% Mizar problem: t10_card_lar,card_lar,270,34 
fof(t10_card_lar,conjecture,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( ( v1_card_lar(C,A)
                  & r2_hidden(B,A) )
               => ( r2_hidden(k2_card_lar(A,C,B),C)
                  & r2_hidden(B,k2_card_lar(A,C,B)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_card_5,cc1_ordinal1,cc2_arytm_3,cc2_card_lar,cc2_ordinal1,cc3_ordinal1,d1_setfam_1,d6_card_lar,d6_ordinal2,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_lar,dt_k2_ordinal2,dt_k6_ordinal2,dt_m1_subset_1,existence_m1_subset_1,fc1_subset_1,fc2_ordinal1,fraenkel_a_0_0_domain_1,fraenkel_a_3_0_card_lar,fraenkel_a_3_1_card_lar,rc1_arytm_3,rc1_card_5,rc1_ordinal1,rc1_ordinal2,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,reflexivity_r1_tarski,s1_card_fil__e2_19_1__card_lar,s7_domain_1__e6_19__card_lar,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_card_lar,t8_ordinal3,t9_card_lar]),
    [file(card_lar,t10_card_lar)]).

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

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

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

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

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v3_ordinal1(A)
        & v4_ordinal1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_finset_1(A) ) ) ),
    file(card_lar,cc2_card_lar),
    []).

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(d1_setfam_1,axiom,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    []).

fof(d6_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( v1_card_lar(B,A)
                  & r2_hidden(C,A) )
               => k2_card_lar(A,B,C) = k6_ordinal2(a_3_1_card_lar(A,B,C)) ) ) ) ) ),
    file(card_lar,d6_card_lar),
    []).

fof(d6_ordinal2,axiom,(
    ! [A] : k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A)) ),
    file(ordinal2,d6_ordinal2),
    []).

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_card_lar,axiom,(
    ! [A,B,C] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & v3_ordinal1(C) )
     => m1_subset_1(k2_card_lar(A,B,C),B) ) ),
    file(card_lar,k2_card_lar),
    []).

fof(dt_k2_ordinal2,axiom,(
    $true ),
    file(ordinal2,k2_ordinal2),
    []).

fof(dt_k6_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k6_ordinal2(A)) ),
    file(ordinal2,k6_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_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_0_0_domain_1,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_domain_1)
    <=> ? [B] : 
          ( m1_subset_1(B,f1_s7_domain_1)
          & A = B
          & p1_s7_domain_1(B) ) ) ),
    file(domain_1,a_0_0_domain_1),
    []).

fof(fraenkel_a_3_0_card_lar,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(B)
        & v4_ordinal1(B)
        & ~ v1_finset_1(B)
        & v3_ordinal1(C)
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_3_0_card_lar(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,B)
            & A = E
            & r2_hidden(E,D)
            & r2_hidden(C,E) ) ) ) ),
    file(card_lar,a_3_0_card_lar),
    []).

fof(fraenkel_a_3_1_card_lar,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(B)
        & v4_ordinal1(B)
        & ~ v1_finset_1(B)
        & m1_subset_1(C,k1_zfmisc_1(B))
        & v3_ordinal1(D) )
     => ( r2_hidden(A,a_3_1_card_lar(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,B)
            & A = E
            & r2_hidden(E,C)
            & r2_hidden(D,E) ) ) ) ),
    file(card_lar,a_3_1_card_lar),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

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

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

fof(s1_card_fil__e2_19_1__card_lar,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A)
        & v3_ordinal1(B)
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => ( r2_hidden(D,a_3_0_card_lar(A,B,C))
       => ( r2_hidden(D,C)
          & r2_hidden(B,D) ) ) ) ),
    file(card_lar,s1_card_fil__e2_19_1__card_lar),
    []).

fof(s7_domain_1__e6_19__card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(A)) ) ),
    file(card_lar,s7_domain_1__e6_19__card_lar),
    []).

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(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),
    []).

fof(t8_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ~ ( v1_card_lar(B,A)
              & v1_xboole_0(B) ) ) ) ),
    file(card_lar,t8_card_lar),
    []).

fof(t8_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => k2_ordinal2(B) = B ) ) ),
    file(ordinal3,t8_ordinal3),
    []).

fof(t9_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ~ ( v1_card_lar(C,A)
                  & r2_hidden(B,A)
                  & ! [D] : 
                      ( m1_subset_1(D,A)
                     => ~ r2_hidden(D,a_3_0_card_lar(A,B,C)) ) ) ) ) ) ),
    file(card_lar,t9_card_lar),
    []).