% Mizar problem: t14_taxonom2,taxonom2,755,23 
fof(t14_taxonom2,conjecture,(
    ! [A,B] : 
      ( ( v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_taxonom2(B,A) )
     => ! [C] : 
          ( ( v4_taxonom2(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
         => ( ( r1_tarski(C,B)
              & ! [D] : 
                  ( ( v4_taxonom2(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
                 => ( ( r1_tarski(D,B)
                      & r1_tarski(k5_setfam_1(A,C),k5_setfam_1(A,D)) )
                   => C = D ) ) )
           => m1_eqrel_1(C,A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_eqrel_1,cc2_eqrel_1,d1_tarski,d5_taxonom2,d6_eqrel_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_tarski,dt_k5_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m1_taxonom2,existence_m1_eqrel_1,existence_m1_subset_1,existence_m1_taxonom2,fc1_subset_1,fc1_xboole_0,fc2_subset_1,l17_taxonom2,l18_taxonom2,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_taxonom2,redefinition_k5_setfam_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,t1_subset,t1_zfmisc_1,t2_subset,t39_zfmisc_1,t3_subset,t3_xboole_1,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(taxonom2,t14_taxonom2)]).

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

fof(cc1_eqrel_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    []).

fof(cc2_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_1),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d5_taxonom2,axiom,(
    ! [A] : 
      ( v4_taxonom2(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => ( B = C
            | r1_xboole_0(B,C) ) ) ) ),
    file(taxonom2,d5_taxonom2),
    []).

fof(d6_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    []).

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

fof(dt_m1_taxonom2,axiom,(
    ! [A,B] : 
      ( m1_taxonom2(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(taxonom2,m1_taxonom2),
    []).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_1),
    []).

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

fof(existence_m1_taxonom2,axiom,(
    ! [A] : 
    ? [B] : m1_taxonom2(B,A) ),
    file(taxonom2,m1_taxonom2),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(l17_taxonom2,axiom,(
    ! [A,B] : 
      ( m1_taxonom2(B,A)
     => ( v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
       => ! [C] : 
            ( ( v4_taxonom2(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( ( r1_tarski(C,B)
                & ! [D] : 
                    ( ( v4_taxonom2(D)
                      & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
                   => ( ( r1_tarski(D,B)
                        & r1_tarski(k5_setfam_1(A,C),k5_setfam_1(A,D)) )
                     => C = D ) ) )
             => k5_setfam_1(A,C) = A ) ) ) ) ),
    file(taxonom2,l17_taxonom2),
    []).

fof(l18_taxonom2,axiom,(
    ! [A,B] : 
      ( m1_taxonom2(B,A)
     => ! [C] : 
          ( ( v4_taxonom2(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
         => ( ( r1_tarski(C,B)
              & ! [D] : 
                  ( ( v4_taxonom2(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
                 => ( ( r1_tarski(D,B)
                      & r1_tarski(k5_setfam_1(A,C),k5_setfam_1(A,D)) )
                   => C = D ) ) )
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ~ ( r2_hidden(D,C)
                    & D = k1_xboole_0 ) ) ) ) ) ),
    file(taxonom2,l18_taxonom2),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

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

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

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

fof(rc3_taxonom2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & v4_taxonom2(B) ) ),
    file(taxonom2,rc3_taxonom2),
    []).

fof(redefinition_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    []).

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

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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

fof(t1_zfmisc_1,axiom,(
    k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    file(zfmisc_1,t1_zfmisc_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(t39_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,t39_zfmisc_1),
    []).

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

fof(t3_xboole_1,axiom,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    []).

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(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),
    []).