%------------------------------------------------------------------------------
% File     : NUN074+1 : TPTP v9.0.0. Released v7.3.0.
% Domain   : Number Theory
% Problem  : Robinson arithmetic: Primes exist
% Version  : Especial.
% English  :

% Refs     : [BBJ03] Boolos et al. (2003), Computability and Logic
%          : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
%          : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% Source   : [Lam18]
% Names    : primeexistid [Lam18]

% Status   : Theorem
% Rating   : 1.00 v7.3.0
% Syntax   : Number of formulae    :   19 (   1 unt;   0 def)
%            Number of atoms       :   89 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  112 (  42   ~;  34   |;  36   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   5 usr;   0 prp; 1-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   80 (  55   !;  25   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Translated to FOL without equality.
%------------------------------------------------------------------------------
include('Axioms/NUM009+0.ax').
%------------------------------------------------------------------------------
fof(primeexistid,conjecture,
    ? [Y1] :
      ( ! [X1,X2] :
          ( ! [Y2,Y6] :
              ( ~ id(Y6,Y1)
              | ~ r3(X1,Y2,Y6) )
          | ! [Y3,Y5] :
              ( ~ id(Y5,Y1)
              | ~ r3(X2,Y3,Y5) )
          | ! [Y4] :
              ( ~ id(Y4,Y1)
              | ~ r4(X1,X2,Y4) )
          | ? [Y7] :
              ( id(X1,Y7)
              & ? [Y9] :
                  ( r1(Y9)
                  & r2(Y9,Y7) ) )
          | ? [Y8] :
              ( id(X2,Y8)
              & ? [Y10] :
                  ( r1(Y10)
                  & r2(Y10,Y8) ) ) )
      & ! [Y11] :
          ( ~ id(Y1,Y11)
          | ~ r1(Y11) ) ) ).

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