% Mizar problem: t1_aff_4,aff_4,25,20 
fof(t1_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))
                     => ~ ( ( 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) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_aff_1,dt_k1_xboole_0,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,t13_aff_1,t15_aff_1,t1_subset,t2_subset,t47_diraf,t6_boole,t7_boole,t8_boole]),
    [file(aff_4,t1_aff_4)]).

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

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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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

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

fof(t47_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B = C ) )
        & ! [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))
                               => ( r2_analoaf(A,B,C,C,B)
                                  & r2_analoaf(A,B,C,D,D)
                                  & ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,B,C,F,G) )
                                   => ( B = C
                                      | r2_analoaf(A,D,E,F,G) ) )
                                  & ( r2_analoaf(A,B,C,B,D)
                                   => r2_analoaf(A,C,B,C,D) ) ) ) ) ) ) ) )
        & ~ ! [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,B,D) ) ) )
        & ! [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,D,C,E)
                        & C != E ) ) ) )
        & ! [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,D,C,E) ) ) ) )
        & ! [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,D,B,B,E)
                            & B != D
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_analoaf(A,C,B,B,F)
                                    & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ),
    file(diraf,t47_diraf),
    []).

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),
    []).