% Mizar problem: t10_aff_3,aff_3,182,49 
fof(t10_aff_3,conjecture,(
    ! [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) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_aff_1,d1_aff_3,d2_aff_1,d2_aff_3,d3_aff_1,dt_k1_aff_1,dt_k1_zfmisc_1,dt_k2_aff_1,dt_l1_analoaf,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_analoaf,existence_l1_struct_0,existence_m1_subset_1,redefinition_k2_aff_1,t12_aff_1,t13_aff_1,t15_aff_1,t16_aff_1,t23_aff_1,t26_aff_1,t30_aff_1,t33_aff_1,t39_aff_1]),
    [file(aff_3,t10_aff_3)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(commutativity_k2_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k2_aff_1(A,B,C) = k2_aff_1(A,C,B) ) ),
    file(aff_1,k2_aff_1),
    []).

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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(aff_3,d1_aff_3),
    []).

fof(d2_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( D = k1_aff_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(E,D)
                        <=> r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) ),
    file(aff_1,d2_aff_1),
    []).

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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(aff_3,d2_aff_3),
    []).

fof(d3_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_1(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C != D
                    & B = k2_aff_1(A,C,D) ) ) ) ) ) ),
    file(aff_1,d3_aff_1),
    []).

fof(dt_k1_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_aff_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(aff_1,k1_aff_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_aff_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(aff_1,k2_aff_1),
    []).

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

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

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

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(redefinition_k2_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k2_aff_1(A,B,C) = k1_aff_1(A,B,C) ) ),
    file(aff_1,k2_aff_1),
    []).

fof(t12_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_analoaf(A,B,C,D,D)
                    & r2_analoaf(A,D,D,B,C) ) ) ) ) ) ),
    file(aff_1,t12_aff_1),
    []).

fof(t13_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_analoaf(A,B,C,D,E)
                       => ( r2_analoaf(A,B,C,E,D)
                          & r2_analoaf(A,C,B,D,E)
                          & r2_analoaf(A,C,B,E,D)
                          & r2_analoaf(A,D,E,B,C)
                          & r2_analoaf(A,D,E,C,B)
                          & r2_analoaf(A,E,D,B,C)
                          & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(aff_1,t13_aff_1),
    []).

fof(t15_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                   => ( r1_aff_1(A,B,D,C)
                      & r1_aff_1(A,C,B,D)
                      & r1_aff_1(A,C,D,B)
                      & r1_aff_1(A,D,B,C)
                      & r1_aff_1(A,D,C,B) ) ) ) ) ) ) ),
    file(aff_1,t15_aff_1),
    []).

fof(t16_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_aff_1(A,B,B,C)
                & r1_aff_1(A,B,C,C)
                & r1_aff_1(A,B,C,B) ) ) ) ) ),
    file(aff_1,t16_aff_1),
    []).

fof(t23_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_aff_1(A,B,D,E)
                          & r2_analoaf(A,C,D,C,E) )
                       => ( r1_aff_1(A,B,C,D)
                          | D = E ) ) ) ) ) ) ) ),
    file(aff_1,t23_aff_1),
    []).

fof(t26_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k2_aff_1(A,B,C))
                & r2_hidden(C,k2_aff_1(A,B,C)) ) ) ) ) ),
    file(aff_1,t26_aff_1),
    []).

fof(t30_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & B != C
                          & D != E ) ) ) ) ) ) ),
    file(aff_1,t30_aff_1),
    []).

fof(t33_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                        & v1_aff_1(E,A)
                        & r2_hidden(B,E)
                        & r2_hidden(C,E)
                        & r2_hidden(D,E) ) ) ) ) ) ) ),
    file(aff_1,t33_aff_1),
    []).

fof(t39_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_1(E,A)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & r1_aff_1(A,B,C,D) )
                       => ( B = C
                          | r2_hidden(D,E) ) ) ) ) ) ) ) ),
    file(aff_1,t39_aff_1),
    []).