TPTP Problem File: NUN064+1.p
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% File : NUN064+1 : TPTP v8.2.0. 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 : neggoldbachid [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 : 153 ( 54 ~; 43 |; 56 &)
% ( 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 ( 62 !; 44 ?)
% SPC : FOF_OPN_RFO_NEQ
% Comments : Translated to FOL without equality.
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include('Axioms/NUM009+0.ax').
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fof(neggoldbachid,conjecture,
? [X1] :
( ! [Y1] :
( ! [Y6] :
( ! [Y10] :
( ~ r1(Y10)
| ~ r2(Y10,Y6) )
| ~ r2(Y6,Y1) )
| ~ id(X1,Y1) )
& ! [Y2] :
( ~ id(X1,Y2)
| ~ r1(Y2) )
& ! [Y4,Y7] :
( ! [Y23] :
( ~ id(Y23,X1)
| ~ r3(Y4,Y7,Y23) )
| ? [X2,X4] :
( ! [Y14] :
( ! [Y27] :
( ~ r1(Y27)
| ~ r2(Y27,Y14) )
| ~ id(X2,Y14) )
& ! [Y15] :
( ! [Y28] :
( ~ r1(Y28)
| ~ r2(Y28,Y15) )
| ~ id(X4,Y15) )
& ? [Y11,Y25] :
( id(Y25,Y4)
& r3(X2,Y11,Y25) )
& ? [Y12,Y26] :
( id(Y26,Y4)
& r3(X4,Y12,Y26) )
& ? [Y13] :
( id(Y13,Y4)
& r4(X2,X4,Y13) ) )
| ? [X3,X5] :
( ! [Y19] :
( ! [Y31] :
( ~ r1(Y31)
| ~ r2(Y31,Y19) )
| ~ id(X3,Y19) )
& ! [Y20] :
( ! [Y32] :
( ~ r1(Y32)
| ~ r2(Y32,Y20) )
| ~ id(X5,Y20) )
& ? [Y16,Y29] :
( id(Y29,Y7)
& r3(X3,Y16,Y29) )
& ? [Y17,Y30] :
( id(Y30,Y7)
& r3(X5,Y17,Y30) )
& ? [Y18] :
( id(Y18,Y7)
& r4(X3,X5,Y18) ) )
| ? [Y21] :
( id(Y4,Y21)
& r1(Y21) )
| ? [Y22] :
( id(Y7,Y22)
& r1(Y22) ) )
& ? [Y3,Y5] :
( ? [Y8] :
( id(Y8,X1)
& ? [Y24] :
( r4(Y24,Y3,Y8)
& ? [Y33] :
( r2(Y33,Y24)
& ? [Y34] :
( r1(Y34)
& r2(Y34,Y33) ) ) ) )
& ? [Y9] :
( id(Y9,X1)
& r3(Y3,Y5,Y9) ) ) ) ).
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