SET007 Axioms: SET007+251.ax


%------------------------------------------------------------------------------
% File     : SET007+251 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Analytical Metric Affine Spaces and Planes
% 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    : analmetr [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  131 (  19 unit)
%            Number of atoms       : 1431 ( 120 equality)
%            Maximal formula depth :   41 (  12 average)
%            Number of connectives : 1536 ( 236 ~  ;  15  |; 700  &)
%                                         (  31 <=>; 554 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-7 arity)
%            Number of functors    :   26 (   2 constant; 0-4 arity)
%            Number of variables   :  570 (   0 singleton; 521 !;  49 ?)
%            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_analmetr,axiom,(
    ? [A] :
      ( l1_analmetr(A)
      & v1_analmetr(A) ) )).

fof(rc2_analmetr,axiom,(
    ? [A] :
      ( l1_analmetr(A)
      & ~ v3_struct_0(A) ) )).

fof(fc1_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_analmetr(A,B,C))
        & v1_analmetr(k2_analmetr(A,B,C)) ) ) )).

fof(fc2_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A)) ) ) )).

fof(rc3_analmetr,axiom,(
    ? [A] :
      ( l1_analmetr(A)
      & ~ v3_struct_0(A)
      & v1_analmetr(A)
      & v2_analmetr(A) ) )).

fof(rc4_analmetr,axiom,(
    ? [A] :
      ( l1_analmetr(A)
      & ~ v3_struct_0(A)
      & v1_analmetr(A)
      & v3_analmetr(A) ) )).

fof(fc3_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A)) ) ) )).

fof(fc4_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A)) ) ) )).

fof(cc1_analmetr,axiom,(
    ! [A] :
      ( l1_analmetr(A)
     => ( ( ~ v3_struct_0(A)
          & v3_analmetr(A) )
       => ( ~ v3_struct_0(A)
          & v2_analmetr(A) ) ) ) )).

fof(d1_analmetr,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_analmetr(A,B,C)
              <=> ( ! [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)) ) ) )
                  & ! [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 ) ) ) ) ) ) ) ) ) )).

fof(d2_analmetr,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_analmetr(A,B,C,D,E)
                      <=> ? [F] :
                            ( m1_subset_1(F,k1_numbers)
                            & ? [G] :
                                ( m1_subset_1(G,k1_numbers)
                                & ? [H] :
                                    ( m1_subset_1(H,k1_numbers)
                                    & ? [I] :
                                        ( m1_subset_1(I,k1_numbers)
                                        & B = k4_rlvect_1(A,k3_rlvect_1(A,D,F),k3_rlvect_1(A,E,G))
                                        & C = k4_rlvect_1(A,k3_rlvect_1(A,D,H),k3_rlvect_1(A,E,I))
                                        & k3_real_1(k4_real_1(F,H),k4_real_1(G,I)) = np__0 ) ) ) ) ) ) ) ) ) ) )).

fof(t1_analmetr,axiom,(
    $true )).

fof(t2_analmetr,axiom,(
    $true )).

fof(t3_analmetr,axiom,(
    $true )).

fof(t4_analmetr,axiom,(
    $true )).

fof(t5_analmetr,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_analmetr(A,D,E)
                       => ( r2_analmetr(A,B,C,D,E)
                        <=> ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( ( B = k4_rlvect_1(A,k3_rlvect_1(A,D,F),k3_rlvect_1(A,E,G))
                                              & C = k4_rlvect_1(A,k3_rlvect_1(A,D,H),k3_rlvect_1(A,E,I)) )
                                           => k3_real_1(k4_real_1(F,H),k4_real_1(G,I)) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_analmetr,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))
             => r2_analmetr(A,B,C,B,C) ) ) ) )).

fof(t7_analmetr,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_analmetr(A,B,C) ) ) ) )).

fof(t8_analmetr,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_analmetr(A,B,C,D,E)
                       => r2_analmetr(A,C,B,D,E) ) ) ) ) ) ) )).

fof(t9_analmetr,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_analmetr(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_analmetr(A,D,k1_rlvect_1(A),B,C)
                          & r2_analmetr(A,k1_rlvect_1(A),E,B,C) ) ) ) ) ) ) ) )).

fof(t10_analmetr,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,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ( r2_analmetr(A,B,C,D,E)
                               => r2_analmetr(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) )).

fof(t11_analmetr,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,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ( r2_analmetr(A,B,C,D,E)
                               => ( r2_analmetr(A,k3_rlvect_1(A,B,F),C,D,E)
                                  & r2_analmetr(A,B,k3_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) ) )).

fof(t12_analmetr,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_analmetr(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_analmetr(A,D,E,B,C)
                        & E != k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(t13_analmetr,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))
                         => ~ ( r1_analmetr(A,B,C)
                              & r2_analmetr(A,D,E,B,C)
                              & r2_analmetr(A,D,F,B,C)
                              & D != k1_rlvect_1(A)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ~ ( k3_rlvect_1(A,E,G) = k3_rlvect_1(A,F,H)
                                          & ~ ( G = np__0
                                              & H = np__0 ) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_analmetr,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))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_analmetr(A,D,E,B,C)
                              & r2_analmetr(A,D,F,B,C) )
                           => ( r2_analmetr(A,D,k4_rlvect_1(A,E,F),B,C)
                              & r2_analmetr(A,D,k6_rlvect_1(A,E,F),B,C) ) ) ) ) ) ) ) ) )).

fof(t15_analmetr,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_analmetr(A,B,C)
                      & r2_analmetr(A,D,D,B,C) )
                   => D = k1_rlvect_1(A) ) ) ) ) ) )).

fof(t16_analmetr,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))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_analmetr(A,D,k6_rlvect_1(A,E,F),B,C)
                              & r2_analmetr(A,E,k6_rlvect_1(A,F,D),B,C) )
                           => r2_analmetr(A,F,k6_rlvect_1(A,D,E),B,C) ) ) ) ) ) ) ) )).

fof(t17_analmetr,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_analmetr(A,B,C)
                          & D != k1_rlvect_1(A)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ~ r2_analmetr(A,k6_rlvect_1(A,E,k3_rlvect_1(A,D,F)),D,B,C) ) ) ) ) ) ) ) )).

fof(t18_analmetr,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,B,C,E,D) )
                            & ! [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)
                                        & ~ ( F = np__0
                                            & G = np__0 ) ) ) ) )
                        & ~ ( ? [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)
                                    & ~ ( F = np__0
                                        & G = np__0 ) ) )
                            & ~ r1_analoaf(A,B,C,D,E)
                            & ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).

fof(t19_analmetr,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_diraf(u1_struct_0(A),k1_analoaf(A)))
                      <=> ? [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)
                                & ~ ( F = np__0
                                    & G = np__0 ) ) ) ) ) ) ) ) ) )).

fof(d3_analmetr,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))
                             => ( r3_analmetr(A,B,C,D,E,F,G)
                              <=> r2_analmetr(A,k6_rlvect_1(A,C,B),k6_rlvect_1(A,E,D),F,G) ) ) ) ) ) ) ) ) )).

fof(d4_analmetr,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] :
                  ( m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
                 => ( D = k1_analmetr(A,B,C)
                  <=> ! [E,F] :
                        ( r2_hidden(k4_tarski(E,F),D)
                      <=> ? [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))
                                    & ? [J] :
                                        ( m1_subset_1(J,u1_struct_0(A))
                                        & E = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
                                        & F = k1_domain_1(u1_struct_0(A),u1_struct_0(A),I,J)
                                        & r3_analmetr(A,G,H,I,J,B,C) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_analmetr,axiom,(
    $true )).

fof(t21_analmetr,axiom,(
    $true )).

fof(t22_analmetr,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) )
     => u1_struct_0(k2_diraf(k2_analoaf(A))) = u1_struct_0(A) ) )).

fof(t23_analmetr,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) )
     => u1_analoaf(k2_diraf(k2_analoaf(A))) = k1_diraf(u1_struct_0(A),k1_analoaf(A)) ) )).

fof(t24_analmetr,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(k2_diraf(k2_analoaf(A))))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_diraf(k2_analoaf(A))))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                     => ( ( F = B
                                          & G = C
                                          & H = D
                                          & I = E )
                                       => ( r2_analoaf(k2_diraf(k2_analoaf(A)),F,G,H,I)
                                        <=> ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & ? [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                  & k3_rlvect_1(A,k6_rlvect_1(A,C,B),J) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),K)
                                                  & ~ ( J = np__0
                                                      & K = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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))
                     => ( r4_analmetr(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(d6_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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))
                     => ( r5_analmetr(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_analmetr(A)) ) ) ) ) ) ) )).

fof(d7_analmetr,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))
             => k2_analmetr(A,B,C) = g1_analmetr(u1_struct_0(A),k1_diraf(u1_struct_0(A),k1_analoaf(A)),k1_analmetr(A,B,C)) ) ) ) )).

fof(t25_analmetr,axiom,(
    $true )).

fof(t26_analmetr,axiom,(
    $true )).

fof(t27_analmetr,axiom,(
    $true )).

fof(t28_analmetr,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))
             => ( u1_struct_0(k2_analmetr(A,B,C)) = u1_struct_0(A)
                & u1_analoaf(k2_analmetr(A,B,C)) = k1_diraf(u1_struct_0(A),k1_analoaf(A))
                & u1_analmetr(k2_analmetr(A,B,C)) = k1_analmetr(A,B,C) ) ) ) ) )).

fof(d8_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => k3_analmetr(A) = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) )).

fof(t29_analmetr,axiom,(
    $true )).

fof(t30_analmetr,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))
             => k3_analmetr(k2_analmetr(A,B,C)) = k2_diraf(k2_analoaf(A)) ) ) ) )).

fof(t31_analmetr,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))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,F,G)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,F,G)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,F,G)))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,F,G)))
                                             => ( ( H = B
                                                  & I = C
                                                  & J = D
                                                  & K = E )
                                               => ( r5_analmetr(k2_analmetr(A,F,G),H,J,I,K)
                                                <=> r3_analmetr(A,B,D,C,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t32_analmetr,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))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,B,C)))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,B,C)))
                                             => ( ( H = D
                                                  & I = E
                                                  & J = F
                                                  & K = G )
                                               => ( r4_analmetr(k2_analmetr(A,B,C),H,I,J,K)
                                                <=> ? [L] :
                                                      ( m1_subset_1(L,k1_numbers)
                                                      & ? [M] :
                                                          ( m1_subset_1(M,k1_numbers)
                                                          & k3_rlvect_1(A,k6_rlvect_1(A,E,D),L) = k3_rlvect_1(A,k6_rlvect_1(A,G,F),M)
                                                          & ~ ( L = np__0
                                                              & M = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t33_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                             => ( r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                               => r5_analmetr(k2_analmetr(A,B,C),F,G,D,E) ) ) ) ) ) ) ) ) )).

fof(t34_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                             => ( r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                               => r5_analmetr(k2_analmetr(A,B,C),D,E,G,F) ) ) ) ) ) ) ) ) )).

fof(t35_analmetr,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_analmetr(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                           => r5_analmetr(k2_analmetr(A,B,C),D,E,F,F) ) ) ) ) ) ) ) )).

fof(t36_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
                                     => ~ ( r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                                          & r4_analmetr(k2_analmetr(A,B,C),D,E,H,I)
                                          & D != E
                                          & ~ r5_analmetr(k2_analmetr(A,B,C),F,G,H,I) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_analmetr,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_analmetr(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                           => ? [G] :
                                ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                                & r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                                & F != G ) ) ) ) ) ) ) ) )).

fof(t38_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
                                     => ~ ( r1_analmetr(A,B,C)
                                          & r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                                          & r5_analmetr(k2_analmetr(A,B,C),D,E,H,I)
                                          & D != E
                                          & ~ r4_analmetr(k2_analmetr(A,B,C),F,G,H,I) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ( ( r1_analmetr(A,B,C)
                                      & r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                                      & r5_analmetr(k2_analmetr(A,B,C),D,E,F,H) )
                                   => r5_analmetr(k2_analmetr(A,B,C),D,E,G,H) ) ) ) ) ) ) ) ) ) )).

fof(t40_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ( ( r1_analmetr(A,B,C)
                          & r5_analmetr(k2_analmetr(A,B,C),D,E,D,E) )
                       => D = E ) ) ) ) ) ) )).

fof(t41_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                             => ( ( r1_analmetr(A,B,C)
                                  & r5_analmetr(k2_analmetr(A,B,C),D,E,F,G)
                                  & r5_analmetr(k2_analmetr(A,B,C),F,E,G,D) )
                               => r5_analmetr(k2_analmetr(A,B,C),G,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t42_analmetr,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(k2_analmetr(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C)))
                     => ( r1_analmetr(A,B,C)
                       => ( D = E
                          | ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C)))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C)))
                                  & r4_analmetr(k2_analmetr(A,B,C),D,E,D,G)
                                  & r5_analmetr(k2_analmetr(A,B,C),D,E,G,F) ) ) ) ) ) ) ) ) ) )).

fof(d9_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( v2_analmetr(A)
      <=> ( ~ v3_struct_0(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & ~ v3_realset2(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & v1_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & l1_analoaf(g1_analoaf(u1_struct_0(A),u1_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))
                                         => ( ( r5_analmetr(A,B,C,B,C)
                                             => B = C )
                                            & r5_analmetr(A,B,C,D,D)
                                            & ( r5_analmetr(A,B,C,D,E)
                                             => ( r5_analmetr(A,B,C,E,D)
                                                & r5_analmetr(A,D,E,B,C) ) )
                                            & ~ ( r5_analmetr(A,B,C,F,G)
                                                & r4_analmetr(A,B,C,H,I)
                                                & ~ r5_analmetr(A,F,G,H,I)
                                                & B != C )
                                            & ( ( r5_analmetr(A,B,C,F,G)
                                                & r5_analmetr(A,B,C,F,I) )
                                             => r5_analmetr(A,B,C,G,I) ) ) ) ) ) ) ) ) ) )
          & ! [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))
                     => ~ ( B != C
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ~ ( r4_analmetr(A,B,C,B,E)
                                  & r5_analmetr(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))
                          & r5_analmetr(A,B,C,D,E)
                          & D != E ) ) ) ) ) ) ) )).

fof(t43_analmetr,axiom,(
    $true )).

fof(t44_analmetr,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_analmetr(A,B,C)
               => ( ~ v3_struct_0(k2_analmetr(A,B,C))
                  & v2_analmetr(k2_analmetr(A,B,C))
                  & l1_analmetr(k2_analmetr(A,B,C)) ) ) ) ) ) )).

fof(d10_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( v3_analmetr(A)
      <=> ( ~ v3_struct_0(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & ~ v3_realset2(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & v1_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & v2_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A)))
          & l1_analoaf(g1_analoaf(u1_struct_0(A),u1_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))
                                         => ( ( r5_analmetr(A,B,C,B,C)
                                             => B = C )
                                            & r5_analmetr(A,B,C,D,D)
                                            & ( r5_analmetr(A,B,C,D,E)
                                             => ( r5_analmetr(A,B,C,E,D)
                                                & r5_analmetr(A,D,E,B,C) ) )
                                            & ~ ( r5_analmetr(A,B,C,F,G)
                                                & r4_analmetr(A,B,C,H,I)
                                                & ~ r5_analmetr(A,F,G,H,I)
                                                & B != C )
                                            & ~ ( r5_analmetr(A,B,C,F,G)
                                                & r5_analmetr(A,B,C,H,I)
                                                & ~ r4_analmetr(A,F,G,H,I)
                                                & 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))
                          & r5_analmetr(A,B,C,D,E)
                          & D != E ) ) ) ) ) ) ) )).

fof(t45_analmetr,axiom,(
    $true )).

fof(t46_analmetr,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_analmetr(A,B,C)
               => ( ~ v3_struct_0(k2_analmetr(A,B,C))
                  & v3_analmetr(k2_analmetr(A,B,C))
                  & l1_analmetr(k2_analmetr(A,B,C)) ) ) ) ) ) )).

fof(t47_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
        <=> m1_subset_1(B,u1_struct_0(k3_analmetr(A))) ) ) )).

fof(t48_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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(k3_analmetr(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k3_analmetr(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k3_analmetr(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k3_analmetr(A)))
                                     => ( ( B = F
                                          & C = G
                                          & D = H
                                          & E = I )
                                       => ( r4_analmetr(A,B,C,D,E)
                                        <=> r2_analoaf(k3_analmetr(A),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t49_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) ) ) )).

fof(t50_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( ( ~ v3_struct_0(k3_analmetr(A))
          & ~ v3_realset2(k3_analmetr(A))
          & v1_diraf(k3_analmetr(A))
          & v2_diraf(k3_analmetr(A))
          & l1_analoaf(k3_analmetr(A)) )
       => ( ~ v3_struct_0(A)
          & v3_analmetr(A)
          & l1_analmetr(A) ) ) ) )).

fof(t51_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( v3_analmetr(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))
                                         => ( r4_analmetr(A,B,C,C,B)
                                            & r4_analmetr(A,B,C,D,D)
                                            & ~ ( r4_analmetr(A,B,C,F,G)
                                                & r4_analmetr(A,B,C,H,I)
                                                & ~ r4_analmetr(A,F,G,H,I)
                                                & B != C )
                                            & ( r4_analmetr(A,B,C,B,D)
                                             => r4_analmetr(A,C,B,C,D) )
                                            & ? [J] :
                                                ( m1_subset_1(J,u1_struct_0(A))
                                                & r4_analmetr(A,B,C,D,J)
                                                & r4_analmetr(A,B,D,C,J) )
                                            & ~ ! [J] :
                                                  ( m1_subset_1(J,u1_struct_0(A))
                                                 => ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(A))
                                                     => ! [L] :
                                                          ( m1_subset_1(L,u1_struct_0(A))
                                                         => r4_analmetr(A,J,K,J,L) ) ) )
                                            & ? [J] :
                                                ( m1_subset_1(J,u1_struct_0(A))
                                                & r4_analmetr(A,B,C,D,J)
                                                & D != J )
                                            & ~ ( r4_analmetr(A,B,C,C,E)
                                                & C != B
                                                & ! [J] :
                                                    ( m1_subset_1(J,u1_struct_0(A))
                                                   => ~ ( r4_analmetr(A,D,C,C,J)
                                                        & r4_analmetr(A,D,B,E,J) ) ) )
                                            & ( r5_analmetr(A,B,C,B,C)
                                             => B = C )
                                            & r5_analmetr(A,B,C,D,D)
                                            & ( r5_analmetr(A,B,C,D,E)
                                             => ( r5_analmetr(A,B,C,E,D)
                                                & r5_analmetr(A,D,E,B,C) ) )
                                            & ~ ( r5_analmetr(A,B,C,F,G)
                                                & r4_analmetr(A,B,C,H,I)
                                                & ~ r5_analmetr(A,F,G,H,I)
                                                & B != C )
                                            & ~ ( r5_analmetr(A,B,C,F,G)
                                                & r5_analmetr(A,B,C,H,I)
                                                & ~ r4_analmetr(A,F,G,H,I)
                                                & B != C )
                                            & ? [J] :
                                                ( m1_subset_1(J,u1_struct_0(A))
                                                & r5_analmetr(A,B,C,D,J)
                                                & D != J )
                                            & ~ ( ~ r4_analmetr(A,B,C,D,E)
                                                & ! [J] :
                                                    ( m1_subset_1(J,u1_struct_0(A))
                                                   => ~ ( r4_analmetr(A,B,C,B,J)
                                                        & r4_analmetr(A,D,E,D,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d11_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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))
                 => ( r6_analmetr(A,B,C,D)
                  <=> r4_analmetr(A,B,C,B,D) ) ) ) ) ) )).

fof(d12_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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_zfmisc_1(u1_struct_0(A)))
                 => ( D = k4_analmetr(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(E,D)
                        <=> r6_analmetr(A,B,C,E) ) ) ) ) ) ) ) )).

fof(d13_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_analmetr(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C != D
                    & B = k4_analmetr(A,C,D) ) ) ) ) ) )).

fof(t52_analmetr,axiom,(
    $true )).

fof(t53_analmetr,axiom,(
    $true )).

fof(t54_analmetr,axiom,(
    $true )).

fof(t55_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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(k3_analmetr(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k3_analmetr(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k3_analmetr(A)))
                             => ( ( B = E
                                  & C = F
                                  & D = G )
                               => ( r6_analmetr(A,B,C,D)
                                <=> r1_aff_1(k3_analmetr(A),E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t56_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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(k3_analmetr(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k3_analmetr(A)))
                     => ( ( B = D
                          & C = E )
                       => k4_analmetr(A,B,C) = k2_aff_1(k3_analmetr(A),D,E) ) ) ) ) ) ) )).

fof(t57_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        <=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) ) ) )).

fof(t58_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
             => ( B = C
               => ( v4_analmetr(B,A)
                <=> v1_aff_1(C,k3_analmetr(A)) ) ) ) ) ) )).

fof(d14_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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_zfmisc_1(u1_struct_0(A)))
                 => ( r7_analmetr(A,B,C,D)
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & ? [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                            & E != F
                            & D = k4_analmetr(A,E,F)
                            & r5_analmetr(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(d15_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r8_analmetr(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & D != E
                        & B = k4_analmetr(A,D,E)
                        & r7_analmetr(A,D,E,C) ) ) ) ) ) ) )).

fof(d16_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r9_analmetr(A,B,C)
              <=> ? [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))
                                & D != E
                                & F != G
                                & B = k4_analmetr(A,D,E)
                                & C = k4_analmetr(A,F,G)
                                & r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t59_analmetr,axiom,(
    $true )).

fof(t60_analmetr,axiom,(
    $true )).

fof(t61_analmetr,axiom,(
    $true )).

fof(t62_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r7_analmetr(A,B,C,D)
                         => v4_analmetr(D,A) )
                        & ( r8_analmetr(A,D,E)
                         => ( v4_analmetr(D,A)
                            & v4_analmetr(E,A) ) ) ) ) ) ) ) ) )).

fof(t63_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r8_analmetr(A,B,C)
              <=> ? [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))
                                & D != E
                                & F != G
                                & B = k4_analmetr(A,D,E)
                                & C = k4_analmetr(A,F,G)
                                & r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t64_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
                     => ( ( B = D
                          & C = E )
                       => ( r9_analmetr(A,B,C)
                        <=> r4_aff_1(k3_analmetr(A),D,E) ) ) ) ) ) ) ) )).

fof(t65_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( v4_analmetr(B,A)
               => r7_analmetr(A,C,C,B) ) ) ) ) )).

fof(t66_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(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))
                         => ( r7_analmetr(A,C,D,B)
                           => ( ( ~ r4_analmetr(A,C,D,E,F)
                                & ~ r4_analmetr(A,E,F,C,D) )
                              | C = D
                              | r7_analmetr(A,E,F,B) ) ) ) ) ) ) ) ) )).

fof(t67_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r7_analmetr(A,C,D,B)
                   => r7_analmetr(A,D,C,B) ) ) ) ) ) )).

fof(t68_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r9_analmetr(A,B,C)
               => r9_analmetr(A,C,B) ) ) ) ) )).

fof(t69_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r7_analmetr(A,D,E,B)
                       => ( ( ~ r9_analmetr(A,B,C)
                            & ~ r9_analmetr(A,C,B) )
                          | r7_analmetr(A,D,E,C) ) ) ) ) ) ) ) )).

fof(t70_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r8_analmetr(A,B,C)
               => r8_analmetr(A,C,B) ) ) ) ) )).

fof(t71_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_hidden(C,B)
                      & r2_hidden(D,B)
                      & r7_analmetr(A,C,D,B) )
                   => C = D ) ) ) ) ) )).

fof(t72_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ r11_analmetr(A,B,B) ) ) )).

fof(t73_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( ( r11_analmetr(A,B,C)
                        | r11_analmetr(A,C,B) )
                      & ( r10_analmetr(A,B,D)
                        | r10_analmetr(A,D,B) )
                      & ~ ( r11_analmetr(A,C,D)
                          & r11_analmetr(A,D,C) ) ) ) ) ) ) )).

fof(t74_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( r10_analmetr(A,B,C)
                  & r11_analmetr(A,B,C) ) ) ) ) )).

fof(t75_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(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))
                         => ( ( r2_hidden(C,B)
                              & r2_hidden(D,B)
                              & r7_analmetr(A,E,F,B) )
                           => ( r5_analmetr(A,E,F,C,D)
                              & r5_analmetr(A,C,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t76_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_hidden(C,B)
                      & r2_hidden(D,B)
                      & v4_analmetr(B,A) )
                   => ( C = D
                      | B = k4_analmetr(A,C,D) ) ) ) ) ) ) )).

fof(t77_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(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))
                         => ( ( r2_hidden(C,B)
                              & r2_hidden(D,B)
                              & v4_analmetr(B,A) )
                           => ( C = D
                              | ( ~ r5_analmetr(A,C,D,E,F)
                                & ~ r5_analmetr(A,E,F,C,D) )
                              | r7_analmetr(A,E,F,B) ) ) ) ) ) ) ) ) )).

fof(t78_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(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_hidden(D,B)
                                  & r2_hidden(E,B)
                                  & r2_hidden(F,C)
                                  & r2_hidden(G,C)
                                  & r11_analmetr(A,B,C) )
                               => r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t79_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(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))
                                 => ( ( r2_hidden(F,B)
                                      & r2_hidden(F,C)
                                      & r2_hidden(G,B)
                                      & r2_hidden(H,C)
                                      & r2_hidden(G,D)
                                      & r2_hidden(H,D)
                                      & r11_analmetr(A,E,B)
                                      & r11_analmetr(A,E,C)
                                      & v4_analmetr(D,A) )
                                   => ( G = H
                                      | r11_analmetr(A,E,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t80_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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))
                 => ( r5_analmetr(A,B,C,D,D)
                    & r5_analmetr(A,D,D,B,C)
                    & r4_analmetr(A,B,C,D,D)
                    & r4_analmetr(A,D,D,B,C) ) ) ) ) ) )).

fof(t81_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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))
                     => ( r4_analmetr(A,B,C,D,E)
                       => ( r4_analmetr(A,B,C,E,D)
                          & r4_analmetr(A,C,B,D,E)
                          & r4_analmetr(A,C,B,E,D)
                          & r4_analmetr(A,D,E,B,C)
                          & r4_analmetr(A,D,E,C,B)
                          & r4_analmetr(A,E,D,B,C)
                          & r4_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t82_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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
                                  & ~ ( ~ ( r4_analmetr(A,B,C,D,E)
                                          & r4_analmetr(A,B,C,F,G) )
                                      & ~ ( r4_analmetr(A,B,C,D,E)
                                          & r4_analmetr(A,F,G,B,C) )
                                      & ~ ( r4_analmetr(A,D,E,B,C)
                                          & r4_analmetr(A,F,G,B,C) )
                                      & ~ ( r4_analmetr(A,D,E,B,C)
                                          & r4_analmetr(A,B,C,F,G) ) )
                                  & ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t83_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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))
                     => ( r5_analmetr(A,B,C,D,E)
                       => ( r5_analmetr(A,B,C,E,D)
                          & r5_analmetr(A,C,B,D,E)
                          & r5_analmetr(A,C,B,E,D)
                          & r5_analmetr(A,D,E,B,C)
                          & r5_analmetr(A,D,E,C,B)
                          & r5_analmetr(A,E,D,B,C)
                          & r5_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t84_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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
                                  & ~ ( ~ ( r4_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,B,C,F,G) )
                                      & ~ ( r4_analmetr(A,B,C,F,G)
                                          & r5_analmetr(A,B,C,D,E) )
                                      & ~ ( r4_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r4_analmetr(A,B,C,F,G)
                                          & r5_analmetr(A,D,E,B,C) )
                                      & ~ ( r4_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r4_analmetr(A,F,G,B,C)
                                          & r5_analmetr(A,D,E,B,C) )
                                      & ~ ( r4_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,B,C,F,G) )
                                      & ~ ( r4_analmetr(A,F,G,B,C)
                                          & r5_analmetr(A,B,C,D,E) ) )
                                  & ~ r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t85_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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
                                  & ~ ( ~ ( r5_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,B,C,F,G) )
                                      & ~ ( r5_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r5_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r5_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,B,C,F,G) ) )
                                  & ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t86_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(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_hidden(D,B)
                                  & r2_hidden(E,B)
                                  & v4_analmetr(B,A)
                                  & r2_hidden(F,C)
                                  & r2_hidden(G,C)
                                  & v4_analmetr(C,A)
                                  & r4_analmetr(A,D,E,F,G) )
                               => ( D = E
                                  | F = G
                                  | r10_analmetr(A,B,C) ) ) ) ) ) ) ) ) ) )).

fof(t87_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( ( r11_analmetr(A,B,C)
                        | r11_analmetr(A,C,B) )
                      & ( r11_analmetr(A,B,D)
                        | r11_analmetr(A,D,B) )
                      & ~ ( r10_analmetr(A,C,D)
                          & r10_analmetr(A,D,C) ) ) ) ) ) ) )).

fof(t88_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( r11_analmetr(A,B,C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,B)
                          & r2_hidden(D,C) ) ) ) ) ) ) )).

fof(t89_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ~ ( r5_analmetr(A,B,C,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r6_analmetr(A,B,C,F)
                                  & r6_analmetr(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t90_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r7_analmetr(A,C,D,B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r6_analmetr(A,C,D,E)
                              & r2_hidden(E,B) ) ) ) ) ) ) ) )).

fof(t91_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                      & r5_analmetr(A,B,E,C,D)
                      & r6_analmetr(A,C,D,E) ) ) ) ) ) )).

fof(t92_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( v4_analmetr(B,A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r7_analmetr(A,C,D,B)
                          & r2_hidden(D,B) ) ) ) ) ) ) )).

fof(dt_l1_analmetr,axiom,(
    ! [A] :
      ( l1_analmetr(A)
     => l1_analoaf(A) ) )).

fof(existence_l1_analmetr,axiom,(
    ? [A] : l1_analmetr(A) )).

fof(abstractness_v1_analmetr,axiom,(
    ! [A] :
      ( l1_analmetr(A)
     => ( v1_analmetr(A)
       => A = g1_analmetr(u1_struct_0(A),u1_analoaf(A),u1_analmetr(A)) ) ) )).

fof(symmetry_r10_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r10_analmetr(A,B,C)
       => r10_analmetr(A,C,B) ) ) )).

fof(redefinition_r10_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r10_analmetr(A,B,C)
      <=> r9_analmetr(A,B,C) ) ) )).

fof(symmetry_r11_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r11_analmetr(A,B,C)
       => r11_analmetr(A,C,B) ) ) )).

fof(redefinition_r11_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r11_analmetr(A,B,C)
      <=> r8_analmetr(A,B,C) ) ) )).

fof(dt_k1_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m2_relset_1(k1_analmetr(A,B,C),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_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_analmetr(k2_analmetr(A,B,C))
        & l1_analmetr(k2_analmetr(A,B,C)) ) ) )).

fof(dt_k3_analmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( v1_analoaf(k3_analmetr(A))
        & l1_analoaf(k3_analmetr(A)) ) ) )).

fof(dt_k4_analmetr,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_analmetr(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_u1_analmetr,axiom,(
    ! [A] :
      ( l1_analmetr(A)
     => m2_relset_1(u1_analmetr(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_analmetr,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
        & m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
     => ( v1_analmetr(g1_analmetr(A,B,C))
        & l1_analmetr(g1_analmetr(A,B,C)) ) ) )).

fof(free_g1_analmetr,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
        & m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
     => ! [D,E,F] :
          ( g1_analmetr(A,B,C) = g1_analmetr(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------