SET007 Axioms: SET007+289.ax


%------------------------------------------------------------------------------
% File     : SET007+289 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Planes 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   79 (   0 unit)
%            Number of atoms       : 1104 (  59 equality)
%            Maximal formula depth :   44 (  15 average)
%            Number of connectives : 1276 ( 251 ~  ;  54  |; 557  &)
%                                         (  12 <=>; 402 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   0 propositional; 1-5 arity)
%            Number of functors    :    9 (   1 constant; 0-3 arity)
%            Number of variables   :  373 (   0 singleton; 361 !;  12 ?)
%            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(t1_aff_4,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,D,C) )
                          & B != C
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_aff_1(A,B,E,F)
                                  & r2_analoaf(A,C,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t2_aff_4,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_hidden(B,D)
                   => ( ( ~ r2_aff_1(A,B,C,D)
                        & ~ r2_aff_1(A,C,B,D) )
                      | r2_hidden(C,D) ) ) ) ) ) ) )).

fof(t3_aff_4,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,C,B,D) )
                          & ( r4_aff_1(A,D,E)
                            | r4_aff_1(A,E,D) )
                          & ~ ( r2_aff_1(A,B,C,E)
                              & r2_aff_1(A,C,B,E) ) ) ) ) ) ) ) )).

fof(t4_aff_4,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_aff_1(A,C,B,F) )
                              & ( r2_analoaf(A,B,C,D,E)
                                | r2_analoaf(A,D,E,B,C) )
                              & B != C
                              & ~ ( r2_aff_1(A,D,E,F)
                                  & r2_aff_1(A,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t5_aff_4,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,C,B,D) )
                          & ( r2_aff_1(A,B,C,E)
                            | r2_aff_1(A,C,B,E) )
                          & B != C
                          & ~ ( r4_aff_1(A,D,E)
                              & r4_aff_1(A,E,D) ) ) ) ) ) ) ) )).

fof(t6_aff_4,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_aff_1(A,C,B,F) )
                              & ( r2_aff_1(A,D,E,F)
                                | r2_aff_1(A,E,D,F) )
                              & ~ ( r2_analoaf(A,B,C,D,E)
                                  & r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) )).

fof(t7_aff_4,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) )
                               => ( ( ~ r4_aff_1(A,F,G)
                                    & ~ r4_aff_1(A,G,F) )
                                  | B = C
                                  | ( ~ r2_analoaf(A,B,C,D,E)
                                    & ~ r2_analoaf(A,D,E,B,C) )
                                  | r2_hidden(E,G) ) ) ) ) ) ) ) ) ) )).

fof(t8_aff_4,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)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ( ( r2_hidden(B,G)
                                      & r2_hidden(B,H)
                                      & r2_hidden(C,G)
                                      & r2_hidden(D,G)
                                      & r2_hidden(E,H)
                                      & r2_hidden(F,H)
                                      & v1_aff_1(G,A)
                                      & v1_aff_1(H,A)
                                      & B = D )
                                   => ( B = C
                                      | B = E
                                      | G = H
                                      | ( ~ r2_analoaf(A,C,E,D,F)
                                        & ~ r2_analoaf(A,E,C,F,D) )
                                      | B = F ) ) ) ) ) ) ) ) ) ) )).

fof(t9_aff_4,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)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ( ( r2_hidden(B,G)
                                      & r2_hidden(B,H)
                                      & r2_hidden(C,G)
                                      & r2_hidden(D,G)
                                      & r2_hidden(E,H)
                                      & r2_hidden(F,H)
                                      & v1_aff_1(G,A)
                                      & v1_aff_1(H,A)
                                      & C = D )
                                   => ( B = C
                                      | B = E
                                      | G = H
                                      | ( ~ r2_analoaf(A,C,E,D,F)
                                        & ~ r2_analoaf(A,E,C,F,D) )
                                      | E = F ) ) ) ) ) ) ) ) ) ) )).

fof(t10_aff_4,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)
                                  & B = C )
                               => ( ( ~ r4_aff_1(A,F,G)
                                    & ~ r4_aff_1(A,G,F) )
                                  | F = G
                                  | ( ~ r2_analoaf(A,B,D,C,E)
                                    & ~ r2_analoaf(A,D,B,E,C) )
                                  | D = E ) ) ) ) ) ) ) ) ) )).

fof(t11_aff_4,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_hidden(B,D)
                  & r2_hidden(C,D)
                  & v1_aff_1(D,A) ) ) ) ) )).

fof(t12_aff_4,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))
                 => r2_hidden(C,B) ) ) ) ) )).

fof(d2_aff_4,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_4(B,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)))
                    & v1_aff_1(C,A)
                    & v1_aff_1(D,A)
                    & ~ r4_aff_1(A,C,D)
                    & B = k1_aff_4(A,C,D) ) ) ) ) ) )).

fof(t13_aff_4,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)))
             => ( ~ v1_aff_1(B,A)
               => k1_aff_4(A,B,C) = k1_xboole_0 ) ) ) ) )).

fof(t14_aff_4,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)))
             => ( v1_aff_1(B,A)
               => r1_tarski(C,k1_aff_4(A,B,C)) ) ) ) ) )).

fof(t15_aff_4,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)))
             => ( r4_aff_1(A,B,C)
               => k1_aff_4(A,B,C) = C ) ) ) ) )).

fof(t16_aff_4,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)
                   => k1_aff_4(A,B,D) = k1_aff_4(A,C,D) ) ) ) ) ) )).

fof(t17_aff_4,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)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] :
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ~ ( r2_hidden(B,G)
                                              & r2_hidden(C,G)
                                              & r2_hidden(D,G)
                                              & r2_hidden(B,H)
                                              & r2_hidden(E,H)
                                              & r2_hidden(F,H)
                                              & ~ r2_hidden(B,I)
                                              & ~ r2_hidden(B,J)
                                              & G != H
                                              & r2_hidden(C,I)
                                              & r2_hidden(E,I)
                                              & r2_hidden(D,J)
                                              & r2_hidden(F,J)
                                              & v1_aff_1(G,A)
                                              & v1_aff_1(H,A)
                                              & v1_aff_1(I,A)
                                              & v1_aff_1(J,A)
                                              & ~ r4_aff_1(A,I,J)
                                              & ! [K] :
                                                  ( m1_subset_1(K,u1_struct_0(A))
                                                 => ~ ( r2_hidden(K,I)
                                                      & r2_hidden(K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_aff_4,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)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ~ ( r2_hidden(B,F)
                                          & r2_hidden(C,F)
                                          & r2_hidden(D,G)
                                          & r2_hidden(E,G)
                                          & r2_hidden(B,H)
                                          & r2_hidden(D,H)
                                          & r2_hidden(C,I)
                                          & r2_hidden(E,I)
                                          & F != G
                                          & r4_aff_1(A,F,G)
                                          & v1_aff_1(H,A)
                                          & v1_aff_1(I,A)
                                          & ~ r4_aff_1(A,H,I)
                                          & ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ~ ( r2_hidden(J,H)
                                                  & r2_hidden(J,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_aff_4,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_4(D,A)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => ( B = C
                      | r1_tarski(k2_aff_1(A,B,C),D) ) ) ) ) ) ) )).

fof(t20_aff_4,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)))
                 => ( ( v1_aff_1(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(D,k1_aff_4(A,B,C)) )
                   => ( r4_aff_1(A,B,C)
                      | r4_aff_1(A,B,D)
                      | k1_aff_4(A,B,D) = k1_aff_4(A,B,C) ) ) ) ) ) ) )).

fof(t21_aff_4,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)))
                 => ~ ( v1_aff_1(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(D,k1_aff_4(A,B,C))
                      & ~ r4_aff_1(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,C)
                              & r2_hidden(E,D) ) ) ) ) ) ) ) )).

fof(t22_aff_4,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)))
                 => ~ ( v1_aff_4(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(C,B)
                      & r1_tarski(D,B)
                      & ~ r4_aff_1(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,C)
                              & r2_hidden(E,D) ) ) ) ) ) ) ) )).

fof(t23_aff_4,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)))
                     => ( ( v1_aff_4(C,A)
                          & r2_hidden(B,C)
                          & r1_tarski(D,C)
                          & r2_hidden(B,E) )
                       => ( ( ~ r4_aff_1(A,D,E)
                            & ~ r4_aff_1(A,E,D) )
                          | r1_tarski(E,C) ) ) ) ) ) ) ) )).

fof(t24_aff_4,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_4(D,A)
                          & v1_aff_4(E,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E) )
                       => ( D = E
                          | B = C
                          | v1_aff_1(k5_subset_1(u1_struct_0(A),D,E),A) ) ) ) ) ) ) ) )).

fof(t25_aff_4,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)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_4(E,A)
                              & v1_aff_4(F,A)
                              & r2_hidden(B,E)
                              & r2_hidden(C,E)
                              & r2_hidden(D,E)
                              & r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F) )
                           => ( r1_aff_1(A,B,C,D)
                              | E = F ) ) ) ) ) ) ) ) )).

fof(t26_aff_4,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)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_4(B,A)
                          & v1_aff_4(C,A)
                          & v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r1_tarski(D,B)
                          & r1_tarski(E,B)
                          & r1_tarski(D,C)
                          & r1_tarski(E,C) )
                       => ( D = E
                          | B = C ) ) ) ) ) ) ) )).

fof(d3_aff_4,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)))
                   => ( D = k2_aff_4(A,B,C)
                    <=> ( r2_hidden(B,D)
                        & r4_aff_1(A,C,D) ) ) ) ) ) ) ) )).

fof(t27_aff_4,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)
               => v1_aff_1(k2_aff_4(A,B,C),A) ) ) ) ) )).

fof(t28_aff_4,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)))
                 => ( ( v1_aff_4(C,A)
                      & v1_aff_1(D,A)
                      & r2_hidden(B,C)
                      & r1_tarski(D,C) )
                   => r1_tarski(k2_aff_4(A,B,D),C) ) ) ) ) ) )).

fof(t29_aff_4,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_4(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(t30_aff_4,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_hidden(B,C)
                <=> k2_aff_4(A,B,C) = C ) ) ) ) ) )).

fof(t31_aff_4,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)
                   => k2_aff_4(A,B,D) = k2_aff_4(A,B,k2_aff_4(A,C,D)) ) ) ) ) ) )).

fof(t32_aff_4,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)
                   => k2_aff_4(A,B,C) = k2_aff_4(A,B,D) ) ) ) ) ) )).

fof(d4_aff_4,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)))
             => ( r1_aff_4(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( ( r2_hidden(D,C)
                            & v1_aff_1(E,A)
                            & r1_tarski(E,B) )
                         => r1_tarski(k2_aff_4(A,D,E),C) ) ) ) ) ) ) ) )).

fof(t33_aff_4,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)))
             => ( r1_tarski(B,C)
               => ( ( ~ ( v1_aff_1(B,A)
                        & v1_aff_1(C,A) )
                    & ~ ( v1_aff_4(B,A)
                        & v1_aff_4(C,A) ) )
                  | B = C ) ) ) ) ) )).

fof(t34_aff_4,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_4(B,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(C,B)
                              & r2_hidden(D,B)
                              & r2_hidden(E,B)
                              & ~ r1_aff_1(A,C,D,E) ) ) ) ) ) ) ) )).

fof(t35_aff_4,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)))
             => ~ ( v1_aff_1(B,A)
                  & v1_aff_4(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ~ r2_hidden(D,B) ) ) ) ) ) ) )).

fof(t36_aff_4,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)
                          & r1_tarski(C,D)
                          & v1_aff_4(D,A) ) ) ) ) ) ) )).

fof(t37_aff_4,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_hidden(D,E)
                      & v1_aff_4(E,A) ) ) ) ) ) )).

fof(t38_aff_4,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)))
                 => ~ ( r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( r1_tarski(C,E)
                              & r1_tarski(D,E)
                              & v1_aff_4(E,A) ) ) ) ) ) ) ) )).

fof(t39_aff_4,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)))
             => ~ ( r4_aff_1(A,B,C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r1_tarski(B,D)
                          & r1_tarski(C,D)
                          & v1_aff_4(D,A) ) ) ) ) ) ) )).

fof(t40_aff_4,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)))
             => ( ( v1_aff_1(B,A)
                  & v1_aff_1(C,A) )
               => ( r4_aff_1(A,B,C)
                <=> r1_aff_4(A,B,C) ) ) ) ) ) )).

fof(t41_aff_4,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)))
             => ( ( v1_aff_1(B,A)
                  & v1_aff_4(C,A) )
               => ( r1_aff_4(A,B,C)
                <=> ? [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                      & r1_tarski(D,C)
                      & ( r4_aff_1(A,B,D)
                        | r4_aff_1(A,D,B) ) ) ) ) ) ) ) )).

fof(t42_aff_4,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)))
             => ( ( v1_aff_1(B,A)
                  & v1_aff_4(C,A)
                  & r1_tarski(B,C) )
               => r1_aff_4(A,B,C) ) ) ) ) )).

fof(t43_aff_4,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)))
                 => ( ( v1_aff_1(C,A)
                      & v1_aff_4(D,A)
                      & r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & r1_aff_4(A,C,D) )
                   => r1_tarski(C,D) ) ) ) ) ) )).

fof(d5_aff_4,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)))
                 => ( r2_aff_4(A,B,C,D)
                  <=> ? [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                        & r1_tarski(B,E)
                        & r1_tarski(C,E)
                        & r1_tarski(D,E)
                        & v1_aff_4(E,A) ) ) ) ) ) ) )).

fof(t44_aff_4,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)))
                 => ( r2_aff_4(A,B,C,D)
                   => ( r2_aff_4(A,B,D,C)
                      & r2_aff_4(A,C,B,D)
                      & r2_aff_4(A,C,D,B)
                      & r2_aff_4(A,D,B,C)
                      & r2_aff_4(A,D,C,B) ) ) ) ) ) ) )).

fof(t45_aff_4,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)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_1(B,A)
                          & v1_aff_1(C,A)
                          & v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r2_aff_4(A,D,E,C)
                          & r2_aff_4(A,D,E,B) )
                       => ( D = E
                          | r2_aff_4(A,D,C,B) ) ) ) ) ) ) ) )).

fof(t46_aff_4,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)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_1(B,A)
                          & v1_aff_1(C,A)
                          & v1_aff_4(D,A)
                          & r1_tarski(B,D)
                          & r1_tarski(C,D) )
                       => ( B = C
                          | ( r2_aff_4(A,B,C,E)
                          <=> r1_tarski(E,D) ) ) ) ) ) ) ) ) )).

fof(t47_aff_4,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)))
                 => ( ( r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A) )
                   => ( r2_aff_4(A,C,D,D)
                      & r2_aff_4(A,D,C,D)
                      & r2_aff_4(A,D,D,C) ) ) ) ) ) ) )).

fof(t48_aff_4,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)))
         => ~ ( ~ ( ~ v3_struct_0(A)
                  & ~ v3_realset2(A)
                  & v1_diraf(A)
                  & v2_diraf(A)
                  & l1_analoaf(A) )
              & v1_aff_4(B,A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => r2_hidden(C,B) ) ) ) ) )).

fof(t49_aff_4,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))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] :
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ! [K] :
                                              ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                             => ( ( r2_hidden(B,I)
                                                  & r2_hidden(B,J)
                                                  & r2_hidden(B,K)
                                                  & r2_hidden(C,I)
                                                  & r2_hidden(F,I)
                                                  & r2_hidden(D,J)
                                                  & r2_hidden(G,J)
                                                  & r2_hidden(E,K)
                                                  & r2_hidden(H,K)
                                                  & v1_aff_1(I,A)
                                                  & v1_aff_1(J,A)
                                                  & v1_aff_1(K,A)
                                                  & r2_analoaf(A,C,D,F,G)
                                                  & r2_analoaf(A,C,E,F,H) )
                                               => ( ( ~ v3_struct_0(A)
                                                    & ~ v3_realset2(A)
                                                    & v1_diraf(A)
                                                    & v2_diraf(A)
                                                    & l1_analoaf(A) )
                                                  | B = C
                                                  | B = D
                                                  | B = E
                                                  | I = J
                                                  | I = K
                                                  | r2_analoaf(A,D,E,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t50_aff_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ( ~ v3_struct_0(A)
            & ~ v3_realset2(A)
            & v1_diraf(A)
            & v2_diraf(A)
            & l1_analoaf(A) )
       => v4_aff_2(A) ) ) )).

fof(t51_aff_4,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))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] :
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ( ( r4_aff_1(A,H,I)
                                              & r4_aff_1(A,H,J)
                                              & r2_hidden(B,H)
                                              & r2_hidden(C,H)
                                              & r2_hidden(D,I)
                                              & r2_hidden(E,I)
                                              & r2_hidden(F,J)
                                              & r2_hidden(G,J)
                                              & v1_aff_1(H,A)
                                              & v1_aff_1(I,A)
                                              & v1_aff_1(J,A)
                                              & r2_analoaf(A,B,D,C,E)
                                              & r2_analoaf(A,B,F,C,G) )
                                           => ( ( ~ v3_struct_0(A)
                                                & ~ v3_realset2(A)
                                                & v1_diraf(A)
                                                & v2_diraf(A)
                                                & l1_analoaf(A) )
                                              | H = I
                                              | H = J
                                              | r2_analoaf(A,D,F,E,G) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t52_aff_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ( ~ v3_struct_0(A)
            & ~ v3_realset2(A)
            & v1_diraf(A)
            & v2_diraf(A)
            & l1_analoaf(A) )
       => v11_aff_2(A) ) ) )).

fof(t53_aff_4,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))
                         => ~ ( ~ v3_struct_0(A)
                              & ~ v3_realset2(A)
                              & v1_diraf(A)
                              & v2_diraf(A)
                              & l1_analoaf(A)
                              & ~ r1_aff_1(A,B,C,D)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,B,D,E,G)
                                      & r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t54_aff_4,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)
                              & E != F
                              & r2_analoaf(A,B,C,E,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,B,D,E,G)
                                      & r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t55_aff_4,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)))
             => ( ( v1_aff_4(B,A)
                  & v1_aff_4(C,A) )
               => ( r1_aff_4(A,B,C)
                <=> ? [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,k1_zfmisc_1(u1_struct_0(A)))
                              & ? [G] :
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                                  & ~ r4_aff_1(A,D,E)
                                  & r1_tarski(D,B)
                                  & r1_tarski(E,B)
                                  & r1_tarski(F,C)
                                  & r1_tarski(G,C)
                                  & ( r4_aff_1(A,D,F)
                                    | r4_aff_1(A,F,D) )
                                  & ( r4_aff_1(A,E,G)
                                    | r4_aff_1(A,G,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t56_aff_4,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)
                      & r1_aff_4(A,C,D) )
                   => r1_aff_4(A,B,D) ) ) ) ) ) )).

fof(t57_aff_4,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_4(B,A)
           => r1_aff_4(A,B,B) ) ) ) )).

fof(t58_aff_4,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)))
             => ( ( v1_aff_4(B,A)
                  & v1_aff_4(C,A)
                  & r1_aff_4(A,B,C) )
               => r1_aff_4(A,C,B) ) ) ) ) )).

fof(t59_aff_4,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_4(B,A)
              & B = k1_xboole_0 ) ) ) )).

fof(t60_aff_4,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)))
                 => ( ( r1_aff_4(A,B,C)
                      & r1_aff_4(A,C,D) )
                   => ( C = k1_xboole_0
                      | r1_aff_4(A,B,D) ) ) ) ) ) ) )).

fof(t61_aff_4,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)))
                 => ( ( v1_aff_4(B,A)
                      & v1_aff_4(C,A)
                      & v1_aff_4(D,A) )
                   => ( ( ~ ( r1_aff_4(A,B,C)
                            & r1_aff_4(A,C,D) )
                        & ~ ( r1_aff_4(A,B,C)
                            & r1_aff_4(A,D,C) )
                        & ~ ( r1_aff_4(A,C,B)
                            & r1_aff_4(A,C,D) )
                        & ~ ( r1_aff_4(A,C,B)
                            & r1_aff_4(A,D,C) ) )
                      | ( r1_aff_4(A,B,D)
                        & r1_aff_4(A,D,B) ) ) ) ) ) ) ) )).

fof(t62_aff_4,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)))
                 => ( ( v1_aff_4(C,A)
                      & v1_aff_4(D,A)
                      & r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & r1_aff_4(A,C,D) )
                   => C = D ) ) ) ) ) )).

fof(t63_aff_4,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)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ( ( v1_aff_4(F,A)
                                      & v1_aff_4(G,A)
                                      & v1_aff_4(H,A)
                                      & r1_aff_4(A,F,G)
                                      & r2_hidden(B,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(C,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(D,k5_subset_1(u1_struct_0(A),G,H))
                                      & r2_hidden(E,k5_subset_1(u1_struct_0(A),G,H)) )
                                   => ( F = G
                                      | r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t64_aff_4,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)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ( ( v1_aff_4(F,A)
                                      & v1_aff_4(G,A)
                                      & v1_aff_4(H,A)
                                      & r1_aff_4(A,F,G)
                                      & r2_hidden(B,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(C,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(D,k5_subset_1(u1_struct_0(A),G,H))
                                      & r2_hidden(E,k5_subset_1(u1_struct_0(A),G,H)) )
                                   => ( F = G
                                      | B = C
                                      | D = E
                                      | r4_aff_1(A,k5_subset_1(u1_struct_0(A),F,H),k5_subset_1(u1_struct_0(A),G,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t65_aff_4,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_4(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(B,D)
                          & r1_aff_4(A,C,D)
                          & v1_aff_4(D,A) ) ) ) ) ) ) )).

fof(d6_aff_4,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_4(C,A)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = k3_aff_4(A,B,C)
                    <=> ( r2_hidden(B,D)
                        & r1_aff_4(A,C,D)
                        & v1_aff_4(D,A) ) ) ) ) ) ) ) )).

fof(t66_aff_4,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_4(C,A)
               => ( r2_hidden(B,C)
                <=> k3_aff_4(A,B,C) = C ) ) ) ) ) )).

fof(t67_aff_4,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_4(D,A)
                   => k3_aff_4(A,B,D) = k3_aff_4(A,B,k3_aff_4(A,C,D)) ) ) ) ) ) )).

fof(t68_aff_4,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)))
                 => ( ( v1_aff_1(C,A)
                      & v1_aff_4(D,A)
                      & r1_aff_4(A,C,D) )
                   => r1_tarski(k2_aff_4(A,B,C),k3_aff_4(A,B,D)) ) ) ) ) ) )).

fof(t69_aff_4,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)))
                 => ( ( v1_aff_4(C,A)
                      & v1_aff_4(D,A)
                      & r1_aff_4(A,C,D) )
                   => k3_aff_4(A,B,C) = k3_aff_4(A,B,D) ) ) ) ) ) )).

fof(dt_k1_aff_4,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))) )
     => m1_subset_1(k1_aff_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k2_aff_4,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,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_aff_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k3_aff_4,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,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_aff_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(d1_aff_4,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)))
             => k1_aff_4(A,B,C) = a_3_0_aff_4(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_aff_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v3_realset2(B)
        & v1_diraf(B)
        & l1_analoaf(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_aff_4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & ? [F] :
                ( m1_subset_1(F,u1_struct_0(B))
                & r2_aff_1(B,E,F,C)
                & r2_hidden(F,D) ) ) ) ) )).
%------------------------------------------------------------------------------