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
(d&g)
((h>a)>(a&a))
0
0
0
0
not entailment
((a|~(~(g)))&((g|(g>(w>g)))&h))
(~(g)>a)
1
1
1
1
entailment
((d>d)>p)
(p|((h&h)>(h&w)))
1
0
0
0
entailment
((a|~(~(g)))&((g|(g>(w>g)))&h))
(p|((h&h)>(h&w)))
0
1
0
0
not entailment
((d>d)>p)
(~(g)>a)
0
1
0
0
not entailment
(((w>w)&(g>p))&(h&p))
(~((~((w|~((d&w))))&(a|g)))&h)
1
0
0
0
entailment
((a>w)>(a|a))
((~((a&a))&d)>(~(g)>a))
1
0
0
0
entailment
(((w>w)&(g>p))&(h&p))
((~((a&a))&d)>(~(g)>a))
0
0
0
0
not entailment
((a>w)>(a|a))
(~((~((w|~((d&w))))&(a|g)))&h)
0
0
0
0
not entailment
((~((w|d))&~((a>(a>~(p)))))&((a>w)>a))
(~((p|~((w|~((h&d))))))>a)
1
1
0
0
entailment
(d&(w>g))
(~(~(((w|a)|w)))>d)
1
0
0
0
entailment
((~((w|d))&~((a>(a>~(p)))))&((a>w)>a))
(~(~(((w|a)|w)))>d)
0
1
1
0
not entailment
(d&(w>g))
(~((p|~((w|~((h&d))))))>a)
0
0
0
0
not entailment
((p|(h>(w|((w|g)>d))))&((~(d)&d)|(p&d)))
((((p>w)>w)&(w|a))|(d|a))
1
1
0
0
entailment
~((((((a>d)>p)|d)|~(~(d)))|~((h>p))))
~(((p>p)&a))
1
1
1
1
entailment
((p|(h>(w|((w|g)>d))))&((~(d)&d)|(p&d)))
~(((p>p)&a))
0
1
0
0
not entailment
~((((((a>d)>p)|d)|~(~(d)))|~((h>p))))
((((p>w)>w)&(w|a))|(d|a))
0
1
0
0
not entailment
~((((a&p)>(a&p))&(g>p)))
(((~((a|p))>w)>((p|g)&w))|(g|(g|g)))
1
0
0
0
entailment
~((w>(~(g)>((g>w)&p))))
((p|w)|a)
1
1
0
0
entailment
~((((a&p)>(a&p))&(g>p)))
((p|w)|a)
0
1
0
0
not entailment
~((w>(~(g)>((g>w)&p))))
(((~((a|p))>w)>((p|g)&w))|(g|(g|g)))
0
0
0
0
not entailment
(~(~(p))>~((p&p)))
~(((p&((h|(w|((d&w)|(d>d))))&h))&(a>g)))
1
0
0
0
entailment
(((w&a)&~((a>~(h))))&(g|h))
~(~((~(~((g>~(d))))>(~(d)>a))))
1
0
0
0
entailment
(~(~(p))>~((p&p)))
~(~((~(~((g>~(d))))>(~(d)>a))))
0
0
0
0
not entailment
(((w&a)&~((a>~(h))))&(g|h))
~(((p&((h|(w|((d&w)|(d>d))))&h))&(a>g)))
0
0
0
0
not entailment
~(((w|(d&~(~((g|a)))))|p))
(~(w)|(a&(d|w)))
1
1
1
0
entailment
((~(p)>p)&((a|(w&h))>d))
(h|(p&p))
1
1
1
0
entailment
~(((w|(d&~(~((g|a)))))|p))
(h|(p&p))
0
1
0
0
not entailment
((~(p)>p)&((a|(w&h))>d))
(~(w)|(a&(d|w)))
0
1
1
0
not entailment
(w&~(h))
((~((w>p))&(h&~(p)))>(g&w))
1
0
0
0
entailment
~(~((h&~(((~(d)&(d>g))|(p&d))))))
(((p&w)|g)>(((g>a)&p)|(d|h)))
1
1
0
0
entailment
(w&~(h))
(((p&w)|g)>(((g>a)&p)|(d|h)))
0
0
0
0
not entailment
~(~((h&~(((~(d)&(d>g))|(p&d))))))
((~((w>p))&(h&~(p)))>(g&w))
0
1
0
0
not entailment
((w|h)&(w&(((w>p)>g)&g)))
(~(p)>(w|a))
1
1
0
0
entailment
((w|h)&(w&(((w>p)>g)&g)))
(g>h)
0
1
1
0
not entailment
~(g)
(~(p)>(w|a))
0
0
0
0
not entailment
((~((p|h))>d)&a)
(((h|a)&(h>(g&h)))>(d>a))
1
0
0
0
entailment
((p>p)&h)
(g|((w>a)>h))
1
0
0
0
entailment
((~((p|h))>d)&a)
(g|((w>a)>h))
0
1
0
0
not entailment
((p>p)&h)
(((h|a)&(h>(g&h)))>(d>a))
0
0
0
0
not entailment
(~(~((~(~(d))>(w|p))))>(~((a|p))|d))
(d|((g>(a>d))|(w>(d|p))))
1
1
0
0
entailment
(w&(~((p>p))|((p>(~(w)>w))&(h&a))))
~((g&~(w)))
1
1
0
0
entailment
(~(~((~(~(d))>(w|p))))>(~((a|p))|d))
~((g&~(w)))
0
1
0
0
not entailment
(w&(~((p>p))|((p>(~(w)>w))&(h&a))))
(d|((g>(a>d))|(w>(d|p))))
0
1
0
0
not entailment
((((w>a)>a)&((g|~(~(a)))|(g>(g|g))))>d)
((((a>d)|g)|(p|(a>h)))|(a>h))
1
1
0
0
entailment
~(d)
((w>p)|((p>(g&p))&((a&d)>p)))
1
0
0
0
entailment
((((w>a)>a)&((g|~(~(a)))|(g>(g|g))))>d)
((w>p)|((p>(g&p))&((a&d)>p)))
0
1
0
0
not entailment
~(d)
((((a>d)|g)|(p|(a>h)))|(a>h))
0
0
0
0
not entailment
(((z|((z&x)|(x&(x&z))))>(z>z))&(x&x))
((x|((x>z)>x))&(z>x))
1
1
1
1
entailment
(z&(z>z))
(((z&z)|(~((x>(x>z)))>z))|(z|((z>x)&z)))
1
0
0
0
entailment
(((z|((z&x)|(x&(x&z))))>(z>z))&(x&x))
(((z&z)|(~((x>(x>z)))>z))|(z|((z>x)&z)))
0
0
1
1
not entailment
(z&(z>z))
((x|((x>z)>x))&(z>x))
0
0
0
0
not entailment
((((z>(x>z))|x)&(z>((z|x)>z)))>x)
((x&x)&((x&x)&(x|(z|x))))
1
1
1
1
entailment
((z>~((x&z)))>z)
(z|(x&~(x)))
1
1
1
0
entailment
((((z>(x>z))|x)&(z>((z|x)>z)))>x)
(z|(x&~(x)))
0
1
1
1
not entailment
((z>~((x&z)))>z)
((x&x)&((x&x)&(x|(z|x))))
0
0
1
1
not entailment
((((x|~(((x|x)>z)))&(~((x|z))>x))|x)&x)
~((x>(~(x)&z)))
1
1
1
1
entailment
(z|(z&z))
(x>z)
1
1
0
0
entailment
((((x|~(((x|x)>z)))&(~((x|z))>x))|x)&x)
(x>z)
0
1
1
0
not entailment
(z|(z&z))
~((x>(~(x)&z)))
0
0
0
0
not entailment
((z&x)&x)
(((z|z)|(z&x))|((x&z)|(z&z)))
1
0
1
1
entailment
((x>(z&(x&x)))>(z>~((z>z))))
(z>~(((x>x)&z)))
1
1
1
1
entailment
((z&x)&x)
(z>~(((x>x)&z)))
0
0
1
0
not entailment
((x>(z&(x&x)))>(z>~((z>z))))
(((z|z)|(z&x))|((x&z)|(z&z)))
0
1
1
1
not entailment
(z&x)
~(~((((x&z)&x)|~((x|z)))))
1
0
1
0
entailment
~((~((z>z))|(((z&(z&z))|(z>x))>(x>z))))
(x>(z>((z|x)&~(z))))
1
1
1
0
entailment
(z&x)
(x>(z>((z|x)&~(z))))
0
0
1
0
not entailment
~((~((z>z))|(((z&(z&z))|(z>x))>(x>z))))
~(~((((x&z)&x)|~((x|z)))))
0
1
1
0
not entailment
((x>~((z&(x|x))))>~((x>x)))
((~(z)|(x&x))&(x>x))
1
1
1
0
entailment
(~((x|x))&~(~((z|(z|(x&(x|z)))))))
(x>~((x|(z&x))))
1
1
1
0
entailment
((x>~((z&(x|x))))>~((x>x)))
(x>~((x|(z&x))))
0
1
1
0
not entailment
(~((x|x))&~(~((z|(z|(x&(x|z)))))))
((~(z)|(x&x))&(x>x))
0
1
1
0
not entailment
(z>~((z>~(x))))
(z>(x&(z|z)))
1
1
1
1
entailment
((~((x|(z&(x>x))))|z)&(x|z))
~(~(((((x|z)&z)|x)|x)))
1
1
1
1
entailment
(z>~((z>~(x))))
~(~(((((x|z)&z)|x)|x)))
0
0
1
1
not entailment
((~((x|(z&(x>x))))|z)&(x|z))
(z>(x&(z|z)))
0
1
1
1
not entailment
(x|x)
(~((z>z))|x)
1
0
0
0
entailment
~(~(~((z&(z>z)))))
(x>~(z))
1
1
0
0
entailment
(x|x)
(x>~(z))
0
0
0
0
not entailment
~(~(~((z&(z>z)))))
(~((z>z))|x)
0
1
0
0
not entailment
(((x>((z>x)|z))&(((x|z)>(z|z))|x))>x)
(((z&x)>z)>x)
1
1
1
1
entailment
(z&~(~((x>x))))
(((x|z)>z)|z)
1
1
1
0
entailment
(((x>((z>x)|z))&(((x|z)>(z|z))|x))>x)
(((x|z)>z)|z)
0
1
1
1
not entailment
(z&~(~((x>x))))
(((z&x)>z)>x)
0
1
1
0
not entailment
(x>~((x>(x|z))))
((((x&x)|(x&x))|((z|x)&(x&x)))>z)
1
0
1
0
entailment
(x&(x>x))
((((x>z)>(z&~((x&z))))&x)|z)
1
0
0
0
entailment
(x>~((x>(x|z))))
((((x>z)>(z&~((x&z))))&x)|z)
0
0
1
0
not entailment
(x&(x>x))
((((x&x)|(x&x))|((z|x)&(x&x)))>z)
0
0
0
0
not entailment
~(((~((z&(z|x)))&~((x|(z>x))))|x))
((~((z&z))&x)>((z&z)&(z&(x>x))))
1
1
1
1
entailment
((x|z)&x)
((((x&z)>z)>x)|(z|~((z>~((z&z))))))
1
0
1
0
entailment
~(((~((z&(z|x)))&~((x|(z>x))))|x))
((((x&z)>z)>x)|(z|~((z>~((z&z))))))
0
1
1
1
not entailment
((x|z)&x)
((~((z&z))&x)>((z&z)&(z&(x>x))))
0
0
1
0
not entailment
(x&z)
~(~(((x>((z>z)&z))&(z&(z&(z|x))))))
1
0
1
0
entailment
~(((~(x)|x)>x))
(((z&(z|x))|x)>((z>(x&z))>~(z)))
1
0
0
0
entailment
(x&z)
(((z&(z|x))|x)>((z>(x&z))>~(z)))
0
0
1
0
not entailment
~(((~(x)|x)>x))
~(~(((x>((z>z)&z))&(z&(z&(z|x))))))
0
0
0
0
not entailment
~(~(((z|(z|(x&z)))&(z|x))))
(((z|(x>(x>(z>x))))&(z>x))>x)
1
1
1
0
entailment
((~(z)&z)|~(~((~(x)&~((x|x))))))
~((((z>x)&(z|x))|x))
1
1
1
1
entailment
~(~(((z|(z|(x&z)))&(z|x))))
~((((z>x)&(z|x))|x))
0
1
1
0
not entailment
((~(z)&z)|~(~((~(x)&~((x|x))))))
(((z|(x>(x>(z>x))))&(z>x))>x)
0
1
1
0
not entailment