(VAR x y z)
(THEORY (AC or and))
(THEORY (C eq neq))
(RULES
  eq(x, x) -> true
  not(eq(x, y)) -> neq(x, y)
  not(neq(x, y)) -> eq(x, y)
  not(true) -> false
  not(false) -> true
  not(not(x)) -> x
  not(and(x, y)) -> or(not(x), not(y))
  not(or(x, y)) -> and(not(x), not(y))
  neq(x, x) -> false
  or(and(x, y), z) -> and(or(x, z), or(y, z))
  or(x, x) -> x
  or(x, true) -> true
  or(x, false) -> x
  and(x, x) -> x
  and(x, true) -> x
  and(x, false) -> false
  and(x, or(x, y)) -> x
)