ITP001 Axioms: ITP064^5.ax


%------------------------------------------------------------------------------
% File     : ITP064^5 : TPTP v9.0.0. 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    : dft^2.ax [Gau20]
%          : HL4064^5.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_2Edft_2EDFT,type,
    c_2Edft_2EDFT: del > del > $i ).

thf(mem_c_2Edft_2EDFT,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Edft_2EDFT @ 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_2Edft_2ERel,type,
    c_2Edft_2ERel: del > del > del > del > del > $i ).

thf(mem_c_2Edft_2ERel,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del] : ( mem @ ( c_2Edft_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_2Edft_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 ) )
             => ! [V3to__visit: $i] :
                  ( ( mem @ V3to__visit @ ( ty_2Elist_2Elist @ A_27d ) )
                 => ! [V4acc: $i] :
                      ( ( mem @ V4acc @ A_27e )
                     => ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( c_2Edft_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 ) @ V3to__visit ) @ 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 ) @ V3to__visit ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__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 )
                 => ! [V4visit__now: $i] :
                      ( ( mem @ V4visit__now @ A_27a )
                     => ! [V5visit__later: $i] :
                          ( ( mem @ V5visit__later @ ( 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_2Edft_2EDFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V3acc )
                                = V3acc )
                              & ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Edft_2EDFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4visit__now ) @ V5visit__later ) ) @ V3acc )
                                = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4visit__now ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2seen ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Edft_2EDFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V5visit__later ) @ V3acc ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Edft_2EDFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4visit__now ) @ V2seen ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ V0G @ V4visit__now ) ) @ V5visit__later ) ) @ ( ap @ ( ap @ V1f @ V4visit__now ) @ V3acc ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__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 ) )
                   => ! [V4visit__now: $i] :
                        ( ( mem @ V4visit__now @ A_27a )
                       => ! [V5visit__later: $i] :
                            ( ( mem @ V5visit__later @ ( 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 ) @ V4visit__now ) @ ( 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 ) @ V4visit__now ) @ V3seen ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ V1G @ V4visit__now ) ) @ V5visit__later ) ) @ ( ap @ ( ap @ V2f @ V4visit__now ) @ 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 ) @ V4visit__now ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V3seen ) ) ) )
                                       => ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1G ) @ V2f ) @ V3seen ) @ V5visit__later ) @ V6acc ) ) ) )
                                   => ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1G ) @ V2f ) @ V3seen ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4visit__now ) @ V5visit__later ) ) @ 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_2Edft_2EDFT__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 ) )
             => ! [V3to__visit: $i] :
                  ( ( mem @ V3to__visit @ ( 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_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3to__visit ) @ V4acc )
                                  = ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3to__visit ) @ V5a ) ) @ V6b ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__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 ) )
             => ! [V3to__visit: $i] :
                  ( ( mem @ V3to__visit @ ( 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_2Edft_2EDFT @ A_27b @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3to__visit ) @ V4acc )
                          = ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V1f ) @ V4acc ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ V2seen ) @ V3to__visit ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__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 ) )
         => ! [V2to__visit: $i] :
              ( ( mem @ V2to__visit @ ( 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_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ V1seen ) @ V2to__visit ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__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 ) )
             => ! [V3to__visit: $i] :
                  ( ( mem @ V3to__visit @ ( 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_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3to__visit ) @ V4acc ) ) ) )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( ap @ ( c_2EdirGraph_2EREACH__LIST @ A_27a ) @ V0G ) @ V3to__visit ) ) )
                                | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V4acc ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__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 ) )
             => ! [V3to__visit: $i] :
                  ( ( mem @ V3to__visit @ ( 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 ) ) ) @ V3to__visit ) ) )
                              & ~ ( 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_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ V1f ) @ V2seen ) @ V3to__visit ) @ V4acc ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Edft_2EDFT__REACH__THM,axiom,
    ! [A_27a: del,V0G: $i] :
      ( ( mem @ V0G @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) )
     => ! [V1to__visit: $i] :
          ( ( mem @ V1to__visit @ ( 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 ) @ V1to__visit ) ) )
                <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Edft_2EDFT @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ V0G ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V1to__visit ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ) ) ).

%------------------------------------------------------------------------------