TPTP Problem File: NUN092+1.p
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%------------------------------------------------------------------------------
% File : NUN092+1 : TPTP v8.2.0. Released v7.4.0.
% Domain : Number Theory
% Problem : Primitive recursive factorial function applied to 1!=1
% Version : Especial.
% English : The translation of the primitive recursive factorial function
% applied to 1!=1 into FOL with identity.
% Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% : [Lam19] Lampert (2018), Email to Geoff Sutcliffe
% Source : [Lam19]
% Names :
% Status : Unsatisfiable
% Rating : 1.00 v7.4.0
% Syntax : Number of formulae : 12 ( 0 unt; 0 def)
% Number of atoms : 134 ( 40 equ)
% Maximal formula atoms : 90 ( 11 avg)
% Number of connectives : 214 ( 92 ~; 90 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 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 : 133 ( 99 !; 34 ?)
% SPC : FOF_UNS_RFO_SEQ
% Comments : The translation goes from primitive recursive functions to
% L_A-expressions, and from L_A-expressions to FOL as defined in
% [BBJ03] and [Smi07].
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_2,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) )
& Y5 = Y4 )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ) ).
fof(axiom_3,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) )
& Y3 = Y2 )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ) ).
fof(axiom_4,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ r2(X3,Y13)
| Y13 != Y12 )
| ~ r2(X10,Y12) )
| X3 = X10 ) ).
fof(axiom_5,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ) ).
fof(axiom_6,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ) ).
fof(axiom_7,axiom,
! [X6] :
( ? [Y19] :
( r1(Y19)
& X6 = Y19 )
| ? [Y1,Y11] :
( r2(Y1,Y11)
& X6 = Y11 ) ) ).
fof(axiom_8,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(axiom_9,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& X12 != Y21 )
| ( r2(X11,X12)
& X12 = Y21 ) ) ).
fof(axiom_10,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ r3(X13,X14,X15)
& X15 != Y22 )
| ( r3(X13,X14,X15)
& X15 = Y22 ) ) ).
fof(axiom_11,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ r4(X16,X17,X18)
& X18 != Y23 )
| ( r4(X16,X17,X18)
& X18 = Y23 ) ) ).
fof(axiom_12,axiom,
( ! [Y1,Y2] :
( ! [Y5] :
( ! [Y21] :
( ! [Y25] :
( ! [Y36] :
( ! [Y46] :
( ! [Y59] :
( ! [Y69] :
( ~ r1(Y69)
| ~ r2(Y69,Y59) )
| ~ r4(Y2,Y59,Y46) )
| ~ r2(Y46,Y36) )
| ~ r4(Y36,Y5,Y25) )
| ! [Y60] :
( ! [Y70] :
( ~ r1(Y70)
| ~ r2(Y70,Y60) )
| ~ r3(Y25,Y60,Y21) ) )
| Y1 != Y21 )
| ! [Y7,Y45] :
( ! [Y47] :
( ! [Y57] :
( ! [Y67] :
( ~ r1(Y67)
| ~ r2(Y67,Y57) )
| ~ r3(Y7,Y57,Y47) )
| Y47 != Y45 )
| ! [Y58] :
( ! [Y68] :
( ~ r1(Y68)
| ~ r2(Y68,Y58) )
| ~ r4(Y2,Y58,Y45) ) )
| ! [Y8,Y44] :
( ~ r3(Y8,Y5,Y44)
| Y44 != Y1 ) )
| ! [Y6] :
( ! [Y10,Y42] :
( ~ r3(Y10,Y6,Y42)
| Y42 != Y1 )
| ! [Y20] :
( ! [Y24] :
( ! [Y30] :
( ! [Y35] :
( ! [Y56] :
( ! [Y63] :
( ! [Y73] :
( ~ r1(Y73)
| ~ r2(Y73,Y63) )
| ~ r2(Y63,Y56) )
| ~ r4(Y2,Y56,Y35) )
| ~ r2(Y35,Y30) )
| ~ r4(Y30,Y6,Y24) )
| ! [Y64] :
( ! [Y74] :
( ~ r1(Y74)
| ~ r2(Y74,Y64) )
| ~ r3(Y24,Y64,Y20) ) )
| Y1 != Y20 )
| ! [Y9,Y34] :
( ! [Y43] :
( ! [Y61] :
( ! [Y71] :
( ~ r1(Y71)
| ~ r2(Y71,Y61) )
| ~ r3(Y9,Y61,Y43) )
| Y43 != Y34 )
| ! [Y55] :
( ! [Y62] :
( ! [Y72] :
( ~ r1(Y72)
| ~ r2(Y72,Y62) )
| ~ r2(Y62,Y55) )
| ~ r4(Y2,Y55,Y34) ) ) )
| ? [X1] :
( ! [Y4,Y11] :
( ! [Y12] :
( ! [Y14,Y32] :
( ! [Y40] :
( ~ r3(Y14,Y4,Y40)
| Y40 != Y32 )
| ! [Y53] :
( ~ r2(Y12,Y53)
| ~ r4(Y2,Y53,Y32) ) )
| ! [Y15,Y39] :
( ~ r3(Y15,Y12,Y39)
| Y39 != Y1 )
| ! [Y19] :
( ! [Y23] :
( ! [Y29] :
( ! [Y33] :
( ! [Y54] :
( ~ r2(Y12,Y54)
| ~ r4(Y2,Y54,Y33) )
| ~ r2(Y33,Y29) )
| ~ r4(Y29,Y12,Y23) )
| ~ r3(Y23,Y4,Y19) )
| Y1 != Y19 ) )
| ! [Y13] :
( ! [Y16,Y27] :
( ! [Y38] :
( ~ r3(Y16,Y11,Y38)
| Y38 != Y27 )
| ! [Y48] :
( ! [Y51] :
( ~ r2(Y13,Y51)
| ~ r2(Y51,Y48) )
| ~ r4(Y2,Y48,Y27) ) )
| ! [Y17,Y37] :
( ~ r3(Y17,Y13,Y37)
| Y37 != Y1 )
| ! [Y18] :
( ! [Y22] :
( ! [Y26] :
( ! [Y28] :
( ! [Y49] :
( ! [Y52] :
( ~ r2(Y13,Y52)
| ~ r2(Y52,Y49) )
| ~ r4(Y2,Y49,Y28) )
| ~ r2(Y28,Y26) )
| ~ r4(Y26,Y13,Y22) )
| ~ r3(Y22,Y11,Y18) )
| Y1 != Y18 ) )
| ! [Y31] :
( ! [Y50] :
( ~ r2(X1,Y50)
| ~ r4(Y4,Y50,Y31) )
| Y11 != Y31 ) )
& ! [Y66] :
( ! [Y76] :
( ~ r1(Y76)
| ~ r2(Y76,Y66) )
| X1 != Y66 )
& ? [Y3,Y41] :
( r3(Y3,X1,Y41)
& ? [Y65] :
( Y41 = Y65
& ? [Y75] :
( r1(Y75)
& r2(Y75,Y65) ) ) ) ) )
| ! [Y77] :
? [X2] :
( ( ~ r1(X2)
| X2 != Y77 )
& ( r1(X2)
| X2 = Y77 ) )
| ? [X3] :
! [Y78] :
? [X4] :
( ( ~ r2(X3,X4)
| X4 != Y78 )
& ( r2(X3,X4)
| X4 = Y78 ) )
| ? [X5,X6] :
! [Y79] :
? [X7] :
( ( ~ r3(X5,X6,X7)
| X7 != Y79 )
& ( r3(X5,X6,X7)
| X7 = Y79 ) )
| ? [X8,X9] :
! [Y80] :
? [X10] :
( ( ~ r4(X8,X9,X10)
| X10 != Y80 )
& ( r4(X8,X9,X10)
| X10 = Y80 ) ) ) ).
%------------------------------------------------------------------------------