% Mizar ND problem: t1_cantor_1,cantor_1,83,65 
fof(dh_c1_4__cantor_1,definition,
    ( ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1)))
       => r1_tarski(A,k1_cantor_1(c1_4__cantor_1,A)) )
   => ! [B,C] : 
        ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
       => r1_tarski(C,k1_cantor_1(B,C)) ) ),
    introduced(definition,[new_symbol(c1_4__cantor_1),file(cantor_1,c1_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c1_4__cantor_1)]).

fof(dh_c2_4__cantor_1,definition,
    ( ( m1_subset_1(c2_4__cantor_1,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1)))
     => r1_tarski(c2_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1)))
       => r1_tarski(A,k1_cantor_1(c1_4__cantor_1,A)) ) ),
    introduced(definition,[new_symbol(c2_4__cantor_1),file(cantor_1,c2_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c2_4__cantor_1)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_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(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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

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(dt_k1_cantor_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k1_cantor_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(cantor_1,k1_cantor_1),
    [interesting(0.9),axiom,file(cantor_1,k1_cantor_1)]).

fof(dt_c1_4__cantor_1,assumption,(
    $true ),
    introduced(assumption,[file(cantor_1,c1_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c1_4__cantor_1)]).

fof(dt_c2_4__cantor_1,assumption,(
    m1_subset_1(c2_4__cantor_1,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1))) ),
    introduced(assumption,[file(cantor_1,c2_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c2_4__cantor_1)]).

fof(dt_c3_4__cantor_1,assumption,(
    $true ),
    introduced(assumption,[file(cantor_1,c3_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c3_4__cantor_1)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c3_4__cantor_1,definition,
    ( ~ ( r2_hidden(c3_4__cantor_1,c2_4__cantor_1)
        & ~ r2_hidden(c3_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_4__cantor_1)
          & ~ r2_hidden(A,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ) ),
    introduced(definition,[new_symbol(c3_4__cantor_1),file(cantor_1,c3_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c3_4__cantor_1)]).

fof(e1_4__cantor_1,assumption,(
    r2_hidden(c3_4__cantor_1,c2_4__cantor_1) ),
    introduced(assumption,[file(cantor_1,e1_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,e1_4__cantor_1)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,k5_finsub_1)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(redefinition_k2_setwiseo,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k2_setwiseo(A,B) = k1_tarski(B) ) ),
    file(setwiseo,k2_setwiseo),
    [interesting(0.9),axiom,file(setwiseo,k2_setwiseo)]).

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

fof(dt_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) ),
    file(setwiseo,k2_setwiseo),
    [interesting(0.9),axiom,file(setwiseo,k2_setwiseo)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(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(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(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(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(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(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(de_c4_4__cantor_1,definition,(
    c4_4__cantor_1 = c3_4__cantor_1 ),
    introduced(definition,[new_symbol(c4_4__cantor_1),file(cantor_1,c4_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c4_4__cantor_1)]).

fof(e2_4__cantor_1,plain,(
    m1_subset_1(c3_4__cantor_1,k1_zfmisc_1(c1_4__cantor_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t8_boole,reflexivity_r1_tarski,cc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_4__cantor_1]),
    [interesting(0.8),file(cantor_1,e2_4__cantor_1),[file(cantor_1,e2_4__cantor_1)]]).

fof(dt_c4_4__cantor_1,plain,(
    m1_subset_1(c4_4__cantor_1,k1_zfmisc_1(c1_4__cantor_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c3_4__cantor_1,fc1_subset_1,t3_subset,de_c4_4__cantor_1,e2_4__cantor_1]),
    [interesting(0.8),file(cantor_1,c4_4__cantor_1),[file(cantor_1,c4_4__cantor_1)]]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(de_c5_4__cantor_1,definition,(
    c5_4__cantor_1 = k2_setwiseo(k1_zfmisc_1(c1_4__cantor_1),c4_4__cantor_1) ),
    introduced(definition,[new_symbol(c5_4__cantor_1),file(cantor_1,c5_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c5_4__cantor_1)]).

fof(t63_subset_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)) ) ),
    file(subset_1,t63_subset_1),
    [interesting(0.9),axiom,file(subset_1,t63_subset_1)]).

fof(e3_4__cantor_1,plain,(
    m1_subset_1(k2_setwiseo(k1_zfmisc_1(c1_4__cantor_1),c4_4__cantor_1),k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[dt_k1_xboole_0,fc1_xboole_0,reflexivity_r1_tarski,dt_k5_finsub_1,dt_c3_4__cantor_1,cc1_finset_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k2_setwiseo,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_setwiseo,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c4_4__cantor_1,de_c4_4__cantor_1,fc1_finset_1,fc1_subset_1,fc2_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,t63_subset_1]),
    [interesting(0.8),file(cantor_1,e3_4__cantor_1),[file(cantor_1,e3_4__cantor_1)]]).

fof(dt_c5_4__cantor_1,plain,(
    m1_subset_1(c5_4__cantor_1,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,dt_k1_tarski,dt_k5_finsub_1,dt_c3_4__cantor_1,cc1_finset_1,fc1_finset_1,fc2_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k2_setwiseo,dt_k1_zfmisc_1,dt_k2_setwiseo,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c4_4__cantor_1,de_c4_4__cantor_1,fc1_subset_1,t3_subset,de_c5_4__cantor_1,e3_4__cantor_1]),
    [interesting(0.8),file(cantor_1,c5_4__cantor_1),[file(cantor_1,c5_4__cantor_1)]]).

fof(redefinition_k5_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(de_c6_4__cantor_1,definition,(
    c6_4__cantor_1 = c5_4__cantor_1 ),
    introduced(definition,[new_symbol(c6_4__cantor_1),file(cantor_1,c6_4__cantor_1)]),
    [interesting(0.8),axiom,file(cantor_1,c6_4__cantor_1)]).

fof(e4_4__cantor_1,plain,(
    m1_subset_1(c5_4__cantor_1,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k5_finsub_1,dt_c3_4__cantor_1,cc2_finset_1,fc1_finset_1,fc1_xboole_0,fc2_subset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,redefinition_k2_setwiseo,dt_k2_setwiseo,dt_c4_4__cantor_1,de_c4_4__cantor_1,cc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c5_4__cantor_1,de_c5_4__cantor_1,fc1_subset_1,t3_subset]),
    [interesting(0.8),file(cantor_1,e4_4__cantor_1),[file(cantor_1,e4_4__cantor_1)]]).

fof(dt_c6_4__cantor_1,plain,(
    m1_subset_1(c6_4__cantor_1,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k5_finsub_1,dt_c3_4__cantor_1,cc2_finset_1,fc1_finset_1,fc1_xboole_0,fc2_subset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,redefinition_k2_setwiseo,dt_k2_setwiseo,dt_c4_4__cantor_1,de_c4_4__cantor_1,cc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c5_4__cantor_1,de_c5_4__cantor_1,fc1_subset_1,t3_subset,de_c6_4__cantor_1,e4_4__cantor_1]),
    [interesting(0.8),file(cantor_1,c6_4__cantor_1),[file(cantor_1,c6_4__cantor_1)]]).

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    file(zfmisc_1,t31_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t31_zfmisc_1)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t37_zfmisc_1)]).

fof(e5_4__cantor_1,plain,
    ( r1_tarski(c6_4__cantor_1,c2_4__cantor_1)
    & c3_4__cantor_1 = k5_setfam_1(c1_4__cantor_1,c6_4__cantor_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[dt_k5_finsub_1,redefinition_k2_setwiseo,dt_k1_xboole_0,dt_k2_setwiseo,dt_c4_4__cantor_1,de_c4_4__cantor_1,fc1_xboole_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c5_4__cantor_1,de_c5_4__cantor_1,cc1_finset_1,cc2_finset_1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_setfam_1,dt_k1_tarski,dt_k3_tarski,dt_k5_setfam_1,dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,dt_c6_4__cantor_1,de_c6_4__cantor_1,fc1_finset_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e1_4__cantor_1,t31_zfmisc_1,t37_zfmisc_1]),
    [interesting(0.8),file(cantor_1,e5_4__cantor_1),[file(cantor_1,e5_4__cantor_1)]]).

fof(d1_cantor_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k1_cantor_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A)))
                      & r1_tarski(E,B)
                      & D = k5_setfam_1(A,E) ) ) ) ) ) ) ),
    file(cantor_1,d1_cantor_1),
    [interesting(0.9),axiom,file(cantor_1,d1_cantor_1)]).

fof(e6_4__cantor_1,plain,(
    r2_hidden(c3_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[dt_k1_tarski,dt_k5_finsub_1,fc1_finset_1,fc2_subset_1,redefinition_k2_setwiseo,dt_k1_xboole_0,dt_k2_setwiseo,dt_c4_4__cantor_1,de_c4_4__cantor_1,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,dt_k3_tarski,dt_c5_4__cantor_1,de_c5_4__cantor_1,cc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_setfam_1,dt_k1_cantor_1,dt_k1_zfmisc_1,dt_k5_setfam_1,dt_m1_subset_1,dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,dt_c6_4__cantor_1,de_c6_4__cantor_1,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e5_4__cantor_1,d1_cantor_1]),
    [interesting(0.8),file(cantor_1,e6_4__cantor_1),[file(cantor_1,e6_4__cantor_1)]]).

fof(i5_4__cantor_1,theorem,(
    $true ),
    introduced(tautology,[file(cantor_1,i5_4__cantor_1)]),
    [interesting(0.8),trivial,file(cantor_1,i5_4__cantor_1)]).

fof(i4_4__cantor_1,plain,(
    r2_hidden(c3_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1,e1_4__cantor_1])],[e6_4__cantor_1,i5_4__cantor_1]),
    [interesting(0.8),file(cantor_1,i4_4__cantor_1),[file(cantor_1,i4_4__cantor_1)]]).

fof(i3_4__cantor_1,plain,(
    ~ ( r2_hidden(c3_4__cantor_1,c2_4__cantor_1)
      & ~ r2_hidden(c3_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1,dt_c3_4__cantor_1]),discharge_asm(discharge,[e1_4__cantor_1])],[e1_4__cantor_1,i4_4__cantor_1]),
    [interesting(0.8),file(cantor_1,i3_4__cantor_1),[file(cantor_1,i3_4__cantor_1)]]).

fof(i3_4_tmp__cantor_1,plain,(
    ~ ( r2_hidden(c3_4__cantor_1,c2_4__cantor_1)
      & ~ r2_hidden(c3_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1]),discharge_asm(discharge,[dt_c3_4__cantor_1])],[dt_c3_4__cantor_1,i3_4__cantor_1]),
    [interesting(0.8),i2_4__cantor_1]).

fof(i2_4__cantor_1,plain,(
    r1_tarski(c2_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ),
    inference(let,[status(thm),assumptions([dt_c1_4__cantor_1,dt_c2_4__cantor_1])],[i3_4_tmp__cantor_1,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_cantor_1,dt_c1_4__cantor_1,dt_c2_4__cantor_1,d3_tarski,dh_c3_4__cantor_1]),
    [interesting(0.8),file(cantor_1,i2_4__cantor_1),[file(cantor_1,i2_4__cantor_1)]]).

fof(i2_4_tmp__cantor_1,plain,
    ( m1_subset_1(c2_4__cantor_1,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1)))
   => r1_tarski(c2_4__cantor_1,k1_cantor_1(c1_4__cantor_1,c2_4__cantor_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__cantor_1]),discharge_asm(discharge,[dt_c2_4__cantor_1])],[dt_c2_4__cantor_1,i2_4__cantor_1]),
    [interesting(0.8),i1_4__cantor_1]).

fof(i1_4__cantor_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1)))
     => r1_tarski(A,k1_cantor_1(c1_4__cantor_1,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__cantor_1])],[i2_4_tmp__cantor_1,dh_c2_4__cantor_1]),
    [interesting(0.8),file(cantor_1,i1_4__cantor_1),[file(cantor_1,i1_4__cantor_1)]]).

fof(i1_4_tmp__cantor_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_4__cantor_1)))
     => r1_tarski(A,k1_cantor_1(c1_4__cantor_1,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__cantor_1])],[dt_c1_4__cantor_1,i1_4__cantor_1]),
    [interesting(1),t1_cantor_1]).

fof(t1_cantor_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => r1_tarski(B,k1_cantor_1(A,B)) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__cantor_1,dh_c1_4__cantor_1]),
    [interesting(1),file(cantor_1,t1_cantor_1),[file(cantor_1,t1_cantor_1)]]).