SET007 Axioms: SET007+231.ax


%------------------------------------------------------------------------------
% File     : SET007+231 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Affine Localizations of Desargues Axiom
% 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   26 (   8 unit)
%            Number of atoms       :  426 (  52 equality)
%            Maximal formula depth :   45 (  16 average)
%            Number of connectives :  436 (  36 ~  ;  68  |; 196  &)
%                                         (  10 <=>; 126 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-5 arity)
%            Number of functors    :    2 (   0 constant; 1-1 arity)
%            Number of variables   :  110 (   0 singleton; 110 !;   0 ?)
%            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_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v1_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( v1_aff_1(B,A)
                                                            & v1_aff_1(C,A)
                                                            & v1_aff_1(D,A)
                                                            & r2_hidden(E,B)
                                                            & r2_hidden(F,B)
                                                            & r2_hidden(G,B)
                                                            & r2_hidden(E,C)
                                                            & r2_hidden(H,C)
                                                            & r2_hidden(I,C)
                                                            & r2_hidden(E,D)
                                                            & r2_hidden(J,D)
                                                            & r2_hidden(K,D)
                                                            & r1_aff_1(A,H,F,L)
                                                            & r1_aff_1(A,I,G,L)
                                                            & r1_aff_1(A,H,J,M)
                                                            & r1_aff_1(A,I,K,M)
                                                            & r2_analoaf(A,F,J,G,K) )
                                                         => ( C = B
                                                            | C = D
                                                            | B = D
                                                            | E = F
                                                            | E = H
                                                            | E = J
                                                            | L = M
                                                            | r1_aff_1(A,H,F,J)
                                                            | r1_aff_1(A,I,G,K)
                                                            | F = G
                                                            | r2_analoaf(A,F,J,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( v1_aff_1(B,A)
                                                            & v1_aff_1(C,A)
                                                            & v1_aff_1(D,A)
                                                            & r2_hidden(E,B)
                                                            & r2_hidden(F,B)
                                                            & r2_hidden(G,B)
                                                            & r2_hidden(E,C)
                                                            & r2_hidden(H,C)
                                                            & r2_hidden(I,C)
                                                            & r2_hidden(E,D)
                                                            & r2_hidden(J,D)
                                                            & r2_hidden(K,D)
                                                            & r1_aff_1(A,H,F,L)
                                                            & r1_aff_1(A,I,G,L)
                                                            & r1_aff_1(A,H,J,M)
                                                            & r1_aff_1(A,I,K,M)
                                                            & r2_analoaf(A,F,J,L,M) )
                                                         => ( C = B
                                                            | C = D
                                                            | B = D
                                                            | E = F
                                                            | E = H
                                                            | E = J
                                                            | L = M
                                                            | J = M
                                                            | r1_aff_1(A,H,F,J)
                                                            | r1_aff_1(A,I,G,K)
                                                            | r2_analoaf(A,F,J,G,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v3_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( v1_aff_1(B,A)
                                                            & v1_aff_1(C,A)
                                                            & v1_aff_1(D,A)
                                                            & r2_hidden(E,B)
                                                            & r2_hidden(F,B)
                                                            & r2_hidden(G,B)
                                                            & r2_hidden(E,C)
                                                            & r2_hidden(H,C)
                                                            & r2_hidden(I,C)
                                                            & r2_hidden(J,D)
                                                            & r2_hidden(K,D)
                                                            & r1_aff_1(A,H,F,L)
                                                            & r1_aff_1(A,I,G,L)
                                                            & r1_aff_1(A,H,J,M)
                                                            & r1_aff_1(A,I,K,M)
                                                            & r2_analoaf(A,F,J,G,K)
                                                            & r2_analoaf(A,F,J,L,M) )
                                                         => ( C = B
                                                            | C = D
                                                            | B = D
                                                            | E = F
                                                            | E = H
                                                            | E = J
                                                            | L = M
                                                            | r1_aff_1(A,H,F,J)
                                                            | r1_aff_1(A,I,G,K)
                                                            | J = K
                                                            | r2_hidden(E,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( v1_aff_1(B,A)
                                                            & v1_aff_1(C,A)
                                                            & v1_aff_1(D,A)
                                                            & r2_hidden(E,B)
                                                            & r2_hidden(F,B)
                                                            & r2_hidden(G,B)
                                                            & r2_hidden(H,C)
                                                            & r2_hidden(I,C)
                                                            & r2_hidden(E,D)
                                                            & r2_hidden(J,D)
                                                            & r2_hidden(K,D)
                                                            & r1_aff_1(A,H,F,L)
                                                            & r1_aff_1(A,I,G,L)
                                                            & r1_aff_1(A,H,J,M)
                                                            & r1_aff_1(A,I,K,M)
                                                            & r2_analoaf(A,F,J,G,K)
                                                            & r2_analoaf(A,F,J,L,M) )
                                                         => ( C = B
                                                            | C = D
                                                            | B = D
                                                            | E = F
                                                            | E = H
                                                            | E = J
                                                            | L = M
                                                            | r1_aff_1(A,H,F,J)
                                                            | r1_aff_1(A,I,G,K)
                                                            | H = I
                                                            | F = G
                                                            | r2_hidden(E,C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v5_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ( ( v1_aff_1(B,A)
                                                        & v1_aff_1(C,A)
                                                        & v1_aff_1(D,A)
                                                        & r2_hidden(E,B)
                                                        & r2_hidden(F,B)
                                                        & r2_hidden(G,C)
                                                        & r2_hidden(H,C)
                                                        & r2_hidden(I,D)
                                                        & r2_hidden(J,D)
                                                        & r4_aff_1(A,B,C)
                                                        & r4_aff_1(A,B,D)
                                                        & r1_aff_1(A,G,E,K)
                                                        & r1_aff_1(A,H,F,K)
                                                        & r1_aff_1(A,G,I,L)
                                                        & r1_aff_1(A,H,J,L)
                                                        & r2_analoaf(A,E,I,F,J) )
                                                     => ( B = C
                                                        | B = D
                                                        | C = D
                                                        | r1_aff_1(A,G,E,I)
                                                        | r1_aff_1(A,H,F,J)
                                                        | K = L
                                                        | E = F
                                                        | r2_analoaf(A,E,I,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v6_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ( ( v1_aff_1(B,A)
                                                        & v1_aff_1(C,A)
                                                        & v1_aff_1(D,A)
                                                        & r2_hidden(E,B)
                                                        & r2_hidden(F,B)
                                                        & r2_hidden(G,C)
                                                        & r2_hidden(H,C)
                                                        & r2_hidden(I,D)
                                                        & r2_hidden(J,D)
                                                        & r4_aff_1(A,B,C)
                                                        & r4_aff_1(A,B,D)
                                                        & r1_aff_1(A,G,E,K)
                                                        & r1_aff_1(A,H,F,K)
                                                        & r1_aff_1(A,G,I,L)
                                                        & r1_aff_1(A,H,J,L)
                                                        & r2_analoaf(A,E,I,K,L) )
                                                     => ( B = C
                                                        | B = D
                                                        | C = D
                                                        | r1_aff_1(A,G,E,I)
                                                        | r1_aff_1(A,H,F,J)
                                                        | K = L
                                                        | r2_analoaf(A,E,I,F,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v7_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ( ( v1_aff_1(B,A)
                                                        & v1_aff_1(C,A)
                                                        & v1_aff_1(D,A)
                                                        & r2_hidden(E,B)
                                                        & r2_hidden(F,B)
                                                        & r2_hidden(G,C)
                                                        & r2_hidden(H,C)
                                                        & r2_hidden(I,D)
                                                        & r2_hidden(J,D)
                                                        & r4_aff_1(A,B,D)
                                                        & r1_aff_1(A,G,E,K)
                                                        & r1_aff_1(A,H,F,K)
                                                        & r1_aff_1(A,G,I,L)
                                                        & r1_aff_1(A,H,J,L)
                                                        & r2_analoaf(A,E,I,F,J)
                                                        & r2_analoaf(A,E,I,K,L) )
                                                     => ( B = C
                                                        | B = D
                                                        | C = D
                                                        | r1_aff_1(A,G,E,I)
                                                        | r1_aff_1(A,H,F,J)
                                                        | K = L
                                                        | E = F
                                                        | r4_aff_1(A,B,C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v8_aff_3(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,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ( ( v1_aff_1(B,A)
                                                        & v1_aff_1(C,A)
                                                        & v1_aff_1(D,A)
                                                        & r2_hidden(E,B)
                                                        & r2_hidden(F,B)
                                                        & r2_hidden(G,C)
                                                        & r2_hidden(H,C)
                                                        & r2_hidden(I,D)
                                                        & r2_hidden(J,D)
                                                        & r4_aff_1(A,B,C)
                                                        & r1_aff_1(A,G,E,K)
                                                        & r1_aff_1(A,H,F,K)
                                                        & r1_aff_1(A,G,I,L)
                                                        & r1_aff_1(A,H,J,L)
                                                        & r2_analoaf(A,E,I,F,J)
                                                        & r2_analoaf(A,E,I,K,L) )
                                                     => ( B = C
                                                        | B = D
                                                        | C = D
                                                        | r1_aff_1(A,G,E,I)
                                                        | r1_aff_1(A,H,F,J)
                                                        | K = L
                                                        | I = J
                                                        | r4_aff_1(A,B,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t1_aff_3,axiom,(
    $true )).

fof(t2_aff_3,axiom,(
    $true )).

fof(t3_aff_3,axiom,(
    $true )).

fof(t4_aff_3,axiom,(
    $true )).

fof(t5_aff_3,axiom,(
    $true )).

fof(t6_aff_3,axiom,(
    $true )).

fof(t7_aff_3,axiom,(
    $true )).

fof(t8_aff_3,axiom,(
    $true )).

fof(t9_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v1_aff_3(A)
       => v2_aff_3(A) ) ) )).

fof(t10_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_3(A)
       => v1_aff_3(A) ) ) )).

fof(t11_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
       => v1_aff_3(A) ) ) )).

fof(t12_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
       => v3_aff_3(A) ) ) )).

fof(t13_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v3_aff_3(A)
       => v4_aff_3(A) ) ) )).

fof(t14_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v3_aff_3(A)
       => v4_aff_2(A) ) ) )).

fof(t15_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v6_aff_3(A)
       => v5_aff_3(A) ) ) )).

fof(t16_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v6_aff_3(A)
      <=> v8_aff_3(A) ) ) )).

fof(t17_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v5_aff_3(A)
      <=> v7_aff_3(A) ) ) )).

fof(t18_aff_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_3(A)
       => v6_aff_3(A) ) ) )).
%------------------------------------------------------------------------------