% Mizar problem: t17_aff_4,aff_4,200,65 
fof(t17_aff_4,conjecture,(
    ! [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) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_aff_1,d1_aff_1,d3_aff_1,dt_k1_aff_1,dt_k1_xboole_0,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,fc1_struct_0,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k2_aff_1,redefinition_r4_aff_1,reflexivity_r1_tarski,symmetry_r4_aff_1,t13_aff_1,t14_aff_1,t1_aff_4,t1_subset,t26_aff_1,t2_subset,t30_aff_1,t33_aff_1,t39_aff_1,t3_subset,t4_subset,t52_aff_1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(aff_4,t17_aff_4)]).

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_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                  <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ),
    file(aff_1,d1_aff_1),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

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(redefinition_r4_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_aff_1(A,B,C)
      <=> r3_aff_1(A,B,C) ) ) ),
    file(aff_1,r4_aff_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(symmetry_r4_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_aff_1(A,B,C)
       => r4_aff_1(A,C,B) ) ) ),
    file(aff_1,r4_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(t14_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( B != C
                                  & ~ ( ~ ( r2_analoaf(A,B,C,D,E)
                                          & r2_analoaf(A,B,C,F,G) )
                                      & ~ ( r2_analoaf(A,B,C,D,E)
                                          & r2_analoaf(A,F,G,B,C) )
                                      & ~ ( r2_analoaf(A,D,E,B,C)
                                          & r2_analoaf(A,F,G,B,C) )
                                      & ~ ( r2_analoaf(A,D,E,B,C)
                                          & r2_analoaf(A,B,C,F,G) ) )
                                  & ~ r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ),
    file(aff_1,t14_aff_1),
    []).

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) ) ) ) ) ) ) ) ) ),
    file(aff_4,t1_aff_4),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t52_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( v1_aff_1(F,A)
                                  & v1_aff_1(G,A)
                                  & r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G) )
                               => ( B = C
                                  | D = E
                                  | ( r3_aff_1(A,F,G)
                                  <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ),
    file(aff_1,t52_aff_1),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).