%--------------------------------------------------------------------------
% File     : PUZ054-1 : TPTP v9.0.0. Released v2.7.0.
% Domain   : Puzzles
% Problem  : Take black and white balls from a bag
% Version  : [Cla03] axioms : Especial.
% English  : Start with a bag with 10 white balls and 9 black balls.
%            Take out two balls: if they have the same color, put a black
%            ball back; if they have a different color, put a white ball back.
%            The last ball left cannot be white.

% Refs     : [Cla03] Claessen (2003), Email to G. Sutcliffe
% Source   : [Cla03]
% Names    :

% Status   : Satisfiable
% Rating   : 0.00 v2.7.0
% Syntax   : Number of clauses     :    5 (   2 unt;   0 nHn;   5 RR)
%            Number of literals    :    8 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :   11 (   3 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_SAT_RFO_NEQ

% Comments :
%--------------------------------------------------------------------------
cnf(initial_state,axiom,
    p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(s(n0)))))))))) ).

cnf(two_whites_out_one_black_in,axiom,
    ( p(X,s(Y))
    | ~ p(s(s(X)),Y) ) ).

cnf(two_blacks_out_one_black_in,axiom,
    ( p(X,s(Y))
    | ~ p(X,s(s(Y))) ) ).

cnf(two_different_balls_out_one_white_in,axiom,
    ( p(s(X),Y)
    | ~ p(s(X),s(Y)) ) ).

cnf(goal_state,negated_conjecture,
    ~ p(s(n0),n0) ).

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