% Mizar ND problem: t8_bhsp_2,bhsp_2,249,49 
fof(dh_c1_9__bhsp_2,definition,
    ( ( ( ~ v3_struct_0(c1_9__bhsp_2)
        & v3_rlvect_1(c1_9__bhsp_2)
        & v4_rlvect_1(c1_9__bhsp_2)
        & v5_rlvect_1(c1_9__bhsp_2)
        & v6_rlvect_1(c1_9__bhsp_2)
        & v7_rlvect_1(c1_9__bhsp_2)
        & v2_bhsp_1(c1_9__bhsp_2)
        & l1_bhsp_1(c1_9__bhsp_2) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_9__bhsp_2))
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,u1_struct_0(c1_9__bhsp_2))
                & m2_relset_1(B,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
             => ( v1_bhsp_2(B,c1_9__bhsp_2)
               => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,B,A),c1_9__bhsp_2) ) ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & v3_rlvect_1(C)
          & v4_rlvect_1(C)
          & v5_rlvect_1(C)
          & v6_rlvect_1(C)
          & v7_rlvect_1(C)
          & v2_bhsp_1(C)
          & l1_bhsp_1(C) )
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(C))
           => ! [E] : 
                ( ( v1_funct_1(E)
                  & v1_funct_2(E,k5_numbers,u1_struct_0(C))
                  & m2_relset_1(E,k5_numbers,u1_struct_0(C)) )
               => ( v1_bhsp_2(E,C)
                 => v1_bhsp_2(k5_normsp_1(C,E,D),C) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_9__bhsp_2),file(bhsp_2,c1_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,c1_9__bhsp_2)]).

fof(dh_c2_9__bhsp_2,definition,
    ( ( m1_subset_1(c2_9__bhsp_2,u1_struct_0(c1_9__bhsp_2))
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,k5_numbers,u1_struct_0(c1_9__bhsp_2))
            & m2_relset_1(A,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
         => ( v1_bhsp_2(A,c1_9__bhsp_2)
           => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,A,c2_9__bhsp_2),c1_9__bhsp_2) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_9__bhsp_2))
       => ! [C] : 
            ( ( v1_funct_1(C)
              & v1_funct_2(C,k5_numbers,u1_struct_0(c1_9__bhsp_2))
              & m2_relset_1(C,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
           => ( v1_bhsp_2(C,c1_9__bhsp_2)
             => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,C,B),c1_9__bhsp_2) ) ) ) ),
    introduced(definition,[new_symbol(c2_9__bhsp_2),file(bhsp_2,c2_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,c2_9__bhsp_2)]).

fof(dh_c3_9__bhsp_2,definition,
    ( ( ( v1_funct_1(c3_9__bhsp_2)
        & v1_funct_2(c3_9__bhsp_2,k5_numbers,u1_struct_0(c1_9__bhsp_2))
        & m2_relset_1(c3_9__bhsp_2,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
     => ( v1_bhsp_2(c3_9__bhsp_2,c1_9__bhsp_2)
       => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,c3_9__bhsp_2,c2_9__bhsp_2),c1_9__bhsp_2) ) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,u1_struct_0(c1_9__bhsp_2))
          & m2_relset_1(A,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
       => ( v1_bhsp_2(A,c1_9__bhsp_2)
         => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,A,c2_9__bhsp_2),c1_9__bhsp_2) ) ) ),
    introduced(definition,[new_symbol(c3_9__bhsp_2),file(bhsp_2,c3_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,c3_9__bhsp_2)]).

fof(e1_9__bhsp_2,assumption,(
    v1_bhsp_2(c3_9__bhsp_2,c1_9__bhsp_2) ),
    introduced(assumption,[file(bhsp_2,e1_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,e1_9__bhsp_2)]).

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(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(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(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(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(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(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(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(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

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

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    [interesting(0.9),axiom,file(struct_0,l2_struct_0)]).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    [interesting(0.9),axiom,file(struct_0,l2_struct_0)]).

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

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

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(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(rc4_struct_0,theorem,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc4_struct_0)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_l2_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) ),
    file(rlvect_1,l2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(rlvect_1,l2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_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(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_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

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(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(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

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(existence_l1_bhsp_1,axiom,(
    ? [A] : l1_bhsp_1(A) ),
    file(bhsp_1,l1_bhsp_1),
    [interesting(0.9),axiom,file(bhsp_1,l1_bhsp_1)]).

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(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_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_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k5_normsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_funct_1(k5_normsp_1(A,B,C))
        & v1_funct_2(k5_normsp_1(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k5_normsp_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ),
    file(normsp_1,k5_normsp_1),
    [interesting(0.9),axiom,file(normsp_1,k5_normsp_1)]).

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_k5_rlvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ),
    file(rlvect_1,k5_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k5_rlvect_1)]).

fof(dt_k7_bhsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_funct_1(k7_bhsp_1(A,B,C))
        & v1_funct_2(k7_bhsp_1(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k7_bhsp_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ),
    file(bhsp_1,k7_bhsp_1),
    [interesting(0.9),axiom,file(bhsp_1,k7_bhsp_1)]).

fof(dt_l1_bhsp_1,axiom,(
    ! [A] : 
      ( l1_bhsp_1(A)
     => l2_rlvect_1(A) ) ),
    file(bhsp_1,l1_bhsp_1),
    [interesting(0.9),axiom,file(bhsp_1,l1_bhsp_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(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_9__bhsp_2,assumption,
    ( ~ v3_struct_0(c1_9__bhsp_2)
    & v3_rlvect_1(c1_9__bhsp_2)
    & v4_rlvect_1(c1_9__bhsp_2)
    & v5_rlvect_1(c1_9__bhsp_2)
    & v6_rlvect_1(c1_9__bhsp_2)
    & v7_rlvect_1(c1_9__bhsp_2)
    & v2_bhsp_1(c1_9__bhsp_2)
    & l1_bhsp_1(c1_9__bhsp_2) ),
    introduced(assumption,[file(bhsp_2,c1_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,c1_9__bhsp_2)]).

fof(dt_c2_9__bhsp_2,assumption,(
    m1_subset_1(c2_9__bhsp_2,u1_struct_0(c1_9__bhsp_2)) ),
    introduced(assumption,[file(bhsp_2,c2_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,c2_9__bhsp_2)]).

fof(dt_c3_9__bhsp_2,assumption,
    ( v1_funct_1(c3_9__bhsp_2)
    & v1_funct_2(c3_9__bhsp_2,k5_numbers,u1_struct_0(c1_9__bhsp_2))
    & m2_relset_1(c3_9__bhsp_2,k5_numbers,u1_struct_0(c1_9__bhsp_2)) ),
    introduced(assumption,[file(bhsp_2,c3_9__bhsp_2)]),
    [interesting(0.8),axiom,file(bhsp_2,c3_9__bhsp_2)]).

fof(t7_bhsp_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( v1_bhsp_2(C,A)
               => v1_bhsp_2(k7_bhsp_1(A,C,B),A) ) ) ) ) ),
    file(bhsp_2,t7_bhsp_2),
    [interesting(0.9),axiom,file(bhsp_2,t7_bhsp_2)]).

fof(e2_9__bhsp_2,plain,(
    v1_bhsp_2(k7_bhsp_1(c1_9__bhsp_2,c3_9__bhsp_2,k5_rlvect_1(c1_9__bhsp_2,c2_9__bhsp_2)),c1_9__bhsp_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bhsp_2,dt_c2_9__bhsp_2,dt_c3_9__bhsp_2,e1_9__bhsp_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_xreal_0,cc7_xreal_0,fc6_membered,rc1_xreal_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_membered,rc1_arytm_3,rc1_membered,rc4_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,cc1_relset_1,cc3_arytm_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc2_membered,fc5_membered,rc3_struct_0,t3_subset,existence_l1_bhsp_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_numbers,dt_k5_rlvect_1,dt_k7_bhsp_1,dt_l1_bhsp_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_9__bhsp_2,dt_c2_9__bhsp_2,dt_c3_9__bhsp_2,e1_9__bhsp_2,t7_bhsp_2]),
    [interesting(0.8),file(bhsp_2,e2_9__bhsp_2),[file(bhsp_2,e2_9__bhsp_2)]]).

fof(t78_bhsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => k5_normsp_1(A,C,B) = k7_bhsp_1(A,C,k5_rlvect_1(A,B)) ) ) ) ),
    file(bhsp_1,t78_bhsp_1),
    [interesting(0.9),axiom,file(bhsp_1,t78_bhsp_1)]).

fof(e3_9__bhsp_2,plain,(
    v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,c3_9__bhsp_2,c2_9__bhsp_2),c1_9__bhsp_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bhsp_2,dt_c2_9__bhsp_2,dt_c3_9__bhsp_2,e1_9__bhsp_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_xreal_0,cc7_xreal_0,fc6_membered,rc1_xreal_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_membered,rc1_arytm_3,rc1_membered,rc4_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,cc1_relset_1,cc3_arytm_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc2_membered,fc5_membered,rc3_struct_0,t3_subset,existence_l1_bhsp_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_normsp_1,dt_k5_numbers,dt_k5_rlvect_1,dt_k7_bhsp_1,dt_l1_bhsp_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_9__bhsp_2,dt_c2_9__bhsp_2,dt_c3_9__bhsp_2,e2_9__bhsp_2,t78_bhsp_1]),
    [interesting(0.8),file(bhsp_2,e3_9__bhsp_2),[file(bhsp_2,e3_9__bhsp_2)]]).

fof(i5_9__bhsp_2,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_2,i5_9__bhsp_2)]),
    [interesting(0.8),trivial,file(bhsp_2,i5_9__bhsp_2)]).

fof(i4_9__bhsp_2,plain,(
    v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,c3_9__bhsp_2,c2_9__bhsp_2),c1_9__bhsp_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__bhsp_2,dt_c2_9__bhsp_2,dt_c3_9__bhsp_2,e1_9__bhsp_2])],[e3_9__bhsp_2,i5_9__bhsp_2]),
    [interesting(0.8),file(bhsp_2,i4_9__bhsp_2),[file(bhsp_2,i4_9__bhsp_2)]]).

fof(i3_9__bhsp_2,plain,
    ( v1_bhsp_2(c3_9__bhsp_2,c1_9__bhsp_2)
   => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,c3_9__bhsp_2,c2_9__bhsp_2),c1_9__bhsp_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__bhsp_2,dt_c2_9__bhsp_2,dt_c3_9__bhsp_2]),discharge_asm(discharge,[e1_9__bhsp_2])],[e1_9__bhsp_2,i4_9__bhsp_2]),
    [interesting(0.8),file(bhsp_2,i3_9__bhsp_2),[file(bhsp_2,i3_9__bhsp_2)]]).

fof(i3_9_tmp__bhsp_2,plain,
    ( ( v1_funct_1(c3_9__bhsp_2)
      & v1_funct_2(c3_9__bhsp_2,k5_numbers,u1_struct_0(c1_9__bhsp_2))
      & m2_relset_1(c3_9__bhsp_2,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
   => ( v1_bhsp_2(c3_9__bhsp_2,c1_9__bhsp_2)
     => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,c3_9__bhsp_2,c2_9__bhsp_2),c1_9__bhsp_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__bhsp_2,dt_c2_9__bhsp_2]),discharge_asm(discharge,[dt_c3_9__bhsp_2])],[dt_c3_9__bhsp_2,i3_9__bhsp_2]),
    [interesting(0.8),i2_9__bhsp_2]).

fof(i2_9__bhsp_2,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,u1_struct_0(c1_9__bhsp_2))
        & m2_relset_1(A,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
     => ( v1_bhsp_2(A,c1_9__bhsp_2)
       => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,A,c2_9__bhsp_2),c1_9__bhsp_2) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__bhsp_2,dt_c2_9__bhsp_2])],[i3_9_tmp__bhsp_2,dh_c3_9__bhsp_2]),
    [interesting(0.8),file(bhsp_2,i2_9__bhsp_2),[file(bhsp_2,i2_9__bhsp_2)]]).

fof(i2_9_tmp__bhsp_2,plain,
    ( m1_subset_1(c2_9__bhsp_2,u1_struct_0(c1_9__bhsp_2))
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,u1_struct_0(c1_9__bhsp_2))
          & m2_relset_1(A,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
       => ( v1_bhsp_2(A,c1_9__bhsp_2)
         => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,A,c2_9__bhsp_2),c1_9__bhsp_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__bhsp_2]),discharge_asm(discharge,[dt_c2_9__bhsp_2])],[dt_c2_9__bhsp_2,i2_9__bhsp_2]),
    [interesting(0.8),i1_9__bhsp_2]).

fof(i1_9__bhsp_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_9__bhsp_2))
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(c1_9__bhsp_2))
            & m2_relset_1(B,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
         => ( v1_bhsp_2(B,c1_9__bhsp_2)
           => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,B,A),c1_9__bhsp_2) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__bhsp_2])],[i2_9_tmp__bhsp_2,dh_c2_9__bhsp_2]),
    [interesting(0.8),file(bhsp_2,i1_9__bhsp_2),[file(bhsp_2,i1_9__bhsp_2)]]).

fof(i1_9_tmp__bhsp_2,plain,
    ( ( ~ v3_struct_0(c1_9__bhsp_2)
      & v3_rlvect_1(c1_9__bhsp_2)
      & v4_rlvect_1(c1_9__bhsp_2)
      & v5_rlvect_1(c1_9__bhsp_2)
      & v6_rlvect_1(c1_9__bhsp_2)
      & v7_rlvect_1(c1_9__bhsp_2)
      & v2_bhsp_1(c1_9__bhsp_2)
      & l1_bhsp_1(c1_9__bhsp_2) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_9__bhsp_2))
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,u1_struct_0(c1_9__bhsp_2))
              & m2_relset_1(B,k5_numbers,u1_struct_0(c1_9__bhsp_2)) )
           => ( v1_bhsp_2(B,c1_9__bhsp_2)
             => v1_bhsp_2(k5_normsp_1(c1_9__bhsp_2,B,A),c1_9__bhsp_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_9__bhsp_2])],[dt_c1_9__bhsp_2,i1_9__bhsp_2]),
    [interesting(1),t8_bhsp_2]).

fof(t8_bhsp_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( v1_bhsp_2(C,A)
               => v1_bhsp_2(k5_normsp_1(A,C,B),A) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_9_tmp__bhsp_2,dh_c1_9__bhsp_2]),
    [interesting(1),file(bhsp_2,t8_bhsp_2),[file(bhsp_2,t8_bhsp_2)]]).