TPTP Axioms File: COL001-0.ax


%------------------------------------------------------------------------------
% File     : COL001-0 : TPTP v7.5.0. 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 (   1 non-Horn;   8 unit;   2 RR)
%            Number of atoms      :   12 (  12 equality)
%            Maximal clause size  :    2 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    8 (   4 constant; 0-2 arity)
%            Number of variables  :   18 (   3 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      : 

% Comments :
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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 )).

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