ITP001 Axioms: ITP075^7.ax
%------------------------------------------------------------------------------
% File : ITP075^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : string_num.ax [Gau19]
% : HL4075^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 18 unt; 43 typ; 0 def)
% Number of atoms : 53 ( 25 equ; 2 cnn)
% Maximal formula atoms : 4 ( 0 avg)
% Number of connectives : 466 ( 2 ~; 1 |; 5 &; 445 @)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg; 445 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 3 con; 0-7 aty)
% Number of variables : 76 ( 12 ^ 40 !; 3 ?; 76 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Estring_2Echar,type,
tyop_2Estring_2Echar: $tType ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2A,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Esum_2E_2B_2B,type,
c_2Esum_2E_2B_2B:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( A_27a > A_27c ) > ( A_27b > A_27d ) > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ).
thf(c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Emin_2E_40,type,
c_2Emin_2E_40:
!>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Estring_2ECHR,type,
c_2Estring_2ECHR: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Earithmetic_2EDIV,type,
c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ecombin_2EI,type,
c_2Ecombin_2EI:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
thf(c_2Esum_2EINL,type,
c_2Esum_2EINL:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ).
thf(c_2Esum_2EINR,type,
c_2Esum_2EINR:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ).
thf(c_2Ebool_2ELET,type,
c_2Ebool_2ELET:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Earithmetic_2EMOD,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EODD,type,
c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).
thf(c_2Estring_2EORD,type,
c_2Estring_2EORD: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).
thf(c_2Erelation_2EWF,type,
c_2Erelation_2EWF:
!>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > $o ) ).
thf(c_2Erelation_2EWFREC,type,
c_2Erelation_2EWFREC:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27a > $o ) > ( ( A_27a > A_27b ) > A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Estring__num_2En2nsum,type,
c_2Estring__num_2En2nsum: tyop_2Enum_2Enum > ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ).
thf(c_2Estring__num_2En2s,type,
c_2Estring__num_2En2s: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).
thf(c_2Estring__num_2Ensum2n,type,
c_2Estring__num_2Ensum2n: ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
thf(c_2Estring__num_2Es2n,type,
c_2Estring__num_2Es2n: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).
thf(c_2Estring__num_2Es2ssum,type,
c_2Estring__num_2Es2ssum: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Esum_2Esum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).
thf(c_2Estring__num_2Essum2s,type,
c_2Estring__num_2Essum2s: ( tyop_2Esum_2Esum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Estring__num_2En2s__primitive__def,axiom,
( c_2Estring__num_2En2s
= ( c_2Erelation_2EWFREC @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ( c_2Emin_2E_40 @ ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o )
@ ^ [V0R: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o] :
( c_2Ebool_2E_2F_5C @ ( c_2Erelation_2EWF @ tyop_2Enum_2Enum @ V0R )
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V1n: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V2r0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V3r: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V1n @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2r0 @ ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3r @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2r0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ V2r0 ) ) ) ) @ ( V0R @ ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ V1n @ V3r ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ V1n ) ) ) ) ) ) )
@ ^ [V4n2s: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ),V5a: tyop_2Enum_2Enum] :
( c_2Ecombin_2EI @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V5a @ c_2Enum_2E0 ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar )
@ ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ^ [V6r0: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ^ [V7r: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ^ [V8s0: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2E_2D @ V7r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V8s0 )
@ ( V4n2s @ ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ V5a @ V7r ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
@ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V6r0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ V6r0 ) )
@ ( c_2Earithmetic_2EMOD @ V5a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Estring__num_2Es2n__def,axiom,
( ( ( c_2Estring__num_2Es2n @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
= c_2Enum_2E0 )
& ! [V0c: tyop_2Estring_2Echar,V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( c_2Estring__num_2Es2n @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1s ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Estring__num_2Es2n @ V1s ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Estring__num_2En2nsum__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Estring__num_2En2nsum @ V0n )
= ( c_2Ebool_2ECOND @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Earithmetic_2EODD @ V0n ) @ ( c_2Esum_2EINL @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EDIV @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Esum_2EINR @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EDIV @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Estring__num_2Ensum2n__def,axiom,
( ! [V0n: tyop_2Enum_2Enum] :
( ( c_2Estring__num_2Ensum2n @ ( c_2Esum_2EINL @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V0n ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ! [V1n: tyop_2Enum_2Enum] :
( ( c_2Estring__num_2Ensum2n @ ( c_2Esum_2EINR @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1n ) )
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V1n ) ) ) ).
thf(thm_2Estring__num_2Es2ssum__def,axiom,
! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( c_2Estring__num_2Es2ssum @ V0s )
= ( c_2Esum_2E_2B_2B @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2Estring__num_2En2s @ c_2Estring__num_2En2s @ ( c_2Estring__num_2En2nsum @ ( c_2Estring__num_2Es2n @ V0s ) ) ) ) ).
thf(thm_2Estring__num_2Essum2s__def,axiom,
! [V0sm: tyop_2Esum_2Esum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )] :
( ( c_2Estring__num_2Essum2s @ V0sm )
= ( c_2Estring__num_2En2s @ ( c_2Estring__num_2Ensum2n @ ( c_2Esum_2E_2B_2B @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Estring__num_2Es2n @ c_2Estring__num_2Es2n @ V0sm ) ) ) ) ).
thf(thm_2Estring__num_2En2s__ind,axiom,
! [V0P: tyop_2Enum_2Enum > $o] :
( ! [V1n: tyop_2Enum_2Enum] :
( ! [V2r0: tyop_2Enum_2Enum,V3r: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V1n = c_2Enum_2E0 ) )
& ( V2r0
= ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
& ( V3r
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2r0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ V2r0 ) ) )
=> ( V0P @ ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ V1n @ V3r ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( V0P @ V1n ) )
=> ! [V4v: tyop_2Enum_2Enum] : ( V0P @ V4v ) ) ).
thf(thm_2Estring__num_2En2s__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Estring__num_2En2s @ V0n )
= ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V0n @ c_2Enum_2E0 ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar )
@ ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ^ [V1r0: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ^ [V2r: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
@ ^ [V3s0: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2E_2D @ V2r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V3s0 )
@ ( c_2Estring__num_2En2s @ ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ V0n @ V2r ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
@ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V1r0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ V1r0 ) )
@ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Estring__num_2Es2n__n2s,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Estring__num_2Es2n @ ( c_2Estring__num_2En2s @ V0n ) )
= V0n ) ).
thf(thm_2Estring__num_2En2s__s2n,axiom,
! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( c_2Estring__num_2En2s @ ( c_2Estring__num_2Es2n @ V0s ) )
= V0s ) ).
thf(thm_2Estring__num_2En2s__11,axiom,
! [V0y: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum] :
( ( ( c_2Estring__num_2En2s @ V1x )
= ( c_2Estring__num_2En2s @ V0y ) )
<=> ( V1x = V0y ) ) ).
thf(thm_2Estring__num_2Es2n__11,axiom,
! [V0y: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1x: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( ( c_2Estring__num_2Es2n @ V1x )
= ( c_2Estring__num_2Es2n @ V0y ) )
<=> ( V1x = V0y ) ) ).
thf(thm_2Estring__num_2En2s__onto,axiom,
! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
? [V1n: tyop_2Enum_2Enum] :
( V0s
= ( c_2Estring__num_2En2s @ V1n ) ) ).
thf(thm_2Estring__num_2Es2n__onto,axiom,
! [V0n: tyop_2Enum_2Enum] :
? [V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( V0n
= ( c_2Estring__num_2Es2n @ V1s ) ) ).
thf(thm_2Estring__num_2En2nsum__nsum2n,axiom,
! [V0ns: tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( ( c_2Estring__num_2En2nsum @ ( c_2Estring__num_2Ensum2n @ V0ns ) )
= V0ns ) ).
thf(thm_2Estring__num_2Ensum2n__n2nsum,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Estring__num_2Ensum2n @ ( c_2Estring__num_2En2nsum @ V0n ) )
= V0n ) ).
thf(thm_2Estring__num_2Es2ssum__ssum2s,axiom,
! [V0sm: tyop_2Esum_2Esum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )] :
( ( c_2Estring__num_2Es2ssum @ ( c_2Estring__num_2Essum2s @ V0sm ) )
= V0sm ) ).
thf(thm_2Estring__num_2Essum2s__s2ssum,axiom,
! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( c_2Estring__num_2Essum2s @ ( c_2Estring__num_2Es2ssum @ V0s ) )
= V0s ) ).
%------------------------------------------------------------------------------