% Mizar ND problem: t1_bhsp_5,bhsp_5,41,44 
fof(dh_c1_1__bhsp_5,definition,
    ( ! [A] : 
        ( m2_finseq_1(A,c1_1__bhsp_5)
       => ! [B] : 
            ( m2_finseq_1(B,c1_1__bhsp_5)
           => ( ( v2_funct_1(A)
                & v2_funct_1(B)
                & k2_relat_1(A) = k2_relat_1(B) )
             => ( k5_finsop_1(A) = k5_finsop_1(B)
                & ? [C] : 
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k5_finsop_1(A),k5_finsop_1(A))
                    & v3_funct_2(C,k5_finsop_1(A),k5_finsop_1(A))
                    & m2_relset_1(C,k5_finsop_1(A),k5_finsop_1(A))
                    & B = k5_relat_1(C,A)
                    & k1_relat_1(C) = k5_finsop_1(A)
                    & k2_relat_1(C) = k5_finsop_1(A) ) ) ) ) )
   => ! [D,E] : 
        ( m2_finseq_1(E,D)
       => ! [F] : 
            ( m2_finseq_1(F,D)
           => ( ( v2_funct_1(E)
                & v2_funct_1(F)
                & k2_relat_1(E) = k2_relat_1(F) )
             => ( k5_finsop_1(E) = k5_finsop_1(F)
                & ? [G] : 
                    ( v1_funct_1(G)
                    & v1_funct_2(G,k5_finsop_1(E),k5_finsop_1(E))
                    & v3_funct_2(G,k5_finsop_1(E),k5_finsop_1(E))
                    & m2_relset_1(G,k5_finsop_1(E),k5_finsop_1(E))
                    & F = k5_relat_1(G,E)
                    & k1_relat_1(G) = k5_finsop_1(E)
                    & k2_relat_1(G) = k5_finsop_1(E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__bhsp_5),file(bhsp_5,c1_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,c1_1__bhsp_5)]).

fof(dh_c2_1__bhsp_5,definition,
    ( ( m2_finseq_1(c2_1__bhsp_5,c1_1__bhsp_5)
     => ! [A] : 
          ( m2_finseq_1(A,c1_1__bhsp_5)
         => ( ( v2_funct_1(c2_1__bhsp_5)
              & v2_funct_1(A)
              & k2_relat_1(c2_1__bhsp_5) = k2_relat_1(A) )
           => ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(A)
              & ? [B] : 
                  ( v1_funct_1(B)
                  & v1_funct_2(B,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
                  & v3_funct_2(B,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
                  & m2_relset_1(B,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
                  & A = k5_relat_1(B,c2_1__bhsp_5)
                  & k1_relat_1(B) = k5_finsop_1(c2_1__bhsp_5)
                  & k2_relat_1(B) = k5_finsop_1(c2_1__bhsp_5) ) ) ) ) )
   => ! [C] : 
        ( m2_finseq_1(C,c1_1__bhsp_5)
       => ! [D] : 
            ( m2_finseq_1(D,c1_1__bhsp_5)
           => ( ( v2_funct_1(C)
                & v2_funct_1(D)
                & k2_relat_1(C) = k2_relat_1(D) )
             => ( k5_finsop_1(C) = k5_finsop_1(D)
                & ? [E] : 
                    ( v1_funct_1(E)
                    & v1_funct_2(E,k5_finsop_1(C),k5_finsop_1(C))
                    & v3_funct_2(E,k5_finsop_1(C),k5_finsop_1(C))
                    & m2_relset_1(E,k5_finsop_1(C),k5_finsop_1(C))
                    & D = k5_relat_1(E,C)
                    & k1_relat_1(E) = k5_finsop_1(C)
                    & k2_relat_1(E) = k5_finsop_1(C) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__bhsp_5),file(bhsp_5,c2_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,c2_1__bhsp_5)]).

fof(dh_c3_1__bhsp_5,definition,
    ( ( m2_finseq_1(c3_1__bhsp_5,c1_1__bhsp_5)
     => ( ( v2_funct_1(c2_1__bhsp_5)
          & v2_funct_1(c3_1__bhsp_5)
          & k2_relat_1(c2_1__bhsp_5) = k2_relat_1(c3_1__bhsp_5) )
       => ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5)
          & ? [A] : 
              ( v1_funct_1(A)
              & v1_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
              & v3_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
              & m2_relset_1(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
              & c3_1__bhsp_5 = k5_relat_1(A,c2_1__bhsp_5)
              & k1_relat_1(A) = k5_finsop_1(c2_1__bhsp_5)
              & k2_relat_1(A) = k5_finsop_1(c2_1__bhsp_5) ) ) ) )
   => ! [B] : 
        ( m2_finseq_1(B,c1_1__bhsp_5)
       => ( ( v2_funct_1(c2_1__bhsp_5)
            & v2_funct_1(B)
            & k2_relat_1(c2_1__bhsp_5) = k2_relat_1(B) )
         => ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(B)
            & ? [C] : 
                ( v1_funct_1(C)
                & v1_funct_2(C,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
                & v3_funct_2(C,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
                & m2_relset_1(C,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
                & B = k5_relat_1(C,c2_1__bhsp_5)
                & k1_relat_1(C) = k5_finsop_1(c2_1__bhsp_5)
                & k2_relat_1(C) = k5_finsop_1(c2_1__bhsp_5) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_1__bhsp_5),file(bhsp_5,c3_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,c3_1__bhsp_5)]).

fof(cc1_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

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_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(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(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

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_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_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(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(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_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(rc4_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc4_finseq_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(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(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

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

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_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(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_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_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(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc3_funct_2)]).

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(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(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(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]).

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(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(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(rc2_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]).

fof(rc2_funct_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc2_funct_2)]).

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

fof(redefinition_m2_finseq_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,k5_finsub_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_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(dt_c1_1__bhsp_5,assumption,(
    $true ),
    introduced(assumption,[file(bhsp_5,c1_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,c1_1__bhsp_5)]).

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_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(cc2_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc2_funct_2)]).

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_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

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_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_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

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(redefinition_k5_finsop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k5_finsop_1(A) = k1_relat_1(A) ) ),
    file(finsop_1,k5_finsop_1),
    [interesting(0.9),axiom,file(finsop_1,k5_finsop_1)]).

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_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

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

fof(dt_k5_finsop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k5_finsop_1(A),k5_finsub_1(k5_numbers)) ) ),
    file(finsop_1,k5_finsop_1),
    [interesting(0.9),axiom,file(finsop_1,k5_finsop_1)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_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_c2_1__bhsp_5,assumption,(
    m2_finseq_1(c2_1__bhsp_5,c1_1__bhsp_5) ),
    introduced(assumption,[file(bhsp_5,c2_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,c2_1__bhsp_5)]).

fof(dt_c3_1__bhsp_5,assumption,(
    m2_finseq_1(c3_1__bhsp_5,c1_1__bhsp_5) ),
    introduced(assumption,[file(bhsp_5,c3_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,c3_1__bhsp_5)]).

fof(e1_1__bhsp_5,assumption,(
    v2_funct_1(c2_1__bhsp_5) ),
    introduced(assumption,[file(bhsp_5,e1_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,e1_1__bhsp_5)]).

fof(e2_1__bhsp_5,assumption,(
    v2_funct_1(c3_1__bhsp_5) ),
    introduced(assumption,[file(bhsp_5,e2_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,e2_1__bhsp_5)]).

fof(e3_1__bhsp_5,assumption,(
    k2_relat_1(c2_1__bhsp_5) = k2_relat_1(c3_1__bhsp_5) ),
    introduced(assumption,[file(bhsp_5,e3_1__bhsp_5)]),
    [interesting(0.8),axiom,file(bhsp_5,e3_1__bhsp_5)]).

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

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_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(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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

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_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(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    [interesting(0.9),axiom,file(funct_1,k2_funct_1)]).

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

fof(dh_c1_1_4__bhsp_5,definition,
    ( ( r2_hidden(c1_1_4__bhsp_5,k5_finsop_1(c3_1__bhsp_5))
     => k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) )
   => ! [A] : 
        ( r2_hidden(A,k5_finsop_1(c3_1__bhsp_5))
       => k1_funct_1(c3_1__bhsp_5,A) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),A) ) ),
    introduced(definition,[new_symbol(c1_1_4__bhsp_5),file(bhsp_5,c1_1_4__bhsp_5)]),
    [interesting(0.65),axiom,file(bhsp_5,c1_1_4__bhsp_5)]).

fof(e1_1_4__bhsp_5,assumption,(
    r2_hidden(c1_1_4__bhsp_5,k5_finsop_1(c3_1__bhsp_5)) ),
    introduced(assumption,[file(bhsp_5,e1_1_4__bhsp_5)]),
    [interesting(0.65),axiom,file(bhsp_5,e1_1_4__bhsp_5)]).

fof(dt_c1_1_4__bhsp_5,assumption,(
    $true ),
    introduced(assumption,[file(bhsp_5,c1_1_4__bhsp_5)]),
    [interesting(0.65),axiom,file(bhsp_5,c1_1_4__bhsp_5)]).

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_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]).

fof(fc1_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]).

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_k2_finseq_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(redefinition_k3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

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_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

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(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_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(t77_finseq_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v2_funct_1(A)
      <=> k4_card_1(k2_relat_1(A)) = k3_finseq_1(A) ) ) ),
    file(finseq_4,t77_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,t77_finseq_4)]).

fof(e1_1_1_1__bhsp_5,plain,(
    k3_finseq_1(c2_1__bhsp_5) = k4_card_1(k2_relat_1(c3_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5])],[rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,fc14_finset_1,fc2_finseq_1,fc6_membered,rc1_membered,rc2_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_1__bhsp_5,fc11_finseq_1,fc2_membered,redefinition_k3_finseq_1,redefinition_k4_card_1,dt_k2_relat_1,dt_k3_finseq_1,dt_k4_card_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,rc3_funct_1,e1_1__bhsp_5,e3_1__bhsp_5,t77_finseq_4]),
    [interesting(0.5),file(bhsp_5,e1_1_1_1__bhsp_5),[file(bhsp_5,e1_1_1_1__bhsp_5)]]).

fof(e2_1_1_1__bhsp_5,plain,(
    k4_card_1(k2_relat_1(c3_1__bhsp_5)) = k3_finseq_1(c3_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c3_1__bhsp_5,e2_1__bhsp_5])],[rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,fc14_finset_1,fc2_finseq_1,fc6_membered,rc1_membered,rc2_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_1__bhsp_5,fc11_finseq_1,fc2_membered,redefinition_k3_finseq_1,redefinition_k4_card_1,dt_k2_relat_1,dt_k3_finseq_1,dt_k4_card_1,dt_c3_1__bhsp_5,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,rc3_funct_1,e2_1__bhsp_5,t77_finseq_4]),
    [interesting(0.5),file(bhsp_5,e2_1_1_1__bhsp_5),[file(bhsp_5,e2_1_1_1__bhsp_5)]]).

fof(e1_1_1__bhsp_5,plain,(
    k3_finseq_1(c2_1__bhsp_5) = k3_finseq_1(c3_1__bhsp_5) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5,e2_1__bhsp_5])],[rc2_finset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,fc14_finset_1,rc1_membered,rc2_finseq_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_finset_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_1__bhsp_5,cc1_finseq_1,fc11_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,redefinition_k3_finseq_1,redefinition_k4_card_1,dt_k2_relat_1,dt_k3_finseq_1,dt_k4_card_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_1_1__bhsp_5,e2_1_1_1__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e1_1_1__bhsp_5),[file(bhsp_5,e1_1_1__bhsp_5)]]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,d3_finseq_1)]).

fof(e1_1_1_2__bhsp_5,plain,(
    k5_finsop_1(c2_1__bhsp_5) = k2_finseq_1(k3_finseq_1(c3_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5,e2_1__bhsp_5])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,fc5_membered,rc1_finset_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k5_finsop_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k5_finsop_1,dt_k5_numbers,dt_m2_subset_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,e1_1_1__bhsp_5,d3_finseq_1]),
    [interesting(0.5),file(bhsp_5,e1_1_1_2__bhsp_5),[file(bhsp_5,e1_1_1_2__bhsp_5)]]).

fof(e2_1_1_2__bhsp_5,plain,(
    k2_finseq_1(k3_finseq_1(c3_1__bhsp_5)) = k5_finsop_1(c3_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c3_1__bhsp_5])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,fc5_membered,rc1_finset_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k5_finsop_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k5_finsop_1,dt_k5_numbers,dt_m2_subset_1,dt_c3_1__bhsp_5,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,d3_finseq_1]),
    [interesting(0.5),file(bhsp_5,e2_1_1_2__bhsp_5),[file(bhsp_5,e2_1_1_2__bhsp_5)]]).

fof(e2_1_1__bhsp_5,plain,(
    k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,e2_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5])],[e1_1_1_2__bhsp_5,e2_1_1_2__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e2_1_1__bhsp_5),[file(bhsp_5,e2_1_1__bhsp_5)]]).

fof(e3_1_1__bhsp_5,plain,(
    k5_finsop_1(c3_1__bhsp_5) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,e2_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,t3_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,redefinition_k5_finsop_1,dt_k5_finsop_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e2_1_1__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e3_1_1__bhsp_5),[file(bhsp_5,e3_1_1__bhsp_5)]]).

fof(i1_1_1__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i1_1_1__bhsp_5)]),
    [interesting(0.65),trivial,file(bhsp_5,i1_1_1__bhsp_5)]).

fof(e4_1__bhsp_5,plain,(
    k5_finsop_1(c3_1__bhsp_5) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,e2_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5])],[e3_1_1__bhsp_5,i1_1_1__bhsp_5]),
    [interesting(0.8),file(bhsp_5,e4_1__bhsp_5),[file(bhsp_5,e4_1__bhsp_5)]]).

fof(dt_c1_1_2_3__bhsp_5,assumption,(
    $true ),
    introduced(assumption,[file(bhsp_5,c1_1_2_3__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c1_1_2_3__bhsp_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_1_2_3__bhsp_5,definition,
    ( ~ ( r2_hidden(c1_1_2_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5))
        & ~ r2_hidden(c1_1_2_3__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k5_finsop_1(c2_1__bhsp_5))
          & ~ r2_hidden(A,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ) ),
    introduced(definition,[new_symbol(c1_1_2_3__bhsp_5),file(bhsp_5,c1_1_2_3__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c1_1_2_3__bhsp_5)]).

fof(e1_1_2_3__bhsp_5,assumption,(
    r2_hidden(c1_1_2_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ),
    introduced(assumption,[file(bhsp_5,e1_1_2_3__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,e1_1_2_3__bhsp_5)]).

fof(dh_c3_1_2_3__bhsp_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,k5_finsop_1(c3_1__bhsp_5))
        & c2_1_2_3__bhsp_5 = k1_funct_1(c3_1__bhsp_5,A) )
   => ( r2_hidden(c3_1_2_3__bhsp_5,k5_finsop_1(c3_1__bhsp_5))
      & c2_1_2_3__bhsp_5 = k1_funct_1(c3_1__bhsp_5,c3_1_2_3__bhsp_5) ) ),
    introduced(definition,[new_symbol(c3_1_2_3__bhsp_5),file(bhsp_5,c3_1_2_3__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c3_1_2_3__bhsp_5)]).

fof(dh_c2_1_2_3__bhsp_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funct_1(c2_1__bhsp_5)))
        & c1_1_2_3__bhsp_5 = k1_funct_1(k2_funct_1(c2_1__bhsp_5),A) )
   => ( r2_hidden(c2_1_2_3__bhsp_5,k1_relat_1(k2_funct_1(c2_1__bhsp_5)))
      & c1_1_2_3__bhsp_5 = k1_funct_1(k2_funct_1(c2_1__bhsp_5),c2_1_2_3__bhsp_5) ) ),
    introduced(definition,[new_symbol(c2_1_2_3__bhsp_5),file(bhsp_5,c2_1_2_3__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c2_1_2_3__bhsp_5)]).

fof(t55_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    file(funct_1,t55_funct_1),
    [interesting(0.9),axiom,file(funct_1,t55_funct_1)]).

fof(e2_1_2_3__bhsp_5,plain,(
    r2_hidden(c1_1_2_3__bhsp_5,k2_relat_1(k2_funct_1(c2_1__bhsp_5))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_1_2_3__bhsp_5,e1_1__bhsp_5,t55_funct_1]),
    [interesting(0.5),file(bhsp_5,e2_1_2_3__bhsp_5),[file(bhsp_5,e2_1_2_3__bhsp_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(e3_1_2_3__bhsp_5,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(k2_funct_1(c2_1__bhsp_5)))
      & c1_1_2_3__bhsp_5 = k1_funct_1(k2_funct_1(c2_1__bhsp_5),A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,rc2_finset_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc3_finset_1,rc4_finset_1,rc4_funct_1,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,rc1_funct_1,t1_subset,t7_boole,e2_1_2_3__bhsp_5,d5_funct_1]),
    [interesting(0.5),file(bhsp_5,e3_1_2_3__bhsp_5),[file(bhsp_5,e3_1_2_3__bhsp_5)]]).

fof(dt_c2_1_2_3__bhsp_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[dh_c2_1_2_3__bhsp_5,e3_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,c2_1_2_3__bhsp_5),[file(bhsp_5,c2_1_2_3__bhsp_5)]]).

fof(e4_1_2_3__bhsp_5,plain,(
    r2_hidden(c2_1_2_3__bhsp_5,k1_relat_1(k2_funct_1(c2_1__bhsp_5))) ),
    inference(consider,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[dh_c2_1_2_3__bhsp_5,e3_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,e4_1_2_3__bhsp_5),[file(bhsp_5,e4_1_2_3__bhsp_5)]]).

fof(e6_1_2_3__bhsp_5,plain,(
    r2_hidden(c2_1_2_3__bhsp_5,k2_relat_1(c3_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,rc2_finset_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc3_finset_1,rc4_finset_1,rc4_funct_1,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_c2_1__bhsp_5,dt_c2_1_2_3__bhsp_5,dt_c3_1__bhsp_5,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_1__bhsp_5,e3_1__bhsp_5,e4_1_2_3__bhsp_5,t55_funct_1]),
    [interesting(0.5),file(bhsp_5,e6_1_2_3__bhsp_5),[file(bhsp_5,e6_1_2_3__bhsp_5)]]).

fof(e7_1_2_3__bhsp_5,plain,(
    ? [A] : 
      ( r2_hidden(A,k5_finsop_1(c3_1__bhsp_5))
      & c2_1_2_3__bhsp_5 = k1_funct_1(c3_1__bhsp_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_finsop_1,dt_c2_1_2_3__bhsp_5,dt_c3_1__bhsp_5,rc1_funct_1,t1_subset,t7_boole,e6_1_2_3__bhsp_5,d5_funct_1]),
    [interesting(0.5),file(bhsp_5,e7_1_2_3__bhsp_5),[file(bhsp_5,e7_1_2_3__bhsp_5)]]).

fof(dt_c3_1_2_3__bhsp_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[dh_c3_1_2_3__bhsp_5,e7_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,c3_1_2_3__bhsp_5),[file(bhsp_5,c3_1_2_3__bhsp_5)]]).

fof(e5_1_2_3__bhsp_5,plain,(
    c1_1_2_3__bhsp_5 = k1_funct_1(k2_funct_1(c2_1__bhsp_5),c2_1_2_3__bhsp_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[dh_c2_1_2_3__bhsp_5,e3_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,e5_1_2_3__bhsp_5),[file(bhsp_5,e5_1_2_3__bhsp_5)]]).

fof(e8_1_2_3__bhsp_5,plain,(
    r2_hidden(c3_1_2_3__bhsp_5,k5_finsop_1(c3_1__bhsp_5)) ),
    inference(consider,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[dh_c3_1_2_3__bhsp_5,e7_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,e8_1_2_3__bhsp_5),[file(bhsp_5,e8_1_2_3__bhsp_5)]]).

fof(e9_1_2_3__bhsp_5,plain,(
    c2_1_2_3__bhsp_5 = k1_funct_1(c3_1__bhsp_5,c3_1_2_3__bhsp_5) ),
    inference(consider,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[dh_c3_1_2_3__bhsp_5,e7_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,e9_1_2_3__bhsp_5),[file(bhsp_5,e9_1_2_3__bhsp_5)]]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.9),axiom,file(funct_1,t23_funct_1)]).

fof(e10_1_2_3__bhsp_5,plain,(
    c1_1_2_3__bhsp_5 = k1_funct_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c3_1_2_3__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,dt_c2_1_2_3__bhsp_5,dt_c3_1__bhsp_5,dt_c3_1_2_3__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e5_1_2_3__bhsp_5,e8_1_2_3__bhsp_5,e9_1_2_3__bhsp_5,t23_funct_1]),
    [interesting(0.5),file(bhsp_5,e10_1_2_3__bhsp_5),[file(bhsp_5,e10_1_2_3__bhsp_5)]]).

fof(dh_c1_1_2_1__bhsp_5,definition,
    ( ( r2_hidden(c1_1_2_1__bhsp_5,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
    <=> r2_hidden(c1_1_2_1__bhsp_5,k5_finsop_1(c3_1__bhsp_5)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
      <=> r2_hidden(A,k5_finsop_1(c3_1__bhsp_5)) ) ),
    introduced(definition,[new_symbol(c1_1_2_1__bhsp_5),file(bhsp_5,c1_1_2_1__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c1_1_2_1__bhsp_5)]).

fof(dt_c1_1_2_1__bhsp_5,assumption,(
    $true ),
    introduced(assumption,[file(bhsp_5,c1_1_2_1__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c1_1_2_1__bhsp_5)]).

fof(e1_1_2_1__bhsp_5,plain,
    ( k1_relat_1(k2_funct_1(c2_1__bhsp_5)) = k2_relat_1(c2_1__bhsp_5)
    & k2_relat_1(k2_funct_1(c2_1__bhsp_5)) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,rc2_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,t3_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,rc1_finseq_1,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_c2_1__bhsp_5,rc1_funct_1,rc3_funct_1,e1_1__bhsp_5,t55_funct_1]),
    [interesting(0.5),file(bhsp_5,e1_1_2_1__bhsp_5),[file(bhsp_5,e1_1_2_1__bhsp_5)]]).

fof(t12_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ),
    file(funct_1,t12_funct_1),
    [interesting(0.9),axiom,file(funct_1,t12_funct_1)]).

fof(e2_1_2_1__bhsp_5,plain,
    ( r2_hidden(c1_1_2_1__bhsp_5,k5_finsop_1(c3_1__bhsp_5))
   => r2_hidden(k1_funct_1(c3_1__bhsp_5,c1_1_2_1__bhsp_5),k1_relat_1(k2_funct_1(c2_1__bhsp_5))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_2_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_c1_1_2_1__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,rc1_funct_1,t1_subset,t7_boole,e1_1_2_1__bhsp_5,e3_1__bhsp_5,t12_funct_1]),
    [interesting(0.5),file(bhsp_5,e2_1_2_1__bhsp_5),[file(bhsp_5,e2_1_2_1__bhsp_5)]]).

fof(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [interesting(0.9),axiom,file(funct_1,t21_funct_1)]).

fof(e3_1_2_1__bhsp_5,plain,
    ( r2_hidden(c1_1_2_1__bhsp_5,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
  <=> r2_hidden(c1_1_2_1__bhsp_5,k5_finsop_1(c3_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_2_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_2_1__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e2_1_2_1__bhsp_5,t21_funct_1]),
    [interesting(0.5),file(bhsp_5,e3_1_2_1__bhsp_5),[file(bhsp_5,e3_1_2_1__bhsp_5)]]).

fof(i2_1_2_1__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i2_1_2_1__bhsp_5)]),
    [interesting(0.5),trivial,file(bhsp_5,i2_1_2_1__bhsp_5)]).

fof(i1_1_2_1__bhsp_5,plain,
    ( r2_hidden(c1_1_2_1__bhsp_5,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
  <=> r2_hidden(c1_1_2_1__bhsp_5,k5_finsop_1(c3_1__bhsp_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_2_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5])],[rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_2_1__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e3_1_2_1__bhsp_5,i2_1_2_1__bhsp_5]),
    [interesting(0.5),file(bhsp_5,i1_1_2_1__bhsp_5),[file(bhsp_5,i1_1_2_1__bhsp_5)]]).

fof(i1_1_2_1_tmp__bhsp_5,plain,
    ( r2_hidden(c1_1_2_1__bhsp_5,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
  <=> r2_hidden(c1_1_2_1__bhsp_5,k5_finsop_1(c3_1__bhsp_5)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5]),discharge_asm(discharge,[dt_c1_1_2_1__bhsp_5])],[dt_c1_1_2_1__bhsp_5,i1_1_2_1__bhsp_5]),
    [interesting(0.65),e1_1_2__bhsp_5]).

fof(e1_1_2__bhsp_5,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
    <=> r2_hidden(A,k5_finsop_1(c3_1__bhsp_5)) ) ),
    inference(let,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5])],[i1_1_2_1_tmp__bhsp_5,dh_c1_1_2_1__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e1_1_2__bhsp_5),[file(bhsp_5,e1_1_2__bhsp_5)]]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(e2_1_2__bhsp_5,plain,(
    k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))) = k5_finsop_1(c3_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,t1_subset,t7_boole,e1_1_2__bhsp_5,t2_tarski]),
    [interesting(0.65),file(bhsp_5,e2_1_2__bhsp_5),[file(bhsp_5,e2_1_2__bhsp_5)]]).

fof(e11_1_2_3__bhsp_5,plain,(
    r2_hidden(c1_1_2_3__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,dt_c3_1_2_3__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e10_1_2_3__bhsp_5,e2_1_2__bhsp_5,e8_1_2_3__bhsp_5,d5_funct_1]),
    [interesting(0.5),file(bhsp_5,e11_1_2_3__bhsp_5),[file(bhsp_5,e11_1_2_3__bhsp_5)]]).

fof(i3_1_2_3__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i3_1_2_3__bhsp_5)]),
    [interesting(0.5),trivial,file(bhsp_5,i3_1_2_3__bhsp_5)]).

fof(i2_1_2_3__bhsp_5,plain,(
    r2_hidden(c1_1_2_3__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1_2_3__bhsp_5,e1_1__bhsp_5])],[e11_1_2_3__bhsp_5,i3_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,i2_1_2_3__bhsp_5),[file(bhsp_5,i2_1_2_3__bhsp_5)]]).

fof(i1_1_2_3__bhsp_5,plain,(
    ~ ( r2_hidden(c1_1_2_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5))
      & ~ r2_hidden(c1_1_2_3__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_2_3__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5]),discharge_asm(discharge,[e1_1_2_3__bhsp_5])],[e1_1_2_3__bhsp_5,i2_1_2_3__bhsp_5]),
    [interesting(0.5),file(bhsp_5,i1_1_2_3__bhsp_5),[file(bhsp_5,i1_1_2_3__bhsp_5)]]).

fof(i1_1_2_3_tmp__bhsp_5,plain,(
    ~ ( r2_hidden(c1_1_2_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5))
      & ~ r2_hidden(c1_1_2_3__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5]),discharge_asm(discharge,[dt_c1_1_2_3__bhsp_5])],[dt_c1_1_2_3__bhsp_5,i1_1_2_3__bhsp_5]),
    [interesting(0.65),e5_1_2__bhsp_5]).

fof(e5_1_2__bhsp_5,plain,(
    r1_tarski(k5_finsop_1(c2_1__bhsp_5),k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ),
    inference(let,[status(thm),assumptions([dt_c3_1__bhsp_5,e3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[i1_1_2_3_tmp__bhsp_5,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,d3_tarski,dh_c1_1_2_3__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e5_1_2__bhsp_5),[file(bhsp_5,e5_1_2__bhsp_5)]]).

fof(dt_c1_1_2_2__bhsp_5,assumption,(
    $true ),
    introduced(assumption,[file(bhsp_5,c1_1_2_2__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c1_1_2_2__bhsp_5)]).

fof(dh_c1_1_2_2__bhsp_5,definition,
    ( ~ ( r2_hidden(c1_1_2_2__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
        & ~ r2_hidden(c1_1_2_2__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
          & ~ r2_hidden(A,k5_finsop_1(c2_1__bhsp_5)) ) ),
    introduced(definition,[new_symbol(c1_1_2_2__bhsp_5),file(bhsp_5,c1_1_2_2__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,c1_1_2_2__bhsp_5)]).

fof(e1_1_2_2__bhsp_5,assumption,(
    r2_hidden(c1_1_2_2__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))) ),
    introduced(assumption,[file(bhsp_5,e1_1_2_2__bhsp_5)]),
    [interesting(0.5),axiom,file(bhsp_5,e1_1_2_2__bhsp_5)]).

fof(e3_1_2__bhsp_5,plain,
    ( k1_relat_1(k2_funct_1(c2_1__bhsp_5)) = k2_relat_1(c2_1__bhsp_5)
    & k2_relat_1(k2_funct_1(c2_1__bhsp_5)) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,rc2_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,t3_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,rc1_finseq_1,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_c2_1__bhsp_5,rc1_funct_1,rc3_funct_1,e1_1__bhsp_5,t55_funct_1]),
    [interesting(0.65),file(bhsp_5,e3_1_2__bhsp_5),[file(bhsp_5,e3_1_2__bhsp_5)]]).

fof(t25_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k2_relat_1(k5_relat_1(C,B)))
           => r2_hidden(A,k2_relat_1(B)) ) ) ) ),
    file(funct_1,t25_funct_1),
    [interesting(0.9),axiom,file(funct_1,t25_funct_1)]).

fof(e2_1_2_2__bhsp_5,plain,(
    r2_hidden(c1_1_2_2__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_2_2__bhsp_5,dt_c3_1__bhsp_5,e1_1_2_2__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_2_2__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e1_1_2_2__bhsp_5,e3_1_2__bhsp_5,t25_funct_1]),
    [interesting(0.5),file(bhsp_5,e2_1_2_2__bhsp_5),[file(bhsp_5,e2_1_2_2__bhsp_5)]]).

fof(i3_1_2_2__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i3_1_2_2__bhsp_5)]),
    [interesting(0.5),trivial,file(bhsp_5,i3_1_2_2__bhsp_5)]).

fof(i2_1_2_2__bhsp_5,plain,(
    r2_hidden(c1_1_2_2__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_2_2__bhsp_5,dt_c3_1__bhsp_5,e1_1_2_2__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[e2_1_2_2__bhsp_5,i3_1_2_2__bhsp_5]),
    [interesting(0.5),file(bhsp_5,i2_1_2_2__bhsp_5),[file(bhsp_5,i2_1_2_2__bhsp_5)]]).

fof(i1_1_2_2__bhsp_5,plain,(
    ~ ( r2_hidden(c1_1_2_2__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
      & ~ r2_hidden(c1_1_2_2__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1_2_2__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5]),discharge_asm(discharge,[e1_1_2_2__bhsp_5])],[e1_1_2_2__bhsp_5,i2_1_2_2__bhsp_5]),
    [interesting(0.5),file(bhsp_5,i1_1_2_2__bhsp_5),[file(bhsp_5,i1_1_2_2__bhsp_5)]]).

fof(i1_1_2_2_tmp__bhsp_5,plain,(
    ~ ( r2_hidden(c1_1_2_2__bhsp_5,k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
      & ~ r2_hidden(c1_1_2_2__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5]),discharge_asm(discharge,[dt_c1_1_2_2__bhsp_5])],[dt_c1_1_2_2__bhsp_5,i1_1_2_2__bhsp_5]),
    [interesting(0.65),e4_1_2__bhsp_5]).

fof(e4_1_2__bhsp_5,plain,(
    r1_tarski(k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))),k5_finsop_1(c2_1__bhsp_5)) ),
    inference(let,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[i1_1_2_2_tmp__bhsp_5,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,d3_tarski,dh_c1_1_2_2__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e4_1_2__bhsp_5),[file(bhsp_5,e4_1_2__bhsp_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(e6_1_2__bhsp_5,plain,
    ( k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))) = k5_finsop_1(c2_1__bhsp_5)
    & k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc9_membered,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc2_funct_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,t1_subset,t3_subset,t7_boole,e5_1_2__bhsp_5,e4_1__bhsp_5,e1_1_2__bhsp_5,e4_1_2__bhsp_5,t2_tarski,d10_xboole_0]),
    [interesting(0.65),file(bhsp_5,e6_1_2__bhsp_5),[file(bhsp_5,e6_1_2__bhsp_5)]]).

fof(i1_1_2__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i1_1_2__bhsp_5)]),
    [interesting(0.65),trivial,file(bhsp_5,i1_1_2__bhsp_5)]).

fof(e5_1__bhsp_5,plain,
    ( k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))) = k5_finsop_1(c2_1__bhsp_5)
    & k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(conclusion,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e6_1_2__bhsp_5,i1_1_2__bhsp_5]),
    [interesting(0.8),file(bhsp_5,e5_1__bhsp_5),[file(bhsp_5,e5_1__bhsp_5)]]).

fof(e1_1_4_1__bhsp_5,plain,(
    k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) = k1_funct_1(c2_1__bhsp_5,k1_funct_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c1_1_4__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_4__bhsp_5,e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5,e1_1_4__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e4_1__bhsp_5,e5_1__bhsp_5,e1_1_4__bhsp_5,t23_funct_1]),
    [interesting(0.5),file(bhsp_5,e1_1_4_1__bhsp_5),[file(bhsp_5,e1_1_4_1__bhsp_5)]]).

fof(e2_1_4_1__bhsp_5,plain,(
    k1_funct_1(c2_1__bhsp_5,k1_funct_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c1_1_4__bhsp_5)) = k1_funct_1(c2_1__bhsp_5,k1_funct_1(k2_funct_1(c2_1__bhsp_5),k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_4__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e1_1_4__bhsp_5,t23_funct_1]),
    [interesting(0.5),file(bhsp_5,e2_1_4_1__bhsp_5),[file(bhsp_5,e2_1_4_1__bhsp_5)]]).

fof(e2_1_4__bhsp_5,plain,(
    r2_hidden(k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5),k2_relat_1(c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_4__bhsp_5,e3_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_finsop_1,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,rc1_funct_1,t1_subset,t7_boole,e1_1_4__bhsp_5,e3_1__bhsp_5,t12_funct_1]),
    [interesting(0.65),file(bhsp_5,e2_1_4__bhsp_5),[file(bhsp_5,e2_1_4__bhsp_5)]]).

fof(t57_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( v2_funct_1(B)
          & r2_hidden(A,k2_relat_1(B)) )
       => ( A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A))
          & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) ) ) ) ),
    file(funct_1,t57_funct_1),
    [interesting(0.9),axiom,file(funct_1,t57_funct_1)]).

fof(e3_1_4_1__bhsp_5,plain,(
    k1_funct_1(c2_1__bhsp_5,k1_funct_1(k2_funct_1(c2_1__bhsp_5),k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5))) = k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_4__bhsp_5,e3_1__bhsp_5])],[reflexivity_r1_tarski,rc2_finset_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc3_finset_1,rc4_finset_1,rc4_funct_1,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_relat_1,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e1_1__bhsp_5,e2_1_4__bhsp_5,t57_funct_1]),
    [interesting(0.5),file(bhsp_5,e3_1_4_1__bhsp_5),[file(bhsp_5,e3_1_4_1__bhsp_5)]]).

fof(e3_1_4__bhsp_5,plain,(
    k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) = k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) ),
    inference(iterative_eq,[status(thm),assumptions([e2_1__bhsp_5,e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_4__bhsp_5,e3_1__bhsp_5])],[e1_1_4_1__bhsp_5,e2_1_4_1__bhsp_5,e3_1_4_1__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e3_1_4__bhsp_5),[file(bhsp_5,e3_1_4__bhsp_5)]]).

fof(e4_1_4__bhsp_5,plain,(
    k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_1__bhsp_5,e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_4__bhsp_5,e3_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,rc1_finset_1,rc1_membered,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,t3_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,rc1_finseq_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,fc1_funct_1,rc1_funct_1,dt_k1_funct_1,dt_k2_funct_1,dt_k5_relat_1,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e3_1_4__bhsp_5]),
    [interesting(0.65),file(bhsp_5,e4_1_4__bhsp_5),[file(bhsp_5,e4_1_4__bhsp_5)]]).

fof(i3_1_4__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i3_1_4__bhsp_5)]),
    [interesting(0.65),trivial,file(bhsp_5,i3_1_4__bhsp_5)]).

fof(i2_1_4__bhsp_5,plain,(
    k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) ),
    inference(conclusion,[status(thm),assumptions([e2_1__bhsp_5,e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e1_1_4__bhsp_5,e3_1__bhsp_5])],[e4_1_4__bhsp_5,i3_1_4__bhsp_5]),
    [interesting(0.65),file(bhsp_5,i2_1_4__bhsp_5),[file(bhsp_5,i2_1_4__bhsp_5)]]).

fof(i1_1_4__bhsp_5,plain,
    ( r2_hidden(c1_1_4__bhsp_5,k5_finsop_1(c3_1__bhsp_5))
   => k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) ),
    inference(discharge_asm,[status(thm),assumptions([e2_1__bhsp_5,e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c1_1_4__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e3_1__bhsp_5]),discharge_asm(discharge,[e1_1_4__bhsp_5])],[e1_1_4__bhsp_5,i2_1_4__bhsp_5]),
    [interesting(0.65),file(bhsp_5,i1_1_4__bhsp_5),[file(bhsp_5,i1_1_4__bhsp_5)]]).

fof(i1_1_4_tmp__bhsp_5,plain,
    ( r2_hidden(c1_1_4__bhsp_5,k5_finsop_1(c3_1__bhsp_5))
   => k1_funct_1(c3_1__bhsp_5,c1_1_4__bhsp_5) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),c1_1_4__bhsp_5) ),
    inference(discharge_asm,[status(thm),assumptions([e2_1__bhsp_5,e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e3_1__bhsp_5]),discharge_asm(discharge,[dt_c1_1_4__bhsp_5])],[dt_c1_1_4__bhsp_5,i1_1_4__bhsp_5]),
    [interesting(0.8),e11_1__bhsp_5]).

fof(e11_1__bhsp_5,plain,(
    ! [A] : 
      ( r2_hidden(A,k5_finsop_1(c3_1__bhsp_5))
     => k1_funct_1(c3_1__bhsp_5,A) = k1_funct_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5),A) ) ),
    inference(let,[status(thm),assumptions([e2_1__bhsp_5,e1_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e3_1__bhsp_5])],[i1_1_4_tmp__bhsp_5,dh_c1_1_4__bhsp_5]),
    [interesting(0.8),file(bhsp_5,e11_1__bhsp_5),[file(bhsp_5,e11_1__bhsp_5)]]).

fof(dh_c1_1_3__bhsp_5,definition,
    ( ( r2_hidden(c1_1_3__bhsp_5,k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)))
    <=> r2_hidden(c1_1_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)))
      <=> r2_hidden(A,k5_finsop_1(c2_1__bhsp_5)) ) ),
    introduced(definition,[new_symbol(c1_1_3__bhsp_5),file(bhsp_5,c1_1_3__bhsp_5)]),
    [interesting(0.65),axiom,file(bhsp_5,c1_1_3__bhsp_5)]).

fof(dt_c1_1_3__bhsp_5,assumption,(
    $true ),
    introduced(assumption,[file(bhsp_5,c1_1_3__bhsp_5)]),
    [interesting(0.65),axiom,file(bhsp_5,c1_1_3__bhsp_5)]).

fof(e1_1_3__bhsp_5,plain,
    ( r2_hidden(c1_1_3__bhsp_5,k1_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))))
   => r2_hidden(k1_funct_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c1_1_3__bhsp_5),k5_finsop_1(c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_3__bhsp_5,e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_3__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e5_1__bhsp_5,t12_funct_1]),
    [interesting(0.65),file(bhsp_5,e1_1_3__bhsp_5),[file(bhsp_5,e1_1_3__bhsp_5)]]).

fof(e2_1_3__bhsp_5,plain,
    ( r2_hidden(c1_1_3__bhsp_5,k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)))
  <=> r2_hidden(c1_1_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_3__bhsp_5,e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_3__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e1_1_3__bhsp_5,e5_1__bhsp_5,t21_funct_1]),
    [interesting(0.65),file(bhsp_5,e2_1_3__bhsp_5),[file(bhsp_5,e2_1_3__bhsp_5)]]).

fof(i2_1_3__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i2_1_3__bhsp_5)]),
    [interesting(0.65),trivial,file(bhsp_5,i2_1_3__bhsp_5)]).

fof(i1_1_3__bhsp_5,plain,
    ( r2_hidden(c1_1_3__bhsp_5,k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)))
  <=> r2_hidden(c1_1_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_3__bhsp_5,e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c1_1_3__bhsp_5,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e2_1_3__bhsp_5,i2_1_3__bhsp_5]),
    [interesting(0.65),file(bhsp_5,i1_1_3__bhsp_5),[file(bhsp_5,i1_1_3__bhsp_5)]]).

fof(i1_1_3_tmp__bhsp_5,plain,
    ( r2_hidden(c1_1_3__bhsp_5,k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)))
  <=> r2_hidden(c1_1_3__bhsp_5,k5_finsop_1(c2_1__bhsp_5)) ),
    inference(discharge_asm,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5]),discharge_asm(discharge,[dt_c1_1_3__bhsp_5])],[dt_c1_1_3__bhsp_5,i1_1_3__bhsp_5]),
    [interesting(0.8),e9_1__bhsp_5]).

fof(e9_1__bhsp_5,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)))
    <=> r2_hidden(A,k5_finsop_1(c2_1__bhsp_5)) ) ),
    inference(let,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[i1_1_3_tmp__bhsp_5,dh_c1_1_3__bhsp_5]),
    [interesting(0.8),file(bhsp_5,e9_1__bhsp_5),[file(bhsp_5,e9_1__bhsp_5)]]).

fof(e10_1__bhsp_5,plain,(
    k5_finsop_1(c3_1__bhsp_5) = k1_relat_1(k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,e2_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,t1_subset,t7_boole,e9_1__bhsp_5,e4_1__bhsp_5,t2_tarski]),
    [interesting(0.8),file(bhsp_5,e10_1__bhsp_5),[file(bhsp_5,e10_1__bhsp_5)]]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.9),axiom,file(funct_1,t9_funct_1)]).

fof(e12_1__bhsp_5,plain,(
    c3_1__bhsp_5 = k5_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),c2_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bhsp_5,e1_1__bhsp_5,e3_1__bhsp_5,e2_1__bhsp_5,dt_c1_1__bhsp_5,dt_c3_1__bhsp_5])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc2_finset_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_finsop_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e11_1__bhsp_5,e10_1__bhsp_5,t9_funct_1]),
    [interesting(0.8),file(bhsp_5,e12_1__bhsp_5),[file(bhsp_5,e12_1__bhsp_5)]]).

fof(t62_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => v2_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,t62_funct_1),
    [interesting(0.9),axiom,file(funct_1,t62_funct_1)]).

fof(e6_1__bhsp_5,plain,(
    v2_funct_1(k2_funct_1(c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,rc2_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,rc1_finset_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,t3_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,rc1_finseq_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,dt_k2_funct_1,dt_c2_1__bhsp_5,rc1_funct_1,rc3_funct_1,e1_1__bhsp_5,t62_funct_1]),
    [interesting(0.8),file(bhsp_5,e6_1__bhsp_5),[file(bhsp_5,e6_1__bhsp_5)]]).

fof(t46_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => v2_funct_1(k5_relat_1(A,B)) ) ) ) ),
    file(funct_1,t46_funct_1),
    [interesting(0.9),axiom,file(funct_1,t46_funct_1)]).

fof(e7_1__bhsp_5,plain,
    ( v2_funct_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))
    & k2_relat_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5))) = k5_finsop_1(c2_1__bhsp_5) ),
    inference(mizar_by,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,rc2_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc2_finseq_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_finset_1,cc6_membered,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,t3_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,rc1_finseq_1,redefinition_k5_finsop_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,rc3_funct_1,e6_1__bhsp_5,e2_1__bhsp_5,e5_1__bhsp_5,t46_funct_1]),
    [interesting(0.8),file(bhsp_5,e7_1__bhsp_5),[file(bhsp_5,e7_1__bhsp_5)]]).

fof(t3_funct_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A))
        & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ),
    file(funct_2,t3_funct_2),
    [interesting(0.9),axiom,file(funct_2,t3_funct_2)]).

fof(t83_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( ( v2_funct_1(B)
          & k2_relat_1(B) = A )
       => ( v1_funct_1(B)
          & v1_funct_2(B,A,A)
          & v3_funct_2(B,A,A)
          & m2_relset_1(B,A,A) ) ) ) ),
    file(funct_2,t83_funct_2),
    [interesting(0.9),axiom,file(funct_2,t83_funct_2)]).

fof(e8_1__bhsp_5,plain,
    ( v1_funct_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)))
    & v1_funct_2(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
    & v3_funct_2(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
    & m2_relset_1(k5_relat_1(c3_1__bhsp_5,k2_funct_1(c2_1__bhsp_5)),k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5)) ),
    inference(mizar_by,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,fc2_finseq_1,fc6_membered,t1_subset,t4_subset,t5_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,rc1_finset_1,rc1_membered,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_finseq_1,dt_k1_numbers,dt_k5_ordinal2,dt_m1_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_funct_2,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc2_funct_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,cc1_relset_1,cc2_funct_2,cc9_membered,rc1_finseq_1,rc1_funct_2,t3_subset,existence_m2_relset_1,redefinition_k5_finsop_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_m2_relset_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,fc1_funct_1,rc1_funct_1,rc3_funct_1,e7_1__bhsp_5,e5_1__bhsp_5,t3_funct_2,t83_funct_2]),
    [interesting(0.8),file(bhsp_5,e8_1__bhsp_5),[file(bhsp_5,e8_1__bhsp_5)]]).

fof(e13_1__bhsp_5,plain,
    ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5)
    & ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
        & v3_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
        & m2_relset_1(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
        & c3_1__bhsp_5 = k5_relat_1(A,c2_1__bhsp_5)
        & k1_relat_1(A) = k5_finsop_1(c2_1__bhsp_5)
        & k2_relat_1(A) = k5_finsop_1(c2_1__bhsp_5) ) ),
    inference(mizar_by,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,fc2_finseq_1,fc6_membered,t1_subset,t4_subset,t5_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,rc1_finset_1,rc1_membered,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_finseq_1,dt_k1_numbers,dt_k5_ordinal2,dt_m1_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_funct_2,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc2_funct_2,rc3_funct_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,cc1_relset_1,cc2_funct_2,cc9_membered,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc1_funct_2,t3_subset,existence_m2_relset_1,redefinition_k5_finsop_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_m2_relset_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e12_1__bhsp_5,e4_1__bhsp_5,e5_1__bhsp_5,e8_1__bhsp_5]),
    [interesting(0.8),file(bhsp_5,e13_1__bhsp_5),[file(bhsp_5,e13_1__bhsp_5)]]).

fof(i4_1__bhsp_5,theorem,(
    $true ),
    introduced(tautology,[file(bhsp_5,i4_1__bhsp_5)]),
    [interesting(0.8),trivial,file(bhsp_5,i4_1__bhsp_5)]).

fof(i3_1__bhsp_5,plain,
    ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5)
    & ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
        & v3_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
        & m2_relset_1(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
        & c3_1__bhsp_5 = k5_relat_1(A,c2_1__bhsp_5)
        & k1_relat_1(A) = k5_finsop_1(c2_1__bhsp_5)
        & k2_relat_1(A) = k5_finsop_1(c2_1__bhsp_5) ) ),
    inference(conclusion,[status(thm),assumptions([e2_1__bhsp_5,e3_1__bhsp_5,dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5,e1_1__bhsp_5])],[cc1_funct_2,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,rc1_finset_1,rc1_membered,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_numbers,dt_k5_ordinal2,dt_m1_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_funct_2,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc2_funct_2,rc3_funct_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,cc1_relset_1,cc2_funct_2,cc9_membered,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc1_funct_2,redefinition_k5_finsop_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_m2_relset_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,e13_1__bhsp_5,i4_1__bhsp_5]),
    [interesting(0.8),file(bhsp_5,i3_1__bhsp_5),[file(bhsp_5,i3_1__bhsp_5)]]).

fof(i3_1_tmp__bhsp_5,plain,
    ( ( v2_funct_1(c2_1__bhsp_5)
      & v2_funct_1(c3_1__bhsp_5)
      & k2_relat_1(c2_1__bhsp_5) = k2_relat_1(c3_1__bhsp_5) )
   => ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5)
      & ? [A] : 
          ( v1_funct_1(A)
          & v1_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
          & v3_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
          & m2_relset_1(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
          & c3_1__bhsp_5 = k5_relat_1(A,c2_1__bhsp_5)
          & k1_relat_1(A) = k5_finsop_1(c2_1__bhsp_5)
          & k2_relat_1(A) = k5_finsop_1(c2_1__bhsp_5) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5]),discharge_asm(discharge,[e1_1__bhsp_5,e2_1__bhsp_5,e3_1__bhsp_5])],[e1_1__bhsp_5,e2_1__bhsp_5,e3_1__bhsp_5,i3_1__bhsp_5]),
    [interesting(0.8),i2_1__bhsp_5]).

fof(i2_1__bhsp_5,plain,
    ( ( v2_funct_1(c2_1__bhsp_5)
      & v2_funct_1(c3_1__bhsp_5)
      & k2_relat_1(c2_1__bhsp_5) = k2_relat_1(c3_1__bhsp_5) )
   => ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5)
      & ? [A] : 
          ( v1_funct_1(A)
          & v1_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
          & v3_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
          & m2_relset_1(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
          & c3_1__bhsp_5 = k5_relat_1(A,c2_1__bhsp_5)
          & k1_relat_1(A) = k5_finsop_1(c2_1__bhsp_5)
          & k2_relat_1(A) = k5_finsop_1(c2_1__bhsp_5) ) ) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c3_1__bhsp_5,dt_c1_1__bhsp_5,dt_c2_1__bhsp_5])],[i3_1_tmp__bhsp_5,cc1_funct_2,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,rc1_finset_1,rc1_membered,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_numbers,dt_k5_ordinal2,dt_m1_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_funct_2,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc2_funct_2,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_finsub_1,dt_k5_numbers,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_c1_1__bhsp_5,cc1_finseq_1,cc1_relset_1,cc2_funct_2,cc9_membered,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc1_funct_2,rc3_funct_1,redefinition_k5_finsop_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_finsop_1,dt_k5_relat_1,dt_m2_relset_1,dt_c2_1__bhsp_5,dt_c3_1__bhsp_5]),
    [interesting(0.8),file(bhsp_5,i2_1__bhsp_5),[file(bhsp_5,i2_1__bhsp_5)]]).

fof(i2_1_tmp__bhsp_5,plain,
    ( ( m2_finseq_1(c2_1__bhsp_5,c1_1__bhsp_5)
      & m2_finseq_1(c3_1__bhsp_5,c1_1__bhsp_5) )
   => ( ( v2_funct_1(c2_1__bhsp_5)
        & v2_funct_1(c3_1__bhsp_5)
        & k2_relat_1(c2_1__bhsp_5) = k2_relat_1(c3_1__bhsp_5) )
     => ( k5_finsop_1(c2_1__bhsp_5) = k5_finsop_1(c3_1__bhsp_5)
        & ? [A] : 
            ( v1_funct_1(A)
            & v1_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
            & v3_funct_2(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
            & m2_relset_1(A,k5_finsop_1(c2_1__bhsp_5),k5_finsop_1(c2_1__bhsp_5))
            & c3_1__bhsp_5 = k5_relat_1(A,c2_1__bhsp_5)
            & k1_relat_1(A) = k5_finsop_1(c2_1__bhsp_5)
            & k2_relat_1(A) = k5_finsop_1(c2_1__bhsp_5) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bhsp_5]),discharge_asm(discharge,[dt_c2_1__bhsp_5,dt_c3_1__bhsp_5])],[dt_c2_1__bhsp_5,dt_c3_1__bhsp_5,i2_1__bhsp_5]),
    [interesting(0.8),i1_1__bhsp_5]).

fof(i1_1__bhsp_5,plain,(
    ! [A] : 
      ( m2_finseq_1(A,c1_1__bhsp_5)
     => ! [B] : 
          ( m2_finseq_1(B,c1_1__bhsp_5)
         => ( ( v2_funct_1(A)
              & v2_funct_1(B)
              & k2_relat_1(A) = k2_relat_1(B) )
           => ( k5_finsop_1(A) = k5_finsop_1(B)
              & ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k5_finsop_1(A),k5_finsop_1(A))
                  & v3_funct_2(C,k5_finsop_1(A),k5_finsop_1(A))
                  & m2_relset_1(C,k5_finsop_1(A),k5_finsop_1(A))
                  & B = k5_relat_1(C,A)
                  & k1_relat_1(C) = k5_finsop_1(A)
                  & k2_relat_1(C) = k5_finsop_1(A) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__bhsp_5])],[i2_1_tmp__bhsp_5,dh_c2_1__bhsp_5,dh_c3_1__bhsp_5]),
    [interesting(0.8),file(bhsp_5,i1_1__bhsp_5),[file(bhsp_5,i1_1__bhsp_5)]]).

fof(i1_1_tmp__bhsp_5,plain,(
    ! [A] : 
      ( m2_finseq_1(A,c1_1__bhsp_5)
     => ! [B] : 
          ( m2_finseq_1(B,c1_1__bhsp_5)
         => ( ( v2_funct_1(A)
              & v2_funct_1(B)
              & k2_relat_1(A) = k2_relat_1(B) )
           => ( k5_finsop_1(A) = k5_finsop_1(B)
              & ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k5_finsop_1(A),k5_finsop_1(A))
                  & v3_funct_2(C,k5_finsop_1(A),k5_finsop_1(A))
                  & m2_relset_1(C,k5_finsop_1(A),k5_finsop_1(A))
                  & B = k5_relat_1(C,A)
                  & k1_relat_1(C) = k5_finsop_1(A)
                  & k2_relat_1(C) = k5_finsop_1(A) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__bhsp_5])],[dt_c1_1__bhsp_5,i1_1__bhsp_5]),
    [interesting(1),t1_bhsp_5]).

fof(t1_bhsp_5,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ! [C] : 
          ( m2_finseq_1(C,A)
         => ( ( v2_funct_1(B)
              & v2_funct_1(C)
              & k2_relat_1(B) = k2_relat_1(C) )
           => ( k5_finsop_1(B) = k5_finsop_1(C)
              & ? [D] : 
                  ( v1_funct_1(D)
                  & v1_funct_2(D,k5_finsop_1(B),k5_finsop_1(B))
                  & v3_funct_2(D,k5_finsop_1(B),k5_finsop_1(B))
                  & m2_relset_1(D,k5_finsop_1(B),k5_finsop_1(B))
                  & C = k5_relat_1(D,B)
                  & k1_relat_1(D) = k5_finsop_1(B)
                  & k2_relat_1(D) = k5_finsop_1(B) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__bhsp_5,dh_c1_1__bhsp_5]),
    [interesting(1),file(bhsp_5,t1_bhsp_5),[file(bhsp_5,t1_bhsp_5)]]).