%------------------------------------------------------------------------------
% File     : NUN064+2 : TPTP v9.0.0. Released v7.3.0.
% Domain   : Number Theory
% Problem  : Robinson arithmetic: Negated Goldbach conjecture
% 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    : neggoldbach [Lam18]

% Status   : Open
% Rating   : 1.00 v7.3.0
% Syntax   : Number of formulae    :   12 (   0 unt;   0 def)
%            Number of atoms       :   87 (  34 equ)
%            Maximal formula atoms :   43 (   7 avg)
%            Number of connectives :  109 (  34   ~;  27   |;  48   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   0 prp; 1-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   82 (  38   !;  44   ?)
% SPC      : FOF_OPN_RFO_SEQ

% Comments : Translated to FOL with equality.
%------------------------------------------------------------------------------
include('Axioms/NUM008+0.ax').
%------------------------------------------------------------------------------
fof(neggoldbach,conjecture,
    ? [X1] :
      ( ! [Y1] :
          ( ! [Y6] :
              ( ! [Y10] :
                  ( ~ r1(Y10)
                  | ~ r2(Y10,Y6) )
              | ~ r2(Y6,Y1) )
          | X1 != Y1 )
      & ! [Y2] :
          ( ~ r1(Y2)
          | X1 != Y2 )
      & ! [Y4,Y7] :
          ( ! [Y23] :
              ( ~ r3(Y4,Y7,Y23)
              | Y23 != X1 )
          | ? [X2,X4] :
              ( ! [Y14] :
                  ( ! [Y27] :
                      ( ~ r1(Y27)
                      | ~ r2(Y27,Y14) )
                  | X2 != Y14 )
              & ! [Y15] :
                  ( ! [Y28] :
                      ( ~ r1(Y28)
                      | ~ r2(Y28,Y15) )
                  | X4 != Y15 )
              & ? [Y11,Y25] :
                  ( r3(X2,Y11,Y25)
                  & Y25 = Y4 )
              & ? [Y12,Y26] :
                  ( r3(X4,Y12,Y26)
                  & Y26 = Y4 )
              & ? [Y13] :
                  ( r4(X2,X4,Y13)
                  & Y13 = Y4 ) )
          | ? [X3,X5] :
              ( ! [Y19] :
                  ( ! [Y31] :
                      ( ~ r1(Y31)
                      | ~ r2(Y31,Y19) )
                  | X3 != Y19 )
              & ! [Y20] :
                  ( ! [Y32] :
                      ( ~ r1(Y32)
                      | ~ r2(Y32,Y20) )
                  | X5 != Y20 )
              & ? [Y16,Y29] :
                  ( r3(X3,Y16,Y29)
                  & Y29 = Y7 )
              & ? [Y17,Y30] :
                  ( r3(X5,Y17,Y30)
                  & Y30 = Y7 )
              & ? [Y18] :
                  ( r4(X3,X5,Y18)
                  & Y18 = Y7 ) )
          | ? [Y21] :
              ( r1(Y21)
              & Y4 = Y21 )
          | ? [Y22] :
              ( r1(Y22)
              & Y7 = Y22 ) )
      & ? [Y3,Y5] :
          ( ? [Y8] :
              ( ? [Y24] :
                  ( r4(Y24,Y3,Y8)
                  & ? [Y33] :
                      ( r2(Y33,Y24)
                      & ? [Y34] :
                          ( r1(Y34)
                          & r2(Y34,Y33) ) ) )
              & Y8 = X1 )
          & ? [Y9] :
              ( r3(Y3,Y5,Y9)
              & Y9 = X1 ) ) ) ).

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