% Mizar problem: t13_card_fil,card_fil,341,70 
fof(t13_card_fil,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ! [C] : 
              ( m1_card_fil(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( r2_hidden(D,k3_card_fil(A,C,B))
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(A))
                        & r2_hidden(E,C)
                        & r1_tarski(k5_subset_1(A,E,B),D) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,commutativity_k3_xboole_0,commutativity_k5_subset_1,d8_card_fil,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_card_fil,dt_k3_xboole_0,dt_k5_subset_1,dt_m1_card_fil,dt_m1_subset_1,existence_m1_card_fil,existence_m1_subset_1,fc10_finset_1,fc11_finset_1,fc1_subset_1,fc2_ordinal1,fraenkel_a_3_0_card_fil,fraenkel_a_3_1_card_fil,fraenkel_a_3_2_card_fil,fraenkel_a_3_3_card_fil,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc1_card_5,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_subset_1,rc2_funct_1,rc2_ordinal1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc4_funct_1,redefinition_k5_subset_1,reflexivity_r1_tarski,s1_card_fil__e3_26_1__card_fil,t1_subset,t2_boole,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(card_fil,t13_card_fil)]).

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

fof(cc1_card_5,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(card_5,cc1_card_5),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

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_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d8_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => k3_card_fil(A,B,C) = a_3_0_card_fil(A,B,C) ) ) ) ),
    file(card_fil,d8_card_fil),
    []).

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_k3_card_fil,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_card_fil(B,A)
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => ( ~ v1_xboole_0(k3_card_fil(A,B,C))
        & m1_subset_1(k3_card_fil(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(card_fil,k3_card_fil),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_m1_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ),
    file(card_fil,m1_card_fil),
    []).

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

fof(existence_m1_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_card_fil(B,A) ) ),
    file(card_fil,m1_card_fil),
    []).

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

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_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(fraenkel_a_3_0_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & m1_card_fil(C,B)
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_3_0_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(B))
            & A = E
            & ? [F] : 
                ( m1_subset_1(F,k1_zfmisc_1(B))
                & r2_hidden(F,a_3_1_card_fil(B,C,D))
                & r1_tarski(F,E) ) ) ) ) ),
    file(card_fil,a_3_0_card_fil),
    []).

fof(fraenkel_a_3_1_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & m1_card_fil(C,B)
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_3_1_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(B))
            & A = k5_subset_1(B,E,D)
            & r2_hidden(E,C) ) ) ) ),
    file(card_fil,a_3_1_card_fil),
    []).

fof(fraenkel_a_3_2_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(C,k1_zfmisc_1(B))
        & m1_card_fil(D,B) )
     => ( r2_hidden(A,a_3_2_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(B))
            & A = E
            & ? [F] : 
                ( m1_subset_1(F,k1_zfmisc_1(B))
                & r2_hidden(F,a_3_3_card_fil(B,C,D))
                & r1_tarski(F,E) ) ) ) ) ),
    file(card_fil,a_3_2_card_fil),
    []).

fof(fraenkel_a_3_3_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(C,k1_zfmisc_1(B))
        & m1_card_fil(D,B) )
     => ( r2_hidden(A,a_3_3_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(B))
            & A = k5_subset_1(B,E,C)
            & r2_hidden(E,D) ) ) ) ),
    file(card_fil,a_3_3_card_fil),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

fof(rc1_card_5,axiom,(
    ? [A] : ~ v1_finset_1(A) ),
    file(card_5,rc1_card_5),
    []).

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

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(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_finset_1,axiom,(
    ! [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),
    []).

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_finset_1,axiom,(
    ! [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),
    []).

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_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

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

fof(s1_card_fil__e3_26_1__card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & m1_card_fil(C,A)
        & m1_subset_1(D,k1_zfmisc_1(A)) )
     => ( r2_hidden(D,a_3_2_card_fil(A,B,C))
       => ? [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(A))
            & r2_hidden(E,a_3_3_card_fil(A,B,C))
            & r1_tarski(E,D) ) ) ) ),
    file(card_fil,s1_card_fil__e3_26_1__card_fil),
    []).

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

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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(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),
    []).