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tasksource
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logical-entailment

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B
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2 values
((m>m)&(((m>m)>(m>m))&((m>m)>(m|m))))
~(~((((m|m)&~(m))|m)))
1
1
1
1
entailment
~((((m&m)|(m&m))&(m&m)))
~(((((m>m)&m)&m)|(m|m)))
1
1
1
0
entailment
((m>m)&(((m>m)>(m>m))&((m>m)>(m|m))))
~(((((m>m)&m)&m)|(m|m)))
0
1
1
1
not entailment
~((((m&m)|(m&m))&(m&m)))
~(~((((m|m)&~(m))|m)))
0
1
1
0
not entailment
~((~(m)&~((m&m))))
((((m|m)&m)|m)|(~(~((((m|m)>m)&m)))|m))
1
0
1
0
entailment
~((m|m))
((m|((m>m)>m))>((m&m)&~((m&(m&(m>m))))))
1
0
1
0
entailment
~((~(m)&~((m&m))))
((m|((m>m)>m))>((m&m)&~((m&(m&(m>m))))))
0
0
1
0
not entailment
~((m|m))
((((m|m)&m)|m)|(~(~((((m|m)>m)&m)))|m))
0
0
1
0
not entailment
(m|(m|m))
((m>m)&m)
1
1
1
0
entailment
~((m|(m&(m|m))))
~((m&m))
1
1
1
1
entailment
(m|(m|m))
~((m&m))
0
1
1
0
not entailment
~((m|(m&(m|m))))
((m>m)&m)
0
1
1
0
not entailment
(m|(m|m))
(m|(m|((m&m)&((m|m)>(m>(m&m))))))
1
0
1
0
entailment
(m>~((m|(m>((((m|m)|m)>(m&m))>(m>m))))))
(((m>m)&~(m))&~((m&(m|m))))
1
1
1
1
entailment
(m|(m|m))
(((m>m)&~(m))&~((m&(m|m))))
0
0
1
0
not entailment
(m>~((m|(m>((((m|m)|m)>(m&m))>(m>m))))))
(m|(m|((m&m)&((m|m)>(m>(m&m))))))
0
1
1
1
not entailment
~(~(((~(m)&(~(m)&m))|m)))
((m|m)|m)
1
1
1
1
entailment
~((~(m)>(m|m)))
~(m)
1
1
1
1
entailment
~(~(((~(m)&(~(m)&m))|m)))
~(m)
0
1
1
1
not entailment
~((~(m)>(m|m)))
((m|m)|m)
0
1
1
0
not entailment
(m|((((m&m)|(m|m))>~(m))>((m&m)&(m>m))))
(m&m)
1
1
1
1
entailment
~(~(~(((m&m)&~(~(m))))))
~((m|m))
1
1
1
1
entailment
(m|((((m&m)|(m|m))>~(m))>((m&m)&(m>m))))
~((m|m))
0
1
1
1
not entailment
~(~(~(((m&m)&~(~(m))))))
(m&m)
0
1
1
0
not entailment
(~((m>((m|m)&~(m))))|m)
~(~((m|((m>m)&m))))
1
1
1
1
entailment
((m&(m&m))>((m|(m|(m&(m|m))))&~(m)))
((m>(m&m))&~((~(m)>m)))
1
1
1
1
entailment
(~((m>((m|m)&~(m))))|m)
((m>(m&m))&~((~(m)>m)))
0
1
1
1
not entailment
((m&(m&m))>((m|(m|(m&(m|m))))&~(m)))
~(~((m|((m>m)&m))))
0
1
1
1
not entailment
((m&m)&(m|(m>m)))
(~(~((((m&m)|m)|~(m))))>((m>(m|m))>m))
1
0
1
1
entailment
(((m>m)&~(~(~(m))))&~(m))
(~(m)|~(~((~(m)|~(m)))))
1
1
1
1
entailment
((m&m)&(m|(m>m)))
(~(m)|~(~((~(m)|~(m)))))
0
0
1
1
not entailment
(((m>m)&~(~(~(m))))&~(m))
(~(~((((m&m)|m)|~(m))))>((m>(m|m))>m))
0
0
1
1
not entailment
((m>~(m))>((m&m)|m))
((((m|m)&(m|(m&(m|m))))&((m|m)>m))|(m|m))
1
0
1
0
entailment
~((m&(m|((m>(m&m))|m))))
((m|~(m))&~(m))
1
1
1
1
entailment
((m>~(m))>((m&m)|m))
((m|~(m))&~(m))
0
1
1
0
not entailment
~((m&(m|((m>(m&m))|m))))
((((m|m)&(m|(m&(m|m))))&((m|m)>m))|(m|m))
0
0
1
1
not entailment
~(~(o))
(~(~(s))|o)
1
0
0
0
entailment
~((i>g))
((~(s)>((q>i)|s))>(x|~((((i&x)>r)>g))))
1
0
0
0
entailment
~(~(o))
((~(s)>((q>i)|s))>(x|~((((i&x)>r)>g))))
0
0
0
0
not entailment
~((i>g))
(~(~(s))|o)
0
0
0
0
not entailment
((s&~((g>r)))&s)
((s|(g|o))|((~((c|x))&g)&(o|x)))
1
0
0
0
entailment
((i&i)&((q|(q&g))&((~(i)>r)&(c>i))))
((x&v)>(((i&o)|o)|q))
1
1
0
0
entailment
((s&~((g>r)))&s)
((x&v)>(((i&o)|o)|q))
0
0
0
0
not entailment
((i&i)&((q|(q&g))&((~(i)>r)&(c>i))))
((s|(g|o))|((~((c|x))&g)&(o|x)))
0
1
0
0
not entailment
((((g>c)>(~(x)&o))>s)>~(i))
~((x&((c&c)&i)))
1
1
1
1
entailment
(~(((q>~(v))|g))&(x|~((x|(g>q)))))
~(((i&g)&(o|o)))
1
1
0
0
entailment
((((g>c)>(~(x)&o))>s)>~(i))
~(((i&g)&(o|o)))
0
1
1
0
not entailment
(~(((q>~(v))|g))&(x|~((x|(g>q)))))
~((x&((c&c)&i)))
0
1
0
0
not entailment
(((c>c)&~((x>((i&o)|~(o)))))&(r&q))
(~(r)|((q|x)&(v|r)))
1
1
0
0
entailment
~(((o|(r>v))|g))
(v>g)
1
1
1
0
entailment
(((c>c)&~((x>((i&o)|~(o)))))&(r&q))
(v>g)
0
1
0
0
not entailment
~(((o|(r>v))|g))
(~(r)|((q|x)&(v|r)))
0
0
0
0
not entailment
(i&q)
(i|g)
1
1
0
0
entailment
~(~(o))
(~(v)>((x>o)&~(~(o))))
1
0
0
0
entailment
(i&q)
(~(v)>((x>o)&~(~(o))))
0
0
0
0
not entailment
~(~(o))
(i|g)
0
1
0
0
not entailment
(i|i)
((r>c)>((r>v)|i))
1
0
0
0
entailment
((((g|i)|s)>(g>g))&r)
(r&(r>r))
1
1
1
0
entailment
(i|i)
(r&(r>r))
0
0
0
0
not entailment
((((g|i)|s)>(g>g))&r)
((r>c)>((r>v)|i))
0
1
0
0
not entailment
~(((s>q)>s))
((x|(x&s))>((r&~(((o|~(s))|q)))>(o&q)))
1
0
0
0
entailment
(((s&i)&(x>(s>c)))&((r>g)>((x|x)>r)))
(q>(~(s)>(~(o)&(((g&q)|v)>(s|(o>i))))))
1
0
0
0
entailment
~(((s>q)>s))
(q>(~(s)>(~(o)&(((g&q)|v)>(s|(o>i))))))
0
0
0
0
not entailment
(((s&i)&(x>(s>c)))&((r>g)>((x|x)>r)))
((x|(x&s))>((r&~(((o|~(s))|q)))>(o&q)))
0
0
0
0
not entailment
~((~(~((v&o)))>i))
~(~((((((v|s)&(r>s))|r)&g)|o)))
1
0
0
0
entailment
(((g&g)>(c>((v|o)>(g|x))))&c)
~(~(~(~(((g|c)|(c&x))))))
1
1
1
1
entailment
~((~(~((v&o)))>i))
~(~(~(~(((g|c)|(c&x))))))
0
0
0
0
not entailment
(((g&g)>(c>((v|o)>(g|x))))&c)
~(~((((((v|s)&(r>s))|r)&g)|o)))
0
0
0
0
not entailment
(o&(~(((r>c)&(o|(i&q))))&(v|x)))
((((i&v)|v)&c)>(((i>o)&i)|(r>(q&~(r)))))
1
0
1
0
entailment
~((~(o)>g))
(o>(((o|g)>v)&~((c&v))))
1
0
0
0
entailment
(o&(~(((r>c)&(o|(i&q))))&(v|x)))
(o>(((o|g)>v)&~((c&v))))
0
1
0
0
not entailment
~((~(o)>g))
((((i&v)|v)&c)>(((i>o)&i)|(r>(q&~(r)))))
0
0
0
0
not entailment
~(r)
((((o>v)&(c>(c>s)))|(~(r)&(i|o)))>(r>i))
1
0
0
0
entailment
(v&(q|(v|~(r))))
(x|(v|((i|i)>v)))
1
1
0
0
entailment
~(r)
(x|(v|((i|i)>v)))
0
0
0
0
not entailment
(v&(q|(v|~(r))))
((((o>v)&(c>(c>s)))|(~(r)&(i|o)))>(r>i))
0
0
0
0
not entailment
((g>((x|s)|((q&i)&o)))&(s&((i|v)|x)))
(~(((r|s)|q))>(~((q&(q|(s|r))))>(v|r)))
1
0
0
0
entailment
((~(g)&(o>i))&(~((s|o))|((q>x)>(c>c))))
(~((g>(s>~(o))))>v)
1
1
0
0
entailment
((g>((x|s)|((q&i)&o)))&(s&((i|v)|x)))
(~((g>(s>~(o))))>v)
0
1
1
0
not entailment
((~(g)&(o>i))&(~((s|o))|((q>x)>(c>c))))
(~(((r|s)|q))>(~((q&(q|(s|r))))>(v|r)))
0
1
0
0
not entailment
~(((~(r)|s)|((g>c)>(c>(i|v)))))
~((((i|(q&v))>(o>c))>v))
1
1
0
0
entailment
(((x&(i>v))&((((g&v)>x)&(i|i))>i))&i)
(i|(x&c))
1
1
0
0
entailment
~(((~(r)|s)|((g>c)>(c>(i|v)))))
(i|(x&c))
0
1
0
0
not entailment
(((x&(i>v))&((((g&v)>x)&(i|i))>i))&i)
~((((i|(q&v))>(o>c))>v))
0
1
0
0
not entailment
((x|((g>~(x))>g))&s)
((c|(q|x))>(s|(v>(q>r))))
1
0
0
0
entailment
~((~(~((g&(~(r)|(g|x)))))&g))
~(~(~(g)))
1
1
1
1
entailment
((x|((g>~(x))>g))&s)
~(~(~(g)))
0
1
1
0
not entailment
~((~(~((g&(~(r)|(g|x)))))&g))
((c|(q|x))>(s|(v>(q>r))))
0
1
0
0
not entailment
(o|r)
((~(((q>c)>q))>((v>(o|c))|r))|(c&~(x)))
1
0
0
0
entailment
((s>(~(g)>~(x)))&~((x>(s>r))))
(x|(g&g))
1
1
1
1
entailment
(o|r)
(x|(g&g))
0
0
0
0
not entailment
((s>(~(g)>~(x)))&~((x>(s>r))))
((~(((q>c)>q))>((v>(o|c))|r))|(c&~(x)))
0
0
0
0
not entailment
((((i>g)&~(i))|((x|c)&c))>((v&x)&x))
((c&~((q|i)))|(x|(r>(c>(q>i)))))
1
1
0
0
entailment
(v&(q&q))
~(~((v|(g&~(x)))))
1
0
0
0
entailment
((((i>g)&~(i))|((x|c)&c))>((v&x)&x))
~(~((v|(g&~(x)))))
0
1
1
0
not entailment
(v&(q&q))
((c&~((q|i)))|(x|(r>(c>(q>i)))))
0
0
0
0
not entailment
((((~(s)&x)|s)>((q>c)|((g|q)&(g>v))))&x)
((g&o)>(((s>x)|i)|(r&g)))
1
1
0
0
entailment
(s&~((o>r)))
(s|i)
1
1
0
0
entailment
((((~(s)&x)|s)>((q>c)|((g|q)&(g>v))))&x)
(s|i)
0
1
0
0
not entailment
(s&~((o>r)))
((g&o)>(((s>x)|i)|(r&g)))
0
0
0
0
not entailment
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https://github.com/google-deepmind/logical-entailment-dataset

@inproceedings{
evans2018can,
title={Can Neural Networks Understand Logical Entailment?},
author={Richard Evans and David Saxton and David Amos and Pushmeet Kohli and Edward Grefenstette},
booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=SkZxCk-0Z},
}
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