% Mizar problem: t71_classes2,classes2,1262,25 
fof(t71_classes2,conjecture,(
    k13_classes2 = k4_classes1(k5_ordinal2) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_classes2,cc1_ordinal1,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,connectedness_r1_ordinal1,d10_xboole_0,d1_classes2,d2_classes2,d3_classes1,d4_classes1,d5_ordinal2,dt_k13_classes2,dt_k1_classes1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ordinal2,dt_k4_classes1,dt_k5_ordinal2,dt_m1_subset_1,existence_m1_subset_1,fc1_classes1,fc1_classes2,fc1_ordinal2,fc1_subset_1,fc2_classes2,fc2_ordinal1,fc3_classes2,fc4_classes2,rc1_classes2,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc1_subset_1,rc2_classes2,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,redefinition_r1_ordinal1,reflexivity_r1_ordinal1,reflexivity_r1_tarski,t10_ordinal3,t19_ordinal2,t1_subset,t2_subset,t37_classes1,t3_subset,t43_classes1,t44_classes1,t4_subset,t54_classes2,t55_classes2,t5_subset,t6_boole,t70_classes2,t7_boole,t8_boole]),
    [file(classes2,t71_classes2)]).

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_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_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(connectedness_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_classes2,axiom,(
    ! [A] : 
      ( v1_classes2(A)
    <=> ( v1_ordinal1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,d1_classes2),
    []).

fof(d2_classes2,axiom,(
    k13_classes2 = k1_classes1(k1_xboole_0) ),
    file(classes2,d2_classes2),
    []).

fof(d3_classes1,axiom,(
    ! [A,B] : 
      ( r1_classes1(A,B)
    <=> ( r2_hidden(A,B)
        & v2_classes1(B) ) ) ),
    file(classes1,d3_classes1),
    []).

fof(d4_classes1,axiom,(
    ! [A,B] : 
      ( B = k1_classes1(A)
    <=> ( r1_classes1(A,B)
        & ! [C] : 
            ( r1_classes1(A,C)
           => r1_tarski(B,C) ) ) ) ),
    file(classes1,d4_classes1),
    []).

fof(d5_ordinal2,axiom,(
    ! [A] : 
      ( A = k5_ordinal2
    <=> ( r2_hidden(k1_xboole_0,A)
        & v4_ordinal1(A)
        & v3_ordinal1(A)
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( ( r2_hidden(k1_xboole_0,B)
                & v4_ordinal1(B) )
             => r1_tarski(A,B) ) ) ) ) ),
    file(ordinal2,d5_ordinal2),
    []).

fof(dt_k13_classes2,axiom,
    ( ~ v1_xboole_0(k13_classes2)
    & v1_classes2(k13_classes2) ),
    file(classes2,k13_classes2),
    []).

fof(dt_k1_classes1,axiom,(
    $true ),
    file(classes1,k1_classes1),
    []).

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_k4_classes1,axiom,(
    $true ),
    file(classes1,k4_classes1),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

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(fc1_classes1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_classes1(A)) ),
    file(classes1,fc1_classes1),
    []).

fof(fc1_classes2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_classes1(A))
      & v1_classes1(k1_classes1(A))
      & v2_classes1(k1_classes1(A)) ) ),
    file(classes2,fc1_classes2),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

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_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_ordinal1(k1_classes1(A))
        & ~ v1_xboole_0(k1_classes1(A))
        & v1_classes1(k1_classes1(A))
        & v2_classes1(k1_classes1(A))
        & v1_classes2(k1_classes1(A)) ) ) ),
    file(classes2,fc3_classes2),
    []).

fof(fc4_classes2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k1_classes1(A))
        & ~ v1_xboole_0(k1_classes1(A))
        & v1_classes1(k1_classes1(A))
        & v2_classes1(k1_classes1(A))
        & v1_classes2(k1_classes1(A)) ) ) ),
    file(classes2,fc4_classes2),
    []).

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_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_ordinal2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    []).

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(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(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_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_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(redefinition_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    []).

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

fof(t10_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( A != k1_xboole_0
       => r2_hidden(k1_xboole_0,A) ) ) ),
    file(ordinal3,t10_ordinal3),
    []).

fof(t19_ordinal2,axiom,
    ( r2_hidden(k1_xboole_0,k5_ordinal2)
    & v4_ordinal1(k5_ordinal2)
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( ( r2_hidden(k1_xboole_0,A)
            & v4_ordinal1(A) )
         => r1_ordinal1(k5_ordinal2,A) ) ) ),
    file(ordinal2,t19_ordinal2),
    []).

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(t37_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v1_ordinal1(k4_classes1(A)) ) ),
    file(classes1,t37_classes1),
    []).

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

fof(t43_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
          <=> r1_tarski(k4_classes1(A),k4_classes1(B)) ) ) ) ),
    file(classes1,t43_classes1),
    []).

fof(t44_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => r1_tarski(A,k4_classes1(A)) ) ),
    file(classes1,t44_classes1),
    []).

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(t54_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => A = k4_classes1(k2_ordinal2(A)) ) ),
    file(classes2,t54_classes2),
    []).

fof(t55_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( k2_ordinal2(A) != k1_xboole_0
        & v4_ordinal1(k2_ordinal2(A)) ) ) ),
    file(classes2,t55_classes2),
    []).

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(t70_classes2,axiom,(
    v2_classes1(k4_classes1(k5_ordinal2)) ),
    file(classes2,t70_classes2),
    []).

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),
    []).