% Mizar problem: t28_zf_refle,zf_refle,637,25 
fof(t28_zf_refle,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( r2_hidden(B,A)
         => r2_hidden(k7_ordinal2(B),A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_classes2,cc1_funct_1,cc1_ordinal1,cc2_classes2,cc2_funct_1,cc2_ordinal1,cc3_classes2,cc3_ordinal1,d1_classes1,d2_ordinal4,dt_k1_ordinal1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ordinal2,dt_k3_tarski,dt_k6_ordinal4,dt_k7_ordinal2,dt_m1_ordinal4,dt_m1_subset_1,existence_m1_ordinal4,existence_m1_subset_1,fc1_ordinal1,fc1_subset_1,fc2_classes2,fc2_ordinal1,fc3_ordinal1,fc4_ordinal1,rc1_classes2,rc1_funct_1,rc1_ordinal1,rc1_subset_1,rc1_zf_refle,rc2_classes2,rc2_funct_1,rc2_ordinal1,rc2_subset_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,redefinition_k6_ordinal4,reflexivity_r1_tarski,t1_subset,t27_zf_refle,t2_subset,t3_subset,t4_subset,t5_subset,t65_classes2,t6_boole,t7_boole,t7_ordinal3,t8_boole,t9_ordinal2]),
    [file(zf_refle,t28_zf_refle)]).

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

fof(cc1_classes2,axiom,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

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

fof(cc2_classes2,axiom,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

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

fof(cc3_classes2,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    []).

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

fof(d1_classes1,axiom,(
    ! [A] : 
      ( v1_classes1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r1_tarski(C,B) )
         => r2_hidden(C,A) ) ) ),
    file(classes1,d1_classes1),
    []).

fof(d2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( m1_ordinal4(B,A)
          <=> r2_hidden(B,A) ) ) ) ),
    file(ordinal4,d2_ordinal4),
    []).

fof(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    []).

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_k2_ordinal2,axiom,(
    $true ),
    file(ordinal2,k2_ordinal2),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k6_ordinal4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_ordinal4(B,A) )
     => ( ~ v1_xboole_0(k6_ordinal4(A,B))
        & m1_ordinal4(k6_ordinal4(A,B),A) ) ) ),
    file(ordinal4,k6_ordinal4),
    []).

fof(dt_k7_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k7_ordinal2(A)) ),
    file(ordinal2,k7_ordinal2),
    []).

fof(dt_m1_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal4(B,A)
         => v3_ordinal1(B) ) ) ),
    file(ordinal4,m1_ordinal4),
    []).

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

fof(existence_m1_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : m1_ordinal4(B,A) ) ),
    file(ordinal4,m1_ordinal4),
    []).

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

fof(fc1_ordinal1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    []).

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

fof(fc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_ordinal1(k2_ordinal2(A))
        & v2_ordinal1(k2_ordinal2(A))
        & v3_ordinal1(k2_ordinal2(A)) ) ) ),
    file(classes2,fc2_classes2),
    []).

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(fc3_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    []).

fof(fc4_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    []).

fof(rc1_classes2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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

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_zf_refle,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(zf_refle,rc1_zf_refle),
    []).

fof(rc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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(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(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

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

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(redefinition_k6_ordinal4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_ordinal4(B,A) )
     => k6_ordinal4(A,B) = k1_ordinal1(B) ) ),
    file(ordinal4,k6_ordinal4),
    []).

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

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

fof(t27_zf_refle,axiom,(
    ! [A] : r1_tarski(k7_ordinal2(A),k1_ordinal1(k3_tarski(k2_ordinal2(A)))) ),
    file(zf_refle,t27_zf_refle),
    []).

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(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(t65_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B) )
     => ( r2_hidden(A,B)
       => ( r2_hidden(k1_zfmisc_1(A),B)
          & r2_hidden(k3_tarski(A),B)
          & r2_hidden(k1_setfam_1(A),B) ) ) ) ),
    file(classes2,t65_classes2),
    []).

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(t7_ordinal3,axiom,(
    ! [A] : v3_ordinal1(k3_tarski(k2_ordinal2(A))) ),
    file(ordinal3,t7_ordinal3),
    []).

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

fof(t9_ordinal2,axiom,(
    ! [A] : r1_tarski(k2_ordinal2(A),A) ),
    file(ordinal2,t9_ordinal2),
    []).