SET007 Axioms: SET007+229.ax


%------------------------------------------------------------------------------
% File     : SET007+229 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Parallelity and Lines in 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    : aff_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   85 (  14 unit)
%            Number of atoms       :  853 (  56 equality)
%            Maximal formula depth :   24 (  12 average)
%            Number of connectives :  961 ( 193 ~  ;  21  |; 391  &)
%                                         (  14 <=>; 342 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   16 (   1 propositional; 0-5 arity)
%            Number of functors    :    4 (   0 constant; 1-3 arity)
%            Number of variables   :  327 (   0 singleton; 312 !;  15 ?)
%            Maximal term depth    :    3 (   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(d1_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                  <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) )).

fof(t1_aff_1,axiom,(
    $true )).

fof(t2_aff_1,axiom,(
    $true )).

fof(t3_aff_1,axiom,(
    $true )).

fof(t4_aff_1,axiom,(
    $true )).

fof(t5_aff_1,axiom,(
    $true )).

fof(t6_aff_1,axiom,(
    $true )).

fof(t7_aff_1,axiom,(
    $true )).

fof(t8_aff_1,axiom,(
    $true )).

fof(t9_aff_1,axiom,(
    $true )).

fof(t10_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) )).

fof(t11_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_analoaf(A,B,C,C,B)
                & r2_analoaf(A,B,C,B,C) ) ) ) ) )).

fof(t12_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_analoaf(A,B,C,D,D)
                    & r2_analoaf(A,D,D,B,C) ) ) ) ) ) )).

fof(t13_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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)
                          & r2_analoaf(A,C,B,D,E)
                          & r2_analoaf(A,C,B,E,D)
                          & r2_analoaf(A,D,E,B,C)
                          & r2_analoaf(A,D,E,C,B)
                          & r2_analoaf(A,E,D,B,C)
                          & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t14_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( B != C
                                  & ~ ( ~ ( r2_analoaf(A,B,C,D,E)
                                          & r2_analoaf(A,B,C,F,G) )
                                      & ~ ( r2_analoaf(A,B,C,D,E)
                                          & r2_analoaf(A,F,G,B,C) )
                                      & ~ ( r2_analoaf(A,D,E,B,C)
                                          & r2_analoaf(A,F,G,B,C) )
                                      & ~ ( r2_analoaf(A,D,E,B,C)
                                          & r2_analoaf(A,B,C,F,G) ) )
                                  & ~ r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t15_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                   => ( r1_aff_1(A,B,D,C)
                      & r1_aff_1(A,C,B,D)
                      & r1_aff_1(A,C,D,B)
                      & r1_aff_1(A,D,B,C)
                      & r1_aff_1(A,D,C,B) ) ) ) ) ) ) )).

fof(t16_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_aff_1(A,B,B,C)
                & r1_aff_1(A,B,C,C)
                & r1_aff_1(A,B,C,B) ) ) ) ) )).

fof(t17_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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_aff_1(A,B,C,D)
                              & r1_aff_1(A,B,C,E)
                              & r1_aff_1(A,B,C,F) )
                           => ( B = C
                              | r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t18_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_aff_1(A,B,C,D)
                          & r2_analoaf(A,B,C,D,E) )
                       => ( B = C
                          | r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t19_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_aff_1(A,B,C,D)
                          & r1_aff_1(A,B,C,E) )
                       => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t20_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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_aff_1(A,D,E,B)
                              & r1_aff_1(A,D,E,C)
                              & r1_aff_1(A,B,C,F) )
                           => ( B = C
                              | r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t21_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ~ ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_aff_1(A,B,C,D) ) ) ) ) )).

fof(t22_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r1_aff_1(A,B,C,D) ) ) ) ) ) )).

fof(t23_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_aff_1(A,B,D,E)
                          & r2_analoaf(A,C,D,C,E) )
                       => ( r1_aff_1(A,B,C,D)
                          | D = E ) ) ) ) ) ) ) )).

fof(d2_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( D = k1_aff_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(E,D)
                        <=> r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t24_aff_1,axiom,(
    $true )).

fof(t25_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_aff_1(A,B,C) = k1_aff_1(A,C,B) ) ) ) )).

fof(t26_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k2_aff_1(A,B,C))
                & r2_hidden(C,k2_aff_1(A,B,C)) ) ) ) ) )).

fof(t27_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(B,k2_aff_1(A,C,D))
                          & r2_hidden(E,k2_aff_1(A,C,D)) )
                       => ( B = E
                          | r1_tarski(k2_aff_1(A,B,E),k2_aff_1(A,C,D)) ) ) ) ) ) ) ) )).

fof(t28_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(B,k2_aff_1(A,C,D))
                          & r2_hidden(E,k2_aff_1(A,C,D)) )
                       => ( C = D
                          | r1_tarski(k2_aff_1(A,C,D),k2_aff_1(A,B,E)) ) ) ) ) ) ) ) )).

fof(d3_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_1(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C != D
                    & B = k2_aff_1(A,C,D) ) ) ) ) ) )).

fof(t29_aff_1,axiom,(
    $true )).

fof(t30_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & B != C
                          & D != E ) ) ) ) ) ) )).

fof(t31_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_aff_1(B,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)
                          & C != D ) ) ) ) ) ) )).

fof(t32_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( B != D
                          & r2_hidden(D,C) ) ) ) ) ) ) )).

fof(t33_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                  <=> ? [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                        & v1_aff_1(E,A)
                        & r2_hidden(B,E)
                        & r2_hidden(C,E)
                        & r2_hidden(D,E) ) ) ) ) ) ) )).

fof(d4_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_aff_1(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 = k2_aff_1(A,E,F)
                            & r2_analoaf(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(d5_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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)))
             => ( r3_aff_1(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & B = k2_aff_1(A,D,E)
                        & D != E
                        & r2_aff_1(A,D,E,C) ) ) ) ) ) ) )).

fof(t34_aff_1,axiom,(
    $true )).

fof(t35_aff_1,axiom,(
    $true )).

fof(t36_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_hidden(B,k2_aff_1(A,C,D))
                       => ( C = D
                          | ( r2_hidden(E,k2_aff_1(A,C,D))
                          <=> r2_analoaf(A,C,D,B,E) ) ) ) ) ) ) ) ) )).

fof(t37_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(D,A)
                      & r2_hidden(B,D) )
                   => ( r2_hidden(C,D)
                    <=> r2_aff_1(A,B,C,D) ) ) ) ) ) ) )).

fof(t38_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( D = k2_aff_1(A,B,C)
                     => ( B = C
                        | ( v1_aff_1(D,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & B != C ) ) )
                    & ( ( v1_aff_1(D,A)
                        & r2_hidden(B,D)
                        & r2_hidden(C,D) )
                     => ( B = C
                        | ( B != C
                          & D = k2_aff_1(A,B,C) ) ) ) ) ) ) ) ) )).

fof(t39_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_1(E,A)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & r1_aff_1(A,B,C,D) )
                       => ( B = C
                          | r2_hidden(D,E) ) ) ) ) ) ) ) )).

fof(t40_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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_aff_1(A,C,D,B) ) )
           => v1_aff_1(B,A) ) ) ) )).

fof(t41_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & v1_aff_1(F,A) )
                           => ( B = C
                              | ( r2_aff_1(A,D,E,F)
                              <=> r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) ) ) )).

fof(t42_aff_1,axiom,(
    $true )).

fof(t43_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B != C
               => r2_aff_1(A,B,C,k2_aff_1(A,B,C)) ) ) ) ) )).

fof(t44_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v1_aff_1(D,A)
                   => ( r2_aff_1(A,B,C,D)
                    <=> ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & ? [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                              & E != F
                              & r2_hidden(E,D)
                              & r2_hidden(F,D)
                              & r2_analoaf(A,B,C,E,F) ) ) ) ) ) ) ) ) )).

fof(t45_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_1(F,A)
                              & r2_aff_1(A,B,C,F)
                              & r2_aff_1(A,D,E,F) )
                           => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t46_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( r2_aff_1(A,B,C,F)
                              & r2_analoaf(A,B,C,D,E) )
                           => ( B = C
                              | r2_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t47_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_1(C,A)
               => r2_aff_1(A,B,B,C) ) ) ) ) )).

fof(t48_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_aff_1(A,B,C,D)
                   => r2_aff_1(A,C,B,D) ) ) ) ) ) )).

fof(t49_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r2_aff_1(A,B,C,D)
                      & ~ r2_hidden(B,D)
                      & r2_hidden(C,D) ) ) ) ) ) )).

fof(t50_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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)))
             => ( r3_aff_1(A,B,C)
               => ( v1_aff_1(B,A)
                  & v1_aff_1(C,A) ) ) ) ) ) )).

fof(t51_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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)))
             => ( r3_aff_1(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
                                & r2_analoaf(A,D,E,F,G)
                                & B = k2_aff_1(A,D,E)
                                & C = k2_aff_1(A,F,G) ) ) ) ) ) ) ) ) )).

fof(t52_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( v1_aff_1(F,A)
                                  & v1_aff_1(G,A)
                                  & r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G) )
                               => ( B = C
                                  | D = E
                                  | ( r3_aff_1(A,F,G)
                                  <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t53_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G)
                                  & r3_aff_1(A,F,G) )
                               => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) )).

fof(t54_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r3_aff_1(A,D,E) )
                       => r2_aff_1(A,B,C,E) ) ) ) ) ) ) )).

fof(t55_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_1(B,A)
           => r3_aff_1(A,B,B) ) ) ) )).

fof(t56_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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)))
             => ( r3_aff_1(A,B,C)
               => r3_aff_1(A,C,B) ) ) ) ) )).

fof(t57_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_aff_1(A,B,C,D)
                          & r4_aff_1(A,D,E) )
                       => r2_aff_1(A,B,C,E) ) ) ) ) ) ) )).

fof(t58_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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)))
                 => ( ~ ( ~ ( r4_aff_1(A,B,C)
                            & r4_aff_1(A,C,D) )
                        & ~ ( r4_aff_1(A,B,C)
                            & r4_aff_1(A,D,C) )
                        & ~ ( r4_aff_1(A,C,B)
                            & r4_aff_1(A,C,D) )
                        & ~ ( r4_aff_1(A,C,B)
                            & r4_aff_1(A,D,C) ) )
                   => r4_aff_1(A,B,D) ) ) ) ) ) )).

fof(t59_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r4_aff_1(A,C,D)
                      & r2_hidden(B,C)
                      & r2_hidden(B,D) )
                   => C = D ) ) ) ) ) )).

fof(t60_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(B,E)
                          & ~ r2_hidden(C,E)
                          & r2_aff_1(A,C,D,E)
                          & C != D
                          & r1_aff_1(A,B,C,D) ) ) ) ) ) ) )).

fof(t61_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( r2_aff_1(A,B,C,G)
                                  & r2_aff_1(A,D,E,G)
                                  & r1_aff_1(A,F,B,D)
                                  & r1_aff_1(A,F,C,E)
                                  & r2_hidden(F,G)
                                  & B = C )
                               => ( r2_hidden(B,G)
                                  | D = E ) ) ) ) ) ) ) ) ) )).

fof(t62_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_1(F,A)
                              & r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & r2_analoaf(A,B,C,D,E) )
                           => ( B = C
                              | r2_hidden(E,F) ) ) ) ) ) ) ) ) )).

fof(t63_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(B,D)
                          & r4_aff_1(A,C,D) ) ) ) ) ) ) )).

fof(t64_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,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)))
                     => ( ( r4_aff_1(A,C,D)
                          & r4_aff_1(A,C,E)
                          & r2_hidden(B,D)
                          & r2_hidden(B,E) )
                       => D = E ) ) ) ) ) ) )).

fof(t65_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_1(F,A)
                              & r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & r2_hidden(E,F) )
                           => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t66_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(D,A)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => r2_aff_1(A,B,C,D) ) ) ) ) ) )).

fof(t67_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_aff_1(A,B,C,D)
                          & r2_aff_1(A,B,C,E) )
                       => ( B = C
                          | r4_aff_1(A,D,E) ) ) ) ) ) ) ) )).

fof(t68_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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_aff_1(A,B,C,E)
                              & r1_aff_1(A,B,D,F)
                              & r2_analoaf(A,C,D,E,F)
                              & E = F )
                           => ( r1_aff_1(A,B,C,D)
                              | ( E = B
                                & F = B ) ) ) ) ) ) ) ) ) )).

fof(t69_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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_aff_1(A,B,C,E)
                              & r1_aff_1(A,B,D,F)
                              & r2_analoaf(A,C,D,E,F)
                              & E = B )
                           => ( r1_aff_1(A,B,C,D)
                              | F = B ) ) ) ) ) ) ) ) )).

fof(t70_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [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_aff_1(A,B,C,E)
                                  & r1_aff_1(A,B,D,F)
                                  & r1_aff_1(A,B,D,G)
                                  & r2_analoaf(A,C,D,E,F)
                                  & r2_analoaf(A,C,D,E,G) )
                               => ( r1_aff_1(A,B,C,D)
                                  | F = G ) ) ) ) ) ) ) ) ) )).

fof(t71_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(D,A)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => ( B = C
                      | D = k2_aff_1(A,B,C) ) ) ) ) ) ) )).

fof(t72_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(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)))
             => ~ ( v1_aff_1(B,A)
                  & v1_aff_1(C,A)
                  & ~ r4_aff_1(A,B,C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,B)
                          & r2_hidden(D,C) ) ) ) ) ) ) )).

fof(t73_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( v1_aff_1(D,A)
                      & ~ r2_aff_1(A,B,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,D)
                              & r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t74_aff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( ~ r2_analoaf(A,B,C,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_aff_1(A,B,C,F)
                                  & r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(symmetry_r4_aff_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_aff_1(A,B,C)
       => r4_aff_1(A,C,B) ) ) )).

fof(redefinition_r4_aff_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_aff_1(A,B,C)
      <=> r3_aff_1(A,B,C) ) ) )).

fof(dt_k1_aff_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_aff_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k2_aff_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_aff_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(commutativity_k2_aff_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k2_aff_1(A,B,C) = k2_aff_1(A,C,B) ) )).

fof(redefinition_k2_aff_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k2_aff_1(A,B,C) = k1_aff_1(A,B,C) ) )).
%------------------------------------------------------------------------------