fof(t3_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => m2_bhsp_5(k1_xboole_0,A) ) ),
    inference(mizar_proof,[status(thm)],[t2_bhsp_5,d9_bhsp_5]),
    [file(bhsp_5,t3_bhsp_5),interesting(1.00)]).

fof(t2_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => m1_bhsp_5(k1_xboole_0,A) ) ),
    inference(mizar_proof,[status(thm)],[t4_subset_1,d8_bhsp_5]),
    [file(bhsp_5,t2_bhsp_5),interesting(0.97)]).

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(mizar_proof,[status(thm)],[t77_finseq_4,t77_finseq_4,d3_finseq_1,d3_finseq_1,t55_funct_1,t12_funct_1,t21_funct_1,t2_tarski,t55_funct_1,d3_tarski,t25_funct_1,d3_tarski,t55_funct_1,d5_funct_1,t55_funct_1,d5_funct_1,t23_funct_1,d5_funct_1,t2_tarski,d10_xboole_0,t62_funct_1,t46_funct_1,t3_funct_2,t83_funct_2,t12_funct_1,t21_funct_1,t2_tarski,t12_funct_1,t23_funct_1,t23_funct_1,t57_funct_1,t9_funct_1]),
    [file(bhsp_5,t1_bhsp_5),interesting(0.85)]).

fof(t4_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B = k1_rlvect_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_bhsp_1(A,B,C) = 0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_bhsp_1,t19_bhsp_1]),
    [file(bhsp_5,t4_bhsp_5),interesting(0.77)]).

fof(t6_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_bhsp_1(A,B,C)
               => k7_square_1(k3_bhsp_1(A,k4_rlvect_1(A,B,C))) = k9_binop_2(k7_square_1(k3_bhsp_1(A,B)),k7_square_1(k3_bhsp_1(A,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_bhsp_1,d2_bhsp_1,d2_bhsp_1,d2_bhsp_1,d4_bhsp_1,d4_square_1,t21_bhsp_1,d4_square_1,d4_square_1,d4_bhsp_1,d4_bhsp_1]),
    [file(bhsp_5,t6_bhsp_5),interesting(0.74)]).

fof(t13_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( ( v1_finset_1(C)
                  & m2_bhsp_5(C,A) )
               => ( ~ v1_xboole_0(C)
                 => ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),k1_numbers)
                        & m2_relset_1(D,u1_struct_0(A),k1_numbers) )
                     => ( ( r1_tarski(C,k1_relat_1(D))
                          & ! [E] : 
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( r2_hidden(E,C)
                               => k1_funct_1(D,E) = k7_square_1(k2_bhsp_1(A,B,E)) ) ) )
                       => r1_xreal_0(k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,C,D),k7_square_1(k3_bhsp_1(A,B))) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_bhsp_1,d4_rlvect_1,s2_funct_2,d1_funct_2,d1_bhsp_1,d4_rlvect_1,t11_bhsp_5,t12_bhsp_5,t18_bhsp_1,t12_bhsp_5,d2_bhsp_1,t21_xreal_1,d2_bhsp_1,d4_square_1,d4_bhsp_1]),
    [file(bhsp_5,t13_bhsp_5),interesting(0.63)]).

fof(t5_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_binop_2(k7_square_1(k3_bhsp_1(A,k4_rlvect_1(A,B,C))),k7_square_1(k3_bhsp_1(A,k6_rlvect_1(A,B,C)))) = k9_binop_2(k11_binop_2(2,k7_square_1(k3_bhsp_1(A,B))),k11_binop_2(2,k7_square_1(k3_bhsp_1(A,C)))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_bhsp_1,d2_bhsp_1,d2_bhsp_1,d2_bhsp_1,d4_bhsp_1,d4_square_1,d4_bhsp_1,d4_square_1,t21_bhsp_1,t23_bhsp_1,d4_square_1,d4_square_1,d4_bhsp_1,d4_bhsp_1]),
    [file(bhsp_5,t5_bhsp_5),interesting(0.59)]).

fof(t14_bhsp_5,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_binop_1(C,A)
                  & v2_binop_1(C,A)
                  & v1_setwiseo(C,A) )
               => ! [D] : 
                    ( ( v1_finset_1(D)
                      & m1_subset_1(D,k1_zfmisc_1(B)) )
                   => ! [E] : 
                        ( ( v1_finset_1(E)
                          & m1_subset_1(E,k1_zfmisc_1(B)) )
                       => ( r1_xboole_0(D,E)
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,A)
                                & m2_relset_1(F,B,A) )
                             => ( ( r1_tarski(D,k1_relat_1(F))
                                  & r1_tarski(E,k1_relat_1(F)) )
                               => ! [G] : 
                                    ( ( v1_finset_1(G)
                                      & m1_subset_1(G,k1_zfmisc_1(B)) )
                                   => ( G = k2_xboole_0(D,E)
                                     => k5_bhsp_5(A,B,C,G,F) = k2_binop_1(A,A,A,C,k5_bhsp_5(A,B,C,D,F),k5_bhsp_5(A,B,C,E,F)) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_xboole_1,d5_bhsp_5,d5_bhsp_5,t98_finseq_3,t44_finseq_1,d5_bhsp_5,t1_hilbasis,t6_finsop_1]),
    [file(bhsp_5,t14_bhsp_5),interesting(0.47)]).

fof(t8_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( r1_xreal_0(1,k3_finseq_1(C))
               => ! [D] : 
                    ( m2_finseq_1(D,k1_numbers)
                   => ( ( k5_finsop_1(C) = k5_finsop_1(D)
                        & ! [E] : 
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(E,k5_finsop_1(D))
                             => k1_funct_1(D,E) = k1_funct_1(u1_bhsp_1(A),k4_tarski(B,k1_funct_1(C,E))) ) ) )
                     => k2_bhsp_1(A,B,k2_finsop_1(u1_struct_0(A),C,u1_rlvect_1(A))) = k2_finsop_1(k1_numbers,D,k33_binop_2) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_finsop_1,d3_finseq_1,d3_finseq_1,t8_finseq_1,t8_finseq_1,t2_finsop_1,t3_finseq_1,d3_finseq_1,t19_nat_1,t20_int_1,t92_real_1,t3_finseq_1,d3_finseq_1,d3_finseq_1,d1_funct_2,t12_funct_1,t12_relset_1,t12_funct_1,t12_relset_1,d1_bhsp_1,d1_bhsp_1,d9_binop_2,t7_bhsp_1,d1_bhsp_1,t5_rlvect_1,s1_nat_1,t8_finseq_1,t8_finseq_1,d1_bhsp_1]),
    [file(bhsp_5,t8_bhsp_5),interesting(0.45)]).

fof(t7_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( ( r1_xreal_0(1,k3_finseq_1(B))
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ( r2_hidden(C,k5_finsop_1(B))
                          & r2_hidden(D,k5_finsop_1(B)) )
                       => ( C = D
                          | k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D))) = 0 ) ) ) ) )
           => ! [C] : 
                ( m2_finseq_1(C,k1_numbers)
               => ( ( k5_finsop_1(B) = k5_finsop_1(C)
                    & ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( r2_hidden(D,k5_finsop_1(C))
                         => k1_funct_1(C,D) = k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(B,D),k1_funct_1(B,D))) ) ) )
                 => k2_bhsp_1(A,k2_finsop_1(u1_struct_0(A),B,u1_rlvect_1(A)),k2_finsop_1(u1_struct_0(A),B,u1_rlvect_1(A))) = k2_finsop_1(k1_numbers,C,k33_binop_2) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_finseq_3,t2_finsop_1,d1_bhsp_1,d3_finseq_1,d3_finseq_1,t8_finseq_1,t8_finseq_1,t2_finsop_1,t29_nat_1,t3_finseq_1,d3_finseq_1,t19_nat_1,t20_int_1,t2_xreal_1,t92_real_1,t8_finseq_1,t3_finseq_1,d3_finseq_1,d3_finseq_1,d1_funct_2,t12_funct_1,t12_relset_1,t12_funct_1,t12_relset_1,t19_nat_1,t2_xreal_1,t27_finseq_3,t12_funct_1,t12_relset_1,t2_xreal_1,t27_finseq_3,t12_funct_1,t12_relset_1,t92_real_1,t19_nat_1,t20_int_1,t31_xreal_1,t2_xreal_1,d1_bhsp_1,t10_xreal_1,t5_rlvect_1,d1_bhsp_1,t7_bhsp_1,d1_bhsp_1,s1_nat_1,d1_bhsp_1,d1_bhsp_1,d1_bhsp_1,d9_binop_2,t7_bhsp_1,t7_bhsp_1,t7_bhsp_1,d1_bhsp_1,t5_rlvect_1,t5_rlvect_1,s1_nat_1]),
    [file(bhsp_5,t7_bhsp_5),interesting(0.27)]).

fof(t12_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( ( v1_finset_1(C)
                  & m2_bhsp_5(C,A) )
               => ( ~ v1_xboole_0(C)
                 => ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( r1_tarski(C,k1_relat_1(D))
                          & ! [E] : 
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( r2_hidden(E,C)
                               => k1_funct_1(D,E) = k3_rlvect_1(A,E,k2_bhsp_1(A,B,E)) ) ) )
                       => ! [E] : 
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(A),k1_numbers)
                              & m2_relset_1(E,u1_struct_0(A),k1_numbers) )
                           => ( ( r1_tarski(C,k1_relat_1(E))
                                & ! [F] : 
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => ( r2_hidden(F,C)
                                     => k1_funct_1(E,F) = k7_square_1(k2_bhsp_1(A,B,F)) ) ) )
                             => k2_bhsp_1(A,k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),C,D),k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),C,D)) = k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,C,E) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_bhsp_5,d9_bhsp_5,d8_bhsp_5,d1_bhsp_1,t8_bhsp_1,t8_bhsp_1,d9_bhsp_5,t8_bhsp_1,t8_bhsp_1,d1_bhsp_1,d1_bhsp_1,t9_bhsp_5,d5_bhsp_5]),
    [file(bhsp_5,t12_bhsp_5),interesting(0.22)]).

fof(t11_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( ( v1_finset_1(C)
                  & m2_bhsp_5(C,A) )
               => ( ~ v1_xboole_0(C)
                 => ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),k1_numbers)
                        & m2_relset_1(D,u1_struct_0(A),k1_numbers) )
                     => ( ( r1_tarski(C,k1_relat_1(D))
                          & ! [E] : 
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( r2_hidden(E,C)
                               => k1_funct_1(D,E) = k7_square_1(k2_bhsp_1(A,B,E)) ) ) )
                       => ! [E] : 
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                              & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                           => ( ( r1_tarski(C,k1_relat_1(E))
                                & ! [F] : 
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => ( r2_hidden(F,C)
                                     => k1_funct_1(E,F) = k3_rlvect_1(A,F,k2_bhsp_1(A,B,F)) ) ) )
                             => k2_bhsp_1(A,B,k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),C,E)) = k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,C,D) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_bhsp_5,t8_bhsp_1,d1_bhsp_1,d5_bhsp_5,d1_bhsp_1,t10_bhsp_5]),
    [file(bhsp_5,t11_bhsp_5),interesting(0.19)]).

fof(t10_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( r1_tarski(C,k1_relat_1(D))
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(A),k1_numbers)
                          & m2_relset_1(E,u1_struct_0(A),k1_numbers) )
                       => ( ( r1_tarski(C,k1_relat_1(E))
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ( r2_hidden(F,C)
                                 => k1_funct_1(E,F) = k1_funct_1(u1_bhsp_1(A),k4_tarski(B,k1_funct_1(D,F))) ) ) )
                         => ! [F] : 
                              ( m2_finseq_1(F,u1_struct_0(A))
                             => ( ( v2_funct_1(F)
                                  & k2_relat_1(F) = C )
                               => k1_funct_1(u1_bhsp_1(A),k4_tarski(B,k2_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),D,F),u1_rlvect_1(A)))) = k2_finsop_1(k1_numbers,k4_bhsp_5(k1_numbers,u1_struct_0(A),E,F),k33_binop_2) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_1,t21_funct_1,t2_tarski,t12_funct_1,t21_funct_1,t2_tarski,t12_funct_1,t23_funct_1,t23_funct_1,d3_finseq_1,d3_finseq_1,t77_finseq_4,t59_card_2,t19_nat_1,t20_int_1,t8_finseq_1,t8_bhsp_5,d1_bhsp_1]),
    [file(bhsp_5,t10_bhsp_5),interesting(0.14)]).

fof(d1_bhsp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_bhsp_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers,u1_bhsp_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ),
    file(bhsp_1,d1_bhsp_1),
    [interesting(0.00)]).

fof(d4_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) ) ) ) ),
    file(rlvect_1,d4_rlvect_1),
    [interesting(0.00)]).

fof(s2_funct_2,theorem,
    ( ! [A] : 
        ( r2_hidden(A,f1_s2_funct_2)
       => r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2)
        & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2)
        & ! [B] : 
            ( r2_hidden(B,f1_s2_funct_2)
           => k1_funct_1(A,B) = f3_s2_funct_2(B) ) ) ),
    file(funct_2,s2_funct_2),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(d5_bhsp_5,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_binop_1(C,A)
                  & v2_binop_1(C,A)
                  & v1_setwiseo(C,A) )
               => ! [D] : 
                    ( ( v1_finset_1(D)
                      & m1_subset_1(D,k1_zfmisc_1(B)) )
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,B,A)
                          & m2_relset_1(E,B,A) )
                       => ( r1_tarski(D,k1_relat_1(E))
                         => ! [F] : 
                              ( m1_subset_1(F,A)
                             => ( F = k5_bhsp_5(A,B,C,D,E)
                              <=> ? [G] : 
                                    ( m2_finseq_1(G,B)
                                    & v2_funct_1(G)
                                    & k2_relat_1(G) = D
                                    & F = k2_finsop_1(A,k4_bhsp_5(A,B,E,G),C) ) ) ) ) ) ) ) ) ) ) ),
    file(bhsp_5,d5_bhsp_5),
    [interesting(0.00)]).

fof(t8_bhsp_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_bhsp_1(B)
            & l1_bhsp_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k2_bhsp_1(B,C,k3_rlvect_1(B,D,A)) = k4_real_1(A,k2_bhsp_1(B,C,D)) ) ) ) ) ),
    file(bhsp_1,t8_bhsp_1),
    [interesting(0.00)]).

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(0.00)]).

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(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

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(0.00)]).

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(0.00)]).

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(0.00)]).

fof(t59_card_2,theorem,(
    ! [A] : 
      ( k1_card_1(A) = 0
     => A = k1_xboole_0 ) ),
    file(card_2,t59_card_2),
    [interesting(0.00)]).

fof(t19_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( 0 != A
          & r1_xreal_0(A,0) ) ) ),
    file(nat_1,t19_nat_1),
    [interesting(0.00)]).

fof(t20_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ~ r1_xreal_0(B,A)
           => r1_xreal_0(k2_xcmplx_0(A,1),B) ) ) ) ),
    file(int_1,t20_int_1),
    [interesting(0.00)]).

fof(t8_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_finseq_1(A) = k2_finseq_1(B)
           => A = B ) ) ) ),
    file(finseq_1,t8_finseq_1),
    [interesting(0.00)]).

fof(t2_finsop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ~ ( r1_xreal_0(1,k3_finseq_1(B))
                  & ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,A)
                        & m2_relset_1(D,k5_numbers,A) )
                     => ~ ( k8_funct_2(k5_numbers,A,D,1) = k1_funct_1(B,1)
                          & ! [E] : 
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ~ ( 0 != E
                                  & ~ r1_xreal_0(k3_finseq_1(B),E)
                                  & k8_funct_2(k5_numbers,A,D,k1_nat_1(E,1)) != k1_binop_1(C,k8_funct_2(k5_numbers,A,D,E),k1_funct_1(B,k1_nat_1(E,1))) ) )
                          & k2_finsop_1(A,B,C) = k8_funct_2(k5_numbers,A,D,k3_finseq_1(B)) ) ) ) ) ) ) ),
    file(finsop_1,t2_finsop_1),
    [interesting(0.00)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.00)]).

fof(t92_real_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( ( r1_xreal_0(A,B)
                        & r1_xreal_0(C,D) )
                     => r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) )
                    & ~ ( ( ( ~ r1_xreal_0(B,A)
                            & r1_xreal_0(C,D) )
                          | ( r1_xreal_0(A,B)
                            & ~ r1_xreal_0(D,C) ) )
                        & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ) ),
    file(real_1,t92_real_1),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(d9_binop_2,definition,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k33_binop_2
      <=> ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ! [C] : 
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C) ) ) ) ) ),
    file(binop_2,d9_binop_2),
    [interesting(0.00)]).

fof(t7_bhsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k2_bhsp_1(A,B,k4_rlvect_1(A,C,D)) = k3_real_1(k2_bhsp_1(A,B,C),k2_bhsp_1(A,B,D)) ) ) ) ) ),
    file(bhsp_1,t7_bhsp_1),
    [interesting(0.00)]).

fof(t5_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) ),
    file(rlvect_1,t5_rlvect_1),
    [interesting(0.00)]).

fof(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(d9_bhsp_5,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( m2_bhsp_5(B,A)
          <=> ( m1_bhsp_5(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r2_hidden(C,B)
                   => k2_bhsp_1(A,C,C) = 1 ) ) ) ) ) ) ),
    file(bhsp_5,d9_bhsp_5),
    [interesting(0.00)]).

fof(d8_bhsp_5,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( m1_bhsp_5(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => ( C = D
                        | k2_bhsp_1(A,C,D) = 0 ) ) ) ) ) ) ) ),
    file(bhsp_5,d8_bhsp_5),
    [interesting(0.00)]).

fof(t22_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)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

fof(t27_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(B,k4_finseq_1(A))
          <=> ( r1_xreal_0(1,B)
              & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ),
    file(finseq_3,t27_finseq_3),
    [interesting(0.00)]).

fof(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.00)]).

fof(t31_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ),
    file(xreal_1,t31_xreal_1),
    [interesting(0.00)]).

fof(t10_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & r1_xreal_0(C,D)
                      & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ),
    file(xreal_1,t10_xreal_1),
    [interesting(0.00)]).

fof(t9_bhsp_5,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( r1_tarski(B,k1_relat_1(C))
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_hidden(D,B)
                              & r2_hidden(E,B) )
                           => ( D = E
                              | k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E))) = 0 ) ) ) ) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),k1_numbers)
                      & m2_relset_1(D,u1_struct_0(A),k1_numbers) )
                   => ( ( r1_tarski(B,k1_relat_1(D))
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( r2_hidden(E,B)
                             => k1_funct_1(D,E) = k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(C,E),k1_funct_1(C,E))) ) ) )
                     => ! [E] : 
                          ( m2_finseq_1(E,u1_struct_0(A))
                         => ( ( v2_funct_1(E)
                              & k2_relat_1(E) = B )
                           => k1_funct_1(u1_bhsp_1(A),k4_tarski(k2_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),C,E),u1_rlvect_1(A)),k2_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),C,E),u1_rlvect_1(A)))) = k2_finsop_1(k1_numbers,k4_bhsp_5(k1_numbers,u1_struct_0(A),D,E),k33_binop_2) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_1,t21_funct_1,t2_tarski,d3_finseq_1,d3_finseq_1,t77_finseq_4,t59_card_2,t19_nat_1,t20_int_1,t8_finseq_1,t12_funct_1,t12_funct_1,t22_funct_1,d8_funct_1,t12_funct_1,t21_funct_1,t2_tarski,t12_funct_1,t23_funct_1,t23_funct_1,t23_funct_1,d1_bhsp_1,t7_bhsp_5]),
    [file(bhsp_5,t9_bhsp_5),interesting(0.00)]).

fof(t18_bhsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k2_bhsp_1(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,D,E)) = k3_real_1(k5_real_1(k5_real_1(k2_bhsp_1(A,B,D),k2_bhsp_1(A,B,E)),k2_bhsp_1(A,C,D)),k2_bhsp_1(A,C,E)) ) ) ) ) ) ),
    file(bhsp_1,t18_bhsp_1),
    [interesting(0.00)]).

fof(d2_bhsp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_bhsp_1(A) )
     => ( v2_bhsp_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ( ( k1_bhsp_1(A,B,B) = 0
                           => B = k1_rlvect_1(A) )
                          & ( B = k1_rlvect_1(A)
                           => k1_bhsp_1(A,B,B) = 0 )
                          & r1_xreal_0(0,k1_bhsp_1(A,B,B))
                          & k1_bhsp_1(A,B,C) = k1_bhsp_1(A,C,B)
                          & k1_bhsp_1(A,k2_rlvect_1(A,B,C),D) = k3_real_1(k1_bhsp_1(A,B,D),k1_bhsp_1(A,C,D))
                          & k1_bhsp_1(A,k3_rlvect_1(A,B,E),C) = k4_real_1(E,k1_bhsp_1(A,B,C)) ) ) ) ) ) ) ) ),
    file(bhsp_1,d2_bhsp_1),
    [interesting(0.00)]).

fof(t21_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(k2_xcmplx_0(A,B),C)
              <=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ),
    file(xreal_1,t21_xreal_1),
    [interesting(0.00)]).

fof(d4_square_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( r1_xreal_0(0,A)
       => ! [B] : 
            ( v1_xreal_0(B)
           => ( B = k8_square_1(A)
            <=> ( r1_xreal_0(0,B)
                & k5_square_1(B) = A ) ) ) ) ) ),
    file(square_1,d4_square_1),
    [interesting(0.00)]).

fof(d4_bhsp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_bhsp_1(A,B) = k9_square_1(k2_bhsp_1(A,B,B)) ) ) ),
    file(bhsp_1,d4_bhsp_1),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

fof(t98_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( r1_xboole_0(k2_relat_1(A),k2_relat_1(B))
              & v2_funct_1(A)
              & v2_funct_1(B) )
          <=> v2_funct_1(k7_finseq_1(A,B)) ) ) ) ),
    file(finseq_3,t98_finseq_3),
    [interesting(0.00)]).

fof(t44_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(finseq_1,t44_finseq_1),
    [interesting(0.00)]).

fof(t1_hilbasis,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ~ ( r1_tarski(k2_xboole_0(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C))
                  & ! [D] : 
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v1_finseq_1(D) )
                     => ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ~ ( D = k5_relat_1(A,C)
                              & E = k5_relat_1(B,C)
                              & k5_relat_1(k7_finseq_1(A,B),C) = k7_finseq_1(D,E) ) ) ) ) ) ) ) ),
    file(hilbasis,t1_hilbasis),
    [interesting(0.00)]).

fof(t6_finsop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ! [C] : 
              ( m2_finseq_1(C,A)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( v2_binop_1(D,A)
                   => ( ( ~ v1_setwiseo(D,A)
                        & ~ ( r1_xreal_0(1,k3_finseq_1(B))
                            & r1_xreal_0(1,k3_finseq_1(C)) ) )
                      | k2_finsop_1(A,k8_finseq_1(A,B,C),D) = k2_binop_1(A,A,A,D,k2_finsop_1(A,B,D),k2_finsop_1(A,C,D)) ) ) ) ) ) ) ),
    file(finsop_1,t6_finsop_1),
    [interesting(0.00)]).

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(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

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(0.00)]).

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(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

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(0.00)]).

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(0.00)]).

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(0.00)]).

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(0.00)]).

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(0.00)]).

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(0.00)]).

fof(t4_subset_1,theorem,(
    ! [A] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(A)) ),
    file(subset_1,t4_subset_1),
    [interesting(0.00)]).

fof(t19_bhsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_bhsp_1(A,k1_rlvect_1(A),B) = 0 ) ) ),
    file(bhsp_1,t19_bhsp_1),
    [interesting(0.00)]).

fof(t21_bhsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_bhsp_1(A,k4_rlvect_1(A,B,C),k4_rlvect_1(A,B,C)) = k3_real_1(k3_real_1(k2_bhsp_1(A,B,B),k4_real_1(2,k2_bhsp_1(A,B,C))),k2_bhsp_1(A,C,C)) ) ) ) ),
    file(bhsp_1,t21_bhsp_1),
    [interesting(0.00)]).

fof(t23_bhsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_bhsp_1(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,B,C)) = k3_real_1(k5_real_1(k2_bhsp_1(A,B,B),k4_real_1(2,k2_bhsp_1(A,B,C))),k2_bhsp_1(A,C,C)) ) ) ) ),
    file(bhsp_1,t23_bhsp_1),
    [interesting(0.00)]).

fof(d3_bhsp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_bhsp_1(A)
        & l1_bhsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_bhsp_1(A,B,C)
              <=> k2_bhsp_1(A,B,C) = 0 ) ) ) ) ),
    file(bhsp_1,d3_bhsp_1),
    [interesting(0.00)]).