% Mizar problem: t27_card_lar,card_lar,908,40 
fof(t27_card_lar,conjecture,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ( v5_card_lar(A)
       => v4_card_lar(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_card_1,cc1_card_5,cc1_card_lar,cc1_ordinal1,cc2_arytm_3,cc2_card_5,cc2_card_fil,cc2_card_lar,cc2_ordinal1,cc3_card_fil,cc3_card_lar,cc3_ordinal1,cc4_card_fil,cc5_card_fil,cc6_card_fil,d10_card_lar,d11_card_lar,dt_k1_xboole_0,dt_m1_subset_1,existence_m1_subset_1,fc2_ordinal1,fraenkel_a_1_0_card_lar,fraenkel_a_1_1_card_lar,rc1_arytm_3,rc1_card_1,rc1_card_5,rc1_card_lar,rc1_ordinal1,rc1_ordinal2,rc2_card_1,rc2_card_5,rc2_card_fil,rc2_card_lar,rc2_ordinal1,rc3_ordinal1,t1_subset,t2_subset,t2_tarski,t6_boole,t7_boole,t8_boole]),
    [file(card_lar,t27_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_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

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

fof(cc1_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal1(A) ) ) ),
    file(card_lar,cc1_card_lar),
    []).

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_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(card_5,cc2_card_5),
    []).

fof(cc2_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v4_card_fil(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_xboole_0(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & v2_card_1(A)
        & v1_card_5(A) ) ) ),
    file(card_fil,cc2_card_fil),
    []).

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_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v5_card_fil(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_xboole_0(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & v2_card_1(A) ) ) ),
    file(card_fil,cc3_card_fil),
    []).

fof(cc3_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) ) ) ),
    file(card_lar,cc3_card_lar),
    []).

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

fof(cc4_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v6_card_fil(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_xboole_0(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & v2_card_1(A)
        & v1_card_5(A)
        & v5_card_fil(A) ) ) ),
    file(card_fil,cc4_card_fil),
    []).

fof(cc5_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v6_card_fil(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_xboole_0(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & v2_card_1(A)
        & v1_card_5(A)
        & v4_card_fil(A) ) ) ),
    file(card_fil,cc5_card_fil),
    []).

fof(cc6_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_xboole_0(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & v1_card_5(A) ) ) ),
    file(card_fil,cc6_card_fil),
    []).

fof(d10_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ( v4_card_lar(A)
      <=> r4_card_lar(A,a_1_0_card_lar(A)) ) ) ),
    file(card_lar,d10_card_lar),
    []).

fof(d11_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ( v5_card_lar(A)
      <=> r4_card_lar(A,a_1_1_card_lar(A)) ) ) ),
    file(card_lar,d11_card_lar),
    []).

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

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(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_1_0_card_lar,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v1_card_4(B) )
     => ( r2_hidden(A,a_1_0_card_lar(B))
      <=> ? [C] : 
            ( ~ v1_finset_1(C)
            & v1_card_1(C)
            & m1_subset_1(C,B)
            & A = C
            & v1_card_5(C) ) ) ) ),
    file(card_lar,a_1_0_card_lar),
    []).

fof(fraenkel_a_1_1_card_lar,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v1_card_4(B) )
     => ( r2_hidden(A,a_1_1_card_lar(B))
      <=> ? [C] : 
            ( ~ v1_finset_1(C)
            & v1_card_1(C)
            & m1_subset_1(C,B)
            & A = C
            & v6_card_fil(C) ) ) ) ),
    file(card_lar,a_1_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_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

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

fof(rc1_card_lar,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A)
      & v1_card_5(A)
      & ~ v1_card_4(A) ) ),
    file(card_lar,rc1_card_lar),
    []).

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(rc2_card_1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    []).

fof(rc2_card_5,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_5,rc2_card_5),
    []).

fof(rc2_card_fil,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_xboole_0(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A)
      & ~ v2_card_1(A) ) ),
    file(card_fil,rc2_card_fil),
    []).

fof(rc2_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_ordinal1(B)
          & v2_ordinal1(B)
          & v3_ordinal1(B)
          & v4_ordinal1(B)
          & ~ v1_finset_1(B)
          & v1_card_1(B) ) ) ),
    file(card_lar,rc2_card_lar),
    []).

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

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(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),
    []).