ITP001 Axioms: ITP062^5.ax
%------------------------------------------------------------------------------
% File : ITP062^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : bft^2.ax [Gau20]
% : HL4062^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 13 ( 0 unt; 2 typ; 0 def)
% Number of atoms : 477 ( 9 equ; 0 cnn)
% Maximal formula atoms : 101 ( 36 avg)
% Number of connectives : 893 ( 2 ~; 1 |; 11 &; 813 @)
% ( 1 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 23 avg; 813 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 28 usr; 26 con; 0-5 aty)
% Number of variables : 76 ( 0 ^ 76 !; 0 ?; 76 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Ebft_2EBFT,type,
c_2Ebft_2EBFT: del > del > $i ).
thf(mem_c_2Ebft_2EBFT,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebft_2EBFT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27a @ A_27a ) ) @ ( arr @ ( ty_2Elist_2Elist @ A_27b ) @ ( arr @ ( ty_2Elist_2Elist @ A_27b ) @ ( arr @ A_27a @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2Ebft_2ERel,type,
c_2Ebft_2ERel: del > del > del > del > del > $i ).
thf(mem_c_2Ebft_2ERel,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del] : ( mem @ ( c_2Ebft_2ERel @ A_27a @ A_27b @ A_27c @ A_27d @ A_27e ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ty_2Epair_2Eprod @ A_27c @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(ax_thm_2Ebft_2ERel__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27b ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ A_27c )
=> ! [V2seen: $i] :
( ( mem @ V2seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3fringe: $i] :
( ( mem @ V3fringe @ ( ty_2Elist_2Elist @ A_27d ) )
=> ! [V4acc: $i] :
( ( mem @ V4acc @ A_27e )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( c_2Ebft_2ERel @ A_27a @ A_27b @ A_27c @ A_27d @ A_27e ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ty_2Epair_2Eprod @ A_27c @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ V0G ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27c @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ V1f ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ V2seen ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27d ) @ A_27e ) @ V3fringe ) @ V4acc ) ) ) ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27b ) @ V0G ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2seen ) ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27d ) @ V3fringe ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__def,axiom,
! [A_27a: del,A_27b: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V2seen: $i] :
( ( mem @ V2seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3acc: $i] :
( ( mem @ V3acc @ A_27b )
=> ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V3acc )
= V3acc )
& ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ V5t ) ) @ V3acc )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4h ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2seen ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V5t ) @ V3acc ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ V2seen ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V5t ) @ ( ap @ V0G @ V4h ) ) ) @ ( ap @ ( ap @ V1f @ V4h ) @ V3acc ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ A_27b @ bool ) ) ) ) ) )
=> ( ! [V1G: $i] :
( ( mem @ V1G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V3seen: $i] :
( ( mem @ V3seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V6acc: $i] :
( ( mem @ V6acc @ A_27b )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1G ) @ V2f ) @ V3seen ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V6acc ) )
& ( ( ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V1G ) ) )
& ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4h ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V3seen ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1G ) @ V2f ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ V3seen ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V5t ) @ ( ap @ V1G @ V4h ) ) ) @ ( ap @ ( ap @ V2f @ V4h ) @ V6acc ) ) ) )
& ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V1G ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4h ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V3seen ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1G ) @ V2f ) @ V3seen ) @ V5t ) @ V6acc ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1G ) @ V2f ) @ V3seen ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ V5t ) ) @ V6acc ) ) ) ) ) ) ) ) ) )
=> ! [V7v: $i] :
( ( mem @ V7v @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V8v1: $i] :
( ( mem @ V8v1 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V9v2: $i] :
( ( mem @ V9v2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V10v3: $i] :
( ( mem @ V10v3 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V11v4: $i] :
( ( mem @ V11v4 @ A_27b )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) @ V9v2 ) @ V10v3 ) @ V11v4 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__CONS,axiom,
! [A_27a: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
=> ! [V2seen: $i] :
( ( mem @ V2seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3fringe: $i] :
( ( mem @ V3fringe @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4acc: $i] :
( ( mem @ V4acc @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5a: $i] :
( ( mem @ V5a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V6b: $i] :
( ( mem @ V6b @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
& ( V1f
= ( c_2Elist_2ECONS @ A_27a ) )
& ( V4acc
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V5a ) @ V6b ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3fringe ) @ V4acc )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3fringe ) @ V5a ) ) @ V6b ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__FOLD,axiom,
! [A_27a: del,A_27b: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V2seen: $i] :
( ( mem @ V2seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3fringe: $i] :
( ( mem @ V3fringe @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4acc: $i] :
( ( mem @ V4acc @ A_27b )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3fringe ) @ V4acc )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V1f ) @ V4acc ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ V2seen ) @ V3fringe ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__ALL__DISTINCT,axiom,
! [A_27a: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1seen: $i] :
( ( mem @ V1seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2fringe: $i] :
( ( mem @ V2fringe @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
=> ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ V1seen ) @ V2fringe ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__REACH__1,axiom,
! [A_27a: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
=> ! [V2seen: $i] :
( ( mem @ V2seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3fringe: $i] :
( ( mem @ V3fringe @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4acc: $i] :
( ( mem @ V4acc @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
& ( V1f
= ( c_2Elist_2ECONS @ A_27a ) ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3fringe ) @ V4acc ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( ap @ ( c_2EdirGraph_2EREACH__LIST @ A_27a ) @ V0G ) @ V3fringe ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V4acc ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__REACH__2,axiom,
! [A_27a: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
=> ! [V2seen: $i] :
( ( mem @ V2seen @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3fringe: $i] :
( ( mem @ V3fringe @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4acc: $i] :
( ( mem @ V4acc @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
& ( V1f
= ( c_2Elist_2ECONS @ A_27a ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( ap @ ( c_2EdirGraph_2EREACH__LIST @ A_27a ) @ ( ap @ ( ap @ ( c_2EdirGraph_2EEXCLUDE @ A_27a @ A_27a ) @ V0G ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2seen ) ) ) @ V3fringe ) ) )
& ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2seen ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3fringe ) @ V4acc ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebft_2EBFT__REACH__THM,axiom,
! [A_27a: del,V0G: $i] :
( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V1fringe: $i] :
( ( mem @ V1fringe @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2EdirGraph_2EParents @ A_27a @ A_27a ) @ V0G ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2EdirGraph_2EREACH__LIST @ A_27a ) @ V0G ) @ V1fringe ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebft_2EBFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V1fringe ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------