%--------------------------------------------------------------------------
% File     : COL029-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Combinatory Logic
% Problem  : Strong fixed point for U
% Version  : [WM88] (equality) axioms.
% English  : The strong fixed point property holds for the set
%            P consisting of the combinator U, where (Ux)y = y((xx)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
%          : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb
%          : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
% Source   : [MW88]
% Names    : - [MW88]
%          : Question 1 [Wos93]

% Status   : Unsatisfiable
% Rating   : 0.05 v8.2.0, 0.08 v8.1.0, 0.15 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.11 v7.1.0, 0.06 v7.0.0, 0.00 v6.0.0, 0.05 v5.5.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :    2 (   2 unt;   0 nHn;   1 RR)
%            Number of literals    :    2 (   2 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :    3 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
cnf(u_definition,axiom,
    apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ).

cnf(prove_fixed_point,negated_conjecture,
    apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).

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