Datasets:
tasksource
/
logical-entailment

Dataset card Data Studio Files 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
~((((k|(a|k))>k)|~(~(((x&x)|k)))))
(x>k)
1
1
1
1
entailment
(x&a)
(x|k)
1
1
0
0
entailment
~((((k|(a|k))>k)|~(~(((x&x)|k)))))
(x|k)
0
1
1
0
not entailment
(x&a)
(x>k)
0
1
0
0
not entailment
(((x|a)&k)|(a&(k|k)))
(k|~((~(~((x>x)))|(~((k|~(k)))>k))))
1
0
1
0
entailment
(((a>a)&x)&((a&k)|(k|a)))
(x|x)
1
1
1
1
entailment
(((x|a)&k)|(a&(k|k)))
(x|x)
0
1
1
1
not entailment
(((a>a)&x)&((a&k)|(k|a)))
(k|~((~(~((x>x)))|(~((k|~(k)))>k))))
0
0
1
0
not entailment
~(~(((~((k>x))|(x>(k|k)))>(x&x))))
(~(k)>((a>~(a))>(x|x)))
1
1
0
0
entailment
((~(x)|a)&~((a|k)))
~(k)
1
1
1
1
entailment
~(~(((~((k>x))|(x>(k|k)))>(x&x))))
~(k)
0
1
1
1
not entailment
((~(x)|a)&~((a|k)))
(~(k)>((a>~(a))>(x|x)))
0
0
1
0
not entailment
((~(a)>(x|a))&a)
(((k|a)&(a&k))|(a|((a|(k|x))&a)))
1
0
0
0
entailment
~(a)
~(((a|a)&(x|(a|x))))
1
0
0
0
entailment
((~(a)>(x|a))&a)
~(((a|a)&(x|(a|x))))
0
0
1
0
not entailment
~(a)
(((k|a)&(a&k))|(a|((a|(k|x))&a)))
0
0
0
0
not entailment
~(((a>k)|x))
(k>((a>a)>a))
1
1
1
0
entailment
~(((k|(x>~(x)))>(x>a)))
(~((k>(k&~(((x>k)|x)))))&(k&x))
1
0
1
0
entailment
~(((a>k)|x))
(~((k>(k&~(((x>k)|x)))))&(k&x))
0
0
1
0
not entailment
~(((k|(x>~(x)))>(x>a)))
(k>((a>a)>a))
0
1
1
0
not entailment
((x&((k&x)|k))|k)
((~(((k>(~(x)|k))|k))|(a|k))|x)
1
0
0
0
entailment
(x>((~(~(k))>a)&~((x&(x&x)))))
~((~(~((((k>x)&k)|(x&((x>a)>k)))))|x))
1
0
1
0
entailment
((x&((k&x)|k))|k)
~((~(~((((k>x)&k)|(x&((x>a)>k)))))|x))
0
0
0
0
not entailment
(x>((~(~(k))>a)&~((x&(x&x)))))
((~(((k>(~(x)|k))|k))|(a|k))|x)
0
1
1
0
not entailment
((~((a|(k>k)))|(~(a)|(x>k)))&((k>k)>a))
((k|~(x))&(((a&x)>a)|x))
1
1
1
0
entailment
((a|~(k))&x)
(a>(~(((x|(x>a))>k))>x))
1
0
1
0
entailment
((~((a|(k>k)))|(~(a)|(x>k)))&((k>k)>a))
(a>(~(((x|(x>a))>k))>x))
0
1
1
0
not entailment
((a|~(k))&x)
((k|~(x))&(((a&x)>a)|x))
0
0
1
0
not entailment
(((~(x)&~(~(k)))&a)&((a&a)|~((x&k))))
(x>((((k&k)&k)&x)|k))
1
1
1
0
entailment
(((x|k)|~((a&k)))&x)
(((~(x)&k)>x)&((k&x)>x))
1
0
1
0
entailment
(((~(x)&~(~(k)))&a)&((a&a)|~((x&k))))
(((~(x)&k)>x)&((k&x)>x))
0
1
1
0
not entailment
(((x|k)|~((a&k)))&x)
(x>((((k&k)&k)&x)|k))
0
1
1
0
not entailment
((k>a)>k)
(x>((~(k)|~((x>x)))>((a|k)&k)))
1
0
0
0
entailment
~((x>(~(k)&a)))
((x|x)|~(k))
1
1
1
0
entailment
((k>a)>k)
((x|x)|~(k))
0
0
0
0
not entailment
~((x>(~(k)&a)))
(x>((~(k)|~((x>x)))>((a|k)&k)))
0
0
1
0
not entailment
~(~((((x|x)|((x&(a|a))&(x&k)))&k)))
(x|k)
1
1
1
1
entailment
((a|a)&((k&a)>~((x&a))))
((((x&(a&a))&x)>k)>a)
1
1
1
0
entailment
~(~((((x|x)|((x&(a|a))&(x&k)))&k)))
((((x&(a&a))&x)>k)>a)
0
1
1
0
not entailment
((a|a)&((k&a)>~((x&a))))
(x|k)
0
1
1
0
not entailment
((a&(x|k))|(k&x))
(~(~(~(~((k|x)))))|(x&((x>k)>x)))
1
0
1
0
entailment
((a>k)>~(((x|(a>a))>(k|~(a)))))
((a&(k&a))>x)
1
1
1
1
entailment
((a&(x|k))|(k&x))
((a&(k&a))>x)
0
1
1
0
not entailment
((a>k)>~(((x|(a>a))>(k|~(a)))))
(~(~(~(~((k|x)))))|(x&((x>k)>x)))
0
0
1
0
not entailment
((k>x)&(a&k))
((x>k)>(k|x))
1
1
1
1
entailment
(((x>a)>((a&(x&a))>((a|k)&x)))&~(a))
~((((x|x)|k)&(k&a)))
1
1
1
0
entailment
((k>x)&(a&k))
~((((x|x)|k)&(k&a)))
0
0
1
0
not entailment
(((x>a)>((a&(x&a))>((a|k)&x)))&~(a))
((x>k)>(k|x))
0
1
1
0
not entailment
((x>(k>x))&x)
((~((k&a))&(k>k))>~(~(~(~((a|x))))))
1
0
0
0
entailment
((k&a)|k)
(k|((a&k)&((k>(x>~(x)))>(k>(x>k)))))
1
0
0
0
entailment
((x>(k>x))&x)
(k|((a&k)&((k>(x>~(x)))>(k>(x>k)))))
0
0
0
0
not entailment
((k&a)|k)
((~((k&a))&(k>k))>~(~(~(~((a|x))))))
0
0
0
0
not entailment
((((a&(a&x))>x)&~((k&a)))>(a&x))
~((~(((x|k)&a))&((k>k)|k)))
1
1
1
0
entailment
((~((k|(x>a)))|~((a&x)))&a)
(x>k)
1
1
1
0
entailment
((((a&(a&x))>x)&~((k&a)))>(a&x))
(x>k)
0
1
1
1
not entailment
((~((k|(x>a)))|~((a&x)))&a)
~((~(((x|k)&a))&((k>k)|k)))
0
1
1
0
not entailment
~((~((a&a))|(((k>x)|(x&(a&x)))>x)))
(((k>(x&~(x)))>~(((k>a)&(k&a))))&(a|a))
1
0
1
0
entailment
~((a|(k|x)))
((k|a)>k)
1
1
1
0
entailment
~((~((a&a))|(((k>x)|(x&(a&x)))>x)))
((k|a)>k)
0
1
1
0
not entailment
~((a|(k|x)))
(((k>(x&~(x)))>~(((k>a)&(k&a))))&(a|a))
0
0
1
0
not entailment
~((~((a|a))&(k|(k|a))))
~(~((k>a)))
1
1
1
1
entailment
(x&k)
(((k>(x>a))>(a&x))&((((x&k)>x)>(x>k))|k))
1
0
0
0
entailment
~((~((a|a))&(k|(k|a))))
(((k>(x>a))>(a&x))&((((x&k)>x)>(x>k))|k))
0
0
0
0
not entailment
(x&k)
~(~((k>a)))
0
0
0
0
not entailment
~((((k&x)>~((a&a)))&~((x&(a&~(a))))))
(k&((a|(~(k)&k))|(k&x)))
1
1
1
0
entailment
~(a)
~((((a|(a>x))|x)&(((a&a)|a)&k)))
1
0
0
0
entailment
~((((k&x)>~((a&a)))&~((x&(a&~(a))))))
~((((a|(a>x))|x)&(((a&a)|a)&k)))
0
1
1
0
not entailment
~(a)
(k&((a|(~(k)&k))|(k&x)))
0
0
0
0
not entailment
((a|~(a))>(~(((a|(k>k))>a))&k))
((((a|(((k>x)|a)>x))&x)&a)|(a>(k&(x&x))))
1
0
0
0
entailment
(a&(~(((x>x)>k))|(k>a)))
(a&(x>x))
1
1
1
1
entailment
((a|~(a))>(~(((a|(k>k))>a))&k))
(a&(x>x))
0
1
0
0
not entailment
(a&(~(((x>x)>k))|(k>a)))
((((a|(((k>x)|a)>x))&x)&a)|(a>(k&(x&x))))
0
0
1
0
not entailment
(((~((~(t)&c))>u)&(t&~(f)))&(u>(u|c)))
((f>(f>k))>(t|t))
1
1
0
0
entailment
((~(k)&~((~(f)>f)))&u)
~((k&t))
1
1
0
0
entailment
(((~((~(t)&c))>u)&(t&~(f)))&(u>(u|c)))
~((k&t))
0
1
0
0
not entailment
((~(k)&~((~(f)>f)))&u)
((f>(f>k))>(t|t))
0
1
0
0
not entailment
(u&(t&c))
(~((((f&((t&c)&~(f)))>~(k))&t))>(u|c))
1
0
0
0
entailment
~((f|f))
~(((~((k|(c&k)))&(k|f))&((u&c)|(k&k))))
1
0
0
0
entailment
(u&(t&c))
~(((~((k|(c&k)))&(k|f))&((u&c)|(k&k))))
0
0
0
0
not entailment
~((f|f))
(~((((f&((t&c)&~(f)))>~(k))&t))>(u|c))
0
0
0
0
not entailment
(((u>t)&t)&(k>(k&(f>~(t)))))
(((~(k)>~(f))&(u>(u&f)))>((c&f)>t))
1
0
0
0
entailment
((f&~(~(c)))&~(t))
~(~((~(~((f|k)))|(k|u))))
1
0
0
0
entailment
(((u>t)&t)&(k>(k&(f>~(t)))))
~(~((~(~((f|k)))|(k|u))))
0
1
1
0
not entailment
((f&~(~(c)))&~(t))
(((~(k)>~(f))&(u>(u&f)))>((c&f)>t))
0
0
0
0
not entailment
((~(c)&(~(u)>u))&(~((((k|u)>u)|f))>f))
(f>(u&~((c&k))))
1
1
1
0
entailment
(((u>t)>((u|~(t))|t))>c)
(c|(~(f)&u))
1
1
0
0
entailment
((~(c)&(~(u)>u))&(~((((k|u)>u)|f))>f))
(c|(~(f)&u))
0
1
1
0
not entailment
(((u>t)>((u|~(t))|t))>c)
(f>(u&~((c&k))))
0
1
0
0
not entailment
(f&((t>f)|((~(~(k))|(t>c))>(f|k))))
((c&u)>(u>(u&(f&u))))
1
1
0
0
entailment
(((~(~(c))&u)&t)&k)
(((k|c)&t)|~(k))
1
1
1
0
entailment
(f&((t>f)|((~(~(k))|(t>c))>(f|k))))
(((k|c)&t)|~(k))
0
1
1
0
not entailment
(((~(~(c))&u)&t)&k)
((c&u)>(u>(u&(f&u))))
0
1
0
0
not entailment
((~(((k&f)&(k|f)))>k)&(c&(u>f)))
((u&(f|k))>(k&u))
1
1
1
0
entailment
(t&~(c))
(((u&c)|(f>(t|f)))>(((c|u)|c)>~(c)))
1
0
0
0
entailment
((~(((k&f)&(k|f)))>k)&(c&(u>f)))
(((u&c)|(f>(t|f)))>(((c|u)|c)>~(c)))
0
0
0
0
not entailment
(t&~(c))
((u&(f|k))>(k&u))
0
0
0
0
not entailment
((c|u)&(c&(k&c)))
((~((c&f))&(k&~((~(~(t))&u))))|k)
1
0
0
0
entailment
~(((t|c)|~((u&((u&(k>k))|t)))))
((c|t)>(u&~((u|(~(k)|k)))))
1
1
1
0
entailment
((c|u)&(c&(k&c)))
((c|t)>(u&~((u|(~(k)|k)))))
0
0
0
0
not entailment
~(((t|c)|~((u&((u&(k>k))|t)))))
((~((c&f))&(k&~((~(~(t))&u))))|k)
0
0
0
0
not entailment