TPTP Problem File: NUN092+2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUN092+2 : 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 without 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 : 19 ( 1 unt; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 121 ( 10 avg)
% Number of connectives : 300 ( 123 ~; 121 |; 56 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 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 : 181 ( 123 !; 58 ?)
% SPC : FOF_UNS_RFO_NEQ
% 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] :
( ( id(X19,Y24)
& r1(X19) )
| ( ~ r1(X19)
& ~ id(X19,Y24) ) ) ).
fof(axiom_2,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( id(Y5,Y4)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ) ).
fof(axiom_3,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( id(Y3,Y2)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ) ).
fof(axiom_4,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ id(Y13,Y12)
| ~ r2(X3,Y13) )
| ~ r2(X10,Y12) )
| id(X3,X10) ) ).
fof(axiom_5,axiom,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ) ).
fof(axiom_6,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( id(Y8,Y18)
& r1(Y18) ) ) ).
fof(axiom_7,axiom,
! [X6] :
( ? [Y19] :
( id(X6,Y19)
& r1(Y19) )
| ? [Y1,Y11] :
( id(X6,Y11)
& r2(Y1,Y11) ) ) ).
fof(axiom_8,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) )
| ~ r2(X7,Y10) ) ).
fof(axiom_9,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( id(X12,Y21)
& r2(X11,X12) )
| ( ~ r2(X11,X12)
& ~ id(X12,Y21) ) ) ).
fof(axiom_10,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( id(X15,Y22)
& r3(X13,X14,X15) )
| ( ~ r3(X13,X14,X15)
& ~ id(X15,Y22) ) ) ).
fof(axiom_11,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( id(X18,Y23)
& r4(X16,X17,X18) )
| ( ~ r4(X16,X17,X18)
& ~ id(X18,Y23) ) ) ).
fof(axiom_12,axiom,
! [X20] : id(X20,X20) ).
fof(axiom_13,axiom,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ) ).
fof(axiom_14,axiom,
! [X23,X24,X25] :
( ~ id(X23,X24)
| id(X23,X25)
| ~ id(X24,X25) ) ).
fof(axiom_15,axiom,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ) ).
fof(axiom_16,axiom,
! [X28,X29,X30,X31] :
( ~ id(X28,X30)
| ~ id(X29,X31)
| ( ~ r2(X28,X29)
& ~ r2(X30,X31) )
| ( r2(X28,X29)
& r2(X30,X31) ) ) ).
fof(axiom_17,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r3(X32,X33,X34)
& ~ r3(X35,X36,X37) )
| ( r3(X32,X33,X34)
& r3(X35,X36,X37) ) ) ).
fof(axiom_18,axiom,
! [X38,X39,X40,X41,X42,X43] :
( ~ id(X38,X41)
| ~ id(X39,X42)
| ~ id(X40,X43)
| ( ~ r4(X38,X39,X40)
& ~ r4(X41,X42,X43) )
| ( r4(X38,X39,X40)
& r4(X41,X42,X43) ) ) ).
fof(axiom_19,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) ) )
| ~ id(Y1,Y21) )
| ! [Y7,Y45] :
( ! [Y47] :
( ! [Y57] :
( ! [Y67] :
( ~ r1(Y67)
| ~ r2(Y67,Y57) )
| ~ r3(Y7,Y57,Y47) )
| ~ id(Y47,Y45) )
| ! [Y58] :
( ! [Y68] :
( ~ r1(Y68)
| ~ r2(Y68,Y58) )
| ~ r4(Y2,Y58,Y45) ) )
| ! [Y8,Y44] :
( ~ id(Y44,Y1)
| ~ r3(Y8,Y5,Y44) ) )
| ! [Y6] :
( ! [Y10,Y42] :
( ~ id(Y42,Y1)
| ~ r3(Y10,Y6,Y42) )
| ! [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) ) )
| ~ id(Y1,Y20) )
| ! [Y9,Y34] :
( ! [Y43] :
( ! [Y61] :
( ! [Y71] :
( ~ r1(Y71)
| ~ r2(Y71,Y61) )
| ~ r3(Y9,Y61,Y43) )
| ~ id(Y43,Y34) )
| ! [Y55] :
( ! [Y62] :
( ! [Y72] :
( ~ r1(Y72)
| ~ r2(Y72,Y62) )
| ~ r2(Y62,Y55) )
| ~ r4(Y2,Y55,Y34) ) ) )
| ? [X1] :
( ! [Y4,Y11] :
( ! [Y12] :
( ! [Y14,Y32] :
( ! [Y40] :
( ~ id(Y40,Y32)
| ~ r3(Y14,Y4,Y40) )
| ! [Y53] :
( ~ r2(Y12,Y53)
| ~ r4(Y2,Y53,Y32) ) )
| ! [Y15,Y39] :
( ~ id(Y39,Y1)
| ~ r3(Y15,Y12,Y39) )
| ! [Y19] :
( ! [Y23] :
( ! [Y29] :
( ! [Y33] :
( ! [Y54] :
( ~ r2(Y12,Y54)
| ~ r4(Y2,Y54,Y33) )
| ~ r2(Y33,Y29) )
| ~ r4(Y29,Y12,Y23) )
| ~ r3(Y23,Y4,Y19) )
| ~ id(Y1,Y19) ) )
| ! [Y13] :
( ! [Y16,Y27] :
( ! [Y38] :
( ~ id(Y38,Y27)
| ~ r3(Y16,Y11,Y38) )
| ! [Y48] :
( ! [Y51] :
( ~ r2(Y13,Y51)
| ~ r2(Y51,Y48) )
| ~ r4(Y2,Y48,Y27) ) )
| ! [Y17,Y37] :
( ~ id(Y37,Y1)
| ~ r3(Y17,Y13,Y37) )
| ! [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) )
| ~ id(Y1,Y18) ) )
| ! [Y31] :
( ! [Y50] :
( ~ r2(X1,Y50)
| ~ r4(Y4,Y50,Y31) )
| ~ id(Y11,Y31) ) )
& ! [Y66] :
( ! [Y76] :
( ~ r1(Y76)
| ~ r2(Y76,Y66) )
| ~ id(X1,Y66) )
& ? [Y3,Y41] :
( r3(Y3,X1,Y41)
& ? [Y65] :
( id(Y41,Y65)
& ? [Y75] :
( r1(Y75)
& r2(Y75,Y65) ) ) ) ) )
| ! [Y77] :
? [X2] :
( ( id(X2,Y77)
| r1(X2) )
& ( ~ r1(X2)
| ~ id(X2,Y77) ) )
| ? [X11] : ~ id(X11,X11)
| ? [X12,X13] :
( id(X12,X13)
& ~ id(X13,X12) )
| ? [X14,X15,X16] :
( id(X14,X15)
& ~ id(X14,X16)
& id(X15,X16) )
| ? [X17,X18] :
( id(X17,X18)
& ( ~ r1(X17)
| ~ r1(X18) )
& ( r1(X17)
| r1(X18) ) )
| ? [X19,X20,X21,X22] :
( id(X19,X21)
& id(X20,X22)
& ( ~ r2(X19,X20)
| ~ r2(X21,X22) )
& ( r2(X19,X20)
| r2(X21,X22) ) )
| ? [X23,X24,X25,X26,X27,X28] :
( id(X23,X26)
& id(X24,X27)
& id(X25,X28)
& ( ~ r3(X23,X24,X25)
| ~ r3(X26,X27,X28) )
& ( r3(X23,X24,X25)
| r3(X26,X27,X28) ) )
| ? [X29,X30,X31,X32,X33,X34] :
( id(X29,X32)
& id(X30,X33)
& id(X31,X34)
& ( ~ r4(X29,X30,X31)
| ~ r4(X32,X33,X34) )
& ( r4(X29,X30,X31)
| r4(X32,X33,X34) ) )
| ? [X3] :
! [Y78] :
? [X4] :
( ( id(X4,Y78)
| r2(X3,X4) )
& ( ~ r2(X3,X4)
| ~ id(X4,Y78) ) )
| ? [X5,X6] :
! [Y79] :
? [X7] :
( ( id(X7,Y79)
| r3(X5,X6,X7) )
& ( ~ r3(X5,X6,X7)
| ~ id(X7,Y79) ) )
| ? [X8,X9] :
! [Y80] :
? [X10] :
( ( id(X10,Y80)
| r4(X8,X9,X10) )
& ( ~ r4(X8,X9,X10)
| ~ id(X10,Y80) ) ) ) ).
%------------------------------------------------------------------------------