% Mizar ND problem: t82_classes2,classes2,1507,39 
fof(dh_c1_76__classes2,definition,
    ( ( v3_ordinal1(c1_76__classes2)
     => ! [A] : 
          ( v3_ordinal1(A)
         => ( r1_ordinal1(c1_76__classes2,A)
          <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(A)) ) ) )
   => ! [B] : 
        ( v3_ordinal1(B)
       => ! [C] : 
            ( v3_ordinal1(C)
           => ( r1_ordinal1(B,C)
            <=> r1_tarski(k16_classes2(B),k16_classes2(C)) ) ) ) ),
    introduced(definition,[new_symbol(c1_76__classes2),file(classes2,c1_76__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_76__classes2)]).

fof(dh_c2_76__classes2,definition,
    ( ( v3_ordinal1(c2_76__classes2)
     => ( r1_ordinal1(c1_76__classes2,c2_76__classes2)
      <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ) )
   => ! [A] : 
        ( v3_ordinal1(A)
       => ( r1_ordinal1(c1_76__classes2,A)
        <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(A)) ) ) ),
    introduced(definition,[new_symbol(c2_76__classes2),file(classes2,c2_76__classes2)]),
    [interesting(0.8),axiom,file(classes2,c2_76__classes2)]).

fof(cc1_classes2,theorem,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    [interesting(0.9),axiom,file(classes2,cc1_classes2)]).

fof(cc2_classes2,theorem,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    [interesting(0.9),axiom,file(classes2,cc2_classes2)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

fof(cc3_classes2,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    [interesting(0.9),axiom,file(classes2,cc3_classes2)]).

fof(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

fof(rc1_classes2,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    [interesting(0.9),axiom,file(classes2,rc1_classes2)]).

fof(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

fof(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

fof(cc1_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(fc8_classes2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k16_classes2(A))
        & ~ v1_xboole_0(k16_classes2(A))
        & v1_classes1(k16_classes2(A))
        & v2_classes1(k16_classes2(A))
        & v1_classes2(k16_classes2(A)) ) ) ),
    file(classes2,fc8_classes2),
    [interesting(0.9),axiom,file(classes2,fc8_classes2)]).

fof(reflexivity_r1_ordinal1,theorem,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,r1_ordinal1)]).

fof(connectedness_r1_ordinal1,theorem,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,r1_ordinal1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(redefinition_r1_ordinal1,definition,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,r1_ordinal1)]).

fof(dt_k16_classes2,axiom,(
    $true ),
    file(classes2,k16_classes2),
    [interesting(0.9),axiom,file(classes2,k16_classes2)]).

fof(dt_c1_76__classes2,assumption,(
    v3_ordinal1(c1_76__classes2) ),
    introduced(assumption,[file(classes2,c1_76__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_76__classes2)]).

fof(dt_c2_76__classes2,assumption,(
    v3_ordinal1(c2_76__classes2) ),
    introduced(assumption,[file(classes2,c2_76__classes2)]),
    [interesting(0.8),axiom,file(classes2,c2_76__classes2)]).

fof(e1_76_1__classes2,assumption,(
    r1_ordinal1(c1_76__classes2,c2_76__classes2) ),
    introduced(assumption,[file(classes2,e1_76_1__classes2)]),
    [interesting(0.65),axiom,file(classes2,e1_76_1__classes2)]).

fof(e2_76_1__classes2,assumption,(
    ~ r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ),
    introduced(assumption,[file(classes2,e2_76_1__classes2)]),
    [interesting(0.65),axiom,file(classes2,e2_76_1__classes2)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

fof(rc2_ordinal1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc2_ordinal1,theorem,
    ( 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),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(rc2_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    [interesting(0.9),axiom,file(classes2,rc2_classes2)]).

fof(t57_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes2(B) )
         => ( r1_tarski(A,B)
            | r2_hidden(B,A) ) ) ) ),
    file(classes2,t57_classes2),
    [interesting(0.9),axiom,file(classes2,t57_classes2)]).

fof(e3_76_1__classes2,plain,(
    r2_hidden(k16_classes2(c2_76__classes2),k16_classes2(c1_76__classes2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e2_76_1__classes2])],[rc1_partfun1,rc2_ordinal1,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_classes2,cc1_ordinal1,cc2_ordinal1,cc3_classes2,fc1_subset_1,fc2_ordinal1,fc8_classes2,rc1_classes2,rc1_ordinal1,rc1_subset_1,rc2_classes2,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2,cc2_classes2,cc3_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,e2_76_1__classes2,t57_classes2]),
    [interesting(0.65),file(classes2,e3_76_1__classes2),[file(classes2,e3_76_1__classes2)]]).

fof(t80_classes2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
          <=> r2_hidden(k16_classes2(A),k16_classes2(B)) ) ) ) ),
    file(classes2,t80_classes2),
    [interesting(0.9),axiom,file(classes2,t80_classes2)]).

fof(e4_76_1__classes2,plain,(
    r2_hidden(c2_76__classes2,c1_76__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e2_76_1__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_classes2,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,rc1_classes2,rc1_ordinal1,rc2_classes2,rc3_ordinal1,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2,cc1_ordinal1,fc8_classes2,t1_subset,t7_boole,e3_76_1__classes2,t80_classes2]),
    [interesting(0.65),file(classes2,e4_76_1__classes2),[file(classes2,e4_76_1__classes2)]]).

fof(t7_ordinal1,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & r1_tarski(B,A) ) ),
    file(ordinal1,t7_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t7_ordinal1)]).

fof(e5_76_1__classes2,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e2_76_1__classes2,e1_76_1__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_c1_76__classes2,dt_c2_76__classes2,t1_subset,t3_subset,t7_boole,e4_76_1__classes2,e1_76_1__classes2,t7_ordinal1]),
    [interesting(0.65),file(classes2,e5_76_1__classes2),[file(classes2,e5_76_1__classes2)]]).

fof(i3_76_1__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i3_76_1__classes2)]),
    [interesting(0.65),trivial,file(classes2,i3_76_1__classes2)]).

fof(i2_76_1__classes2,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e2_76_1__classes2,e1_76_1__classes2])],[e5_76_1__classes2,i3_76_1__classes2]),
    [interesting(0.65),file(classes2,i2_76_1__classes2),[file(classes2,i2_76_1__classes2)]]).

fof(i1_76_1__classes2,plain,(
    r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e1_76_1__classes2]),discharge_asm(discharge,[e2_76_1__classes2])],[e2_76_1__classes2,i2_76_1__classes2]),
    [interesting(0.65),file(classes2,i1_76_1__classes2),[file(classes2,i1_76_1__classes2)]]).

fof(i1_76_1_tmp__classes2,plain,
    ( r1_ordinal1(c1_76__classes2,c2_76__classes2)
   => r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2]),discharge_asm(discharge,[e1_76_1__classes2])],[e1_76_1__classes2,i1_76_1__classes2]),
    [interesting(0.8),e1_76__classes2]).

fof(e1_76__classes2,plain,
    ( r1_ordinal1(c1_76__classes2,c2_76__classes2)
   => r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2])],[i1_76_1_tmp__classes2,cc1_classes2,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,rc1_classes2,rc1_ordinal1,rc3_ordinal1,cc1_ordinal1,fc8_classes2,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,redefinition_r1_ordinal1,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2]),
    [interesting(0.8),file(classes2,e1_76__classes2),[file(classes2,e1_76__classes2)]]).

fof(e2_76__classes2,assumption,(
    r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ),
    introduced(assumption,[file(classes2,e2_76__classes2)]),
    [interesting(0.8),axiom,file(classes2,e2_76__classes2)]).

fof(e3_76__classes2,assumption,(
    ~ r1_ordinal1(c1_76__classes2,c2_76__classes2) ),
    introduced(assumption,[file(classes2,e3_76__classes2)]),
    [interesting(0.8),axiom,file(classes2,e3_76__classes2)]).

fof(t26_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
            | r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t26_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t26_ordinal1)]).

fof(e4_76__classes2,plain,(
    r2_hidden(c2_76__classes2,c1_76__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e3_76__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc2_ordinal1,rc1_subset_1,rc2_subset_1,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,existence_m1_subset_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc3_ordinal1,t2_subset,t3_subset,t6_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_c1_76__classes2,dt_c2_76__classes2,cc1_ordinal1,t1_subset,t7_boole,e3_76__classes2,t26_ordinal1]),
    [interesting(0.8),file(classes2,e4_76__classes2),[file(classes2,e4_76__classes2)]]).

fof(e5_76__classes2,plain,(
    r2_hidden(k16_classes2(c2_76__classes2),k16_classes2(c1_76__classes2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e3_76__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_classes2,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,rc1_classes2,rc1_ordinal1,rc2_classes2,rc3_ordinal1,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2,cc1_ordinal1,fc8_classes2,t1_subset,t7_boole,e4_76__classes2,t80_classes2]),
    [interesting(0.8),file(classes2,e5_76__classes2),[file(classes2,e5_76__classes2)]]).

fof(e6_76__classes2,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e3_76__classes2,e2_76__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_classes2,cc2_classes2,cc2_ordinal1,cc3_classes2,fc2_ordinal1,rc1_classes2,rc1_ordinal1,rc2_classes2,rc3_ordinal1,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_ordinal1,cc3_ordinal1,fc1_subset_1,fc8_classes2,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2,t1_subset,t3_subset,t7_boole,e5_76__classes2,e2_76__classes2,t7_ordinal1]),
    [interesting(0.8),file(classes2,e6_76__classes2),[file(classes2,e6_76__classes2)]]).

fof(i6_76__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i6_76__classes2)]),
    [interesting(0.8),trivial,file(classes2,i6_76__classes2)]).

fof(i5_76__classes2,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e3_76__classes2,e2_76__classes2])],[e6_76__classes2,i6_76__classes2]),
    [interesting(0.8),file(classes2,i5_76__classes2),[file(classes2,i5_76__classes2)]]).

fof(i4_76__classes2,plain,(
    r1_ordinal1(c1_76__classes2,c2_76__classes2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2,e2_76__classes2]),discharge_asm(discharge,[e3_76__classes2])],[e3_76__classes2,i5_76__classes2]),
    [interesting(0.8),file(classes2,i4_76__classes2),[file(classes2,i4_76__classes2)]]).

fof(i4_76_tmp__classes2,plain,
    ( r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2))
   => r1_ordinal1(c1_76__classes2,c2_76__classes2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2]),discharge_asm(discharge,[e2_76__classes2])],[e2_76__classes2,i4_76__classes2]),
    [interesting(0.8),i3_76__classes2]).

fof(i3_76__classes2,plain,
    ( r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2))
   => r1_ordinal1(c1_76__classes2,c2_76__classes2) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2])],[i4_76_tmp__classes2,cc1_classes2,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,rc1_classes2,rc1_ordinal1,rc3_ordinal1,cc1_ordinal1,fc8_classes2,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,redefinition_r1_ordinal1,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2]),
    [interesting(0.8),file(classes2,i3_76__classes2),[file(classes2,i3_76__classes2)]]).

fof(i2_76__classes2,plain,
    ( r1_ordinal1(c1_76__classes2,c2_76__classes2)
  <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_76__classes2,dt_c2_76__classes2])],[cc1_classes2,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,rc1_classes2,rc1_ordinal1,rc3_ordinal1,cc1_ordinal1,fc8_classes2,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,redefinition_r1_ordinal1,dt_k16_classes2,dt_c1_76__classes2,dt_c2_76__classes2,e1_76__classes2,i3_76__classes2]),
    [interesting(0.8),file(classes2,i2_76__classes2),[file(classes2,i2_76__classes2)]]).

fof(i2_76_tmp__classes2,plain,
    ( v3_ordinal1(c2_76__classes2)
   => ( r1_ordinal1(c1_76__classes2,c2_76__classes2)
    <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(c2_76__classes2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_76__classes2]),discharge_asm(discharge,[dt_c2_76__classes2])],[dt_c2_76__classes2,i2_76__classes2]),
    [interesting(0.8),i1_76__classes2]).

fof(i1_76__classes2,plain,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( r1_ordinal1(c1_76__classes2,A)
      <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_76__classes2])],[i2_76_tmp__classes2,dh_c2_76__classes2]),
    [interesting(0.8),file(classes2,i1_76__classes2),[file(classes2,i1_76__classes2)]]).

fof(i1_76_tmp__classes2,plain,
    ( v3_ordinal1(c1_76__classes2)
   => ! [A] : 
        ( v3_ordinal1(A)
       => ( r1_ordinal1(c1_76__classes2,A)
        <=> r1_tarski(k16_classes2(c1_76__classes2),k16_classes2(A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_76__classes2])],[dt_c1_76__classes2,i1_76__classes2]),
    [interesting(1),t82_classes2]).

fof(t82_classes2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
          <=> r1_tarski(k16_classes2(A),k16_classes2(B)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_76_tmp__classes2,dh_c1_76__classes2]),
    [interesting(1),file(classes2,t82_classes2),[file(classes2,t82_classes2)]]).