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
~((u&~(~(u))))
((u|u)|((u>u)&(u|(u|u))))
0
0
1
0
not entailment
(~(~(((u|u)&u)))|(~((u|u))&(u|u)))
(~((u&((u|~((u>u)))>~(u))))>((u>u)>u))
1
0
1
1
entailment
(((u&u)|u)>~(u))
((u>u)>~((u&u)))
1
1
1
0
entailment
(~(~(((u|u)&u)))|(~((u|u))&(u|u)))
((u>u)>~((u&u)))
0
1
1
1
not entailment
(((u&u)|u)>~(u))
(~((u&((u|~((u>u)))>~(u))))>((u>u)>u))
0
0
1
0
not entailment
(~((y&y))>y)
(y|y)
1
1
1
1
entailment
~(((y&y)|(y&~(((y>y)>(y>y))))))
((y>(y|y))&~(y))
1
1
1
1
entailment
(~((y&y))>y)
((y>(y|y))&~(y))
0
0
1
0
not entailment
~(((y&y)|(y&~(((y>y)>(y>y))))))
(y|y)
0
1
1
1
not entailment
((y>(y|(y>y)))&(y&y))
((((~(y)&y)|y)>~(y))>y)
1
0
1
1
entailment
~(y)
((y&y)>~(~(~(y))))
1
0
1
1
entailment
((y>(y|(y>y)))&(y&y))
((y&y)>~(~(~(y))))
0
1
1
1
not entailment
~(y)
((((~(y)&y)|y)>~(y))>y)
0
0
1
0
not entailment
(y|(~((~(y)|y))|~((((y>y)>y)>~(y)))))
(y&(y|(y&(y>y))))
1
1
1
1
entailment
~(y)
~((((y|((y|y)>y))>y)&y))
1
0
1
0
entailment
(y|(~((~(y)|y))|~((((y>y)>y)>~(y)))))
~((((y|((y|y)>y))>y)&y))
0
1
1
1
not entailment
~(y)
(y&(y|(y&(y>y))))
0
0
1
0
not entailment
(y&y)
((~(~((~(y)>y)))&y)|(y|y))
1
0
1
1
entailment
~(((((~((y&y))|y)>(y|y))&(y|y))|(y&y)))
(~(y)&((y|(y&(y&y)))>(y>(~(y)>y))))
1
1
1
1
entailment
(y&y)
(~(y)&((y|(y&(y&y)))>(y>(~(y)>y))))
0
0
1
0
not entailment
~(((((~((y&y))|y)>(y|y))&(y|y))|(y&y)))
((~(~((~(y)>y)))&y)|(y|y))
0
1
1
1
not entailment
~(~((~(y)&~((~(~(((y>y)>y)))&y)))))
~(((~(y)&~(y))>~((y>(y|y)))))
1
1
1
1
entailment
(y|(((y>y)>~((y>y)))|~(((y|y)>(y|y)))))
((y|y)|y)
1
1
1
1
entailment
~(~((~(y)&~((~(~(((y>y)>y)))&y)))))
((y|y)|y)
0
1
1
1
not entailment
(y|(((y>y)>~((y>y)))|~(((y|y)>(y|y)))))
~(((~(y)&~(y))>~((y>(y|y)))))
0
1
1
1
not entailment
((x&o)&(c>x))
(((p&x)>o)|((o>c)&(u>(r>c))))
1
0
0
0
entailment
(u&h)
((p|u)>((u&u)|u))
1
0
0
0
entailment
((x&o)&(c>x))
((p|u)>((u&u)|u))
0
0
0
0
not entailment
(u&h)
(((p&x)>o)|((o>c)&(u>(r>c))))
0
0
0
0
not entailment
(((o>~(u))>~(p))&~(f))
(y>~(f))
1
1
0
0
entailment
(~(~((o>o)))>u)
((h&(x&r))|u)
1
1
0
0
entailment
(((o>~(u))>~(p))&~(f))
((h&(x&r))|u)
0
1
0
0
not entailment
(~(~((o>o)))>u)
(y>~(f))
0
1
0
0
not entailment
(p&r)
(f>(((y|(y&o))>p)|(f>~((p>~(c))))))
1
0
0
0
entailment
(((c&o)&(~(u)|u))&f)
(~(~(~(~((o|(y&p))))))|f)
1
0
0
0
entailment
(p&r)
(~(~(~(~((o|(y&p))))))|f)
0
0
0
0
not entailment
(((c&o)&(~(u)|u))&f)
(f>(((y|(y&o))>p)|(f>~((p>~(c))))))
0
0
0
0
not entailment
(p&(o&((u>c)|(y>((r&x)&h)))))
(o|x)
1
1
1
1
entailment
(f&~(((y>h)|c)))
~(c)
1
1
1
1
entailment
(p&(o&((u>c)|(y>((r&x)&h)))))
~(c)
0
1
1
0
not entailment
(f&~(((y>h)|c)))
(o|x)
0
1
0
0
not entailment
(f&(x>h))
((~((((h|(f&(y>x)))|h)|f))&(~(o)&p))>x)
1
0
0
0
entailment
~((((o>p)|r)>f))
(r>(((~(~(c))|r)&~(x))|~(f)))
1
0
0
0
entailment
(f&(x>h))
(r>(((~(~(c))|r)&~(x))|~(f)))
0
0
0
0
not entailment
~((((o>p)|r)>f))
((~((((h|(f&(y>x)))|h)|f))&(~(o)&p))>x)
0
0
0
0
not entailment
(~(~(u))&(~(y)&~(~(((h|o)&f)))))
(o|(c>h))
1
1
0
0
entailment
(~((~((o>x))|(((c|f)&h)&((c&y)&y))))&p)
((f|o)>(~((x|(o|p)))>(u>(h>c))))
1
1
0
0
entailment
(~(~(u))&(~(y)&~(~(((h|o)&f)))))
((f|o)>(~((x|(o|p)))>(u>(h>c))))
0
1
0
0
not entailment
(~((~((o>x))|(((c|f)&h)&((c&y)&y))))&p)
(o|(c>h))
0
1
1
0
not entailment
(h&((o&c)|(y>((r|p)&(o&u)))))
((~(h)&(o>h))>(x&h))
1
1
0
0
entailment
~(((~(r)&c)|~((((o&c)>x)&f))))
(y>f)
1
1
0
0
entailment
(h&((o&c)|(y>((r|p)&(o&u)))))
(y>f)
0
1
0
0
not entailment
~(((~(r)&c)|~((((o&c)>x)&f))))
((~(h)&(o>h))>(x&h))
0
1
0
0
not entailment
(((u&y)|((y&o)>r))&h)
(h|h)
1
1
1
1
entailment
~((((h|~((o>c)))|(h|y))>h))
(h>((r&h)>(f>~(o))))
1
1
0
0
entailment
(((u&y)|((y&o)>r))&h)
(h>((r&h)>(f>~(o))))
0
1
0
0
not entailment
~((((h|~((o>c)))|(h|y))>h))
(h|h)
0
1
1
1
not entailment
(((o&(c&(r>u)))&~(~(h)))&r)
~(~(u))
1
1
1
1
entailment
~(((o>(y|f))>h))
~((h&(x&r)))
1
1
0
0
entailment
(((o&(c&(r>u)))&~(~(h)))&r)
~((h&(x&r)))
0
1
0
0
not entailment
~(((o>(y|f))>h))
~(~(u))
0
1
0
0
not entailment
((u&(~(h)>f))&(~(((y>o)|u))|p))
((f|p)|~(~(~(~((~(y)&f))))))
1
1
1
0
entailment
(((h&o)&(c|o))&((h&(o>r))>((u>(r|x))|y)))
((((f|~(u))>f)|~(u))>(c|o))
1
1
0
0
entailment
((u&(~(h)>f))&(~(((y>o)|u))|p))
((((f|~(u))>f)|~(u))>(c|o))
0
1
0
0
not entailment
(((h&o)&(c|o))&((h&(o>r))>((u>(r|x))|y)))
((f|p)|~(~(~(~((~(y)&f))))))
0
1
0
0
not entailment
~((o|((y>~(c))>((x|p)>x))))
(o>((y>r)>~(((x|r)&~(~((r&p)))))))
1
0
0
0
entailment
(((p&y)|o)&x)
(r|(h|x))
1
1
0
0
entailment
~((o|((y>~(c))>((x|p)>x))))
(r|(h|x))
0
1
0
0
not entailment
(((p&y)|o)&x)
(o>((y>r)>~(((x|r)&~(~((r&p)))))))
0
0
0
0
not entailment
(p>~(~(u)))
(((p&o)>((c>(~(p)|h))&r))|u)
1
0
0
0
entailment
~((~(((f|f)&o))|y))
~(~((y>~(~((o>c))))))
1
0
0
0
entailment
(p>~(~(u)))
~(~((y>~(~((o>c))))))
0
0
0
0
not entailment
~((~(((f|f)&o))|y))
(((p&o)>((c>(~(p)|h))&r))|u)
0
0
0
0
not entailment
((o>(r>y))&(f&r))
((~(r)|((h>~(r))|r))>~(~(f)))
1
0
0
0
entailment
(p&o)
(((y|y)|y)|(p|h))
1
0
0
0
entailment
((o>(r>y))&(f&r))
(((y|y)|y)|(p|h))
0
1
0
0
not entailment
(p&o)
((~(r)|((h>~(r))|r))>~(~(f)))
0
0
0
0
not entailment
(~(~((o&((o&~(f))>(r&p)))))&f)
~(~((((~((y>u))&x)>(h>f))|((y>u)&p))))
1
0
0
0
entailment
((o>(f|~((f|(((h&o)&u)|u)))))&(r&(c&c)))
((f&u)|c)
1
1
1
0
entailment
(~(~((o&((o&~(f))>(r&p)))))&f)
((f&u)|c)
0
1
0
0
not entailment
((o>(f|~((f|(((h&o)&u)|u)))))&(r&(c&c)))
~(~((((~((y>u))&x)>(h>f))|((y>u)&p))))
0
1
0
0
not entailment
(o|(y>o))
(r>(((r>f)&y)>(r&o)))
1
0
0
0
entailment
~((u|o))
(((((x&o)|y)>(f>y))|(h&x))|(f>y))
1
0
0
0
entailment
(o|(y>o))
(((((x&o)|y)>(f>y))|(h&x))|(f>y))
0
0
0
0
not entailment
~((u|o))
(r>(((r>f)&y)>(r&o)))
0
0
0
0
not entailment
((b>(b>(b&v)))&((b|(b|v))|((b&b)&(v&v))))
(v|(v&~(v)))
1
1
1
0
entailment
(~((v&(b>v)))&b)
(~(~((v|v)))>(~(b)&v))
1
0
1
0
entailment
((b>(b>(b&v)))&((b|(b|v))|((b&b)&(v&v))))
(~(~((v|v)))>(~(b)&v))
0
1
1
0
not entailment
(~((v&(b>v)))&b)
(v|(v&~(v)))
0
1
1
0
not entailment
((~(v)&(v>b))>b)
~(~(((v|(b&v))|((v>v)>b))))
1
0
1
0
entailment
(((b>v)>((b|b)|b))>(b>v))
(b>~(~((b>(b&v)))))
1
1
1
0
entailment
((~(v)&(v>b))>b)
(b>~(~((b>(b&v)))))
0
0
1
1
not entailment
(((b>v)>((b|b)|b))>(b>v))
~(~(((v|(b&v))|((v>v)>b))))
0
0
1
0
not entailment
(v&((v|b)>(v|b)))
~(~(((v&(v>v))|b)))
1
0
1
1
entailment
(((v>b)|b)&(v>v))
(((b>(b|v))&b)|((v&v)>b))
1
0
1
0
entailment
(v&((v|b)>(v|b)))
(((b>(b|v))&b)|((v&v)>b))
0
0
1
1
not entailment
(((v>b)|b)&(v>v))
~(~(((v&(v>v))|b)))
0
0
1
1
not entailment
(b&(~((v&((v&b)>(v&b))))&~((v&~(v)))))
~((v&~(((v|b)&((v&(b|v))>b)))))
1
1
1
1
entailment
~((~(~((v|((v>b)&v))))>b))
((((b&v)>v)>b)>(v&((b>v)|v)))
1
1
1
1
entailment
(b&(~((v&((v&b)>(v&b))))&~((v&~(v)))))
((((b&v)>v)>b)>(v&((b>v)|v)))
0
1
1
1
not entailment