% 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.