%------------------------------------------------------------------------------
% 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 :    4 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    1 (   1 usr;   0 ari;   1 dat;   0 cdt)
%            Number of type conns  :    5 (   3   >;   2   *;   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   :    9 (   9   !;   0   ?;   9   :)
% 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(mul_type,type,
    mul: ( nat * 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,
    ! [Y: nat] : ( mul(zero,Y) = zero ) ).

tff(4,axiom,
    ! [X: nat,Y: nat] : ( mul(s(X),Y) = add(mul(X,Y),Y) ) ).

tff(goal,conjecture,
    ! [X: nat,Y: nat,Z: nat] : ( mul(add(X,Y),Z) = add(mul(Z,X),mul(Y,Z)) ) ).

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