%--------------------------------------------------------------------------
% File     : COL042-8 : TPTP v2.1.0. Released v2.1.0.
% Domain   : Combinatory Logic
% Problem  : Strong fixed point for B and W1
% Version  : [WM88] (equality) axioms.
%            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 W1, where ((Bx)y)z 
%            = x(yz), (W1x)y = (yx)x.

% Refs     : [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   : ? v2.1.0
% Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   2 RR)
%            Number of literals   :    4 (   4 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    5 (   4 constant; 0-2 arity)
%            Number of variables  :    5 (   0 singleton)
%            Maximal term depth   :    7 (   3 average)

% Comments : 
%          : tptp2X -f tptp -t rm_equality:rstfp COL042-8.p 
%--------------------------------------------------------------------------
input_clause(b_definition,axiom,
    [++ equal(apply(apply(apply(b, X), Y), Z), apply(X, apply(Y, Z)))]).

input_clause(w1_definition,axiom,
    [++ equal(apply(apply(w1, X), Y), apply(apply(Y, X), X))]).

input_clause(strong_fixed_point,axiom,
    [++ equal(strong_fixed_point, apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b))]).

input_clause(prove_strong_fixed_point,conjecture,
    [-- equal(apply(strong_fixed_point, fixed_pt), apply(fixed_pt, apply(strong_fixed_point, fixed_pt)))]).
%--------------------------------------------------------------------------