SET007 Axioms: SET007+226.ax


%------------------------------------------------------------------------------
% File     : SET007+226 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Analytical Ordered Affine Spaces
% 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    : analoaf [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   70 (  23 unit)
%            Number of atoms       :  767 (  76 equality)
%            Maximal formula depth :   31 (   9 average)
%            Number of connectives :  832 ( 135 ~  ;  16  |; 395  &)
%                                         (   9 <=>; 277 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-5 arity)
%            Number of functors    :   17 (   2 constant; 0-4 arity)
%            Number of variables   :  291 (   0 singleton; 243 !;  48 ?)
%            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(rc1_analoaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & v1_analoaf(A) ) )).

fof(rc2_analoaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A) ) )).

fof(fc1_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k2_analoaf(A))
        & v1_analoaf(k2_analoaf(A)) ) ) )).

fof(rc3_analoaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v2_analoaf(A) ) )).

fof(rc4_analoaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v2_analoaf(A)
      & v3_analoaf(A) ) )).

fof(d1_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,B,C,D,E)
                      <=> ~ ( B != C
                            & D != E
                            & ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ! [G] :
                                    ( m1_subset_1(G,k1_numbers)
                                   => ~ ( ~ r1_xreal_0(F,np__0)
                                        & ~ r1_xreal_0(G,np__0)
                                        & k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G) ) ) ) ) ) ) ) ) ) ) )).

fof(t1_analoaf,axiom,(
    $true )).

fof(t2_analoaf,axiom,(
    $true )).

fof(t3_analoaf,axiom,(
    $true )).

fof(t4_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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))
                 => k4_rlvect_1(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,B,D) ) ) ) ) )).

fof(t5_analoaf,axiom,(
    $true )).

fof(t6_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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))
                 => k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,B,k6_rlvect_1(A,D,C)) ) ) ) ) )).

fof(t7_analoaf,axiom,(
    $true )).

fof(t8_analoaf,axiom,(
    $true )).

fof(t9_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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))
                     => ( k4_rlvect_1(A,B,C) = k4_rlvect_1(A,D,E)
                       => k6_rlvect_1(A,B,E) = k6_rlvect_1(A,D,C) ) ) ) ) ) ) )).

fof(t10_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => k3_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k5_rlvect_1(A,k3_rlvect_1(A,k6_rlvect_1(A,C,B),D)) ) ) ) ) )).

fof(t11_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => k3_rlvect_1(A,k6_rlvect_1(A,B,C),k5_real_1(D,E)) = k3_rlvect_1(A,k6_rlvect_1(A,C,B),k5_real_1(E,D)) ) ) ) ) ) )).

fof(t12_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( k3_rlvect_1(A,B,D) = C
                   => ( D = np__0
                      | B = k3_rlvect_1(A,C,k2_real_1(D)) ) ) ) ) ) ) )).

fof(t13_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( k3_rlvect_1(A,B,D) = C
                     => ( D = np__0
                        | B = k3_rlvect_1(A,C,k2_real_1(D)) ) )
                    & ( B = k3_rlvect_1(A,C,k2_real_1(D))
                     => ( D = np__0
                        | k3_rlvect_1(A,B,D) = C ) ) ) ) ) ) ) )).

fof(t14_analoaf,axiom,(
    $true )).

fof(t15_analoaf,axiom,(
    $true )).

fof(t16_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,B,C,D,E)
                          & B != C
                          & D != E
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ~ ( k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
                                      & ~ r1_xreal_0(F,np__0)
                                      & ~ r1_xreal_0(G,np__0) ) ) ) ) ) ) ) ) ) )).

fof(t17_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_analoaf(A,B,C,B,C) ) ) ) )).

fof(t18_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,B,C,D,D)
                    & r1_analoaf(A,B,B,C,D) ) ) ) ) ) )).

fof(t19_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analoaf(A,B,C,C,B)
               => B = C ) ) ) ) )).

fof(t20_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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))
                             => ( ( r1_analoaf(A,B,C,D,E)
                                  & r1_analoaf(A,B,C,F,G) )
                               => ( B = C
                                  | r1_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t21_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,B,C,D,E)
                       => ( r1_analoaf(A,C,B,E,D)
                          & r1_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) )).

fof(t22_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,B,C,C,D)
                   => r1_analoaf(A,B,C,B,D) ) ) ) ) ) )).

fof(t23_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,B,C,B,D)
                      & ~ r1_analoaf(A,B,C,C,D)
                      & ~ r1_analoaf(A,B,D,D,C) ) ) ) ) ) )).

fof(t24_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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))
                     => ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,D,E)
                       => r1_analoaf(A,C,B,E,D) ) ) ) ) ) ) )).

fof(t25_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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 = k6_rlvect_1(A,k4_rlvect_1(A,C,D),E)
                       => ( r1_analoaf(A,E,C,D,B)
                          & r1_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t26_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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))
                        & r1_analoaf(A,B,C,D,E)
                        & r1_analoaf(A,B,D,C,E)
                        & C != E ) ) ) ) ) ) )).

fof(t27_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_analoaf(A,C,B,B,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_analoaf(A,E,B,B,F)
                                  & r1_analoaf(A,E,C,D,F) ) ) ) ) ) ) ) ) )).

fof(t28_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                         => ( D = np__0
                            & E = np__0 ) ) ) )
               => ( B != C
                  & B != k1_rlvect_1(A)
                  & C != k1_rlvect_1(A) ) ) ) ) ) )).

fof(t29_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ~ ( ? [B] :
              ( m1_subset_1(B,u1_struct_0(A))
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                           => ( D = np__0
                              & E = np__0 ) ) ) ) ) )
          & ! [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_analoaf(A,B,C,D,E)
                              & ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).

fof(t30_analoaf,axiom,(
    $true )).

fof(t31_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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,k1_numbers)
                        & ? [F] :
                            ( m1_subset_1(F,k1_numbers)
                            & k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) = 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))
                       => ~ ( ~ r1_analoaf(A,B,C,D,E)
                            & ~ r1_analoaf(A,B,C,E,D)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( ( r1_analoaf(A,B,C,B,F)
                                      | r1_analoaf(A,B,C,F,B) )
                                    & ( r1_analoaf(A,D,E,D,F)
                                      | r1_analoaf(A,D,E,F,D) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_analoaf,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_analoaf(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)),u1_analoaf(A)) ) ) ) ) ) ) )).

fof(d3_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
         => ( B = k1_analoaf(A)
          <=> ! [C,D] :
                ( r2_hidden(k4_tarski(C,D),B)
              <=> ? [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))
                            & ? [H] :
                                ( m1_subset_1(H,u1_struct_0(A))
                                & C = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F)
                                & D = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
                                & r1_analoaf(A,E,F,G,H) ) ) ) ) ) ) ) ) )).

fof(t32_analoaf,axiom,(
    $true )).

fof(t33_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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_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_analoaf(A))
                      <=> r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) )).

fof(d4_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => k2_analoaf(A) = g1_analoaf(u1_struct_0(A),k1_analoaf(A)) ) )).

fof(t34_analoaf,axiom,(
    $true )).

fof(t35_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                         => ( D = np__0
                            & E = np__0 ) ) ) ) ) )
       => ( ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
                   => B = C ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k2_analoaf(A)))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(k2_analoaf(A)))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(k2_analoaf(A)))
                                         => ( r2_analoaf(k2_analoaf(A),B,C,D,D)
                                            & ( r2_analoaf(k2_analoaf(A),B,C,C,B)
                                             => B = C )
                                            & ( ( r2_analoaf(k2_analoaf(A),B,C,F,G)
                                                & r2_analoaf(k2_analoaf(A),B,C,H,I) )
                                             => ( B = C
                                                | r2_analoaf(k2_analoaf(A),F,G,H,I) ) )
                                            & ( r2_analoaf(k2_analoaf(A),B,C,D,E)
                                             => r2_analoaf(k2_analoaf(A),C,B,E,D) )
                                            & ( r2_analoaf(k2_analoaf(A),B,C,C,D)
                                             => r2_analoaf(k2_analoaf(A),B,C,B,D) )
                                            & ~ ( r2_analoaf(k2_analoaf(A),B,C,B,D)
                                                & ~ r2_analoaf(k2_analoaf(A),B,C,C,D)
                                                & ~ r2_analoaf(k2_analoaf(A),B,D,D,C) ) ) ) ) ) ) ) ) ) )
          & ? [B] :
              ( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
                  & ? [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
                      & ? [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
                          & ~ r2_analoaf(k2_analoaf(A),B,C,D,E)
                          & ~ r2_analoaf(k2_analoaf(A),B,C,E,D) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
                          & r2_analoaf(k2_analoaf(A),B,C,D,E)
                          & r2_analoaf(k2_analoaf(A),B,D,C,E)
                          & C != E ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
                         => ~ ( B != D
                              & r2_analoaf(k2_analoaf(A),D,B,B,E)
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
                                 => ~ ( r2_analoaf(k2_analoaf(A),C,B,B,F)
                                      & r2_analoaf(k2_analoaf(A),C,D,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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,k1_numbers)
                        & ? [F] :
                            ( m1_subset_1(F,k1_numbers)
                            & k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) = D ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
                       => ~ ( ~ r2_analoaf(k2_analoaf(A),B,C,D,E)
                            & ~ r2_analoaf(k2_analoaf(A),B,C,E,D)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
                               => ~ ( ( r2_analoaf(k2_analoaf(A),B,C,B,F)
                                      | r2_analoaf(k2_analoaf(A),B,C,F,B) )
                                    & ( r2_analoaf(k2_analoaf(A),D,E,D,F)
                                      | r2_analoaf(k2_analoaf(A),D,E,F,D) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v2_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))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ( r2_analoaf(A,B,C,D,D)
                                            & ( r2_analoaf(A,B,C,C,B)
                                             => B = C )
                                            & ( ( r2_analoaf(A,B,C,F,G)
                                                & r2_analoaf(A,B,C,H,I) )
                                             => ( B = C
                                                | r2_analoaf(A,F,G,H,I) ) )
                                            & ( r2_analoaf(A,B,C,D,E)
                                             => r2_analoaf(A,C,B,E,D) )
                                            & ( r2_analoaf(A,B,C,C,D)
                                             => r2_analoaf(A,B,C,B,D) )
                                            & ~ ( r2_analoaf(A,B,C,B,D)
                                                & ~ r2_analoaf(A,B,C,C,D)
                                                & ~ r2_analoaf(A,B,D,D,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))
                          & ~ r2_analoaf(A,B,C,D,E)
                          & ~ r2_analoaf(A,B,C,E,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,C,D,E)
                          & 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))
                         => ~ ( B != D
                              & r2_analoaf(A,D,B,B,E)
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,C,B,B,F)
                                      & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_analoaf,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))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ( r2_analoaf(A,B,C,D,D)
                                            & ( r2_analoaf(A,B,C,C,B)
                                             => B = C )
                                            & ( ( r2_analoaf(A,B,C,F,G)
                                                & r2_analoaf(A,B,C,H,I) )
                                             => ( B = C
                                                | r2_analoaf(A,F,G,H,I) ) )
                                            & ( r2_analoaf(A,B,C,D,E)
                                             => r2_analoaf(A,C,B,E,D) )
                                            & ( r2_analoaf(A,B,C,C,D)
                                             => r2_analoaf(A,B,C,B,D) )
                                            & ~ ( r2_analoaf(A,B,C,B,D)
                                                & ~ r2_analoaf(A,B,C,C,D)
                                                & ~ r2_analoaf(A,B,D,D,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))
                          & ~ r2_analoaf(A,B,C,D,E)
                          & ~ r2_analoaf(A,B,C,E,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,C,D,E)
                          & 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))
                         => ~ ( B != D
                              & r2_analoaf(A,D,B,B,E)
                              & ! [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)
          & v2_analoaf(A)
          & l1_analoaf(A) ) ) ) )).

fof(t38_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                         => ( D = np__0
                            & E = np__0 ) ) ) ) ) )
       => ( ~ v3_struct_0(k2_analoaf(A))
          & ~ v3_realset2(k2_analoaf(A))
          & v2_analoaf(k2_analoaf(A))
          & l1_analoaf(k2_analoaf(A)) ) ) ) )).

fof(d6_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v3_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)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( ( r2_analoaf(A,B,C,B,F)
                                      | r2_analoaf(A,B,C,F,B) )
                                    & ( r2_analoaf(A,D,E,D,F)
                                      | r2_analoaf(A,D,E,F,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_analoaf,axiom,(
    $true )).

fof(t40_analoaf,axiom,(
    $true )).

fof(t41_analoaf,axiom,(
    $true )).

fof(t42_analoaf,axiom,(
    $true )).

fof(t43_analoaf,axiom,(
    $true )).

fof(t44_analoaf,axiom,(
    $true )).

fof(t45_analoaf,axiom,(
    $true )).

fof(t46_analoaf,axiom,(
    $true )).

fof(t47_analoaf,axiom,(
    $true )).

fof(t48_analoaf,axiom,(
    $true )).

fof(t49_analoaf,axiom,(
    $true )).

fof(t50_analoaf,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))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ( r2_analoaf(A,B,C,D,D)
                                            & ( r2_analoaf(A,B,C,C,B)
                                             => B = C )
                                            & ( ( r2_analoaf(A,B,C,F,G)
                                                & r2_analoaf(A,B,C,H,I) )
                                             => ( B = C
                                                | r2_analoaf(A,F,G,H,I) ) )
                                            & ( r2_analoaf(A,B,C,D,E)
                                             => r2_analoaf(A,C,B,E,D) )
                                            & ( r2_analoaf(A,B,C,C,D)
                                             => r2_analoaf(A,B,C,B,D) )
                                            & ~ ( r2_analoaf(A,B,C,B,D)
                                                & ~ r2_analoaf(A,B,C,C,D)
                                                & ~ r2_analoaf(A,B,D,D,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))
                          & ~ r2_analoaf(A,B,C,D,E)
                          & ~ r2_analoaf(A,B,C,E,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,C,D,E)
                          & 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))
                         => ~ ( B != D
                              & r2_analoaf(A,D,B,B,E)
                              & ! [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)
                              & ~ r2_analoaf(A,B,C,E,D)
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( ( r2_analoaf(A,B,C,B,F)
                                        | r2_analoaf(A,B,C,F,B) )
                                      & ( r2_analoaf(A,D,E,D,F)
                                        | r2_analoaf(A,D,E,F,D) ) ) ) ) ) ) ) ) )
      <=> ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_analoaf(A)
          & v3_analoaf(A)
          & l1_analoaf(A) ) ) ) )).

fof(t51_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                         => ( D = np__0
                            & E = np__0 ) ) ) )
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ? [E] :
                        ( m1_subset_1(E,k1_numbers)
                        & ? [F] :
                            ( m1_subset_1(F,k1_numbers)
                            & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) )
       => ( ~ v3_struct_0(k2_analoaf(A))
          & ~ v3_realset2(k2_analoaf(A))
          & v2_analoaf(k2_analoaf(A))
          & v3_analoaf(k2_analoaf(A))
          & l1_analoaf(k2_analoaf(A)) ) ) ) )).

fof(dt_l1_analoaf,axiom,(
    ! [A] :
      ( l1_analoaf(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) )).

fof(abstractness_v1_analoaf,axiom,(
    ! [A] :
      ( l1_analoaf(A)
     => ( v1_analoaf(A)
       => A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) )).

fof(dt_k1_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => m2_relset_1(k1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) )).

fof(dt_k2_analoaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( v1_analoaf(k2_analoaf(A))
        & l1_analoaf(k2_analoaf(A)) ) ) )).

fof(dt_u1_analoaf,axiom,(
    ! [A] :
      ( l1_analoaf(A)
     => m2_relset_1(u1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) )).

fof(dt_g1_analoaf,axiom,(
    ! [A,B] :
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ( v1_analoaf(g1_analoaf(A,B))
        & l1_analoaf(g1_analoaf(A,B)) ) ) )).

fof(free_g1_analoaf,axiom,(
    ! [A,B] :
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ! [C,D] :
          ( g1_analoaf(A,B) = g1_analoaf(C,D)
         => ( A = C
            & B = D ) ) ) )).
%------------------------------------------------------------------------------