%--------------------------------------------------------------------------
% File     : COL081-1 : TPTP v8.2.0. Released v1.2.0.
% Domain   : Combinatory Logic
% Problem  : Abst k(k(X)) = k(k(X))
% Version  : [Jec95] (equality) axioms.
% English  :

% Refs     : [Jec95] Jech (1995), Otter Experiments in a System of Combinat
% Source   : [Jec95]
% Names    : Proposition 2c [Jec95]

% Status   : Unsatisfiable
% Rating   : 0.27 v8.2.0, 0.38 v8.1.0, 0.32 v7.5.0, 0.41 v7.4.0, 0.53 v7.3.0, 0.38 v7.2.0, 0.42 v7.1.0, 0.36 v7.0.0, 0.54 v6.4.0, 0.50 v6.1.0, 0.64 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.56 v5.3.0, 0.70 v5.2.0, 0.50 v5.1.0, 0.56 v5.0.0, 0.60 v4.1.0, 0.56 v4.0.1, 0.62 v4.0.0, 0.57 v3.7.0, 0.29 v3.4.0, 0.17 v3.3.0, 0.33 v3.2.0, 0.22 v3.1.0, 0.20 v2.7.0, 0.25 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.25 v2.2.1, 0.50 v2.2.0, 0.25 v2.1.0, 1.00 v2.0.0
% Syntax   : Number of clauses     :   12 (  10 unt;   1 nHn;   3 RR)
%            Number of literals    :   14 (  14 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   19 (   3 sgn)
% SPC      : CNF_UNS_RFO_PEQ_NUE

% Comments :
%--------------------------------------------------------------------------
%----Include axioms of Type-respecting combinators
include('Axioms/COL001-0.ax').
%--------------------------------------------------------------------------
cnf(identity_definition,axiom,
    apply(identity,X) = X ).

cnf(prove_TRC2c,negated_conjecture,
    k(k(b)) != apply(abstraction,k(k(b))) ).

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