% Mizar ND problem: t3_aff_4,aff_4,39,18 
fof(dh_c1_3__aff_4,definition,
    ( ( ( ~ v3_struct_0(c1_3__aff_4)
        & ~ v3_realset2(c1_3__aff_4)
        & v1_diraf(c1_3__aff_4)
        & l1_analoaf(c1_3__aff_4) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__aff_4))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
                     => ~ ( ( r2_aff_1(c1_3__aff_4,A,B,C)
                            | r2_aff_1(c1_3__aff_4,B,A,C) )
                          & ( r4_aff_1(c1_3__aff_4,C,D)
                            | r4_aff_1(c1_3__aff_4,D,C) )
                          & ~ ( r2_aff_1(c1_3__aff_4,A,B,D)
                              & r2_aff_1(c1_3__aff_4,B,A,D) ) ) ) ) ) ) )
   => ! [E] : 
        ( ( ~ v3_struct_0(E)
          & ~ v3_realset2(E)
          & v1_diraf(E)
          & l1_analoaf(E) )
       => ! [F] : 
            ( m1_subset_1(F,u1_struct_0(E))
           => ! [G] : 
                ( m1_subset_1(G,u1_struct_0(E))
               => ! [H] : 
                    ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(E)))
                   => ! [I] : 
                        ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(E)))
                       => ~ ( ( r2_aff_1(E,F,G,H)
                              | r2_aff_1(E,G,F,H) )
                            & ( r4_aff_1(E,H,I)
                              | r4_aff_1(E,I,H) )
                            & ~ ( r2_aff_1(E,F,G,I)
                                & r2_aff_1(E,G,F,I) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__aff_4),file(aff_4,c1_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c1_3__aff_4)]).

fof(dh_c2_3__aff_4,definition,
    ( ( m1_subset_1(c2_3__aff_4,u1_struct_0(c1_3__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
                 => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,A,B)
                        | r2_aff_1(c1_3__aff_4,A,c2_3__aff_4,B) )
                      & ( r4_aff_1(c1_3__aff_4,B,C)
                        | r4_aff_1(c1_3__aff_4,C,B) )
                      & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,A,C)
                          & r2_aff_1(c1_3__aff_4,A,c2_3__aff_4,C) ) ) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,u1_struct_0(c1_3__aff_4))
       => ! [E] : 
            ( m1_subset_1(E,u1_struct_0(c1_3__aff_4))
           => ! [F] : 
                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
               => ! [G] : 
                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
                   => ~ ( ( r2_aff_1(c1_3__aff_4,D,E,F)
                          | r2_aff_1(c1_3__aff_4,E,D,F) )
                        & ( r4_aff_1(c1_3__aff_4,F,G)
                          | r4_aff_1(c1_3__aff_4,G,F) )
                        & ~ ( r2_aff_1(c1_3__aff_4,D,E,G)
                            & r2_aff_1(c1_3__aff_4,E,D,G) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__aff_4),file(aff_4,c2_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c2_3__aff_4)]).

fof(dh_c3_3__aff_4,definition,
    ( ( m1_subset_1(c3_3__aff_4,u1_struct_0(c1_3__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
             => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
                    | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) )
                  & ( r4_aff_1(c1_3__aff_4,A,B)
                    | r4_aff_1(c1_3__aff_4,B,A) )
                  & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,B)
                      & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,B) ) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,u1_struct_0(c1_3__aff_4))
       => ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
           => ! [E] : 
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
               => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,C,D)
                      | r2_aff_1(c1_3__aff_4,C,c2_3__aff_4,D) )
                    & ( r4_aff_1(c1_3__aff_4,D,E)
                      | r4_aff_1(c1_3__aff_4,E,D) )
                    & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,C,E)
                        & r2_aff_1(c1_3__aff_4,C,c2_3__aff_4,E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__aff_4),file(aff_4,c3_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c3_3__aff_4)]).

fof(dh_c4_3__aff_4,definition,
    ( ( m1_subset_1(c4_3__aff_4,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
         => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
                | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
              & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,A)
                | r4_aff_1(c1_3__aff_4,A,c4_3__aff_4) )
              & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
                  & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) ) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
           => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,B)
                  | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,B) )
                & ( r4_aff_1(c1_3__aff_4,B,C)
                  | r4_aff_1(c1_3__aff_4,C,B) )
                & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,C)
                    & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__aff_4),file(aff_4,c4_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c4_3__aff_4)]).

fof(dh_c5_3__aff_4,definition,
    ( ( m1_subset_1(c5_3__aff_4,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
     => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
            | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
          & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,c5_3__aff_4)
            | r4_aff_1(c1_3__aff_4,c5_3__aff_4,c4_3__aff_4) )
          & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c5_3__aff_4)
              & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c5_3__aff_4) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
       => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
              | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
            & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,A)
              | r4_aff_1(c1_3__aff_4,A,c4_3__aff_4) )
            & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
                & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) ) ) ) ),
    introduced(definition,[new_symbol(c5_3__aff_4),file(aff_4,c5_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c5_3__aff_4)]).

fof(e1_3__aff_4,assumption,
    ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
    | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) ),
    introduced(assumption,[file(aff_4,e1_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e1_3__aff_4)]).

fof(e2_3__aff_4,assumption,
    ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,c5_3__aff_4)
    | r4_aff_1(c1_3__aff_4,c5_3__aff_4,c4_3__aff_4) ),
    introduced(assumption,[file(aff_4,e2_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e2_3__aff_4)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc5_struct_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(symmetry_r4_aff_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(aff_1,r4_aff_1)]).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    [interesting(0.9),axiom,file(analoaf,l1_analoaf)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(redefinition_r4_aff_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(aff_1,r4_aff_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    [interesting(0.9),axiom,file(analoaf,l1_analoaf)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_3__aff_4,assumption,
    ( ~ v3_struct_0(c1_3__aff_4)
    & ~ v3_realset2(c1_3__aff_4)
    & v1_diraf(c1_3__aff_4)
    & l1_analoaf(c1_3__aff_4) ),
    introduced(assumption,[file(aff_4,c1_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c1_3__aff_4)]).

fof(dt_c2_3__aff_4,assumption,(
    m1_subset_1(c2_3__aff_4,u1_struct_0(c1_3__aff_4)) ),
    introduced(assumption,[file(aff_4,c2_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c2_3__aff_4)]).

fof(dt_c3_3__aff_4,assumption,(
    m1_subset_1(c3_3__aff_4,u1_struct_0(c1_3__aff_4)) ),
    introduced(assumption,[file(aff_4,c3_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c3_3__aff_4)]).

fof(dt_c4_3__aff_4,assumption,(
    m1_subset_1(c4_3__aff_4,k1_zfmisc_1(u1_struct_0(c1_3__aff_4))) ),
    introduced(assumption,[file(aff_4,c4_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c4_3__aff_4)]).

fof(dt_c5_3__aff_4,assumption,(
    m1_subset_1(c5_3__aff_4,k1_zfmisc_1(u1_struct_0(c1_3__aff_4))) ),
    introduced(assumption,[file(aff_4,c5_3__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c5_3__aff_4)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t48_aff_1,theorem,(
    ! [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_aff_1(A,B,C,D)
                   => r2_aff_1(A,C,B,D) ) ) ) ) ) ),
    file(aff_1,t48_aff_1),
    [interesting(0.9),axiom,file(aff_1,t48_aff_1)]).

fof(e3_3__aff_4,plain,
    ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
    & r4_aff_1(c1_3__aff_4,c4_3__aff_4,c5_3__aff_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,e1_3__aff_4,e2_3__aff_4])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,t8_boole,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,symmetry_r4_aff_1,existence_l1_analoaf,existence_m1_subset_1,redefinition_r4_aff_1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,t3_subset,e1_3__aff_4,e2_3__aff_4,t48_aff_1]),
    [interesting(0.8),file(aff_4,e3_3__aff_4),[file(aff_4,e3_3__aff_4)]]).

fof(t57_aff_1,theorem,(
    ! [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)
                          & r4_aff_1(A,D,E) )
                       => r2_aff_1(A,B,C,E) ) ) ) ) ) ) ),
    file(aff_1,t57_aff_1),
    [interesting(0.9),axiom,file(aff_1,t57_aff_1)]).

fof(e4_3__aff_4,plain,(
    r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c5_3__aff_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,e1_3__aff_4,e2_3__aff_4])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,t8_boole,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,symmetry_r4_aff_1,existence_l1_analoaf,existence_m1_subset_1,redefinition_r4_aff_1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,t3_subset,e3_3__aff_4,t57_aff_1]),
    [interesting(0.8),file(aff_4,e4_3__aff_4),[file(aff_4,e4_3__aff_4)]]).

fof(e5_3__aff_4,plain,(
    r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c5_3__aff_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,e1_3__aff_4,e2_3__aff_4])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,t8_boole,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_l1_analoaf,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c5_3__aff_4,t3_subset,e4_3__aff_4,t48_aff_1]),
    [interesting(0.8),file(aff_4,e5_3__aff_4),[file(aff_4,e5_3__aff_4)]]).

fof(i8_3__aff_4,theorem,(
    $true ),
    introduced(tautology,[file(aff_4,i8_3__aff_4)]),
    [interesting(0.8),trivial,file(aff_4,i8_3__aff_4)]).

fof(i7_3__aff_4,plain,(
    r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c5_3__aff_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,e1_3__aff_4,e2_3__aff_4])],[e5_3__aff_4,i8_3__aff_4]),
    [interesting(0.8),file(aff_4,i7_3__aff_4),[file(aff_4,i7_3__aff_4)]]).

fof(i6_3__aff_4,plain,
    ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c5_3__aff_4)
    & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c5_3__aff_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4,e1_3__aff_4,e2_3__aff_4])],[e4_3__aff_4,i7_3__aff_4]),
    [interesting(0.8),file(aff_4,i6_3__aff_4),[file(aff_4,i6_3__aff_4)]]).

fof(i5_3__aff_4,plain,(
    ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
        | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
      & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,c5_3__aff_4)
        | r4_aff_1(c1_3__aff_4,c5_3__aff_4,c4_3__aff_4) )
      & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c5_3__aff_4)
          & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c5_3__aff_4) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4,dt_c5_3__aff_4]),discharge_asm(discharge,[e1_3__aff_4,e2_3__aff_4])],[e1_3__aff_4,e2_3__aff_4,i6_3__aff_4]),
    [interesting(0.8),file(aff_4,i5_3__aff_4),[file(aff_4,i5_3__aff_4)]]).

fof(i5_3_tmp__aff_4,plain,
    ( m1_subset_1(c5_3__aff_4,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
   => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
          | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
        & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,c5_3__aff_4)
          | r4_aff_1(c1_3__aff_4,c5_3__aff_4,c4_3__aff_4) )
        & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c5_3__aff_4)
            & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c5_3__aff_4) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4]),discharge_asm(discharge,[dt_c5_3__aff_4])],[dt_c5_3__aff_4,i5_3__aff_4]),
    [interesting(0.8),i4_3__aff_4]).

fof(i4_3__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
     => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
            | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
          & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,A)
            | r4_aff_1(c1_3__aff_4,A,c4_3__aff_4) )
          & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
              & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4,dt_c4_3__aff_4])],[i5_3_tmp__aff_4,dh_c5_3__aff_4]),
    [interesting(0.8),file(aff_4,i4_3__aff_4),[file(aff_4,i4_3__aff_4)]]).

fof(i4_3_tmp__aff_4,plain,
    ( m1_subset_1(c4_3__aff_4,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
       => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,c4_3__aff_4)
              | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,c4_3__aff_4) )
            & ( r4_aff_1(c1_3__aff_4,c4_3__aff_4,A)
              | r4_aff_1(c1_3__aff_4,A,c4_3__aff_4) )
            & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
                & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4]),discharge_asm(discharge,[dt_c4_3__aff_4])],[dt_c4_3__aff_4,i4_3__aff_4]),
    [interesting(0.8),i3_3__aff_4]).

fof(i3_3__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
         => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
                | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) )
              & ( r4_aff_1(c1_3__aff_4,A,B)
                | r4_aff_1(c1_3__aff_4,B,A) )
              & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,B)
                  & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4,dt_c3_3__aff_4])],[i4_3_tmp__aff_4,dh_c4_3__aff_4]),
    [interesting(0.8),file(aff_4,i3_3__aff_4),[file(aff_4,i3_3__aff_4)]]).

fof(i3_3_tmp__aff_4,plain,
    ( m1_subset_1(c3_3__aff_4,u1_struct_0(c1_3__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
           => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,A)
                  | r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,A) )
                & ( r4_aff_1(c1_3__aff_4,A,B)
                  | r4_aff_1(c1_3__aff_4,B,A) )
                & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,c3_3__aff_4,B)
                    & r2_aff_1(c1_3__aff_4,c3_3__aff_4,c2_3__aff_4,B) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4]),discharge_asm(discharge,[dt_c3_3__aff_4])],[dt_c3_3__aff_4,i3_3__aff_4]),
    [interesting(0.8),i2_3__aff_4]).

fof(i2_3__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
             => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,A,B)
                    | r2_aff_1(c1_3__aff_4,A,c2_3__aff_4,B) )
                  & ( r4_aff_1(c1_3__aff_4,B,C)
                    | r4_aff_1(c1_3__aff_4,C,B) )
                  & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,A,C)
                      & r2_aff_1(c1_3__aff_4,A,c2_3__aff_4,C) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__aff_4,dt_c2_3__aff_4])],[i3_3_tmp__aff_4,dh_c3_3__aff_4]),
    [interesting(0.8),file(aff_4,i2_3__aff_4),[file(aff_4,i2_3__aff_4)]]).

fof(i2_3_tmp__aff_4,plain,
    ( m1_subset_1(c2_3__aff_4,u1_struct_0(c1_3__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
               => ~ ( ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,A,B)
                      | r2_aff_1(c1_3__aff_4,A,c2_3__aff_4,B) )
                    & ( r4_aff_1(c1_3__aff_4,B,C)
                      | r4_aff_1(c1_3__aff_4,C,B) )
                    & ~ ( r2_aff_1(c1_3__aff_4,c2_3__aff_4,A,C)
                        & r2_aff_1(c1_3__aff_4,A,c2_3__aff_4,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__aff_4]),discharge_asm(discharge,[dt_c2_3__aff_4])],[dt_c2_3__aff_4,i2_3__aff_4]),
    [interesting(0.8),i1_3__aff_4]).

fof(i1_3__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__aff_4))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
                 => ~ ( ( r2_aff_1(c1_3__aff_4,A,B,C)
                        | r2_aff_1(c1_3__aff_4,B,A,C) )
                      & ( r4_aff_1(c1_3__aff_4,C,D)
                        | r4_aff_1(c1_3__aff_4,D,C) )
                      & ~ ( r2_aff_1(c1_3__aff_4,A,B,D)
                          & r2_aff_1(c1_3__aff_4,B,A,D) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__aff_4])],[i2_3_tmp__aff_4,dh_c2_3__aff_4]),
    [interesting(0.8),file(aff_4,i1_3__aff_4),[file(aff_4,i1_3__aff_4)]]).

fof(i1_3_tmp__aff_4,plain,
    ( ( ~ v3_struct_0(c1_3__aff_4)
      & ~ v3_realset2(c1_3__aff_4)
      & v1_diraf(c1_3__aff_4)
      & l1_analoaf(c1_3__aff_4) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__aff_4))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_3__aff_4)))
                   => ~ ( ( r2_aff_1(c1_3__aff_4,A,B,C)
                          | r2_aff_1(c1_3__aff_4,B,A,C) )
                        & ( r4_aff_1(c1_3__aff_4,C,D)
                          | r4_aff_1(c1_3__aff_4,D,C) )
                        & ~ ( r2_aff_1(c1_3__aff_4,A,B,D)
                            & r2_aff_1(c1_3__aff_4,B,A,D) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__aff_4])],[dt_c1_3__aff_4,i1_3__aff_4]),
    [interesting(1),t3_aff_4]).

fof(t3_aff_4,theorem,(
    ! [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) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__aff_4,dh_c1_3__aff_4]),
    [interesting(1),file(aff_4,t3_aff_4),[file(aff_4,t3_aff_4)]]).