%--------------------------------------------------------------------------
% File     : COL071-1 : TPTP v8.2.0. Released v1.2.0.
% Domain   : Combinatory Logic
% Problem  : Strong fixed point for N and Q
% Version  : [WM88] (equality) axioms.
% English  : The strong fixed point property holds for the set
%            P consisting of the combinators N and Q, where ((Nx)y)z
%            = ((xz)y)z, ((Qx)y)z = y(xz).

% Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq
%          : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
%          : [Zha95] Zhang (1995), Email to G. Sutcliffe
% Source   : [Wos93]
% Names    : Question 14 [Wos93]

% Status   : Satisfiable
% Rating   : 0.33 v8.2.0, 0.20 v8.1.0, 0.50 v7.5.0, 0.25 v7.3.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.4.0, 1.00 v2.3.0, 0.67 v2.2.1, 0.75 v2.2.0, 1.00 v2.0.0
% Syntax   : Number of clauses     :    3 (   3 unt;   0 nHn;   1 RR)
%            Number of literals    :    3 (   3 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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn)
% SPC      : CNF_SAT_RFO_PEQ_UEQ

% Comments : [Zha95] provided a 4 element model of these clauses.
%--------------------------------------------------------------------------
cnf(n_definition,axiom,
    apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ).

cnf(q_definition,axiom,
    apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ).

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

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