% Mizar problem: t17_taxonom2,taxonom2,1050,50 
fof(t17_taxonom2,conjecture,(
    ! [A,B] : 
      ( ( v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v5_taxonom2(B,A)
        & m1_taxonom2(B,A) )
     => ( v6_taxonom2(B,A)
       => ( r2_hidden(k1_xboole_0,B)
          | ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ~ ( r2_hidden(C,B)
                  & ! [D] : 
                      ( m1_eqrel_1(D,A)
                     => ~ ( r2_hidden(C,D)
                          & r1_tarski(D,B) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_eqrel_1,cc2_eqrel_1,d1_tarski,d1_xboole_0,d4_tarski,d5_taxonom2,d9_ordinal1,d9_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_tarski,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,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_taxonom2,rc4_taxonom2,reflexivity_r1_tarski,reflexivity_r3_xboole_0,s1_xboole_0__e4_33__taxonom2,symmetry_r1_xboole_0,symmetry_r3_xboole_0,t10_taxonom2,t16_taxonom2,t175_orders_1,t1_subset,t1_xboole_1,t2_subset,t37_zfmisc_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t92_zfmisc_1,t94_zfmisc_1]),
    [file(taxonom2,t17_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(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_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(d9_ordinal1,axiom,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    []).

fof(d9_xboole_0,axiom,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        | r1_tarski(B,A) ) ) ),
    file(xboole_0,d9_xboole_0),
    []).

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_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(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(rc4_taxonom2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_taxonom2(B,A)
      & v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & v5_taxonom2(B,A) ) ),
    file(taxonom2,rc4_taxonom2),
    []).

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

fof(reflexivity_r3_xboole_0,axiom,(
    ! [A,B] : r3_xboole_0(A,A) ),
    file(xboole_0,r3_xboole_0),
    []).

fof(s1_xboole_0__e4_33__taxonom2,axiom,(
    ! [A,B,C] : 
      ( ( v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v5_taxonom2(B,A)
        & m1_taxonom2(B,A)
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => ? [D] : 
        ! [E] : 
          ( r2_hidden(E,D)
        <=> ( r2_hidden(E,k1_zfmisc_1(k1_zfmisc_1(A)))
            & r2_hidden(C,E)
            & v4_taxonom2(E)
            & r1_tarski(E,B) ) ) ) ),
    file(taxonom2,s1_xboole_0__e4_33__taxonom2),
    []).

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(symmetry_r3_xboole_0,axiom,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
     => r3_xboole_0(B,A) ) ),
    file(xboole_0,r3_xboole_0),
    []).

fof(t10_taxonom2,axiom,(
    ! [A] : v4_taxonom2(k1_tarski(A)) ),
    file(taxonom2,t10_taxonom2),
    []).

fof(t16_taxonom2,axiom,(
    ! [A,B] : 
      ( ( v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v5_taxonom2(B,A)
        & m1_taxonom2(B,A) )
     => ( v6_taxonom2(B,A)
       => ( r2_hidden(k1_xboole_0,B)
          | ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ! [D] : 
                  ( ( v4_taxonom2(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
                 => ( ( r2_hidden(C,D)
                      & r1_tarski(D,B)
                      & ! [E] : 
                          ( ( v4_taxonom2(E)
                            & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
                         => ( ( r2_hidden(C,E)
                              & r1_tarski(E,B)
                              & r1_tarski(D,E) )
                           => D = E ) ) )
                   => m1_eqrel_1(D,A) ) ) ) ) ) ) ),
    file(taxonom2,t16_taxonom2),
    []).

fof(t175_orders_1,axiom,(
    ! [A] : ~ ( A != k1_xboole_0
      & ! [B] : ~ ( r1_tarski(B,A)
          & v6_ordinal1(B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & ! [D] : 
                  ( r2_hidden(D,B)
                 => r1_tarski(D,C) ) ) )
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C] : ~ ( r2_hidden(C,A)
              & C != B
              & r1_tarski(B,C) ) ) ) ),
    file(orders_1,t175_orders_1),
    []).

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_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(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_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(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),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).

fof(t94_zfmisc_1,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(C,B) )
     => r1_tarski(k3_tarski(A),B) ) ),
    file(zfmisc_1,t94_zfmisc_1),
    []).