~(~((o|o))))
0
1
0
0
not entailment
~(~(((((k>k)|(k&o))|l)>o)))
(l|a)
0
1
0
0
not entailment
(k&(~(k)|l))
~(~((l|~(~(a)))))
1
0
0
0
entailment
(((o>o)|a)&~(o))
(o>~((y|k)))
1
1
0
0
entailment
(k&(~(k)|l))
(o>~((y|k)))
0
1
0
0
not entailment
(((o>o)|a)&~(o))
~(~((l|~(~(a)))))
0
0
0
0
not entailment
((((o&a)>(k>(o>y)))&l)&(l|((a|l)&l)))
((((o&l)&k)&~(o))|l)
1
1
1
0
entailment
((k&a)&((k|a)&k))
~(~((o|((k>k)>((k>a)|o)))))
1
0
0
0
entailment
((((o&a)>(k>(o>y)))&l)&(l|((a|l)&l)))
~(~((o|((k>k)>((k>a)|o)))))
0
1
1
0
not entailment
((k&a)&((k|a)&k))
((((o&l)&k)&~(o))|l)
0
0
0
0
not entailment
(((a&a)>(k>~((l&y))))>(k|(k&k)))
(k|((o>~(o))&l))
1
1
0
0
entailment
((l&(l&o))&((a|y)>~((l&l))))
(~(a)>l)
1
1
1
0
entailment
(((a&a)>(k>~((l&y))))>(k|(k&k)))
(~(a)>l)
0
1
1
1
not entailment
((l&(l&o))&((a|y)>~((l&l))))
(k|((o>~(o))&l))
0
1
0
0
not entailment
(q&x)
(q&(x>q))
1
0
1
0
entailment
(e&(x>(e|x)))
(((x&x)&x)>((q>e)&x))
1
0
0
0
entailment
(q&x)
(((x&x)&x)>((q>e)&x))
0
0
0
0
not entailment
(e&(x>(e|x)))
(q&(x>q))
0
1
0
0
not entailment
((((q|x)>(q>x))&(q>((x&x)&q)))>e)
(((x&q)&x)>(q>(q&e)))
1
1
1
1
entailment
(x&~(~(q)))
(x|e)
1
1
0
0
entailment
((((q|x)>(q>x))&(q>((x&x)&q)))>e)
(x|e)
0
1
1
1
not entailment
(x&~(~(q)))
(((x&q)&x)>(q>(q&e)))
0
0
0
0
not entailment
((((x>x)|x)>((x>~((x&q)))>~((q>e))))&e)
((q>q)&e)
1
1
1
0
entailment
(~(~(~(((((e&e)|e)|(e&e))&(q|x)))))&x)
~(e)
1
1
1
1
entailment
((((x>x)|x)>((x>~((x&q)))>~((q>e))))&e)
~(e)
0
1
1
1
not entailment
(~(~(~(((((e&e)|e)|(e&e))&(q|x)))))&x)
((q>q)&e)
0
1
1
0
not entailment
~((e>(~((x|q))&~(((e&(q|e))>~(x))))))
(e&(e|e))
1
1
1
1
entailment
~(~(~((x>e))))
(q|((e|e)>~(x)))
1
1
0
0
entailment
~((e>(~((x|q))&~(((e&(q|e))>~(x))))))
(q|((e|e)>~(x)))
0
1
1
1
not entailment
~(~(~((x>e))))
(e&(e|e))
0
1
1
0
not entailment
(((e&q)&e)&(e|(q&e)))
(q|((((q>x)|q)|q)>~((~(~(x))>x))))
1
0
0
0
entailment
(((((x|x)&(e&x))|(e|(e|x)))&~((q|q)))&e)
(((x>x)|q)&((~(x)&q)>x))
1
1
1
0
entailment
(((e&q)&e)&(e|(q&e)))
(((x>x)|q)&((~(x)&q)>x))
0
0
0
0
not entailment
(((((x|x)&(e&x))|(e|(e|x)))&~((q|q)))&e)
(q|((((q>x)|q)|q)>~((~(~(x))>x))))
0
1
1
0
not entailment
~(~((((e>(x>e))>q)&x)))
(((~(e)>q)|e)>(x&(x>q)))
1
1
1
0
entailment
((x|e)&~(((x>q)>q)))
(e&(e>(~((q|e))>(e|q))))
1
0
1
0
entailment
~(~((((e>(x>e))>q)&x)))
(e&(e>(~((q|e))>(e|q))))
0
1
1
1
not entailment
((x|e)&~(((x>q)>q)))
(((~(e)>q)|e)>(x&(x>q)))
0
0
1
0
not entailment
((q&~(e))&(~(((q>e)|(~((q&e))&e)))|e))
((q|x)>((x>q)&(~(q)|~(e))))
1
1
0
0
entailment
((q|((q|e)&(q|e)))>~((e|(e>e))))
((~(x)|((~(x)&e)|x))&~(~(~(q))))
1
0
0
0
entailment
((q&~(e))&(~(((q>e)|(~((q&e))&e)))|e))
((~(x)|((~(x)&e)|x))&~(~(~(q))))
0
1
0
0
not entailment
((q|((q|e)&(q|e)))>~((e|(e>e))))
((q|x)>((x>q)&(~(q)|~(e))))
0
1
0
0
not entailment
((e&(x&e))&~((q&(e>q))))
((~((q|q))&((x&~(x))>q))>(q|((e|x)|q)))
1
0
1
0
entailment
~(~(((q&(x|e))|~((~((x&q))&x)))))
(x>((x>x)&((q|e)&(~(q)>q))))
1
1
1
1
entailment
((e&(x&e))&~((q&(e>q))))
(x>((x>x)&((q|e)&(~(q)>q))))
0
0
1
0
not entailment
~(~(((q&(x|e))|~((~((x&q))&x)))))
((~((q|q))&((x&~(x))>q))>(q|((e|x)|q)))
0
0
1
0
not entailment
((e&~((e>q)))|((e&e)&q))
(~(((x&q)>q))|e)
1
1
0
0
entailment