% Mizar problem: t10_zfrefle1,zfrefle1,283,22 
fof(t10_zfrefle1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( ( v1_zf_model(A)
              & r2_zfrefle1(A,B)
              & v1_ordinal1(B) )
           => v1_zf_model(B) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k1_zfrefle1,dt_k2_zfrefle1,dt_k9_zf_lang,dt_m1_subset_1,existence_m1_subset_1,fc2_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,redefinition_k2_zfrefle1,reflexivity_r1_tarski,reflexivity_r2_zfrefle1,symmetry_r2_zfrefle1,t1_subset,t2_subset,t3_subset,t4_subset,t4_zfrefle1,t5_subset,t5_zfrefle1,t6_boole,t7_boole,t8_boole,t8_zfrefle1]),
    [file(zfrefle1,t10_zfrefle1)]).

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

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

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_k1_zfrefle1,axiom,(
    $true ),
    file(zfrefle1,k1_zfrefle1),
    []).

fof(dt_k2_zfrefle1,axiom,(
    m1_subset_1(k2_zfrefle1,k1_zfmisc_1(k9_zf_lang)) ),
    file(zfrefle1,k2_zfrefle1),
    []).

fof(dt_k9_zf_lang,axiom,(
    ~ v1_xboole_0(k9_zf_lang) ),
    file(zf_lang,k9_zf_lang),
    []).

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

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

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(redefinition_k2_zfrefle1,axiom,(
    k2_zfrefle1 = k1_zfrefle1 ),
    file(zfrefle1,k2_zfrefle1),
    []).

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

fof(reflexivity_r2_zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => r2_zfrefle1(A,A) ) ),
    file(zfrefle1,r2_zfrefle1),
    []).

fof(symmetry_r2_zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_zfrefle1(A,B)
       => r2_zfrefle1(B,A) ) ) ),
    file(zfrefle1,r2_zfrefle1),
    []).

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(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(t4_zfrefle1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_zf_model(A)
       => r1_zfrefle1(A,k2_zfrefle1) ) ) ),
    file(zfrefle1,t4_zfrefle1),
    []).

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(t5_zfrefle1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ( r1_zfrefle1(A,k2_zfrefle1)
          & v1_ordinal1(A) )
       => v1_zf_model(A) ) ) ),
    file(zfrefle1,t5_zfrefle1),
    []).

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(t8_zfrefle1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( r2_zfrefle1(A,B)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(k9_zf_lang))
               => ( r1_zfrefle1(A,C)
                <=> r1_zfrefle1(B,C) ) ) ) ) ) ),
    file(zfrefle1,t8_zfrefle1),
    []).