%--------------------------------------------------------------------------
% File     : COL003-2 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Combinatory Logic
% Problem  : Strong fixed point for B and W
% Version  : [WM88] (equality) axioms : Augmented > Especial.
%            Theorem formulation : The fixed point is provided and checked.
% English  : The strong fixed point property holds for the set
%            P consisting of the combinators B and W alone, where ((Bx)y)z
%            = x(yz) and (Wx)y = (xy)y.

% Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
%          : [MW87]  McCune & Wos (1987), A Case Study in Automated Theorem
%          : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq
%          : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
% Source   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.12 v8.2.0, 0.25 v8.1.0, 0.00 v7.5.0, 0.20 v7.4.0, 0.11 v7.3.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.44 v5.5.0, 0.69 v5.4.0, 0.67 v5.3.0, 0.75 v5.2.0, 0.38 v5.1.0, 0.29 v5.0.0, 0.57 v4.1.0, 0.44 v4.0.1, 0.33 v3.3.0, 0.29 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0
% Syntax   : Number of clauses     :    4 (   3 unt;   0 nHn;   2 RR)
%            Number of literals    :    5 (   3 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_UNS_RFO_SEQ_HRN

% Comments : This the J sage of [McCune & Wos, 1987], found by Statman.
%--------------------------------------------------------------------------
cnf(b_definition,axiom,
    apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).

cnf(w_definition,axiom,
    apply(apply(w,X),Y) = apply(apply(X,Y),Y) ).

cnf(strong_fixed_point,axiom,
    ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))
    | fixed_point(Strong_fixed_point) ) ).

cnf(prove_strong_fixed_point,negated_conjecture,
    ~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))) ).

%--------------------------------------------------------------------------