% Mizar ND problem: t12_card_5,card_5,109,39 
fof(dh_c1_6__card_5,definition,
    ( ( v1_card_1(c1_6__card_5)
     => ~ ( ~ v1_finset_1(c1_6__card_5)
          & ! [A] : 
              ( v3_ordinal1(A)
             => c1_6__card_5 != k3_card_1(A) ) ) )
   => ! [B] : 
        ( v1_card_1(B)
       => ~ ( ~ v1_finset_1(B)
            & ! [C] : 
                ( v3_ordinal1(C)
               => B != k3_card_1(C) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__card_5),file(card_5,c1_6__card_5)]),
    [interesting(0.8),axiom,file(card_5,c1_6__card_5)]).

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(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(rc2_card_1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    [interesting(0.9),axiom,file(card_1,rc2_card_1)]).

fof(dt_k3_card_1,axiom,(
    $true ),
    file(card_1,k3_card_1),
    [interesting(0.9),axiom,file(card_1,k3_card_1)]).

fof(dt_c1_6__card_5,assumption,(
    v1_card_1(c1_6__card_5) ),
    introduced(assumption,[file(card_5,c1_6__card_5)]),
    [interesting(0.8),axiom,file(card_5,c1_6__card_5)]).

fof(cc1_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    [interesting(0.9),axiom,file(card_1,cc1_card_1)]).

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(fc1_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_card_1(A))
        & v2_ordinal1(k3_card_1(A))
        & v3_ordinal1(k3_card_1(A))
        & v1_card_1(k3_card_1(A)) ) ) ),
    file(card_1,fc1_card_1),
    [interesting(0.9),axiom,file(card_1,fc1_card_1)]).

fof(rc1_card_1,theorem,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    [interesting(0.9),axiom,file(card_1,rc1_card_1)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_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(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc2_arytm_3,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(cc2_funct_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

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(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_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(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

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(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

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(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k2_card_1,axiom,(
    ! [A] : v1_card_1(k2_card_1(A)) ),
    file(card_1,k2_card_1),
    [interesting(0.9),axiom,file(card_1,k2_card_1)]).

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & 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_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

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(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(s1_card_1__e4_6__card_5,theorem,
    ( ( ~ ( ~ v1_finset_1(k1_xboole_0)
          & ! [A] : 
              ( v3_ordinal1(A)
             => k1_xboole_0 != k3_card_1(A) ) )
      & ! [B] : 
          ( v1_card_1(B)
         => ( ~ ( ~ v1_finset_1(B)
                & ! [C] : 
                    ( v3_ordinal1(C)
                   => B != k3_card_1(C) ) )
           => ~ ( ~ v1_finset_1(k2_card_1(B))
                & ! [D] : 
                    ( v3_ordinal1(D)
                   => k2_card_1(B) != k3_card_1(D) ) ) ) )
      & ! [B] : 
          ( v1_card_1(B)
         => ( ( v2_card_1(B)
              & ! [E] : 
                  ( v1_card_1(E)
                 => ( r2_hidden(E,B)
                   => ~ ( ~ v1_finset_1(E)
                        & ! [F] : 
                            ( v3_ordinal1(F)
                           => E != k3_card_1(F) ) ) ) ) )
           => ( B = k1_xboole_0
              | ~ ( ~ v1_finset_1(B)
                  & ! [G] : 
                      ( v3_ordinal1(G)
                     => B != k3_card_1(G) ) ) ) ) ) )
   => ! [B] : 
        ( v1_card_1(B)
       => ~ ( ~ v1_finset_1(B)
            & ! [H] : 
                ( v3_ordinal1(H)
               => B != k3_card_1(H) ) ) ) ),
    file(card_5,s1_card_1__e4_6__card_5),
    [interesting(0.9),axiom,file(card_5,s1_card_1__e4_6__card_5)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc1_arytm_3,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

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(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(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(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(e1_6__card_5,plain,(
    ~ ( ~ v1_finset_1(k1_xboole_0)
      & ! [A] : 
          ( v3_ordinal1(A)
         => k1_xboole_0 != k3_card_1(A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,t2_subset,antisymmetry_r2_hidden,cc1_xreal_0,cc3_nat_1,rc1_arytm_3,t1_subset,cc15_membered,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_arytm_3,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,dt_k1_xboole_0,dt_k3_card_1,cc1_ordinal1,fc1_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,t6_boole]),
    [interesting(0.8),file(card_5,e1_6__card_5),[file(card_5,e1_6__card_5)]]).

fof(dh_c1_6_1__card_5,definition,
    ( ( v1_card_1(c1_6_1__card_5)
     => ( ~ ( ~ v1_finset_1(c1_6_1__card_5)
            & ! [A] : 
                ( v3_ordinal1(A)
               => c1_6_1__card_5 != k3_card_1(A) ) )
       => ~ ( ~ v1_finset_1(k2_card_1(c1_6_1__card_5))
            & ! [A] : 
                ( v3_ordinal1(A)
               => k2_card_1(c1_6_1__card_5) != k3_card_1(A) ) ) ) )
   => ! [B] : 
        ( v1_card_1(B)
       => ( ~ ( ~ v1_finset_1(B)
              & ! [C] : 
                  ( v3_ordinal1(C)
                 => B != k3_card_1(C) ) )
         => ~ ( ~ v1_finset_1(k2_card_1(B))
              & ! [C] : 
                  ( v3_ordinal1(C)
                 => k2_card_1(B) != k3_card_1(C) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_6_1__card_5),file(card_5,c1_6_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,c1_6_1__card_5)]).

fof(e1_6_1__card_5,assumption,(
    ~ ( ~ v1_finset_1(c1_6_1__card_5)
      & ! [A] : 
          ( v3_ordinal1(A)
         => c1_6_1__card_5 != k3_card_1(A) ) ) ),
    introduced(assumption,[file(card_5,e1_6_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,e1_6_1__card_5)]).

fof(e2_6_1__card_5,assumption,(
    ~ v1_finset_1(k2_card_1(c1_6_1__card_5)) ),
    introduced(assumption,[file(card_5,e2_6_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,e2_6_1__card_5)]).

fof(fc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A))
        & v4_ordinal2(k1_ordinal1(A)) ) ) ),
    file(arytm_3,fc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc2_arytm_3)]).

fof(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,k1_ordinal1)]).

fof(dt_c1_6_1__card_5,assumption,(
    v1_card_1(c1_6_1__card_5) ),
    introduced(assumption,[file(card_5,c1_6_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,c1_6_1__card_5)]).

fof(dh_c2_6_1__card_5,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & c1_6_1__card_5 = k3_card_1(A) )
   => ( v3_ordinal1(c2_6_1__card_5)
      & c1_6_1__card_5 = k3_card_1(c2_6_1__card_5) ) ),
    introduced(definition,[new_symbol(c2_6_1__card_5),file(card_5,c2_6_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,c2_6_1__card_5)]).

fof(e1_6_1_1__card_5,assumption,(
    v1_finset_1(c1_6_1__card_5) ),
    introduced(assumption,[file(card_5,e1_6_1_1__card_5)]),
    [interesting(0.5),axiom,file(card_5,e1_6_1_1__card_5)]).

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

fof(rc2_finset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc2_finset_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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

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(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc10_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]).

fof(fc11_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]).

fof(fc12_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]).

fof(fc1_card_4,theorem,
    ( ~ v1_xboole_0(k5_ordinal2)
    & v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_finset_1(k5_ordinal2)
    & v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(card_4,fc1_card_4),
    [interesting(0.9),axiom,file(card_4,fc1_card_4)]).

fof(fc1_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

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(fc3_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]).

fof(fc3_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]).

fof(fc4_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(fc7_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]).

fof(fc8_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]).

fof(fc9_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]).

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_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_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(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(rc3_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc3_nat_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(spc6_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

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(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(commutativity_k2_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(cc1_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

fof(cc2_card_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    [interesting(0.9),axiom,file(card_1,cc2_card_1)]).

fof(cc2_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]).

fof(cc3_card_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    [interesting(0.9),axiom,file(card_1,cc3_card_1)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(commutativity_k1_nat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(redefinition_k1_nat_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(redefinition_k4_card_1,definition,(
    ! [A] : 
      ( v1_finset_1(A)
     => k4_card_1(A) = k1_card_1(A) ) ),
    file(card_1,k4_card_1),
    [interesting(0.9),axiom,file(card_1,k4_card_1)]).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(dt_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ),
    file(card_1,k4_card_1),
    [interesting(0.9),axiom,file(card_1,k4_card_1)]).

fof(de_c1_6_1_1__card_5,definition,(
    c1_6_1_1__card_5 = c1_6_1__card_5 ),
    introduced(definition,[new_symbol(c1_6_1_1__card_5),file(card_5,c1_6_1_1__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_1_1__card_5)]).

fof(e2_6_1_1__card_5,plain,(
    v1_finset_1(c1_6_1__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e1_6_1_1__card_5])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,rc2_card_1,cc1_card_1,rc1_card_1,dt_c1_6_1__card_5,e1_6_1_1__card_5]),
    [interesting(0.5),file(card_5,e2_6_1_1__card_5),[file(card_5,e2_6_1_1__card_5)]]).

fof(dt_c1_6_1_1__card_5,plain,(
    v1_finset_1(c1_6_1_1__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e1_6_1_1__card_5])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,rc2_card_1,cc1_card_1,rc1_card_1,dt_c1_6_1__card_5,de_c1_6_1_1__card_5,e2_6_1_1__card_5]),
    [interesting(0.5),file(card_5,c1_6_1_1__card_5),[file(card_5,c1_6_1_1__card_5)]]).

fof(fc2_card_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_1,fc2_card_1),
    [interesting(0.9),axiom,file(card_1,fc2_card_1)]).

fof(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(symmetry_r2_wellord2,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(reflexivity_r2_wellord2,theorem,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(redefinition_r2_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(d5_card_1,definition,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( B = k1_card_1(A)
      <=> r2_wellord2(A,B) ) ) ),
    file(card_1,d5_card_1),
    [interesting(0.9),axiom,file(card_1,d5_card_1)]).

fof(e3_6_1_1__card_5,plain,
    ( k1_card_1(c1_6_1__card_5) = k1_card_1(k4_card_1(c1_6_1_1__card_5))
    & k1_card_1(c1_6_1__card_5) = c1_6_1__card_5 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e1_6_1_1__card_5])],[cc1_finseq_1,cc2_funct_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,rc1_nat_1,rc1_xreal_0,rc3_nat_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_arytm_3,cc2_card_1,cc2_finset_1,cc2_nat_1,cc3_arytm_3,cc3_card_1,cc3_ordinal1,cc4_membered,cc6_membered,cc9_membered,fc1_card_4,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_finset_1,rc1_subset_1,rc2_nat_1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,cc1_ordinal1,cc2_ordinal1,fc2_card_1,fc2_membered,rc1_ordinal1,rc2_card_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_k4_card_1,redefinition_r2_wellord2,dt_k1_card_1,dt_k4_card_1,dt_c1_6_1__card_5,dt_c1_6_1_1__card_5,de_c1_6_1_1__card_5,cc1_card_1,rc1_card_1,d5_card_1]),
    [interesting(0.5),file(card_5,e3_6_1_1__card_5),[file(card_5,e3_6_1_1__card_5)]]).

fof(t76_card_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_card_1(k1_card_1(A)) = k1_card_1(k1_nat_1(A,1)) ) ),
    file(card_1,t76_card_1),
    [interesting(0.9),axiom,file(card_1,t76_card_1)]).

fof(e4_6_1_1__card_5,plain,(
    k2_card_1(c1_6_1__card_5) = k1_card_1(k1_nat_1(k4_card_1(c1_6_1_1__card_5),1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e1_6_1_1__card_5])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_ordinal1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_nat_1,fc2_finseq_1,fc2_ordinal1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_arytm_3,rc1_membered,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_ordinal1,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_card_1,cc2_finset_1,cc2_nat_1,cc3_arytm_3,cc3_card_1,cc3_ordinal1,cc4_membered,cc6_membered,cc9_membered,fc1_card_4,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc5_membered,rc1_card_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_card_1,dt_k4_card_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_6_1__card_5,dt_c1_6_1_1__card_5,de_c1_6_1_1__card_5,fc2_membered,spc1_numerals,spc1_boole,e3_6_1_1__card_5,t76_card_1]),
    [interesting(0.5),file(card_5,e4_6_1_1__card_5),[file(card_5,e4_6_1_1__card_5)]]).

fof(e5_6_1_1__card_5,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e1_6_1_1__card_5,e2_6_1__card_5])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_card_4,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_arytm_3,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,spc6_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_ordinal1,cc2_arytm_3,cc2_card_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,fc2_membered,rc1_card_1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k4_card_1,dt_k1_card_1,dt_k1_nat_1,dt_k2_card_1,dt_k4_card_1,dt_c1_6_1__card_5,dt_c1_6_1_1__card_5,de_c1_6_1_1__card_5,fc2_card_1,spc1_numerals,spc1_boole,e4_6_1_1__card_5,e2_6_1__card_5]),
    [interesting(0.5),file(card_5,e5_6_1_1__card_5),[file(card_5,e5_6_1_1__card_5)]]).

fof(i2_6_1_1__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i2_6_1_1__card_5)]),
    [interesting(0.5),trivial,file(card_5,i2_6_1_1__card_5)]).

fof(i1_6_1_1__card_5,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_1__card_5,e1_6_1_1__card_5,e2_6_1__card_5])],[e5_6_1_1__card_5,i2_6_1_1__card_5]),
    [interesting(0.5),file(card_5,i1_6_1_1__card_5),[file(card_5,i1_6_1_1__card_5)]]).

fof(e3_6_1__card_5,plain,(
    ~ v1_finset_1(c1_6_1__card_5) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5]),discharge_asm(discharge,[e1_6_1_1__card_5])],[e1_6_1_1__card_5,i1_6_1_1__card_5]),
    [interesting(0.65),file(card_5,e3_6_1__card_5),[file(card_5,e3_6_1__card_5)]]).

fof(e4_6_1__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c1_6_1__card_5 = k3_card_1(A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5,e1_6_1__card_5])],[cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,rc2_card_1,dt_k3_card_1,dt_c1_6_1__card_5,cc1_ordinal1,fc1_card_1,e3_6_1__card_5,e1_6_1__card_5]),
    [interesting(0.65),file(card_5,e4_6_1__card_5),[file(card_5,e4_6_1__card_5)]]).

fof(dt_c2_6_1__card_5,plain,(
    v3_ordinal1(c2_6_1__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5,e1_6_1__card_5])],[dh_c2_6_1__card_5,e4_6_1__card_5]),
    [interesting(0.65),file(card_5,c2_6_1__card_5),[file(card_5,c2_6_1__card_5)]]).

fof(fc1_ordinal1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc1_ordinal1)]).

fof(fc3_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc3_ordinal1)]).

fof(e5_6_1__card_5,plain,(
    c1_6_1__card_5 = k3_card_1(c2_6_1__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5,e1_6_1__card_5])],[dh_c2_6_1__card_5,e4_6_1__card_5]),
    [interesting(0.65),file(card_5,e5_6_1__card_5),[file(card_5,e5_6_1__card_5)]]).

fof(t39_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k3_card_1(k1_ordinal1(A)) = k2_card_1(k3_card_1(A)) ) ),
    file(card_1,t39_card_1),
    [interesting(0.9),axiom,file(card_1,t39_card_1)]).

fof(e6_6_1__card_5,plain,(
    k2_card_1(c1_6_1__card_5) = k3_card_1(k1_ordinal1(c2_6_1__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5,e1_6_1__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,t1_subset,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k1_ordinal1,dt_k2_card_1,dt_k3_card_1,dt_c1_6_1__card_5,dt_c2_6_1__card_5,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,e5_6_1__card_5,t39_card_1]),
    [interesting(0.65),file(card_5,e6_6_1__card_5),[file(card_5,e6_6_1__card_5)]]).

fof(i4_6_1__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i4_6_1__card_5)]),
    [interesting(0.65),trivial,file(card_5,i4_6_1__card_5)]).

fof(i3_6_1__card_5,plain,(
    k2_card_1(c1_6_1__card_5) = k3_card_1(k1_ordinal1(c2_6_1__card_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5,e1_6_1__card_5])],[e6_6_1__card_5,i4_6_1__card_5]),
    [interesting(0.65),file(card_5,i3_6_1__card_5),[file(card_5,i3_6_1__card_5)]]).

fof(i2_6_1__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & k2_card_1(c1_6_1__card_5) = k3_card_1(A) ) ),
    inference(take,[status(thm),assumptions([dt_c1_6_1__card_5,e2_6_1__card_5,e1_6_1__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_arytm_3,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc3_ordinal1,dt_k1_ordinal1,dt_k2_card_1,dt_k3_card_1,dt_c1_6_1__card_5,dt_c2_6_1__card_5,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,i3_6_1__card_5]),
    [interesting(0.65),file(card_5,i2_6_1__card_5),[file(card_5,i2_6_1__card_5)]]).

fof(i1_6_1__card_5,plain,
    ( ~ ( ~ v1_finset_1(c1_6_1__card_5)
        & ! [A] : 
            ( v3_ordinal1(A)
           => c1_6_1__card_5 != k3_card_1(A) ) )
   => ~ ( ~ v1_finset_1(k2_card_1(c1_6_1__card_5))
        & ! [A] : 
            ( v3_ordinal1(A)
           => k2_card_1(c1_6_1__card_5) != k3_card_1(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_1__card_5]),discharge_asm(discharge,[e1_6_1__card_5,e2_6_1__card_5])],[e1_6_1__card_5,e2_6_1__card_5,i2_6_1__card_5]),
    [interesting(0.65),file(card_5,i1_6_1__card_5),[file(card_5,i1_6_1__card_5)]]).

fof(i1_6_1_tmp__card_5,plain,
    ( v1_card_1(c1_6_1__card_5)
   => ( ~ ( ~ v1_finset_1(c1_6_1__card_5)
          & ! [A] : 
              ( v3_ordinal1(A)
             => c1_6_1__card_5 != k3_card_1(A) ) )
     => ~ ( ~ v1_finset_1(k2_card_1(c1_6_1__card_5))
          & ! [A] : 
              ( v3_ordinal1(A)
             => k2_card_1(c1_6_1__card_5) != k3_card_1(A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6_1__card_5])],[dt_c1_6_1__card_5,i1_6_1__card_5]),
    [interesting(0.8),e2_6__card_5]).

fof(e2_6__card_5,plain,(
    ! [A] : 
      ( v1_card_1(A)
     => ( ~ ( ~ v1_finset_1(A)
            & ! [B] : 
                ( v3_ordinal1(B)
               => A != k3_card_1(B) ) )
       => ~ ( ~ v1_finset_1(k2_card_1(A))
            & ! [B] : 
                ( v3_ordinal1(B)
               => k2_card_1(A) != k3_card_1(B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_1_tmp__card_5,dh_c1_6_1__card_5]),
    [interesting(0.8),file(card_5,e2_6__card_5),[file(card_5,e2_6__card_5)]]).

fof(dh_c1_6_2__card_5,definition,
    ( ( v1_card_1(c1_6_2__card_5)
     => ( ( v2_card_1(c1_6_2__card_5)
          & ! [A] : 
              ( v1_card_1(A)
             => ( r2_hidden(A,c1_6_2__card_5)
               => ~ ( ~ v1_finset_1(A)
                    & ! [B] : 
                        ( v3_ordinal1(B)
                       => A != k3_card_1(B) ) ) ) ) )
       => ( c1_6_2__card_5 = k1_xboole_0
          | ~ ( ~ v1_finset_1(c1_6_2__card_5)
              & ! [A] : 
                  ( v3_ordinal1(A)
                 => c1_6_2__card_5 != k3_card_1(A) ) ) ) ) )
   => ! [C] : 
        ( v1_card_1(C)
       => ( ( v2_card_1(C)
            & ! [D] : 
                ( v1_card_1(D)
               => ( r2_hidden(D,C)
                 => ~ ( ~ v1_finset_1(D)
                      & ! [E] : 
                          ( v3_ordinal1(E)
                         => D != k3_card_1(E) ) ) ) ) )
         => ( C = k1_xboole_0
            | ~ ( ~ v1_finset_1(C)
                & ! [D] : 
                    ( v3_ordinal1(D)
                   => C != k3_card_1(D) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_6_2__card_5),file(card_5,c1_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,c1_6_2__card_5)]).

fof(e1_6_2__card_5,assumption,
    ( c1_6_2__card_5 != k1_xboole_0
    & v2_card_1(c1_6_2__card_5) ),
    introduced(assumption,[file(card_5,e1_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,e1_6_2__card_5)]).

fof(e2_6_2__card_5,assumption,(
    ! [A] : 
      ( v1_card_1(A)
     => ( r2_hidden(A,c1_6_2__card_5)
       => ~ ( ~ v1_finset_1(A)
            & ! [B] : 
                ( v3_ordinal1(B)
               => A != k3_card_1(B) ) ) ) ) ),
    introduced(assumption,[file(card_5,e2_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,e2_6_2__card_5)]).

fof(e3_6_2__card_5,assumption,(
    ~ v1_finset_1(c1_6_2__card_5) ),
    introduced(assumption,[file(card_5,e3_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,e3_6_2__card_5)]).

fof(dt_c1_6_2__card_5,assumption,(
    v1_card_1(c1_6_2__card_5) ),
    introduced(assumption,[file(card_5,c1_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,c1_6_2__card_5)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dh_c3_6_2__card_5,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = c2_6_2__card_5
        & ! [B] : 
            ( r2_hidden(B,c2_6_2__card_5)
           => ? [C] : 
                ( v3_ordinal1(C)
                & B = k3_card_1(C)
                & k1_funct_1(A,B) = C ) ) )
   => ( v1_relat_1(c3_6_2__card_5)
      & v1_funct_1(c3_6_2__card_5)
      & k1_relat_1(c3_6_2__card_5) = c2_6_2__card_5
      & ! [D] : 
          ( r2_hidden(D,c2_6_2__card_5)
         => ? [E] : 
              ( v3_ordinal1(E)
              & D = k3_card_1(E)
              & k1_funct_1(c3_6_2__card_5,D) = E ) ) ) ),
    introduced(definition,[new_symbol(c3_6_2__card_5),file(card_5,c3_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,c3_6_2__card_5)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dh_c2_6_2__card_5,definition,
    ( ? [A] : 
      ! [B] : 
        ( r2_hidden(B,A)
      <=> ( r2_hidden(B,c1_6_2__card_5)
          & ? [C] : 
              ( v1_card_1(C)
              & C = B
              & ~ v1_finset_1(C) ) ) )
   => ! [D] : 
        ( r2_hidden(D,c2_6_2__card_5)
      <=> ( r2_hidden(D,c1_6_2__card_5)
          & ? [E] : 
              ( v1_card_1(E)
              & E = D
              & ~ v1_finset_1(E) ) ) ) ),
    introduced(definition,[new_symbol(c2_6_2__card_5),file(card_5,c2_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,c2_6_2__card_5)]).

fof(s1_xboole_0__e4_6_2__card_5,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ? [B] : 
        ! [C] : 
          ( r2_hidden(C,B)
        <=> ( r2_hidden(C,A)
            & ? [D] : 
                ( v1_card_1(D)
                & D = C
                & ~ v1_finset_1(D) ) ) ) ) ),
    file(card_5,s1_xboole_0__e4_6_2__card_5),
    [interesting(0.9),axiom,file(card_5,s1_xboole_0__e4_6_2__card_5)]).

fof(e4_6_2__card_5,plain,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,c1_6_2__card_5)
        & ? [C] : 
            ( v1_card_1(C)
            & C = B
            & ~ v1_finset_1(C) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_6_2__card_5])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,rc2_card_1,antisymmetry_r2_hidden,dt_c1_6_2__card_5,cc1_card_1,rc1_card_1,s1_xboole_0__e4_6_2__card_5]),
    [interesting(0.65),file(card_5,e4_6_2__card_5),[file(card_5,e4_6_2__card_5)]]).

fof(dt_c2_6_2__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2__card_5])],[dh_c2_6_2__card_5,e4_6_2__card_5]),
    [interesting(0.65),file(card_5,c2_6_2__card_5),[file(card_5,c2_6_2__card_5)]]).

fof(s2_funct_1__e8_6_2__card_5,theorem,(
    ! [A] : 
      ( ( ! [B,C,D] : 
            ( ( r2_hidden(B,A)
              & ? [E] : 
                  ( v3_ordinal1(E)
                  & B = k3_card_1(E)
                  & C = E )
              & ? [F] : 
                  ( v3_ordinal1(F)
                  & B = k3_card_1(F)
                  & D = F ) )
           => C = D )
        & ! [B] : 
            ~ ( r2_hidden(B,A)
              & ! [C] : 
                  ~ ? [G] : 
                      ( v3_ordinal1(G)
                      & B = k3_card_1(G)
                      & C = G ) ) )
     => ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => ? [H] : 
                  ( v3_ordinal1(H)
                  & C = k3_card_1(H)
                  & k1_funct_1(B,C) = H ) ) ) ) ),
    file(card_5,s2_funct_1__e8_6_2__card_5),
    [interesting(0.9),axiom,file(card_5,s2_funct_1__e8_6_2__card_5)]).

fof(t42_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k3_card_1(A) = k3_card_1(B)
           => A = B ) ) ) ),
    file(card_1,t42_card_1),
    [interesting(0.9),axiom,file(card_1,t42_card_1)]).

fof(e6_6_2__card_5,plain,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,c2_6_2__card_5)
        & ? [D] : 
            ( v3_ordinal1(D)
            & A = k3_card_1(D)
            & B = D )
        & ? [D] : 
            ( v3_ordinal1(D)
            & A = k3_card_1(D)
            & C = D ) )
     => B = C ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_card_1,dt_c2_6_2__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,t42_card_1]),
    [interesting(0.65),file(card_5,e6_6_2__card_5),[file(card_5,e6_6_2__card_5)]]).

fof(dh_c1_6_2_1__card_5,definition,
    ( ~ ( r2_hidden(c1_6_2_1__card_5,c2_6_2__card_5)
        & ! [A] : 
            ~ ? [B] : 
                ( v3_ordinal1(B)
                & c1_6_2_1__card_5 = k3_card_1(B)
                & A = B ) )
   => ! [C] : 
        ~ ( r2_hidden(C,c2_6_2__card_5)
          & ! [D] : 
              ~ ? [E] : 
                  ( v3_ordinal1(E)
                  & C = k3_card_1(E)
                  & D = E ) ) ),
    introduced(definition,[new_symbol(c1_6_2_1__card_5),file(card_5,c1_6_2_1__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_1__card_5)]).

fof(e1_6_2_1__card_5,assumption,(
    r2_hidden(c1_6_2_1__card_5,c2_6_2__card_5) ),
    introduced(assumption,[file(card_5,e1_6_2_1__card_5)]),
    [interesting(0.5),axiom,file(card_5,e1_6_2_1__card_5)]).

fof(dt_c1_6_2_1__card_5,assumption,(
    $true ),
    introduced(assumption,[file(card_5,c1_6_2_1__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_1__card_5)]).

fof(dh_c2_6_2_1__card_5,definition,
    ( ? [A] : 
        ( v1_card_1(A)
        & A = c1_6_2_1__card_5
        & ~ v1_finset_1(A) )
   => ( v1_card_1(c2_6_2_1__card_5)
      & c2_6_2_1__card_5 = c1_6_2_1__card_5
      & ~ v1_finset_1(c2_6_2_1__card_5) ) ),
    introduced(definition,[new_symbol(c2_6_2_1__card_5),file(card_5,c2_6_2_1__card_5)]),
    [interesting(0.5),axiom,file(card_5,c2_6_2_1__card_5)]).

fof(e5_6_2__card_5,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_6_2__card_5)
    <=> ( r2_hidden(A,c1_6_2__card_5)
        & ? [B] : 
            ( v1_card_1(B)
            & B = A
            & ~ v1_finset_1(B) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2__card_5])],[dh_c2_6_2__card_5,e4_6_2__card_5]),
    [interesting(0.65),file(card_5,e5_6_2__card_5),[file(card_5,e5_6_2__card_5)]]).

fof(e2_6_2_1__card_5,plain,(
    ? [A] : 
      ( v1_card_1(A)
      & A = c1_6_2_1__card_5
      & ~ v1_finset_1(A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_c1_6_2__card_5,dt_c1_6_2_1__card_5,dt_c2_6_2__card_5,cc1_card_1,rc1_card_1,t1_subset,t7_boole,e1_6_2_1__card_5,e5_6_2__card_5]),
    [interesting(0.5),file(card_5,e2_6_2_1__card_5),[file(card_5,e2_6_2_1__card_5)]]).

fof(dt_c2_6_2_1__card_5,plain,(
    v1_card_1(c2_6_2_1__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[dh_c2_6_2_1__card_5,e2_6_2_1__card_5]),
    [interesting(0.5),file(card_5,c2_6_2_1__card_5),[file(card_5,c2_6_2_1__card_5)]]).

fof(e3_6_2_1__card_5,plain,
    ( c2_6_2_1__card_5 = c1_6_2_1__card_5
    & ~ v1_finset_1(c2_6_2_1__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[dh_c2_6_2_1__card_5,e2_6_2_1__card_5]),
    [interesting(0.5),file(card_5,e3_6_2_1__card_5),[file(card_5,e3_6_2_1__card_5)]]).

fof(e4_6_2_1__card_5,plain,(
    r2_hidden(c2_6_2_1__card_5,c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_c1_6_2__card_5,dt_c1_6_2_1__card_5,dt_c2_6_2__card_5,dt_c2_6_2_1__card_5,cc1_card_1,rc1_card_1,t1_subset,t7_boole,e5_6_2__card_5,e1_6_2_1__card_5,e3_6_2_1__card_5]),
    [interesting(0.5),file(card_5,e4_6_2_1__card_5),[file(card_5,e4_6_2_1__card_5)]]).

fof(e5_6_2_1__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c1_6_2_1__card_5 = k3_card_1(A) ) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_card_1,dt_c1_6_2__card_5,dt_c1_6_2_1__card_5,dt_c2_6_2_1__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,rc1_card_1,t1_subset,t7_boole,e4_6_2_1__card_5,e2_6_2__card_5,e3_6_2_1__card_5]),
    [interesting(0.5),file(card_5,e5_6_2_1__card_5),[file(card_5,e5_6_2_1__card_5)]]).

fof(e6_6_2_1__card_5,plain,(
    ? [A,B] : 
      ( v3_ordinal1(B)
      & c1_6_2_1__card_5 = k3_card_1(B)
      & A = B ) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,dt_k3_card_1,dt_c1_6_2_1__card_5,cc1_ordinal1,fc1_card_1,e5_6_2_1__card_5]),
    [interesting(0.5),file(card_5,e6_6_2_1__card_5),[file(card_5,e6_6_2_1__card_5)]]).

fof(i3_6_2_1__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i3_6_2_1__card_5)]),
    [interesting(0.5),trivial,file(card_5,i3_6_2_1__card_5)]).

fof(i2_6_2_1__card_5,plain,(
    ? [A,B] : 
      ( v3_ordinal1(B)
      & c1_6_2_1__card_5 = k3_card_1(B)
      & A = B ) ),
    inference(conclusion,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2_1__card_5,e1_6_2_1__card_5,dt_c1_6_2__card_5])],[e6_6_2_1__card_5,i3_6_2_1__card_5]),
    [interesting(0.5),file(card_5,i2_6_2_1__card_5),[file(card_5,i2_6_2_1__card_5)]]).

fof(i1_6_2_1__card_5,plain,(
    ~ ( r2_hidden(c1_6_2_1__card_5,c2_6_2__card_5)
      & ! [A] : 
          ~ ? [B] : 
              ( v3_ordinal1(B)
              & c1_6_2_1__card_5 = k3_card_1(B)
              & A = B ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2_1__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2_1__card_5])],[e1_6_2_1__card_5,i2_6_2_1__card_5]),
    [interesting(0.5),file(card_5,i1_6_2_1__card_5),[file(card_5,i1_6_2_1__card_5)]]).

fof(i1_6_2_1_tmp__card_5,plain,(
    ~ ( r2_hidden(c1_6_2_1__card_5,c2_6_2__card_5)
      & ! [A] : 
          ~ ? [B] : 
              ( v3_ordinal1(B)
              & c1_6_2_1__card_5 = k3_card_1(B)
              & A = B ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[dt_c1_6_2_1__card_5])],[dt_c1_6_2_1__card_5,i1_6_2_1__card_5]),
    [interesting(0.65),e7_6_2__card_5]).

fof(e7_6_2__card_5,plain,(
    ! [A] : 
      ~ ( r2_hidden(A,c2_6_2__card_5)
        & ! [B] : 
            ~ ? [C] : 
                ( v3_ordinal1(C)
                & A = k3_card_1(C)
                & B = C ) ) ),
    inference(let,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[i1_6_2_1_tmp__card_5,dh_c1_6_2_1__card_5]),
    [interesting(0.65),file(card_5,e7_6_2__card_5),[file(card_5,e7_6_2__card_5)]]).

fof(e8_6_2__card_5,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = c2_6_2__card_5
      & ! [B] : 
          ( r2_hidden(B,c2_6_2__card_5)
         => ? [C] : 
              ( v3_ordinal1(C)
              & B = k3_card_1(C)
              & k1_funct_1(A,B) = C ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c2_6_2__card_5,cc1_ordinal1,fc1_card_1,rc1_funct_1,s2_funct_1__e8_6_2__card_5,e6_6_2__card_5,e7_6_2__card_5]),
    [interesting(0.65),file(card_5,e8_6_2__card_5),[file(card_5,e8_6_2__card_5)]]).

fof(dt_c3_6_2__card_5,plain,
    ( v1_relat_1(c3_6_2__card_5)
    & v1_funct_1(c3_6_2__card_5) ),
    inference(consider,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c3_6_2__card_5,e8_6_2__card_5]),
    [interesting(0.65),file(card_5,c3_6_2__card_5),[file(card_5,c3_6_2__card_5)]]).

fof(de_c4_6_2__card_5,definition,(
    c4_6_2__card_5 = k2_relat_1(c3_6_2__card_5) ),
    introduced(definition,[new_symbol(c4_6_2__card_5),file(card_5,c4_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,c4_6_2__card_5)]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(dh_c1_6_2_2__card_5,definition,
    ( ( r2_hidden(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5))
     => ( v3_ordinal1(c1_6_2_2__card_5)
        & r1_tarski(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c3_6_2__card_5))
       => ( v3_ordinal1(A)
          & r1_tarski(A,k2_relat_1(c3_6_2__card_5)) ) ) ),
    introduced(definition,[new_symbol(c1_6_2_2__card_5),file(card_5,c1_6_2_2__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_2__card_5)]).

fof(e1_6_2_2__card_5,assumption,(
    r2_hidden(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ),
    introduced(assumption,[file(card_5,e1_6_2_2__card_5)]),
    [interesting(0.5),axiom,file(card_5,e1_6_2_2__card_5)]).

fof(dt_c1_6_2_2__card_5,assumption,(
    $true ),
    introduced(assumption,[file(card_5,c1_6_2_2__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_2__card_5)]).

fof(dh_c2_6_2_2__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,c2_6_2__card_5)
        & c1_6_2_2__card_5 = k1_funct_1(c3_6_2__card_5,A) )
   => ( r2_hidden(c2_6_2_2__card_5,c2_6_2__card_5)
      & c1_6_2_2__card_5 = k1_funct_1(c3_6_2__card_5,c2_6_2_2__card_5) ) ),
    introduced(definition,[new_symbol(c2_6_2_2__card_5),file(card_5,c2_6_2_2__card_5)]),
    [interesting(0.5),axiom,file(card_5,c2_6_2_2__card_5)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(e9_6_2__card_5,plain,
    ( k1_relat_1(c3_6_2__card_5) = c2_6_2__card_5
    & ! [A] : 
        ( r2_hidden(A,c2_6_2__card_5)
       => ? [B] : 
            ( v3_ordinal1(B)
            & A = k3_card_1(B)
            & k1_funct_1(c3_6_2__card_5,A) = B ) ) ),
    inference(consider,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c3_6_2__card_5,e8_6_2__card_5]),
    [interesting(0.65),file(card_5,e9_6_2__card_5),[file(card_5,e9_6_2__card_5)]]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_6_2_2__card_5,plain,(
    ? [A] : 
      ( r2_hidden(A,c2_6_2__card_5)
      & c1_6_2_2__card_5 = k1_funct_1(c3_6_2__card_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_c1_6_2_2__card_5,dt_c2_6_2__card_5,dt_c3_6_2__card_5,cc1_ordinal1,fc1_card_1,rc1_funct_1,t1_subset,t7_boole,e1_6_2_2__card_5,e9_6_2__card_5,d5_funct_1]),
    [interesting(0.5),file(card_5,e2_6_2_2__card_5),[file(card_5,e2_6_2_2__card_5)]]).

fof(dt_c2_6_2_2__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c2_6_2_2__card_5,e2_6_2_2__card_5]),
    [interesting(0.5),file(card_5,c2_6_2_2__card_5),[file(card_5,c2_6_2_2__card_5)]]).

fof(dh_c3_6_2_2__card_5,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & c2_6_2_2__card_5 = k3_card_1(A)
        & c1_6_2_2__card_5 = A )
   => ( v3_ordinal1(c3_6_2_2__card_5)
      & c2_6_2_2__card_5 = k3_card_1(c3_6_2_2__card_5)
      & c1_6_2_2__card_5 = c3_6_2_2__card_5 ) ),
    introduced(definition,[new_symbol(c3_6_2_2__card_5),file(card_5,c3_6_2_2__card_5)]),
    [interesting(0.5),axiom,file(card_5,c3_6_2_2__card_5)]).

fof(e3_6_2_2__card_5,plain,
    ( r2_hidden(c2_6_2_2__card_5,c2_6_2__card_5)
    & c1_6_2_2__card_5 = k1_funct_1(c3_6_2__card_5,c2_6_2_2__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c2_6_2_2__card_5,e2_6_2_2__card_5]),
    [interesting(0.5),file(card_5,e3_6_2_2__card_5),[file(card_5,e3_6_2_2__card_5)]]).

fof(e4_6_2_2__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c2_6_2_2__card_5 = k3_card_1(A)
      & c1_6_2_2__card_5 = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c1_6_2_2__card_5,dt_c2_6_2__card_5,dt_c2_6_2_2__card_5,dt_c3_6_2__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e9_6_2__card_5,e3_6_2_2__card_5]),
    [interesting(0.5),file(card_5,e4_6_2_2__card_5),[file(card_5,e4_6_2_2__card_5)]]).

fof(dt_c3_6_2_2__card_5,plain,(
    v3_ordinal1(c3_6_2_2__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c3_6_2_2__card_5,e4_6_2_2__card_5]),
    [interesting(0.5),file(card_5,c3_6_2_2__card_5),[file(card_5,c3_6_2_2__card_5)]]).

fof(e5_6_2_2__card_5,plain,
    ( c2_6_2_2__card_5 = k3_card_1(c3_6_2_2__card_5)
    & c1_6_2_2__card_5 = c3_6_2_2__card_5 ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c3_6_2_2__card_5,e4_6_2_2__card_5]),
    [interesting(0.5),file(card_5,e5_6_2_2__card_5),[file(card_5,e5_6_2_2__card_5)]]).

fof(e6_6_2_2__card_5,plain,(
    v3_ordinal1(c1_6_2_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,dt_k3_card_1,dt_c1_6_2_2__card_5,dt_c2_6_2_2__card_5,dt_c3_6_2_2__card_5,cc1_ordinal1,fc1_card_1,e5_6_2_2__card_5]),
    [interesting(0.5),file(card_5,e6_6_2_2__card_5),[file(card_5,e6_6_2_2__card_5)]]).

fof(dt_c1_6_2_2_1__card_5,assumption,(
    $true ),
    introduced(assumption,[file(card_5,c1_6_2_2_1__card_5)]),
    [interesting(0.35),axiom,file(card_5,c1_6_2_2_1__card_5)]).

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_c1_6_2_2_1__card_5,definition,
    ( ~ ( r2_hidden(c1_6_2_2_1__card_5,c1_6_2_2__card_5)
        & ~ r2_hidden(c1_6_2_2_1__card_5,k2_relat_1(c3_6_2__card_5)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c1_6_2_2__card_5)
          & ~ r2_hidden(A,k2_relat_1(c3_6_2__card_5)) ) ),
    introduced(definition,[new_symbol(c1_6_2_2_1__card_5),file(card_5,c1_6_2_2_1__card_5)]),
    [interesting(0.35),axiom,file(card_5,c1_6_2_2_1__card_5)]).

fof(e1_6_2_2_1__card_5,assumption,(
    r2_hidden(c1_6_2_2_1__card_5,c1_6_2_2__card_5) ),
    introduced(assumption,[file(card_5,e1_6_2_2_1__card_5)]),
    [interesting(0.35),axiom,file(card_5,e1_6_2_2_1__card_5)]).

fof(de_c2_6_2_2_1__card_5,definition,(
    c2_6_2_2_1__card_5 = c1_6_2_2_1__card_5 ),
    introduced(definition,[new_symbol(c2_6_2_2_1__card_5),file(card_5,c2_6_2_2_1__card_5)]),
    [interesting(0.35),axiom,file(card_5,c2_6_2_2_1__card_5)]).

fof(t23_ordinal1,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t23_ordinal1)]).

fof(e2_6_2_2_1__card_5,plain,(
    v3_ordinal1(c1_6_2_2_1__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,e1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_card_1,dt_c1_6_2_2__card_5,dt_c1_6_2_2_1__card_5,dt_c2_6_2_2__card_5,dt_c3_6_2_2__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e1_6_2_2_1__card_5,e5_6_2_2__card_5,t23_ordinal1]),
    [interesting(0.35),file(card_5,e2_6_2_2_1__card_5),[file(card_5,e2_6_2_2_1__card_5)]]).

fof(dt_c2_6_2_2_1__card_5,plain,(
    v3_ordinal1(c2_6_2_2_1__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,e1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc2_ordinal1,rc1_ordinal1,dt_c1_6_2_2_1__card_5,cc1_ordinal1,de_c2_6_2_2_1__card_5,e2_6_2_2_1__card_5]),
    [interesting(0.35),file(card_5,c2_6_2_2_1__card_5),[file(card_5,c2_6_2_2_1__card_5)]]).

fof(t41_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
          <=> r2_hidden(k3_card_1(A),k3_card_1(B)) ) ) ) ),
    file(card_1,t41_card_1),
    [interesting(0.9),axiom,file(card_1,t41_card_1)]).

fof(e3_6_2_2_1__card_5,plain,
    ( r2_hidden(k3_card_1(c2_6_2_2_1__card_5),k3_card_1(c3_6_2_2__card_5))
    & r2_hidden(k3_card_1(c3_6_2_2__card_5),c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_2_1__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc3_ordinal1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c1_6_2_2__card_5,dt_c1_6_2_2_1__card_5,dt_c2_6_2__card_5,dt_c2_6_2_2__card_5,dt_c2_6_2_2_1__card_5,dt_c3_6_2__card_5,dt_c3_6_2_2__card_5,de_c2_6_2_2_1__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,rc1_card_1,t1_subset,t7_boole,e5_6_2__card_5,e3_6_2_2__card_5,e5_6_2_2__card_5,e1_6_2_2_1__card_5,t41_card_1]),
    [interesting(0.35),file(card_5,e3_6_2_2_1__card_5),[file(card_5,e3_6_2_2_1__card_5)]]).

fof(t11_card_5,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ~ v1_finset_1(k3_card_1(A)) ) ),
    file(card_5,t11_card_5),
    [interesting(0.9),axiom,file(card_5,t11_card_5)]).

fof(t19_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v1_ordinal1(C)
             => ( ( r2_hidden(C,A)
                  & r2_hidden(A,B) )
               => r2_hidden(C,B) ) ) ) ) ),
    file(ordinal1,t19_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t19_ordinal1)]).

fof(e4_6_2_2_1__card_5,plain,
    ( r2_hidden(k3_card_1(c2_6_2_2_1__card_5),c1_6_2__card_5)
    & ~ v1_finset_1(k3_card_1(c2_6_2_2_1__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_2_1__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,dt_c1_6_2_2_1__card_5,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_card_1,dt_c1_6_2__card_5,dt_c2_6_2_2_1__card_5,dt_c3_6_2_2__card_5,de_c2_6_2_2_1__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e3_6_2_2_1__card_5,t11_card_5,t19_ordinal1]),
    [interesting(0.35),file(card_5,e4_6_2_2_1__card_5),[file(card_5,e4_6_2_2_1__card_5)]]).

fof(e5_6_2_2_1__card_5,plain,(
    r2_hidden(k3_card_1(c2_6_2_2_1__card_5),c2_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,e1_6_2_2_1__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,dt_c1_6_2_2_1__card_5,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc1_card_1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_card_1,dt_c1_6_2__card_5,dt_c2_6_2__card_5,dt_c2_6_2_2_1__card_5,de_c2_6_2_2_1__card_5,cc1_card_1,rc1_card_1,t1_subset,t7_boole,e4_6_2_2_1__card_5,e5_6_2__card_5]),
    [interesting(0.35),file(card_5,e5_6_2_2_1__card_5),[file(card_5,e5_6_2_2_1__card_5)]]).

fof(e6_6_2_2_1__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & k3_card_1(c2_6_2_2_1__card_5) = k3_card_1(A)
      & k1_funct_1(c3_6_2__card_5,k3_card_1(c2_6_2_2_1__card_5)) = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e1_6_2_2_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,dt_c1_6_2_2_1__card_5,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c2_6_2__card_5,dt_c2_6_2_2_1__card_5,dt_c3_6_2__card_5,de_c2_6_2_2_1__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e5_6_2_2_1__card_5,e9_6_2__card_5]),
    [interesting(0.35),file(card_5,e6_6_2_2_1__card_5),[file(card_5,e6_6_2_2_1__card_5)]]).

fof(e7_6_2_2_1__card_5,plain,(
    c2_6_2_2_1__card_5 = k1_funct_1(c3_6_2__card_5,k3_card_1(c2_6_2_2_1__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e1_6_2_2_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dt_c1_6_2_2_1__card_5,cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,dt_k1_funct_1,dt_k3_card_1,dt_c2_6_2_2_1__card_5,dt_c3_6_2__card_5,de_c2_6_2_2_1__card_5,cc1_ordinal1,fc1_card_1,e6_6_2_2_1__card_5,t42_card_1]),
    [interesting(0.35),file(card_5,e7_6_2_2_1__card_5),[file(card_5,e7_6_2_2_1__card_5)]]).

fof(e8_6_2_2_1__card_5,plain,(
    r2_hidden(c1_6_2_2_1__card_5,k2_relat_1(c3_6_2__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,e1_6_2_2_1__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_c1_6_2_2_1__card_5,dt_c2_6_2__card_5,dt_c2_6_2_2_1__card_5,dt_c3_6_2__card_5,de_c2_6_2_2_1__card_5,cc1_ordinal1,fc1_card_1,rc1_funct_1,t1_subset,t7_boole,e7_6_2_2_1__card_5,e9_6_2__card_5,e5_6_2_2_1__card_5,d5_funct_1]),
    [interesting(0.35),file(card_5,e8_6_2_2_1__card_5),[file(card_5,e8_6_2_2_1__card_5)]]).

fof(i3_6_2_2_1__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i3_6_2_2_1__card_5)]),
    [interesting(0.35),trivial,file(card_5,i3_6_2_2_1__card_5)]).

fof(i2_6_2_2_1__card_5,plain,(
    r2_hidden(c1_6_2_2_1__card_5,k2_relat_1(c3_6_2__card_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,e1_6_2_2_1__card_5,dt_c1_6_2__card_5])],[e8_6_2_2_1__card_5,i3_6_2_2_1__card_5]),
    [interesting(0.35),file(card_5,i2_6_2_2_1__card_5),[file(card_5,i2_6_2_2_1__card_5)]]).

fof(i1_6_2_2_1__card_5,plain,(
    ~ ( r2_hidden(c1_6_2_2_1__card_5,c1_6_2_2__card_5)
      & ~ r2_hidden(c1_6_2_2_1__card_5,k2_relat_1(c3_6_2__card_5)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2_2_1__card_5,dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2_2_1__card_5])],[e1_6_2_2_1__card_5,i2_6_2_2_1__card_5]),
    [interesting(0.35),file(card_5,i1_6_2_2_1__card_5),[file(card_5,i1_6_2_2_1__card_5)]]).

fof(i1_6_2_2_1_tmp__card_5,plain,(
    ~ ( r2_hidden(c1_6_2_2_1__card_5,c1_6_2_2__card_5)
      & ~ r2_hidden(c1_6_2_2_1__card_5,k2_relat_1(c3_6_2__card_5)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[dt_c1_6_2_2_1__card_5])],[dt_c1_6_2_2_1__card_5,i1_6_2_2_1__card_5]),
    [interesting(0.5),e7_6_2_2__card_5]).

fof(e7_6_2_2__card_5,plain,(
    r1_tarski(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ),
    inference(let,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[i1_6_2_2_1_tmp__card_5,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_c1_6_2_2__card_5,dt_c3_6_2__card_5,d3_tarski,dh_c1_6_2_2_1__card_5]),
    [interesting(0.5),file(card_5,e7_6_2_2__card_5),[file(card_5,e7_6_2_2__card_5)]]).

fof(i4_6_2_2__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i4_6_2_2__card_5)]),
    [interesting(0.5),trivial,file(card_5,i4_6_2_2__card_5)]).

fof(i3_6_2_2__card_5,plain,(
    r1_tarski(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[e7_6_2_2__card_5,i4_6_2_2__card_5]),
    [interesting(0.5),file(card_5,i3_6_2_2__card_5),[file(card_5,i3_6_2_2__card_5)]]).

fof(i2_6_2_2__card_5,plain,
    ( v3_ordinal1(c1_6_2_2__card_5)
    & r1_tarski(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_2_2__card_5,e1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[e6_6_2_2__card_5,i3_6_2_2__card_5]),
    [interesting(0.5),file(card_5,i2_6_2_2__card_5),[file(card_5,i2_6_2_2__card_5)]]).

fof(i1_6_2_2__card_5,plain,
    ( r2_hidden(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5))
   => ( v3_ordinal1(c1_6_2_2__card_5)
      & r1_tarski(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2_2__card_5])],[e1_6_2_2__card_5,i2_6_2_2__card_5]),
    [interesting(0.5),file(card_5,i1_6_2_2__card_5),[file(card_5,i1_6_2_2__card_5)]]).

fof(i1_6_2_2_tmp__card_5,plain,
    ( r2_hidden(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5))
   => ( v3_ordinal1(c1_6_2_2__card_5)
      & r1_tarski(c1_6_2_2__card_5,k2_relat_1(c3_6_2__card_5)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[dt_c1_6_2_2__card_5])],[dt_c1_6_2_2__card_5,i1_6_2_2__card_5]),
    [interesting(0.65),e10_6_2__card_5]).

fof(e10_6_2__card_5,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c3_6_2__card_5))
     => ( v3_ordinal1(A)
        & r1_tarski(A,k2_relat_1(c3_6_2__card_5)) ) ) ),
    inference(let,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[i1_6_2_2_tmp__card_5,dh_c1_6_2_2__card_5]),
    [interesting(0.65),file(card_5,e10_6_2__card_5),[file(card_5,e10_6_2__card_5)]]).

fof(t31_ordinal1,theorem,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,A)
         => ( v3_ordinal1(B)
            & r1_tarski(B,A) ) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,t31_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t31_ordinal1)]).

fof(e11_6_2__card_5,plain,(
    v3_ordinal1(k2_relat_1(c3_6_2__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_finset_1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_funct_1,rc1_ordinal1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_c3_6_2__card_5,cc1_ordinal1,t1_subset,t3_subset,t7_boole,e10_6_2__card_5,t31_ordinal1]),
    [interesting(0.65),file(card_5,e11_6_2__card_5),[file(card_5,e11_6_2__card_5)]]).

fof(dt_c4_6_2__card_5,plain,(
    v3_ordinal1(c4_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc2_ordinal1,rc1_funct_1,rc1_ordinal1,dt_k2_relat_1,dt_c3_6_2__card_5,cc1_ordinal1,de_c4_6_2__card_5,e11_6_2__card_5]),
    [interesting(0.65),file(card_5,c4_6_2__card_5),[file(card_5,c4_6_2__card_5)]]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(e1_6_2_5_1_1__card_5,assumption,(
    c4_6_2__card_5 = k1_xboole_0 ),
    introduced(assumption,[file(card_5,e1_6_2_5_1_1__card_5)]),
    [interesting(0.2),axiom,file(card_5,e1_6_2_5_1_1__card_5)]).

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(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(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.9),axiom,file(relat_1,t65_relat_1)]).

fof(e2_6_2_5_1_1__card_5,plain,
    ( ~ r2_hidden(k3_card_1(0),c2_6_2__card_5)
    & ~ v1_finset_1(k3_card_1(0)) ),
    inference(mizar_by,[status(thm),assumptions([e1_6_2_5_1_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k5_ordinal2,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_xreal_0,cc3_arytm_3,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_card_4,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_arytm_3,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_nat_1,cc2_arytm_3,cc2_card_1,cc2_funct_1,cc2_membered,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc3_membered,cc3_ordinal1,cc4_membered,fc17_finseq_1,fc2_membered,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_card_1,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c4_6_2__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc11_finseq_1,fc1_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,t1_subset,t6_boole,t7_boole,spc0_numerals,spc0_boole,e1_6_2_5_1_1__card_5,e9_6_2__card_5,t11_card_5,t65_relat_1]),
    [interesting(0.2),file(card_5,e2_6_2_5_1_1__card_5),[file(card_5,e2_6_2_5_1_1__card_5)]]).

fof(e3_6_2_5_1_1__card_5,plain,(
    ~ r2_hidden(k3_card_1(0),c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e1_6_2_5_1_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_card_4,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_arytm_3,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_ordinal1,cc2_arytm_3,cc2_card_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,fc1_card_1,fc2_membered,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_card_1,dt_c1_6_2__card_5,dt_c2_6_2__card_5,cc1_card_1,rc1_card_1,t1_subset,t7_boole,spc0_numerals,spc0_boole,e2_6_2_5_1_1__card_5,e5_6_2__card_5]),
    [interesting(0.2),file(card_5,e3_6_2_5_1_1__card_5),[file(card_5,e3_6_2_5_1_1__card_5)]]).

fof(t14_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ~ r1_tarski(B,A) ) ) ) ),
    file(card_1,t14_card_1),
    [interesting(0.9),axiom,file(card_1,t14_card_1)]).

fof(t11_card_4,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ( ~ v1_finset_1(A)
      <=> r1_ordinal1(k3_card_1(0),A) ) ) ),
    file(card_4,t11_card_4),
    [interesting(0.9),axiom,file(card_4,t11_card_4)]).

fof(e4_6_2_5_1_1__card_5,plain,
    ( r1_ordinal1(c1_6_2__card_5,k3_card_1(0))
    & r1_ordinal1(k3_card_1(0),c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e1_6_2_5_1_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e3_6_2__card_5])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_card_4,fc1_ordinal2,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_arytm_3,rc1_membered,rc1_nat_1,rc1_xreal_0,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_ordinal1,cc2_arytm_3,cc2_card_1,cc2_finset_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc1_subset_1,fc2_membered,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc2_card_1,rc2_nat_1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k3_card_1,dt_c1_6_2__card_5,cc1_card_1,rc1_card_1,t1_subset,t3_subset,t7_boole,spc0_numerals,spc0_boole,e3_6_2_5_1_1__card_5,e3_6_2__card_5,t14_card_1,t11_card_4]),
    [interesting(0.2),file(card_5,e4_6_2_5_1_1__card_5),[file(card_5,e4_6_2_5_1_1__card_5)]]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(e5_6_2_5_1_1__card_5,plain,(
    c1_6_2__card_5 = k3_card_1(0) ),
    inference(mizar_by,[status(thm),assumptions([e1_6_2_5_1_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e3_6_2__card_5])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_card_4,fc1_ordinal2,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_ordinal1,cc2_arytm_3,cc2_card_1,cc2_nat_1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc1_subset_1,fc2_membered,rc1_card_1,rc1_subset_1,rc2_nat_1,rc2_subset_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,redefinition_r1_ordinal1,dt_k3_card_1,dt_c1_6_2__card_5,t3_subset,spc0_numerals,spc0_boole,e4_6_2_5_1_1__card_5,d10_xboole_0]),
    [interesting(0.2),file(card_5,e5_6_2_5_1_1__card_5),[file(card_5,e5_6_2_5_1_1__card_5)]]).

fof(i2_6_2_5_1_1__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i2_6_2_5_1_1__card_5)]),
    [interesting(0.2),trivial,file(card_5,i2_6_2_5_1_1__card_5)]).

fof(i1_6_2_5_1_1__card_5,plain,(
    c1_6_2__card_5 = k3_card_1(0) ),
    inference(conclusion,[status(thm),assumptions([e1_6_2_5_1_1__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e3_6_2__card_5])],[e5_6_2_5_1_1__card_5,i2_6_2_5_1_1__card_5]),
    [interesting(0.2),file(card_5,i1_6_2_5_1_1__card_5),[file(card_5,i1_6_2_5_1_1__card_5)]]).

fof(i1_6_2_5_1__card_5,plain,
    ( c4_6_2__card_5 = k1_xboole_0
   => ( c4_6_2__card_5 = k1_xboole_0
      & c1_6_2__card_5 = k3_card_1(0) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5,e3_6_2__card_5]),discharge_asm(discharge,[e1_6_2_5_1_1__card_5])],[e1_6_2_5_1_1__card_5,i1_6_2_5_1_1__card_5]),
    [interesting(0.35),file(card_5,i1_6_2_5_1__card_5),[file(card_5,i1_6_2_5_1__card_5)]]).

fof(e1_6_2_5_1_2__card_5,assumption,(
    c4_6_2__card_5 != k1_xboole_0 ),
    introduced(assumption,[file(card_5,e1_6_2_5_1_2__card_5)]),
    [interesting(0.2),axiom,file(card_5,e1_6_2_5_1_2__card_5)]).

fof(e2_6_2_5_1_2__card_5,assumption,(
    c1_6_2__card_5 != k3_card_1(c4_6_2__card_5) ),
    introduced(assumption,[file(card_5,e2_6_2_5_1_2__card_5)]),
    [interesting(0.2),axiom,file(card_5,e2_6_2_5_1_2__card_5)]).

fof(dt_k7_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k7_ordinal2(A)) ),
    file(ordinal2,k7_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k7_ordinal2)]).

fof(fc5_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( v1_ordinal1(k1_relat_1(A))
        & v2_ordinal1(k1_relat_1(A))
        & v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,fc5_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc5_ordinal1)]).

fof(rc4_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc4_ordinal1)]).

fof(dt_k8_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => v3_ordinal1(k8_ordinal2(A)) ) ),
    file(ordinal2,k8_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k8_ordinal2)]).

fof(dh_c1_6_2_5_1_2__card_5,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & k1_card_1(k8_ordinal2(c5_6_2__card_5)) = k3_card_1(A)
        & k1_funct_1(c3_6_2__card_5,k1_card_1(k8_ordinal2(c5_6_2__card_5))) = A )
   => ( v3_ordinal1(c1_6_2_5_1_2__card_5)
      & k1_card_1(k8_ordinal2(c5_6_2__card_5)) = k3_card_1(c1_6_2_5_1_2__card_5)
      & k1_funct_1(c3_6_2__card_5,k1_card_1(k8_ordinal2(c5_6_2__card_5))) = c1_6_2_5_1_2__card_5 ) ),
    introduced(definition,[new_symbol(c1_6_2_5_1_2__card_5),file(card_5,c1_6_2_5_1_2__card_5)]),
    [interesting(0.2),axiom,file(card_5,c1_6_2_5_1_2__card_5)]).

fof(dh_c5_6_2__card_5,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & k1_relat_1(A) = c4_6_2__card_5
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,c4_6_2__card_5)
             => k1_funct_1(A,B) = k3_card_1(B) ) ) )
   => ( v1_relat_1(c5_6_2__card_5)
      & v1_funct_1(c5_6_2__card_5)
      & v5_ordinal1(c5_6_2__card_5)
      & k1_relat_1(c5_6_2__card_5) = c4_6_2__card_5
      & ! [C] : 
          ( v3_ordinal1(C)
         => ( r2_hidden(C,c4_6_2__card_5)
           => k1_funct_1(c5_6_2__card_5,C) = k3_card_1(C) ) ) ) ),
    introduced(definition,[new_symbol(c5_6_2__card_5),file(card_5,c5_6_2__card_5)]),
    [interesting(0.65),axiom,file(card_5,c5_6_2__card_5)]).

fof(s2_ordinal2__e12_6_2__card_5,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & v5_ordinal1(B)
          & k1_relat_1(B) = A
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(C,A)
               => k1_funct_1(B,C) = k3_card_1(C) ) ) ) ) ),
    file(card_5,s2_ordinal2__e12_6_2__card_5),
    [interesting(0.9),axiom,file(card_5,s2_ordinal2__e12_6_2__card_5)]).

fof(e12_6_2__card_5,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & k1_relat_1(A) = c4_6_2__card_5
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(B,c4_6_2__card_5)
           => k1_funct_1(A,B) = k3_card_1(B) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,fc5_ordinal1,rc1_funct_1,rc4_ordinal1,s2_ordinal2__e12_6_2__card_5]),
    [interesting(0.65),file(card_5,e12_6_2__card_5),[file(card_5,e12_6_2__card_5)]]).

fof(dt_c5_6_2__card_5,plain,
    ( v1_relat_1(c5_6_2__card_5)
    & v1_funct_1(c5_6_2__card_5)
    & v5_ordinal1(c5_6_2__card_5) ),
    inference(consider,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c5_6_2__card_5,e12_6_2__card_5]),
    [interesting(0.65),file(card_5,c5_6_2__card_5),[file(card_5,c5_6_2__card_5)]]).

fof(d9_ordinal2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)) ) ),
    file(ordinal2,d9_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,d9_ordinal2)]).

fof(rc1_ordinal2,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,rc1_ordinal2)]).

fof(dh_c1_6_2_3__card_5,definition,
    ( ( v3_ordinal1(c1_6_2_3__card_5)
     => ( r2_hidden(c1_6_2_3__card_5,c4_6_2__card_5)
       => r2_hidden(k1_ordinal1(c1_6_2_3__card_5),c4_6_2__card_5) ) )
   => ! [A] : 
        ( v3_ordinal1(A)
       => ( r2_hidden(A,c4_6_2__card_5)
         => r2_hidden(k1_ordinal1(A),c4_6_2__card_5) ) ) ),
    introduced(definition,[new_symbol(c1_6_2_3__card_5),file(card_5,c1_6_2_3__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_3__card_5)]).

fof(e1_6_2_3__card_5,assumption,(
    r2_hidden(c1_6_2_3__card_5,c4_6_2__card_5) ),
    introduced(assumption,[file(card_5,e1_6_2_3__card_5)]),
    [interesting(0.5),axiom,file(card_5,e1_6_2_3__card_5)]).

fof(dt_c1_6_2_3__card_5,assumption,(
    v3_ordinal1(c1_6_2_3__card_5) ),
    introduced(assumption,[file(card_5,c1_6_2_3__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_3__card_5)]).

fof(dh_c2_6_2_3__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,c2_6_2__card_5)
        & c1_6_2_3__card_5 = k1_funct_1(c3_6_2__card_5,A) )
   => ( r2_hidden(c2_6_2_3__card_5,c2_6_2__card_5)
      & c1_6_2_3__card_5 = k1_funct_1(c3_6_2__card_5,c2_6_2_3__card_5) ) ),
    introduced(definition,[new_symbol(c2_6_2_3__card_5),file(card_5,c2_6_2_3__card_5)]),
    [interesting(0.5),axiom,file(card_5,c2_6_2_3__card_5)]).

fof(e2_6_2_3__card_5,plain,(
    ? [A] : 
      ( r2_hidden(A,c2_6_2__card_5)
      & c1_6_2_3__card_5 = k1_funct_1(c3_6_2__card_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_c1_6_2_3__card_5,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c4_6_2__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,rc1_funct_1,t1_subset,t7_boole,e1_6_2_3__card_5,e9_6_2__card_5,d5_funct_1]),
    [interesting(0.5),file(card_5,e2_6_2_3__card_5),[file(card_5,e2_6_2_3__card_5)]]).

fof(dt_c2_6_2_3__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c2_6_2_3__card_5,e2_6_2_3__card_5]),
    [interesting(0.5),file(card_5,c2_6_2_3__card_5),[file(card_5,c2_6_2_3__card_5)]]).

fof(dh_c3_6_2_3__card_5,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & c2_6_2_3__card_5 = k3_card_1(A)
        & c1_6_2_3__card_5 = A )
   => ( v3_ordinal1(c3_6_2_3__card_5)
      & c2_6_2_3__card_5 = k3_card_1(c3_6_2_3__card_5)
      & c1_6_2_3__card_5 = c3_6_2_3__card_5 ) ),
    introduced(definition,[new_symbol(c3_6_2_3__card_5),file(card_5,c3_6_2_3__card_5)]),
    [interesting(0.5),axiom,file(card_5,c3_6_2_3__card_5)]).

fof(e3_6_2_3__card_5,plain,
    ( r2_hidden(c2_6_2_3__card_5,c2_6_2__card_5)
    & c1_6_2_3__card_5 = k1_funct_1(c3_6_2__card_5,c2_6_2_3__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c2_6_2_3__card_5,e2_6_2_3__card_5]),
    [interesting(0.5),file(card_5,e3_6_2_3__card_5),[file(card_5,e3_6_2_3__card_5)]]).

fof(e4_6_2_3__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c2_6_2_3__card_5 = k3_card_1(A)
      & c1_6_2_3__card_5 = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c1_6_2_3__card_5,dt_c2_6_2__card_5,dt_c2_6_2_3__card_5,dt_c3_6_2__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e9_6_2__card_5,e3_6_2_3__card_5]),
    [interesting(0.5),file(card_5,e4_6_2_3__card_5),[file(card_5,e4_6_2_3__card_5)]]).

fof(dt_c3_6_2_3__card_5,plain,(
    v3_ordinal1(c3_6_2_3__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c3_6_2_3__card_5,e4_6_2_3__card_5]),
    [interesting(0.5),file(card_5,c3_6_2_3__card_5),[file(card_5,c3_6_2_3__card_5)]]).

fof(dh_c4_6_2_3__card_5,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & k3_card_1(k1_ordinal1(c3_6_2_3__card_5)) = k3_card_1(A)
        & k1_funct_1(c3_6_2__card_5,k3_card_1(k1_ordinal1(c3_6_2_3__card_5))) = A )
   => ( v3_ordinal1(c4_6_2_3__card_5)
      & k3_card_1(k1_ordinal1(c3_6_2_3__card_5)) = k3_card_1(c4_6_2_3__card_5)
      & k1_funct_1(c3_6_2__card_5,k3_card_1(k1_ordinal1(c3_6_2_3__card_5))) = c4_6_2_3__card_5 ) ),
    introduced(definition,[new_symbol(c4_6_2_3__card_5),file(card_5,c4_6_2_3__card_5)]),
    [interesting(0.5),axiom,file(card_5,c4_6_2_3__card_5)]).

fof(e5_6_2_3__card_5,plain,
    ( c2_6_2_3__card_5 = k3_card_1(c3_6_2_3__card_5)
    & c1_6_2_3__card_5 = c3_6_2_3__card_5 ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c3_6_2_3__card_5,e4_6_2_3__card_5]),
    [interesting(0.5),file(card_5,e5_6_2_3__card_5),[file(card_5,e5_6_2_3__card_5)]]).

fof(e6_6_2_3__card_5,plain,
    ( k3_card_1(k1_ordinal1(c3_6_2_3__card_5)) = k2_card_1(k3_card_1(c3_6_2_3__card_5))
    & r2_hidden(k3_card_1(c3_6_2_3__card_5),c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc3_ordinal1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_ordinal1,dt_k2_card_1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c1_6_2_3__card_5,dt_c2_6_2__card_5,dt_c2_6_2_3__card_5,dt_c3_6_2__card_5,dt_c3_6_2_3__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,rc1_card_1,t1_subset,t7_boole,e5_6_2__card_5,e3_6_2_3__card_5,e5_6_2_3__card_5,t39_card_1]),
    [interesting(0.5),file(card_5,e6_6_2_3__card_5),[file(card_5,e6_6_2_3__card_5)]]).

fof(d7_card_1,definition,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v2_card_1(A)
      <=> ! [B] : 
            ( v1_card_1(B)
           => A != k2_card_1(B) ) ) ) ),
    file(card_1,d7_card_1),
    [interesting(0.9),axiom,file(card_1,d7_card_1)]).

fof(t22_card_4,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> r1_tarski(k2_card_1(A),B) ) ) ) ),
    file(card_4,t22_card_4),
    [interesting(0.9),axiom,file(card_4,t22_card_4)]).

fof(e7_6_2_3__card_5,plain,
    ( k3_card_1(k1_ordinal1(c3_6_2_3__card_5)) != c1_6_2__card_5
    & r1_tarski(k3_card_1(k1_ordinal1(c3_6_2_3__card_5)),c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc2_arytm_3,rc1_arytm_3,rc1_nat_1,rc1_xreal_0,rc2_finset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_ordinal1,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,fc1_card_1,fc1_subset_1,fc3_ordinal1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc1_subset_1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_ordinal1,dt_k1_xboole_0,dt_k2_card_1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c3_6_2_3__card_5,cc1_card_1,fc1_ordinal1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_card_1,t1_subset,t3_subset,t6_boole,t7_boole,e6_6_2_3__card_5,e1_6_2__card_5,d7_card_1,t22_card_4]),
    [interesting(0.5),file(card_5,e7_6_2_3__card_5),[file(card_5,e7_6_2_3__card_5)]]).

fof(t13_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ( r1_tarski(A,B)
              & A != B ) ) ) ) ),
    file(card_1,t13_card_1),
    [interesting(0.9),axiom,file(card_1,t13_card_1)]).

fof(e8_6_2_3__card_5,plain,
    ( r2_hidden(k3_card_1(k1_ordinal1(c3_6_2_3__card_5)),c1_6_2__card_5)
    & ~ v1_finset_1(k3_card_1(k1_ordinal1(c3_6_2_3__card_5))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_finset_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc2_card_1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_ordinal1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c3_6_2_3__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,rc1_card_1,t1_subset,t3_subset,t7_boole,e7_6_2_3__card_5,t11_card_5,t13_card_1]),
    [interesting(0.5),file(card_5,e8_6_2_3__card_5),[file(card_5,e8_6_2_3__card_5)]]).

fof(e9_6_2_3__card_5,plain,(
    r2_hidden(k3_card_1(k1_ordinal1(c3_6_2_3__card_5)),c2_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e2_6_2__card_5,e1_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_funct_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc1_card_1,fc3_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_ordinal1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c2_6_2__card_5,dt_c3_6_2_3__card_5,cc1_card_1,fc1_ordinal1,rc1_card_1,t1_subset,t7_boole,e8_6_2_3__card_5,e5_6_2__card_5]),
    [interesting(0.5),file(card_5,e9_6_2_3__card_5),[file(card_5,e9_6_2_3__card_5)]]).

fof(e10_6_2_3__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & k3_card_1(k1_ordinal1(c3_6_2_3__card_5)) = k3_card_1(A)
      & k1_funct_1(c3_6_2__card_5,k3_card_1(k1_ordinal1(c3_6_2_3__card_5))) = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc17_finseq_1,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_ordinal1,dt_k1_relat_1,dt_k3_card_1,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c3_6_2_3__card_5,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,t1_subset,t7_boole,e9_6_2_3__card_5,e9_6_2__card_5]),
    [interesting(0.5),file(card_5,e10_6_2_3__card_5),[file(card_5,e10_6_2_3__card_5)]]).

fof(dt_c4_6_2_3__card_5,plain,(
    v3_ordinal1(c4_6_2_3__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c4_6_2_3__card_5,e10_6_2_3__card_5]),
    [interesting(0.5),file(card_5,c4_6_2_3__card_5),[file(card_5,c4_6_2_3__card_5)]]).

fof(e11_6_2_3__card_5,plain,
    ( k3_card_1(k1_ordinal1(c3_6_2_3__card_5)) = k3_card_1(c4_6_2_3__card_5)
    & k1_funct_1(c3_6_2__card_5,k3_card_1(k1_ordinal1(c3_6_2_3__card_5))) = c4_6_2_3__card_5 ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c4_6_2_3__card_5,e10_6_2_3__card_5]),
    [interesting(0.5),file(card_5,e11_6_2_3__card_5),[file(card_5,e11_6_2_3__card_5)]]).

fof(e12_6_2_3__card_5,plain,(
    k1_ordinal1(c3_6_2_3__card_5) = c4_6_2_3__card_5 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,t1_subset,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k1_funct_1,dt_k1_ordinal1,dt_k3_card_1,dt_c3_6_2__card_5,dt_c3_6_2_3__card_5,dt_c4_6_2_3__card_5,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,e11_6_2_3__card_5,t42_card_1]),
    [interesting(0.5),file(card_5,e12_6_2_3__card_5),[file(card_5,e12_6_2_3__card_5)]]).

fof(e13_6_2_3__card_5,plain,(
    r2_hidden(k1_ordinal1(c1_6_2_3__card_5),c4_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_ordinal1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_c1_6_2_3__card_5,dt_c2_6_2__card_5,dt_c2_6_2_3__card_5,dt_c3_6_2__card_5,dt_c3_6_2_3__card_5,dt_c4_6_2__card_5,dt_c4_6_2_3__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,fc1_ordinal1,fc3_ordinal1,rc1_funct_1,t1_subset,t7_boole,e12_6_2_3__card_5,e9_6_2__card_5,e5_6_2_3__card_5,e9_6_2_3__card_5,e11_6_2_3__card_5,d5_funct_1]),
    [interesting(0.5),file(card_5,e13_6_2_3__card_5),[file(card_5,e13_6_2_3__card_5)]]).

fof(i3_6_2_3__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i3_6_2_3__card_5)]),
    [interesting(0.5),trivial,file(card_5,i3_6_2_3__card_5)]).

fof(i2_6_2_3__card_5,plain,(
    r2_hidden(k1_ordinal1(c1_6_2_3__card_5),c4_6_2__card_5) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[e13_6_2_3__card_5,i3_6_2_3__card_5]),
    [interesting(0.5),file(card_5,i2_6_2_3__card_5),[file(card_5,i2_6_2_3__card_5)]]).

fof(i1_6_2_3__card_5,plain,
    ( r2_hidden(c1_6_2_3__card_5,c4_6_2__card_5)
   => r2_hidden(k1_ordinal1(c1_6_2_3__card_5),c4_6_2__card_5) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2_3__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2_3__card_5])],[e1_6_2_3__card_5,i2_6_2_3__card_5]),
    [interesting(0.5),file(card_5,i1_6_2_3__card_5),[file(card_5,i1_6_2_3__card_5)]]).

fof(i1_6_2_3_tmp__card_5,plain,
    ( v3_ordinal1(c1_6_2_3__card_5)
   => ( r2_hidden(c1_6_2_3__card_5,c4_6_2__card_5)
     => r2_hidden(k1_ordinal1(c1_6_2_3__card_5),c4_6_2__card_5) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[dt_c1_6_2_3__card_5])],[dt_c1_6_2_3__card_5,i1_6_2_3__card_5]),
    [interesting(0.65),e14_6_2__card_5]).

fof(e14_6_2__card_5,plain,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( r2_hidden(A,c4_6_2__card_5)
       => r2_hidden(k1_ordinal1(A),c4_6_2__card_5) ) ) ),
    inference(let,[status(thm),assumptions([e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[i1_6_2_3_tmp__card_5,dh_c1_6_2_3__card_5]),
    [interesting(0.65),file(card_5,e14_6_2__card_5),[file(card_5,e14_6_2__card_5)]]).

fof(t41_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k1_ordinal1(B),A) ) ) ) ) ),
    file(ordinal1,t41_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t41_ordinal1)]).

fof(e15_6_2__card_5,plain,(
    v4_ordinal1(c4_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_funct_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_arytm_3,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_funct_1,rc1_membered,rc2_funct_1,rc7_finseq_1,existence_m1_subset_1,dt_k2_relat_1,dt_m1_subset_1,dt_c3_6_2__card_5,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_ordinal2,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_ordinal1,dt_c4_6_2__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc1_ordinal1,fc3_ordinal1,t1_subset,t7_boole,e14_6_2__card_5,t41_ordinal1]),
    [interesting(0.65),file(card_5,e15_6_2__card_5),[file(card_5,e15_6_2__card_5)]]).

fof(e13_6_2__card_5,plain,
    ( k1_relat_1(c5_6_2__card_5) = c4_6_2__card_5
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( r2_hidden(A,c4_6_2__card_5)
         => k1_funct_1(c5_6_2__card_5,A) = k3_card_1(A) ) ) ),
    inference(consider,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c5_6_2__card_5,e12_6_2__card_5]),
    [interesting(0.65),file(card_5,e13_6_2__card_5),[file(card_5,e13_6_2__card_5)]]).

fof(t40_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
       => ( A = k1_xboole_0
          | ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v5_ordinal1(B) )
             => ( ( k1_relat_1(B) = A
                  & ! [C] : 
                      ( v3_ordinal1(C)
                     => ( r2_hidden(C,A)
                       => k1_funct_1(B,C) = k3_card_1(C) ) ) )
               => k3_card_1(A) = k1_card_1(k8_ordinal2(B)) ) ) ) ) ) ),
    file(card_1,t40_card_1),
    [interesting(0.9),axiom,file(card_1,t40_card_1)]).

fof(e16_6_2__card_5,plain,
    ( c4_6_2__card_5 = k1_xboole_0
    | k3_card_1(c4_6_2__card_5) = k1_card_1(k8_ordinal2(c5_6_2__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_nat_1,rc1_xreal_0,existence_m1_subset_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,dt_c3_6_2__card_5,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_arytm_3,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_card_1,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_ordinal2,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k3_card_1,dt_k8_ordinal2,dt_c4_6_2__card_5,dt_c5_6_2__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,fc2_finseq_1,fc2_ordinal1,fc5_ordinal1,fc6_membered,rc1_funct_1,rc4_ordinal1,t1_subset,t6_boole,t7_boole,d9_ordinal2,e15_6_2__card_5,e13_6_2__card_5,t40_card_1]),
    [interesting(0.65),file(card_5,e16_6_2__card_5),[file(card_5,e16_6_2__card_5)]]).

fof(dt_c1_6_2_4__card_5,assumption,(
    $true ),
    introduced(assumption,[file(card_5,c1_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_4__card_5)]).

fof(dh_c1_6_2_4__card_5,definition,
    ( ~ ( r2_hidden(c1_6_2_4__card_5,k8_ordinal2(c5_6_2__card_5))
        & ~ r2_hidden(c1_6_2_4__card_5,c1_6_2__card_5) )
   => ! [A] : 
        ~ ( r2_hidden(A,k8_ordinal2(c5_6_2__card_5))
          & ~ r2_hidden(A,c1_6_2__card_5) ) ),
    introduced(definition,[new_symbol(c1_6_2_4__card_5),file(card_5,c1_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c1_6_2_4__card_5)]).

fof(e1_6_2_4__card_5,assumption,(
    r2_hidden(c1_6_2_4__card_5,k8_ordinal2(c5_6_2__card_5)) ),
    introduced(assumption,[file(card_5,e1_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,e1_6_2_4__card_5)]).

fof(de_c2_6_2_4__card_5,definition,(
    c2_6_2_4__card_5 = c1_6_2_4__card_5 ),
    introduced(definition,[new_symbol(c2_6_2_4__card_5),file(card_5,c2_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c2_6_2_4__card_5)]).

fof(e2_6_2_4__card_5,plain,(
    v3_ordinal1(c1_6_2_4__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k8_ordinal2,dt_c1_6_2_4__card_5,dt_c5_6_2__card_5,cc1_ordinal1,t1_subset,t7_boole,d9_ordinal2,e1_6_2_4__card_5,t23_ordinal1]),
    [interesting(0.5),file(card_5,e2_6_2_4__card_5),[file(card_5,e2_6_2_4__card_5)]]).

fof(dt_c2_6_2_4__card_5,plain,(
    v3_ordinal1(c2_6_2_4__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc2_ordinal1,rc1_ordinal1,dt_c1_6_2_4__card_5,cc1_ordinal1,de_c2_6_2_4__card_5,e2_6_2_4__card_5]),
    [interesting(0.5),file(card_5,c2_6_2_4__card_5),[file(card_5,c2_6_2_4__card_5)]]).

fof(dh_c3_6_2_4__card_5,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & r2_hidden(A,k2_relat_1(c5_6_2__card_5))
        & r1_ordinal1(c2_6_2_4__card_5,A) )
   => ( v3_ordinal1(c3_6_2_4__card_5)
      & r2_hidden(c3_6_2_4__card_5,k2_relat_1(c5_6_2__card_5))
      & r1_ordinal1(c2_6_2_4__card_5,c3_6_2_4__card_5) ) ),
    introduced(definition,[new_symbol(c3_6_2_4__card_5),file(card_5,c3_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c3_6_2_4__card_5)]).

fof(e3_6_2_4__card_5,plain,(
    r2_hidden(c1_6_2_4__card_5,k7_ordinal2(k2_relat_1(c5_6_2__card_5))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc2_ordinal1,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_funct_1,cc3_ordinal1,rc1_funct_1,rc2_funct_1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k7_ordinal2,dt_k8_ordinal2,dt_c1_6_2_4__card_5,dt_c5_6_2__card_5,t1_subset,t7_boole,d9_ordinal2,e1_6_2_4__card_5]),
    [interesting(0.5),file(card_5,e3_6_2_4__card_5),[file(card_5,e3_6_2_4__card_5)]]).

fof(t29_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ~ ( r2_hidden(A,k7_ordinal2(B))
            & ! [C] : 
                ( v3_ordinal1(C)
               => ~ ( r2_hidden(C,B)
                    & r1_ordinal1(A,C) ) ) ) ) ),
    file(ordinal2,t29_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,t29_ordinal2)]).

fof(e4_6_2_4__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & r2_hidden(A,k2_relat_1(c5_6_2__card_5))
      & r1_ordinal1(c2_6_2_4__card_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_subset_1,rc2_finset_1,rc2_ordinal1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t3_subset,t6_boole,t8_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k2_relat_1,dt_k7_ordinal2,dt_c1_6_2_4__card_5,dt_c2_6_2_4__card_5,dt_c5_6_2__card_5,de_c2_6_2_4__card_5,cc1_ordinal1,t1_subset,t7_boole,e3_6_2_4__card_5,t29_ordinal2]),
    [interesting(0.5),file(card_5,e4_6_2_4__card_5),[file(card_5,e4_6_2_4__card_5)]]).

fof(dt_c3_6_2_4__card_5,plain,(
    v3_ordinal1(c3_6_2_4__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[dh_c3_6_2_4__card_5,e4_6_2_4__card_5]),
    [interesting(0.5),file(card_5,c3_6_2_4__card_5),[file(card_5,c3_6_2_4__card_5)]]).

fof(dh_c4_6_2_4__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c5_6_2__card_5))
        & c3_6_2_4__card_5 = k1_funct_1(c5_6_2__card_5,A) )
   => ( r2_hidden(c4_6_2_4__card_5,k1_relat_1(c5_6_2__card_5))
      & c3_6_2_4__card_5 = k1_funct_1(c5_6_2__card_5,c4_6_2_4__card_5) ) ),
    introduced(definition,[new_symbol(c4_6_2_4__card_5),file(card_5,c4_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c4_6_2_4__card_5)]).

fof(e5_6_2_4__card_5,plain,
    ( r2_hidden(c3_6_2_4__card_5,k2_relat_1(c5_6_2__card_5))
    & r1_ordinal1(c2_6_2_4__card_5,c3_6_2_4__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[dh_c3_6_2_4__card_5,e4_6_2_4__card_5]),
    [interesting(0.5),file(card_5,e5_6_2_4__card_5),[file(card_5,e5_6_2_4__card_5)]]).

fof(e6_6_2_4__card_5,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c5_6_2__card_5))
      & c3_6_2_4__card_5 = k1_funct_1(c5_6_2__card_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_subset_1,rc2_finset_1,rc2_ordinal1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_subset_1,dt_m1_subset_1,dt_c1_6_2_4__card_5,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_funct_1,cc3_ordinal1,fc5_ordinal1,rc2_funct_1,rc4_ordinal1,t2_subset,t3_subset,t6_boole,t8_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c2_6_2_4__card_5,dt_c3_6_2_4__card_5,dt_c5_6_2__card_5,de_c2_6_2_4__card_5,rc1_funct_1,t1_subset,t7_boole,e5_6_2_4__card_5,d5_funct_1]),
    [interesting(0.5),file(card_5,e6_6_2_4__card_5),[file(card_5,e6_6_2_4__card_5)]]).

fof(dt_c4_6_2_4__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[dh_c4_6_2_4__card_5,e6_6_2_4__card_5]),
    [interesting(0.5),file(card_5,c4_6_2_4__card_5),[file(card_5,c4_6_2_4__card_5)]]).

fof(de_c5_6_2_4__card_5,definition,(
    c5_6_2_4__card_5 = c4_6_2_4__card_5 ),
    introduced(definition,[new_symbol(c5_6_2_4__card_5),file(card_5,c5_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c5_6_2_4__card_5)]).

fof(e7_6_2_4__card_5,plain,
    ( r2_hidden(c4_6_2_4__card_5,k1_relat_1(c5_6_2__card_5))
    & c3_6_2_4__card_5 = k1_funct_1(c5_6_2__card_5,c4_6_2_4__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[dh_c4_6_2_4__card_5,e6_6_2_4__card_5]),
    [interesting(0.5),file(card_5,e7_6_2_4__card_5),[file(card_5,e7_6_2_4__card_5)]]).

fof(e8_6_2_4__card_5,plain,(
    v3_ordinal1(c4_6_2_4__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_c3_6_2_4__card_5,dt_c4_6_2_4__card_5,dt_c5_6_2__card_5,cc1_ordinal1,t1_subset,t7_boole,e7_6_2_4__card_5,t23_ordinal1]),
    [interesting(0.5),file(card_5,e8_6_2_4__card_5),[file(card_5,e8_6_2_4__card_5)]]).

fof(dt_c5_6_2_4__card_5,plain,(
    v3_ordinal1(c5_6_2_4__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc2_ordinal1,rc1_ordinal1,dt_c4_6_2_4__card_5,cc1_ordinal1,de_c5_6_2_4__card_5,e8_6_2_4__card_5]),
    [interesting(0.5),file(card_5,c5_6_2_4__card_5),[file(card_5,c5_6_2_4__card_5)]]).

fof(dh_c6_6_2_4__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c3_6_2__card_5))
        & c5_6_2_4__card_5 = k1_funct_1(c3_6_2__card_5,A) )
   => ( r2_hidden(c6_6_2_4__card_5,k1_relat_1(c3_6_2__card_5))
      & c5_6_2_4__card_5 = k1_funct_1(c3_6_2__card_5,c6_6_2_4__card_5) ) ),
    introduced(definition,[new_symbol(c6_6_2_4__card_5),file(card_5,c6_6_2_4__card_5)]),
    [interesting(0.5),axiom,file(card_5,c6_6_2_4__card_5)]).

fof(e10_6_2_4__card_5,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c3_6_2__card_5))
      & c5_6_2_4__card_5 = k1_funct_1(c3_6_2__card_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_card_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_c3_6_2__card_5,dt_c3_6_2_4__card_5,dt_c4_6_2__card_5,dt_c4_6_2_4__card_5,dt_c5_6_2__card_5,dt_c5_6_2_4__card_5,de_c4_6_2__card_5,de_c5_6_2_4__card_5,cc1_ordinal1,fc1_card_1,rc1_funct_1,t1_subset,t7_boole,e13_6_2__card_5,e7_6_2_4__card_5,d5_funct_1]),
    [interesting(0.5),file(card_5,e10_6_2_4__card_5),[file(card_5,e10_6_2_4__card_5)]]).

fof(dt_c6_6_2_4__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[dh_c6_6_2_4__card_5,e10_6_2_4__card_5]),
    [interesting(0.5),file(card_5,c6_6_2_4__card_5),[file(card_5,c6_6_2_4__card_5)]]).

fof(e11_6_2_4__card_5,plain,
    ( r2_hidden(c6_6_2_4__card_5,k1_relat_1(c3_6_2__card_5))
    & c5_6_2_4__card_5 = k1_funct_1(c3_6_2__card_5,c6_6_2_4__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[dh_c6_6_2_4__card_5,e10_6_2_4__card_5]),
    [interesting(0.5),file(card_5,e11_6_2_4__card_5),[file(card_5,e11_6_2_4__card_5)]]).

fof(e12_6_2_4__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c6_6_2_4__card_5 = k3_card_1(A)
      & c5_6_2_4__card_5 = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,dt_c4_6_2_4__card_5,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c5_6_2_4__card_5,dt_c6_6_2_4__card_5,de_c5_6_2_4__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e9_6_2__card_5,e11_6_2_4__card_5]),
    [interesting(0.5),file(card_5,e12_6_2_4__card_5),[file(card_5,e12_6_2_4__card_5)]]).

fof(e9_6_2_4__card_5,plain,
    ( c3_6_2_4__card_5 = k3_card_1(c5_6_2_4__card_5)
    & ~ v1_finset_1(k3_card_1(c5_6_2_4__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_k2_relat_1,dt_m1_subset_1,dt_c3_6_2__card_5,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc11_finseq_1,fc17_finseq_1,fc5_ordinal1,rc1_card_1,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c3_6_2_4__card_5,dt_c4_6_2__card_5,dt_c4_6_2_4__card_5,dt_c5_6_2__card_5,dt_c5_6_2_4__card_5,de_c4_6_2__card_5,de_c5_6_2_4__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,e13_6_2__card_5,e7_6_2_4__card_5,t11_card_5]),
    [interesting(0.5),file(card_5,e9_6_2_4__card_5),[file(card_5,e9_6_2_4__card_5)]]).

fof(e13_6_2_4__card_5,plain,
    ( r2_hidden(c3_6_2_4__card_5,c1_6_2__card_5)
    & c1_6_2__card_5 = c1_6_2__card_5 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_membered,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,dt_c4_6_2_4__card_5,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc17_finseq_1,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc3_ordinal1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c3_6_2_4__card_5,dt_c5_6_2_4__card_5,dt_c6_6_2_4__card_5,de_c5_6_2_4__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,rc1_card_1,t1_subset,t7_boole,e12_6_2_4__card_5,e5_6_2__card_5,e9_6_2__card_5,e9_6_2_4__card_5,e11_6_2_4__card_5]),
    [interesting(0.5),file(card_5,e13_6_2_4__card_5),[file(card_5,e13_6_2_4__card_5)]]).

fof(t22_ordinal1,theorem,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_tarski(A,B)
                  & r2_hidden(B,C) )
               => r2_hidden(A,C) ) ) ) ) ),
    file(ordinal1,t22_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t22_ordinal1)]).

fof(e14_6_2_4__card_5,plain,(
    r2_hidden(c1_6_2_4__card_5,c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_finset_1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k2_relat_1,dt_c1_6_2__card_5,dt_c1_6_2_4__card_5,dt_c2_6_2_4__card_5,dt_c3_6_2_4__card_5,dt_c5_6_2__card_5,de_c2_6_2_4__card_5,cc1_ordinal1,t1_subset,t3_subset,t7_boole,e13_6_2_4__card_5,e5_6_2_4__card_5,t22_ordinal1]),
    [interesting(0.5),file(card_5,e14_6_2_4__card_5),[file(card_5,e14_6_2_4__card_5)]]).

fof(i3_6_2_4__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i3_6_2_4__card_5)]),
    [interesting(0.5),trivial,file(card_5,i3_6_2_4__card_5)]).

fof(i2_6_2_4__card_5,plain,(
    r2_hidden(c1_6_2_4__card_5,c1_6_2__card_5) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_4__card_5])],[e14_6_2_4__card_5,i3_6_2_4__card_5]),
    [interesting(0.5),file(card_5,i2_6_2_4__card_5),[file(card_5,i2_6_2_4__card_5)]]).

fof(i1_6_2_4__card_5,plain,(
    ~ ( r2_hidden(c1_6_2_4__card_5,k8_ordinal2(c5_6_2__card_5))
      & ~ r2_hidden(c1_6_2_4__card_5,c1_6_2__card_5) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2_4__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2_4__card_5])],[e1_6_2_4__card_5,i2_6_2_4__card_5]),
    [interesting(0.5),file(card_5,i1_6_2_4__card_5),[file(card_5,i1_6_2_4__card_5)]]).

fof(i1_6_2_4_tmp__card_5,plain,(
    ~ ( r2_hidden(c1_6_2_4__card_5,k8_ordinal2(c5_6_2__card_5))
      & ~ r2_hidden(c1_6_2_4__card_5,c1_6_2__card_5) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[dt_c1_6_2_4__card_5])],[dt_c1_6_2_4__card_5,i1_6_2_4__card_5]),
    [interesting(0.65),e17_6_2__card_5]).

fof(e17_6_2__card_5,plain,(
    r1_ordinal1(k8_ordinal2(c5_6_2__card_5),c1_6_2__card_5) ),
    inference(let,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[i1_6_2_4_tmp__card_5,cc2_ordinal1,rc1_ordinal1,cc1_card_1,cc1_ordinal1,rc1_card_1,rc1_funct_1,rc4_ordinal1,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k8_ordinal2,dt_c1_6_2__card_5,dt_c5_6_2__card_5,d3_tarski,dh_c1_6_2_4__card_5]),
    [interesting(0.65),file(card_5,e17_6_2__card_5),[file(card_5,e17_6_2__card_5)]]).

fof(t27_card_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    [interesting(0.9),axiom,file(card_1,t27_card_1)]).

fof(e18_6_2__card_5,plain,(
    r1_tarski(k1_card_1(k8_ordinal2(c5_6_2__card_5)),k1_card_1(c1_6_2__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_finset_1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,cc1_arytm_3,cc1_card_1,cc1_ordinal1,fc1_subset_1,rc1_card_1,rc1_funct_1,rc4_ordinal1,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,redefinition_r1_ordinal1,dt_k1_card_1,dt_k8_ordinal2,dt_c1_6_2__card_5,dt_c5_6_2__card_5,t3_subset,d9_ordinal2,e17_6_2__card_5,t27_card_1]),
    [interesting(0.65),file(card_5,e18_6_2__card_5),[file(card_5,e18_6_2__card_5)]]).

fof(e19_6_2__card_5,plain,(
    r1_tarski(k1_card_1(k8_ordinal2(c5_6_2__card_5)),c1_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_finset_1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc3_ordinal1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,cc1_arytm_3,cc1_ordinal1,cc2_ordinal1,fc1_subset_1,rc1_funct_1,rc1_ordinal1,rc4_ordinal1,reflexivity_r1_tarski,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k8_ordinal2,dt_c1_6_2__card_5,dt_c5_6_2__card_5,cc1_card_1,rc1_card_1,t3_subset,d9_ordinal2,e18_6_2__card_5,d5_card_1]),
    [interesting(0.65),file(card_5,e19_6_2__card_5),[file(card_5,e19_6_2__card_5)]]).

fof(e3_6_2_5_1_2__card_5,plain,
    ( r2_hidden(k1_card_1(k8_ordinal2(c5_6_2__card_5)),c1_6_2__card_5)
    & ~ v1_finset_1(k3_card_1(c4_6_2__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_5_1_2__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_nat_1,rc1_xreal_0,rc2_finset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,dt_c3_6_2__card_5,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,fc11_finseq_1,fc1_subset_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc1_subset_1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc4_funct_1,rc4_ordinal1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_xboole_0,dt_k3_card_1,dt_k8_ordinal2,dt_c1_6_2__card_5,dt_c4_6_2__card_5,dt_c5_6_2__card_5,de_c4_6_2__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_card_1,t1_subset,t3_subset,t6_boole,t7_boole,d9_ordinal2,e2_6_2_5_1_2__card_5,e16_6_2__card_5,e19_6_2__card_5,e1_6_2_5_1_2__card_5,t11_card_5,t13_card_1]),
    [interesting(0.2),file(card_5,e3_6_2_5_1_2__card_5),[file(card_5,e3_6_2_5_1_2__card_5)]]).

fof(e4_6_2_5_1_2__card_5,plain,(
    r2_hidden(k1_card_1(k8_ordinal2(c5_6_2__card_5)),c2_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5,e1_6_2_5_1_2__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_nat_1,rc1_xreal_0,existence_m1_subset_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,dt_c3_6_2__card_5,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,fc11_finseq_1,fc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc4_ordinal1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_xboole_0,dt_k3_card_1,dt_k8_ordinal2,dt_c1_6_2__card_5,dt_c2_6_2__card_5,dt_c4_6_2__card_5,dt_c5_6_2__card_5,de_c4_6_2__card_5,cc1_card_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_card_1,t1_subset,t6_boole,t7_boole,d9_ordinal2,e3_6_2_5_1_2__card_5,e5_6_2__card_5,e16_6_2__card_5,e1_6_2_5_1_2__card_5]),
    [interesting(0.2),file(card_5,e4_6_2_5_1_2__card_5),[file(card_5,e4_6_2_5_1_2__card_5)]]).

fof(e5_6_2_5_1_2__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & k1_card_1(k8_ordinal2(c5_6_2__card_5)) = k3_card_1(A)
      & k1_funct_1(c3_6_2__card_5,k1_card_1(k8_ordinal2(c5_6_2__card_5))) = A ) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_k2_relat_1,dt_k7_ordinal2,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_funct_1,dt_k1_relat_1,dt_k3_card_1,dt_k8_ordinal2,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c5_6_2__card_5,cc1_ordinal1,fc1_card_1,t1_subset,t7_boole,d9_ordinal2,e4_6_2_5_1_2__card_5,e9_6_2__card_5]),
    [interesting(0.2),file(card_5,e5_6_2_5_1_2__card_5),[file(card_5,e5_6_2_5_1_2__card_5)]]).

fof(dt_c1_6_2_5_1_2__card_5,plain,(
    v3_ordinal1(c1_6_2_5_1_2__card_5) ),
    inference(consider,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c1_6_2_5_1_2__card_5,e5_6_2_5_1_2__card_5]),
    [interesting(0.2),file(card_5,c1_6_2_5_1_2__card_5),[file(card_5,c1_6_2_5_1_2__card_5)]]).

fof(e6_6_2_5_1_2__card_5,plain,
    ( k1_card_1(k8_ordinal2(c5_6_2__card_5)) = k3_card_1(c1_6_2_5_1_2__card_5)
    & k1_funct_1(c3_6_2__card_5,k1_card_1(k8_ordinal2(c5_6_2__card_5))) = c1_6_2_5_1_2__card_5 ),
    inference(consider,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[dh_c1_6_2_5_1_2__card_5,e5_6_2_5_1_2__card_5]),
    [interesting(0.2),file(card_5,e6_6_2_5_1_2__card_5),[file(card_5,e6_6_2_5_1_2__card_5)]]).

fof(e7_6_2_5_1_2__card_5,plain,(
    c4_6_2__card_5 = c1_6_2_5_1_2__card_5 ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,t2_subset,antisymmetry_r2_hidden,cc1_xreal_0,cc3_nat_1,rc1_arytm_3,t1_subset,dt_k2_relat_1,dt_k7_ordinal2,cc15_membered,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_arytm_3,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,fc11_finseq_1,fc2_card_1,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc4_ordinal1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,dt_k1_card_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k3_card_1,dt_k8_ordinal2,dt_c1_6_2_5_1_2__card_5,dt_c3_6_2__card_5,dt_c4_6_2__card_5,dt_c5_6_2__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,t6_boole,d9_ordinal2,e16_6_2__card_5,e1_6_2_5_1_2__card_5,e6_6_2_5_1_2__card_5,t42_card_1]),
    [interesting(0.2),file(card_5,e7_6_2_5_1_2__card_5),[file(card_5,e7_6_2_5_1_2__card_5)]]).

fof(e8_6_2_5_1_2__card_5,plain,(
    r2_hidden(c4_6_2__card_5,c4_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc2_card_1,rc2_ordinal1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_k7_ordinal2,dt_m1_subset_1,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finset_1,cc1_funct_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_card_1,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_k8_ordinal2,dt_c1_6_2_5_1_2__card_5,dt_c2_6_2__card_5,dt_c3_6_2__card_5,dt_c4_6_2__card_5,dt_c5_6_2__card_5,de_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,rc1_funct_1,t1_subset,t7_boole,d9_ordinal2,e7_6_2_5_1_2__card_5,e9_6_2__card_5,e4_6_2_5_1_2__card_5,e6_6_2_5_1_2__card_5,d5_funct_1]),
    [interesting(0.2),file(card_5,e8_6_2_5_1_2__card_5),[file(card_5,e8_6_2_5_1_2__card_5)]]).

fof(e9_6_2_5_1_2__card_5,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_xreal_0,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_nat_1,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_funct_1,rc3_ordinal1,rc7_finseq_1,existence_m1_subset_1,dt_k2_relat_1,dt_m1_subset_1,dt_c3_6_2__card_5,cc15_membered,cc1_arytm_3,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_c4_6_2__card_5,de_c4_6_2__card_5,t1_subset,t7_boole,e8_6_2_5_1_2__card_5]),
    [interesting(0.2),file(card_5,e9_6_2_5_1_2__card_5),[file(card_5,e9_6_2_5_1_2__card_5)]]).

fof(i3_6_2_5_1_2__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i3_6_2_5_1_2__card_5)]),
    [interesting(0.2),trivial,file(card_5,i3_6_2_5_1_2__card_5)]).

fof(i2_6_2_5_1_2__card_5,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e2_6_2_5_1_2__card_5,e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[e9_6_2_5_1_2__card_5,i3_6_2_5_1_2__card_5]),
    [interesting(0.2),file(card_5,i2_6_2_5_1_2__card_5),[file(card_5,i2_6_2_5_1_2__card_5)]]).

fof(i1_6_2_5_1_2__card_5,plain,(
    c1_6_2__card_5 = k3_card_1(c4_6_2__card_5) ),
    inference(discharge_asm,[status(thm),assumptions([e1_6_2__card_5,e1_6_2_5_1_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e2_6_2_5_1_2__card_5])],[e2_6_2_5_1_2__card_5,i2_6_2_5_1_2__card_5]),
    [interesting(0.2),file(card_5,i1_6_2_5_1_2__card_5),[file(card_5,i1_6_2_5_1_2__card_5)]]).

fof(i2_6_2_5_1__card_5,plain,
    ( c4_6_2__card_5 != k1_xboole_0
   => ( c4_6_2__card_5 != k1_xboole_0
      & c1_6_2__card_5 = k3_card_1(c4_6_2__card_5) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2_5_1_2__card_5])],[e1_6_2_5_1_2__card_5,i1_6_2_5_1_2__card_5]),
    [interesting(0.35),file(card_5,i2_6_2_5_1__card_5),[file(card_5,i2_6_2_5_1__card_5)]]).

fof(e1_6_2_5_1__card_5,plain,(
    ~ ( c4_6_2__card_5 != k1_xboole_0
      & c4_6_2__card_5 = k1_xboole_0 ) ),
    inference(mizar_by,[status(thm),assumptions([e2_6_2__card_5,dt_c1_6_2__card_5])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,t2_subset,antisymmetry_r2_hidden,cc1_xreal_0,cc3_nat_1,rc1_arytm_3,t1_subset,dt_k2_relat_1,dt_c3_6_2__card_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,fc11_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,dt_k1_xboole_0,dt_c4_6_2__card_5,de_c4_6_2__card_5,fc2_finseq_1,fc2_ordinal1,fc6_membered,t6_boole]),
    [interesting(0.35),file(card_5,e1_6_2_5_1__card_5),[file(card_5,e1_6_2_5_1__card_5)]]).

fof(e20_6_2__card_5,plain,
    ( ( c4_6_2__card_5 = k1_xboole_0
      & c1_6_2__card_5 = k3_card_1(0) )
    | ( c4_6_2__card_5 != k1_xboole_0
      & c1_6_2__card_5 = k3_card_1(c4_6_2__card_5) ) ),
    inference(percases,[status(thm),assumptions([e3_6_2__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[i1_6_2_5_1__card_5,i2_6_2_5_1__card_5,e1_6_2_5_1__card_5]),
    [interesting(0.65),file(card_5,e20_6_2__card_5),[file(card_5,e20_6_2__card_5)]]).

fof(e21_6_2__card_5,plain,(
    c1_6_2__card_5 = k3_card_1(c4_6_2__card_5) ),
    inference(mizar_by,[status(thm),assumptions([e3_6_2__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k5_ordinal2,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_xreal_0,cc3_arytm_3,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_card_4,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_arytm_3,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_relat_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c3_6_2__card_5,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_arytm_3,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_nat_1,cc1_ordinal1,cc2_arytm_3,cc2_card_1,cc2_funct_1,cc2_membered,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc3_membered,cc3_ordinal1,cc4_membered,fc11_finseq_1,fc1_card_1,fc2_membered,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t7_boole,t8_boole,dt_k1_xboole_0,dt_k3_card_1,dt_c1_6_2__card_5,dt_c4_6_2__card_5,de_c4_6_2__card_5,fc2_finseq_1,fc2_ordinal1,fc6_membered,t6_boole,spc0_numerals,spc0_boole,e20_6_2__card_5]),
    [interesting(0.65),file(card_5,e21_6_2__card_5),[file(card_5,e21_6_2__card_5)]]).

fof(i4_6_2__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i4_6_2__card_5)]),
    [interesting(0.65),trivial,file(card_5,i4_6_2__card_5)]).

fof(i3_6_2__card_5,plain,(
    c1_6_2__card_5 = k3_card_1(c4_6_2__card_5) ),
    inference(conclusion,[status(thm),assumptions([e3_6_2__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[e21_6_2__card_5,i4_6_2__card_5]),
    [interesting(0.65),file(card_5,i3_6_2__card_5),[file(card_5,i3_6_2__card_5)]]).

fof(i2_6_2__card_5,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c1_6_2__card_5 = k3_card_1(A) ) ),
    inference(take,[status(thm),assumptions([e3_6_2__card_5,e1_6_2__card_5,e2_6_2__card_5,dt_c1_6_2__card_5])],[cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,dt_k3_card_1,dt_c1_6_2__card_5,dt_c4_6_2__card_5,cc1_ordinal1,fc1_card_1,i3_6_2__card_5]),
    [interesting(0.65),file(card_5,i2_6_2__card_5),[file(card_5,i2_6_2__card_5)]]).

fof(i1_6_2__card_5,plain,
    ( ( v2_card_1(c1_6_2__card_5)
      & ! [A] : 
          ( v1_card_1(A)
         => ( r2_hidden(A,c1_6_2__card_5)
           => ~ ( ~ v1_finset_1(A)
                & ! [B] : 
                    ( v3_ordinal1(B)
                   => A != k3_card_1(B) ) ) ) ) )
   => ( c1_6_2__card_5 = k1_xboole_0
      | ~ ( ~ v1_finset_1(c1_6_2__card_5)
          & ! [A] : 
              ( v3_ordinal1(A)
             => c1_6_2__card_5 != k3_card_1(A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2__card_5]),discharge_asm(discharge,[e1_6_2__card_5,e2_6_2__card_5,e3_6_2__card_5])],[e1_6_2__card_5,e2_6_2__card_5,e3_6_2__card_5,i2_6_2__card_5]),
    [interesting(0.65),file(card_5,i1_6_2__card_5),[file(card_5,i1_6_2__card_5)]]).

fof(i1_6_2_tmp__card_5,plain,
    ( v1_card_1(c1_6_2__card_5)
   => ( ( v2_card_1(c1_6_2__card_5)
        & ! [A] : 
            ( v1_card_1(A)
           => ( r2_hidden(A,c1_6_2__card_5)
             => ~ ( ~ v1_finset_1(A)
                  & ! [B] : 
                      ( v3_ordinal1(B)
                     => A != k3_card_1(B) ) ) ) ) )
     => ( c1_6_2__card_5 = k1_xboole_0
        | ~ ( ~ v1_finset_1(c1_6_2__card_5)
            & ! [A] : 
                ( v3_ordinal1(A)
               => c1_6_2__card_5 != k3_card_1(A) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6_2__card_5])],[dt_c1_6_2__card_5,i1_6_2__card_5]),
    [interesting(0.8),e3_6__card_5]).

fof(e3_6__card_5,plain,(
    ! [A] : 
      ( v1_card_1(A)
     => ( ( v2_card_1(A)
          & ! [B] : 
              ( v1_card_1(B)
             => ( r2_hidden(B,A)
               => ~ ( ~ v1_finset_1(B)
                    & ! [C] : 
                        ( v3_ordinal1(C)
                       => B != k3_card_1(C) ) ) ) ) )
       => ( A = k1_xboole_0
          | ~ ( ~ v1_finset_1(A)
              & ! [B] : 
                  ( v3_ordinal1(B)
                 => A != k3_card_1(B) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_2_tmp__card_5,dh_c1_6_2__card_5]),
    [interesting(0.8),file(card_5,e3_6__card_5),[file(card_5,e3_6__card_5)]]).

fof(e4_6__card_5,plain,(
    ! [A] : 
      ( v1_card_1(A)
     => ~ ( ~ v1_finset_1(A)
          & ! [B] : 
              ( v3_ordinal1(B)
             => A != k3_card_1(B) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,cc1_xreal_0,cc3_nat_1,rc1_arytm_3,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_arytm_3,cc2_funct_1,cc2_membered,cc2_ordinal1,cc3_membered,cc3_ordinal1,cc4_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_card_1,dt_k3_card_1,cc1_card_1,cc1_ordinal1,fc1_card_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_card_1,s1_card_1__e4_6__card_5,e1_6__card_5,e2_6__card_5,e3_6__card_5]),
    [interesting(0.8),file(card_5,e4_6__card_5),[file(card_5,e4_6__card_5)]]).

fof(e5_6__card_5,plain,(
    ~ ( ~ v1_finset_1(c1_6__card_5)
      & ! [A] : 
          ( v3_ordinal1(A)
         => c1_6__card_5 != k3_card_1(A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_5])],[cc2_ordinal1,rc1_ordinal1,rc2_card_1,dt_k3_card_1,dt_c1_6__card_5,cc1_card_1,cc1_ordinal1,fc1_card_1,rc1_card_1,e4_6__card_5]),
    [interesting(0.8),file(card_5,e5_6__card_5),[file(card_5,e5_6__card_5)]]).

fof(i2_6__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i2_6__card_5)]),
    [interesting(0.8),trivial,file(card_5,i2_6__card_5)]).

fof(i1_6__card_5,plain,(
    ~ ( ~ v1_finset_1(c1_6__card_5)
      & ! [A] : 
          ( v3_ordinal1(A)
         => c1_6__card_5 != k3_card_1(A) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__card_5])],[e5_6__card_5,i2_6__card_5]),
    [interesting(0.8),file(card_5,i1_6__card_5),[file(card_5,i1_6__card_5)]]).

fof(i1_6_tmp__card_5,plain,
    ( v1_card_1(c1_6__card_5)
   => ~ ( ~ v1_finset_1(c1_6__card_5)
        & ! [A] : 
            ( v3_ordinal1(A)
           => c1_6__card_5 != k3_card_1(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__card_5])],[dt_c1_6__card_5,i1_6__card_5]),
    [interesting(1),t12_card_5]).

fof(t12_card_5,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ~ ( ~ v1_finset_1(A)
          & ! [B] : 
              ( v3_ordinal1(B)
             => A != k3_card_1(B) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__card_5,dh_c1_6__card_5]),
    [interesting(1),file(card_5,t12_card_5),[file(card_5,t12_card_5)]]).