TPTP Problem File: NUN063+2.p
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% File : NUN063+2 : TPTP v8.2.0. Released v7.3.0.
% Domain : Number Theory
% Problem : Robinson arithmetic: There exist infinite primes
% 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 : infprimes [Lam18]
% Status : Unknown
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% Number of atoms : 90 ( 37 equ)
% Maximal formula atoms : 46 ( 7 avg)
% Number of connectives : 116 ( 38 ~; 33 |; 45 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 85 ( 45 !; 40 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Translated to FOL with equality.
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include('Axioms/NUM008+0.ax').
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fof(infprimes,conjecture,
( ? [Y4] :
( ! [X1,X3] :
( ! [Y17] :
( ~ r4(X1,X3,Y17)
| Y17 != Y4 )
| ! [Y5,Y19] :
( ~ r3(X1,Y5,Y19)
| Y19 != Y4 )
| ! [Y6,Y18] :
( ~ r3(X3,Y6,Y18)
| Y18 != Y4 )
| ? [Y20] :
( X1 = Y20
& ? [Y26] :
( r1(Y26)
& r2(Y26,Y20) ) )
| ? [Y21] :
( X3 = Y21
& ? [Y27] :
( r1(Y27)
& r2(Y27,Y21) ) ) )
& ! [Y28] :
( ~ r1(Y28)
| Y4 != Y28 ) )
& ! [X2] :
( ? [X4,X6] :
( ! [Y22] :
( ! [Y29] :
( ~ r1(Y29)
| ~ r2(Y29,Y22) )
| X4 != Y22 )
& ! [Y23] :
( ! [Y30] :
( ~ r1(Y30)
| ~ r2(Y30,Y23) )
| X6 != Y23 )
& ? [Y14] :
( r4(X4,X6,Y14)
& Y14 = X2 )
& ? [Y1,Y16] :
( r3(X4,Y1,Y16)
& Y16 = X2 )
& ? [Y2,Y15] :
( r3(X6,Y2,Y15)
& Y15 = X2 ) )
| ? [Y31] :
( r1(Y31)
& X2 = Y31 )
| ? [Y3] :
( ! [X5,X7] :
( ! [Y10] :
( ~ r4(X5,X7,Y10)
| Y10 != Y3 )
| ! [Y7,Y12] :
( ~ r3(X5,Y7,Y12)
| Y12 != Y3 )
| ! [Y8,Y11] :
( ~ r3(X7,Y8,Y11)
| Y11 != Y3 )
| ? [Y24] :
( X5 = Y24
& ? [Y33] :
( r1(Y33)
& r2(Y33,Y24) ) )
| ? [Y25] :
( X7 = Y25
& ? [Y34] :
( r1(Y34)
& r2(Y34,Y25) ) ) )
& ! [Y35] :
( ~ r1(Y35)
| Y3 != Y35 )
& ? [Y9] :
( ! [Y32] :
( ~ r1(Y32)
| Y9 != Y32 )
& ? [Y13] :
( r3(X2,Y9,Y13)
& Y13 = Y3 ) ) ) ) ) ).
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