Lion and Unicorn with Prolog SAT Solver

Seems you are totally off topic and not talking about the two Liars
from the riddle, namely this here what Alice in the forest hears
from the animals:

Lion: Yesterday was one of my lying days.
Unicorn: Yesterday was one of my lying days.

Thats why my predicate is called two_liars/6. First liar is Lion,
the second liar is Unicorn, in total we have two liars.

There is a bug somewhere in your reasoning or how you enter
the formula or how you use your system to check for antinomy.
Since you make a quite far off claim.

But the riddle gives a hint that it is satisfiable. Even uniquely
satisfiable, since the riddle says:

From these statements, Alice, who was a bright girl, was able to
deduce the day of the week. What was it?

You can also verify satisfiable via my Prolog code:

Or via library(clpb) by using the predicate which has this documentation:

labeling(+Vs)
Assigns truth values to the variables Vs such that all constraints are satisfied.

So if I use this SAT solver predicate I also find that it is satisfiable: