April 24, 2002
A preprint (the submitted version) is available: DVI, PS, PDF.
(((y v x) ^ x) v (((z ^ (x v x)) v (u ^ x)) ^ v)) ^ (w v ((v6 v x) ^ (x v v7))) = x. % A1 (((y v x) ^ x) v (((z ^ (x v x)) v (u ^ x)) ^ v)) ^ (((w v x) ^ (v6 v x)) v v7) = x. % A2The McKenzie 4-basis is
x v (y ^ (x ^ z)) = x. x ^ (y v (x v z)) = x. ((y ^ x) v (x ^ z)) v x = x. ((y v x) ^ (x v z)) ^ x = x.
An "automatic" proof of A1 -> McKenzie-4-basis.
An "automatic" proof of A2 -> McKenzie-4-basis.
(((x ^ y) v (y ^ (x v y))) ^ z) v (((x ^ (((x1 ^ y) v (y ^ x2)) v y)) v (((y ^ (((x1 v (y v x2)) ^ (x3 v y)) ^ y)) v (u ^ (y v (((x1 v (y v x2)) ^ (x3 v y)) ^ y)))) ^ (x v (((x1 ^ y) v (y ^ x2)) v y)))) ^ (((x ^ y) v (y ^ (x v y))) v z)) = y.The length-77 axiom (8 variables) from [Veroff:2001]:
(((x ^ y) v (y ^ (x v y))) ^ z) v (((x ^ (((x1 ^ y) v (y ^ x2)) v y)) v (((y ^ (((x1 v (y v x2)) ^ (x3 v y)) ^ y)) v (u ^ (y v (((y v xnew) ^ (x3 v y)) ^ y)))) ^ (x v (((x1 ^ y) v (y ^ x2)) v y)))) ^ (((x ^ y) v (y ^ (x v y))) v z)) = y.