%------------------------------------------------------------------------------
% 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    :   14 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :   15 (   2 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   1   ~;   0   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   1 usr;   0 ari;   1 dat;   0 cdt)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   15 (  15   !;   0   ?;  15   :)
% 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(equal_type,type,
    equal: ( nat * nat * nat ) > $o ).

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,
    ( equal(zero,zero,zero)
  <=> ~ $false ) ).

tff(4,axiom,
    ! [Y: nat,Z: nat] :
      ( equal(zero,s(Y),Z)
    <=> $false ) ).

tff(5,axiom,
    ! [Y: nat,Z: nat] :
      ( equal(zero,Y,s(Z))
    <=> $false ) ).

tff(6,axiom,
    ! [X: nat,Z: nat] :
      ( equal(s(X),zero,Z)
    <=> $false ) ).

tff(7,axiom,
    ! [X: nat,Y: nat] :
      ( equal(s(X),Y,zero)
    <=> $false ) ).

tff(8,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( equal(s(X),s(Y),s(Z))
    <=> equal(X,Y,Z) ) ).

tff(goal,conjecture,
    ! [X: nat] : equal(add(X,add(X,X)),add(add(X,X),X),add(add(X,X),X)) ).

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