%------------------------------------------------------------------------------
% File     : COL001-0 : TPTP v9.0.0. Bugfixed v1.2.0.
% Domain   : Combinatory Logic
% Axioms   : Type-respecting combinators
% Version  : [Jec95] (equality) axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of clauses     :   10 (   8 unt;   1 nHn;   2 RR)
%            Number of literals    :   12 (  12 equ;   2 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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   3 sgn)
% SPC      : 

% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
    apply(k(X),Y) = X ).

cnf(projection1,axiom,
    apply(projection1,pair(X,Y)) = X ).

cnf(projection2,axiom,
    apply(projection2,pair(X,Y)) = Y ).

cnf(pairing,axiom,
    pair(apply(projection1,X),apply(projection2,X)) = X ).

cnf(pairwise_application,axiom,
    apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)) ).

cnf(abstraction,axiom,
    apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ).

cnf(equality,axiom,
    apply(eq,pair(X,X)) = projection1 ).

cnf(extensionality1,axiom,
    ( X = Y
    | apply(eq,pair(X,Y)) = projection2 ) ).

cnf(extensionality2,axiom,
    ( X = Y
    | apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ).

cnf(different_projections,axiom,
    projection1 != projection2 ).

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