include("ortholattice-header").

% OL_SS basis: { A_SS, B_SS, ONE_SS }
% OL    basis: { AJ, B1, DM, CC, ONE }

list(sos).

f(x,f(f(y,z),f(y,z))) = f(y,f(f(x,z),f(x,z))).  % A_SS
f(f(x,x),f(x,y)) = x.                           % B_SS
f(x,f(x,x)) = f(y,f(y,y)).                      % ONE_SS

x v y = f(f(x,x),f(y,y)).  % DEF_J
x ^ y = f(f(x,y),f(x,y)).  % DEF_M
c(x) = f(x,x).             % DEF_C

end_of_list.

assign(max_proofs, 6).

list(passive).

  A v (B v C) != B v (A v C)  | $Ans(AJ).
% A v (A ^ B) != A            | $Ans(B1).
  A v c(c(A) v c(B)) != A     | $Ans(B1_rewritten).
  A ^ B != c(c(A) v c(B))     | $Ans(DM).
  c(c(A)) != A                | $Ans(CC).
  A v c(A) != B v c(B)        | $Ans(ONE).

  f(A,B) != c(A) v c(B)      | $Ans(DEF_SS).

end_of_list.