SET007 Axioms: SET007+228.ax


%------------------------------------------------------------------------------
% File     : SET007+228 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Ordered Affine Spaces Defined in Directed Parallelity - Part I
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : diraf [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   67 (   9 unit)
%            Number of atoms       :  791 (  44 equality)
%            Maximal formula depth :   26 (  12 average)
%            Number of connectives :  916 ( 192 ~  ;  14  |; 329  &)
%                                         (  13 <=>; 368 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   1 propositional; 0-5 arity)
%            Number of functors    :    7 (   0 constant; 1-4 arity)
%            Number of variables   :  355 (   0 singleton; 340 !;  15 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & v1_analoaf(k2_diraf(A)) ) ) )).

fof(rc1_diraf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v1_diraf(A) ) )).

fof(rc2_diraf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v1_diraf(A)
      & v2_diraf(A) ) )).

fof(d1_diraf,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( C = k1_diraf(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => ( r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,F,G)),C)
                                <=> ( r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,F,G)),B)
                                    | r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,G,F)),B) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => k2_diraf(A) = g1_analoaf(u1_struct_0(A),k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) )).

fof(t1_diraf,axiom,(
    $true )).

fof(t2_diraf,axiom,(
    $true )).

fof(t3_diraf,axiom,(
    $true )).

fof(t4_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_analoaf(A,B,C,B,C) ) ) ) )).

fof(t5_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_analoaf(A,B,C,D,E)
                       => ( r2_analoaf(A,C,B,E,D)
                          & r2_analoaf(A,D,E,B,C)
                          & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t6_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r2_analoaf(A,D,E,B,C)
                                  & r2_analoaf(A,B,C,F,G) )
                               => ( B = C
                                  | r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t7_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_analoaf(A,B,B,C,D)
                    & r2_analoaf(A,C,D,B,B) ) ) ) ) ) )).

fof(t8_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_analoaf(A,B,C,D,E)
                          & r2_analoaf(A,B,C,E,D)
                          & B != C
                          & D != E ) ) ) ) ) ) )).

fof(t9_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_analoaf(A,B,C,B,D)
                  <=> ( r2_analoaf(A,B,C,C,D)
                      | r2_analoaf(A,B,D,D,C) ) ) ) ) ) ) )).

fof(d3_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_diraf(A,B,C,D)
                  <=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) )).

fof(t10_diraf,axiom,(
    $true )).

fof(t11_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_analoaf(A,B,C,B,D)
                  <=> ( r1_diraf(A,B,C,D)
                      | r1_diraf(A,B,D,C) ) ) ) ) ) ) )).

fof(t12_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_diraf(A,B,C,B)
               => B = C ) ) ) ) )).

fof(t13_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_diraf(A,B,C,D)
                   => r1_diraf(A,D,C,B) ) ) ) ) ) )).

fof(t14_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_diraf(A,B,B,C)
                & r1_diraf(A,B,C,C) ) ) ) ) )).

fof(t15_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_diraf(A,B,C,D)
                          & r1_diraf(A,B,D,E) )
                       => r1_diraf(A,C,D,E) ) ) ) ) ) ) )).

fof(t16_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_diraf(A,D,B,C)
                          & r1_diraf(A,B,C,E) )
                       => ( B = C
                          | r1_diraf(A,D,C,E) ) ) ) ) ) ) ) )).

fof(t17_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & r1_diraf(A,B,C,D)
                  & C != D ) ) ) ) )).

fof(t18_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_diraf(A,B,C,D)
                      & r1_diraf(A,C,B,D) )
                   => B = C ) ) ) ) ) )).

fof(t19_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( B != C
                          & r1_diraf(A,B,C,D)
                          & r1_diraf(A,B,C,E)
                          & ~ r1_diraf(A,C,D,E)
                          & ~ r1_diraf(A,C,E,D) ) ) ) ) ) ) )).

fof(t20_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( B != C
                          & r1_diraf(A,B,C,D)
                          & r1_diraf(A,B,C,E)
                          & ~ r1_diraf(A,B,D,E)
                          & ~ r1_diraf(A,B,E,D) ) ) ) ) ) ) )).

fof(t21_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r1_diraf(A,B,C,D)
                          & r1_diraf(A,B,E,D)
                          & ~ r1_diraf(A,B,C,E)
                          & ~ r1_diraf(A,B,E,C) ) ) ) ) ) ) )).

fof(d4_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_diraf(A,B,C,D,E)
                      <=> ( r2_analoaf(A,B,C,D,E)
                          | r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).

fof(t22_diraf,axiom,(
    $true )).

fof(t23_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_diraf(A,B,C,D,E)
                      <=> r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ) ) ) ) ) )).

fof(t24_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_diraf(A,B,C,C,B)
                & r2_diraf(A,B,C,B,C) ) ) ) ) )).

fof(t25_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_diraf(A,B,C,D,D)
                    & r2_diraf(A,D,D,B,C) ) ) ) ) ) )).

fof(t26_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_diraf(A,B,C,B,D)
                   => r2_diraf(A,C,B,C,D) ) ) ) ) ) )).

fof(t27_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_diraf(A,B,C,D,E)
                       => ( r2_diraf(A,B,C,E,D)
                          & r2_diraf(A,C,B,D,E)
                          & r2_diraf(A,C,B,E,D)
                          & r2_diraf(A,D,E,B,C)
                          & r2_diraf(A,D,E,C,B)
                          & r2_diraf(A,E,D,B,C)
                          & r2_diraf(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t28_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( B != C
                                  & ~ ( ~ ( r2_diraf(A,B,C,D,E)
                                          & r2_diraf(A,B,C,F,G) )
                                      & ~ ( r2_diraf(A,B,C,D,E)
                                          & r2_diraf(A,F,G,B,C) )
                                      & ~ ( r2_diraf(A,D,E,B,C)
                                          & r2_diraf(A,F,G,B,C) )
                                      & ~ ( r2_diraf(A,D,E,B,C)
                                          & r2_diraf(A,B,C,F,G) ) )
                                  & ~ r2_diraf(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t29_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ~ ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_diraf(A,B,C,B,D) ) ) ) ) )).

fof(t30_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & r2_diraf(A,B,C,D,E)
                      & D != E ) ) ) ) ) )).

fof(t31_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & r2_diraf(A,B,C,D,E)
                      & r2_diraf(A,B,D,C,E) ) ) ) ) ) )).

fof(t32_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_diraf(A,B,C,C,D)
                          & C != B
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_diraf(A,E,C,C,F)
                                  & r2_diraf(A,E,B,D,F) ) ) ) ) ) ) ) ) )).

fof(d5_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_diraf(A,B,C,D)
                  <=> r2_diraf(A,B,C,B,D) ) ) ) ) ) )).

fof(t33_diraf,axiom,(
    $true )).

fof(t34_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_diraf(A,B,C,D)
                   => r3_diraf(A,B,C,D) ) ) ) ) ) )).

fof(t35_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r3_diraf(A,B,C,D)
                      & ~ r1_diraf(A,B,C,D)
                      & ~ r1_diraf(A,C,B,D)
                      & ~ r1_diraf(A,B,D,C) ) ) ) ) ) )).

fof(t36_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_diraf(A,B,C,D)
                   => ( r3_diraf(A,B,D,C)
                      & r3_diraf(A,C,B,D)
                      & r3_diraf(A,C,D,B)
                      & r3_diraf(A,D,B,C)
                      & r3_diraf(A,D,C,B) ) ) ) ) ) ) )).

fof(t37_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_diraf(A,B,B,C)
                & r3_diraf(A,B,C,C)
                & r3_diraf(A,B,C,B) ) ) ) ) )).

fof(t38_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r3_diraf(A,B,C,D)
                              & r3_diraf(A,B,C,E)
                              & r3_diraf(A,B,C,F) )
                           => ( B = C
                              | r3_diraf(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t39_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_diraf(A,B,C,D)
                          & r2_diraf(A,B,C,D,E) )
                       => ( B = C
                          | r3_diraf(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t40_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_diraf(A,B,C,D)
                          & r3_diraf(A,B,C,E) )
                       => r2_diraf(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t41_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r3_diraf(A,D,E,B)
                              & r3_diraf(A,D,E,C)
                              & r3_diraf(A,B,C,F) )
                           => ( B = C
                              | r3_diraf(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t42_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ~ ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r3_diraf(A,B,C,D) ) ) ) ) )).

fof(t43_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r3_diraf(A,B,C,D) ) ) ) ) ) )).

fof(t44_diraf,axiom,(
    $true )).

fof(t45_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_analoaf(B) )
         => ( B = k2_diraf(A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(B))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(B))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(B))
                                           => ( ( C = G
                                                & D = H
                                                & E = I
                                                & F = J )
                                             => ( r2_analoaf(B,G,H,I,J)
                                              <=> r2_diraf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t46_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_analoaf(B) )
         => ( B = k2_diraf(A)
           => ( ~ ! [C] :
                    ( m1_subset_1(C,u1_struct_0(B))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(B))
                       => C = D ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(B))
                                     => ( r2_analoaf(B,C,D,D,C)
                                        & r2_analoaf(B,C,D,E,E)
                                        & ( ( r2_analoaf(B,C,D,E,F)
                                            & r2_analoaf(B,C,D,G,H) )
                                         => ( C = D
                                            | r2_analoaf(B,E,F,G,H) ) )
                                        & ( r2_analoaf(B,C,D,C,E)
                                         => r2_analoaf(B,D,C,D,E) ) ) ) ) ) ) ) )
              & ~ ! [C] :
                    ( m1_subset_1(C,u1_struct_0(B))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(B))
                       => ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => r2_analoaf(B,C,D,C,E) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ? [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                              & r2_analoaf(B,C,E,D,F)
                              & D != F ) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ? [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                              & r2_analoaf(B,C,D,E,F)
                              & r2_analoaf(B,C,E,D,F) ) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ~ ( r2_analoaf(B,E,C,C,F)
                                  & C != E
                                  & ! [G] :
                                      ( m1_subset_1(G,u1_struct_0(B))
                                     => ~ ( r2_analoaf(B,D,C,C,G)
                                          & r2_analoaf(B,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_diraf,axiom,(
    $true )).

fof(d7_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_diraf(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r2_analoaf(A,B,C,C,B)
                                    & r2_analoaf(A,B,C,D,D)
                                    & ( ( r2_analoaf(A,B,C,D,E)
                                        & r2_analoaf(A,B,C,F,G) )
                                     => ( B = C
                                        | r2_analoaf(A,D,E,F,G) ) )
                                    & ( r2_analoaf(A,B,C,B,D)
                                     => r2_analoaf(A,C,B,C,D) ) ) ) ) ) ) ) )
          & ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => r2_analoaf(A,B,C,B,D) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,D,C,E)
                          & C != E ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,C,D,E)
                          & r2_analoaf(A,B,D,C,E) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_analoaf(A,D,B,B,E)
                              & B != D
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,C,B,B,F)
                                      & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t47_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B = C ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( r2_analoaf(A,B,C,C,B)
                                  & r2_analoaf(A,B,C,D,D)
                                  & ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,B,C,F,G) )
                                   => ( B = C
                                      | r2_analoaf(A,D,E,F,G) ) )
                                  & ( r2_analoaf(A,B,C,B,D)
                                   => r2_analoaf(A,C,B,C,D) ) ) ) ) ) ) ) )
        & ~ ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_analoaf(A,B,C,B,D) ) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_analoaf(A,B,D,C,E)
                        & C != E ) ) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_analoaf(A,B,C,D,E)
                        & r2_analoaf(A,B,D,C,E) ) ) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( r2_analoaf(A,D,B,B,E)
                            & B != D
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_analoaf(A,C,B,B,F)
                                    & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t48_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & l1_analoaf(k2_diraf(A)) ) ) )).

fof(t49_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( ( ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => B = C ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r2_analoaf(A,B,C,C,B)
                                    & r2_analoaf(A,B,C,D,D)
                                    & ( ( r2_analoaf(A,B,C,D,E)
                                        & r2_analoaf(A,B,C,F,G) )
                                     => ( B = C
                                        | r2_analoaf(A,D,E,F,G) ) )
                                    & ( r2_analoaf(A,B,C,B,D)
                                     => r2_analoaf(A,C,B,C,D) ) ) ) ) ) ) ) )
          & ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => r2_analoaf(A,B,C,B,D) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,D,C,E)
                          & C != E ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,C,D,E)
                          & r2_analoaf(A,B,D,C,E) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_analoaf(A,D,B,B,E)
                              & B != D
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,C,B,B,F)
                                      & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) )
      <=> ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v1_diraf(A)
          & l1_analoaf(A) ) ) ) )).

fof(t50_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v3_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( ~ r2_diraf(A,B,C,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_diraf(A,B,C,B,F)
                                  & r2_diraf(A,D,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t51_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & v3_analoaf(B)
            & l1_analoaf(B) )
         => ( A = k2_diraf(B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( ~ r2_analoaf(A,C,D,E,F)
                                & ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ~ ( r2_analoaf(A,C,D,C,G)
                                        & r2_analoaf(A,E,F,E,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v2_diraf(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( ~ r2_analoaf(A,B,C,D,E)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_analoaf(A,B,C,B,F)
                                    & r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) )).

fof(t52_diraf,axiom,(
    $true )).

fof(t53_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v3_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v2_diraf(k2_diraf(A))
        & l1_analoaf(k2_diraf(A)) ) ) )).

fof(t54_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v1_diraf(A)
          & v2_diraf(A)
          & l1_analoaf(A) )
      <=> ( ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => B = C ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r2_analoaf(A,B,C,C,B)
                                    & r2_analoaf(A,B,C,D,D)
                                    & ( ( r2_analoaf(A,B,C,D,E)
                                        & r2_analoaf(A,B,C,F,G) )
                                     => ( B = C
                                        | r2_analoaf(A,D,E,F,G) ) )
                                    & ( r2_analoaf(A,B,C,B,D)
                                     => r2_analoaf(A,C,B,C,D) ) ) ) ) ) ) ) )
          & ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => r2_analoaf(A,B,C,B,D) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,D,C,E)
                          & C != E ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,C,D,E)
                          & r2_analoaf(A,B,D,C,E) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_analoaf(A,D,B,B,E)
                              & B != D
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,C,B,B,F)
                                      & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( ~ r2_analoaf(A,B,C,D,E)
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,B,C,B,F)
                                      & r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_diraf,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
     => m2_relset_1(k1_diraf(A,B),k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) ) )).

fof(dt_k2_diraf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_analoaf(k2_diraf(A))
        & l1_analoaf(k2_diraf(A)) ) ) )).
%------------------------------------------------------------------------------