TPTP Problem File: NUM006+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUM006+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Number Theory
% Problem : Robinson arithmetic: 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 : goldbachid [Lam18]
% Status : Open
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 156 ( 57 ~; 51 |; 48 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 106 ( 71 !; 35 ?)
% SPC : FOF_OPN_RFO_NEQ
% Comments : Translated to FOL without equality.
%------------------------------------------------------------------------------
include('Axioms/NUM009+0.ax').
%------------------------------------------------------------------------------
fof(goldbachid,conjecture,
! [X1] :
( ! [Y1,Y3] :
( ! [Y17] :
( ~ id(Y17,X1)
| ~ r3(Y1,Y3,Y17) )
| ! [Y9] :
( ! [Y18] :
( ! [Y20] :
( ! [Y26] :
( ~ r1(Y26)
| ~ r2(Y26,Y20) )
| ~ r2(Y20,Y18) )
| ~ r4(Y18,Y1,Y9) )
| ~ id(Y9,X1) ) )
| ? [Y19] :
( id(X1,Y19)
& ? [Y21] :
( r2(Y21,Y19)
& ? [Y27] :
( r1(Y27)
& r2(Y27,Y21) ) ) )
| ? [Y28] :
( id(X1,Y28)
& r1(Y28) )
| ? [Y2,Y4] :
( ! [X2,X4] :
( ! [Y14] :
( ~ id(Y14,Y2)
| ~ r4(X2,X4,Y14) )
| ! [Y5,Y16] :
( ~ id(Y16,Y2)
| ~ r3(X2,Y5,Y16) )
| ! [Y6,Y15] :
( ~ id(Y15,Y2)
| ~ r3(X4,Y6,Y15) )
| ? [Y22] :
( id(X2,Y22)
& ? [Y29] :
( r1(Y29)
& r2(Y29,Y22) ) )
| ? [Y23] :
( id(X4,Y23)
& ? [Y30] :
( r1(Y30)
& r2(Y30,Y23) ) ) )
& ! [X3,X5] :
( ! [Y11] :
( ~ id(Y11,Y4)
| ~ r4(X3,X5,Y11) )
| ! [Y7,Y13] :
( ~ id(Y13,Y4)
| ~ r3(X3,Y7,Y13) )
| ! [Y8,Y12] :
( ~ id(Y12,Y4)
| ~ r3(X5,Y8,Y12) )
| ? [Y24] :
( id(X3,Y24)
& ? [Y31] :
( r1(Y31)
& r2(Y31,Y24) ) )
| ? [Y25] :
( id(X5,Y25)
& ? [Y32] :
( r1(Y32)
& r2(Y32,Y25) ) ) )
& ! [Y33] :
( ~ id(Y2,Y33)
| ~ r1(Y33) )
& ! [Y34] :
( ~ id(Y4,Y34)
| ~ r1(Y34) )
& ? [Y10] :
( id(Y10,X1)
& r3(Y2,Y4,Y10) ) ) ) ).
%------------------------------------------------------------------------------