%------------------------------------------------------------------------------
% File     : DAT001_1 : TPTP v10.0.0. Released v10.0.0.
% Domain   : Data Structures
% Problem  :
% Version  : Especial.
% English  :

% Refs     :
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : ? v10.0.0
% Syntax   : Number of formulae    :   10 (   5 unt;   5 typ;   0 def)
%            Number of atoms       :    5 (   5 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    0 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    1 (   1 usr;   0 ari;   1 dat;   0 cdt)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    5 (   5   !;   0   ?;   5   :)
% SPC      : TF0_THM_EQU_NAR_DAT

% Comments :
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tff(nat_type,type-datatype,
    nat: $tType ).

tff(zero_type,type-datatype_constructor,
    zero: nat ).

tff(s_type,type-datatype_constructor,
    s: nat > nat ).

tff(add_type,type,
    add: ( nat * nat ) > nat ).

tff(dup_type,type,
    dup: nat > nat ).

tff(1,axiom,
    ! [Y: nat] : ( add(zero,Y) = Y ) ).

tff(2,axiom,
    ! [X: nat,Y: nat] : ( add(s(X),Y) = s(add(X,Y)) ) ).

tff(3,axiom,
    dup(zero) = zero ).

tff(4,axiom,
    ! [X: nat] : ( dup(s(X)) = s(s(dup(X))) ) ).

tff(goal,conjecture,
    ! [V0: nat] : ( dup(V0) = add(V0,V0) ) ).

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