% This is a BAD set of assumptions.
% Here, we'll make 3 assumptions that assume a blatant contradiction:
% a=b and a!=b.
% With this, prover9 can "prove" anything.
% HOWEVER, mace4 is NOT able to find a model that meets these 3 assumptions;
% that gives us a tip-off that the assumptions are probably inconsistent.
% More importantly, if mace4 *can* find a model, then the assumptions
% *are* consistent, and since mace4 can find a model for all of the
% DDC related proofs, this means that the assumptions for each of the proofs
% are consistent.
% Prover9's default naming conventions require hard-to-read names. We'll use
% Prolog conventions instead (e.g., variables begin with an uppercase letter,
% while constants begin with a lowercase letter):
set(prolog_style_variables).
formulas(assumptions).
a = b.
(a = b) -> c.
a != b.
end_of_list.
formulas(goals).
-c.
% We can also prove "c.".
end_of_list.