% Mizar problem: t59_hermitan,hermitan,2076,24 
fof(t59_hermitan,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v12_vectsp_1(A,k1_complfld)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
            & v2_bilinear(B,k1_complfld,A,A)
            & v4_bilinear(B,k1_complfld,A,A)
            & v3_hermitan(B,A)
            & v5_hermitan(B,A)
            & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
         => k15_bilinear(k1_complfld,A,A,B) = k16_bilinear(k1_complfld,A,A,k3_hermitan(A,A,B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v11_vectsp_1,abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_complfld,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_hermitan,cc2_membered,cc2_xcmplx_0,cc2_xreal_0,cc3_hermitan,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_hermitan,cc4_membered,cc4_xreal_0,cc5_hermitan,cc5_xreal_0,cc6_hermitan,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_tarski,d16_bilinear,d17_bilinear,d18_bilinear,d19_bilinear,d20_bilinear,d2_rlvect_1,d5_tarski,dt_g3_vectsp_1,dt_g4_vectsp_1,dt_k12_bilinear,dt_k13_bilinear,dt_k14_bilinear,dt_k15_bilinear,dt_k16_bilinear,dt_k1_complfld,dt_k1_domain_1,dt_k1_funct_1,dt_k1_rlvect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_hermitan,dt_k4_tarski,dt_k8_funct_2,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_l4_vectsp_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_vectsp_4,dt_m2_relset_1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_struct_0,dt_u2_vectsp_1,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_l4_vectsp_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_vectsp_4,existence_m2_relset_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_complfld,fc1_struct_0,fc1_subset_1,fc21_hermitan,fc22_hermitan,fc23_hermitan,fc24_hermitan,fc27_hermitan,fc2_complfld,fc2_subset_1,fc32_bilinear,fc33_bilinear,fc34_bilinear,fc35_bilinear,fc36_bilinear,fc37_bilinear,fc38_bilinear,fc39_bilinear,fc3_complfld,fc3_subset_1,fc4_subset_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,fraenkel_a_3_0_bilinear,fraenkel_a_4_0_bilinear,fraenkel_a_4_1_bilinear,free_g3_vectsp_1,free_g4_vectsp_1,rc1_bilinear,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xcmplx_0,rc1_xreal_0,rc2_bilinear,rc2_subset_1,rc2_vectsp10,rc2_xcmplx_0,rc2_xreal_0,rc3_hermitan,rc3_struct_0,rc3_vectsp10,rc3_xreal_0,rc4_hermitan,rc4_struct_0,rc4_xreal_0,rc5_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t2_tarski,t37_vectsp_4,t3_subset,t4_subset,t55_hermitan,t56_hermitan,t58_hermitan,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(hermitan,t59_hermitan)]).

fof(abstractness_v11_vectsp_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l4_vectsp_1(B,A) )
     => ( v11_vectsp_1(B,A)
       => B = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) ) ) ),
    file(vectsp_1,v11_vectsp_1),
    []).

fof(abstractness_v3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( v3_vectsp_1(A)
       => A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) ),
    file(vectsp_1,v3_vectsp_1),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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

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

fof(cc12_membered,axiom,(
    ! [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),
    []).

fof(cc13_membered,axiom,(
    ! [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),
    []).

fof(cc14_membered,axiom,(
    ! [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),
    []).

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

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

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

fof(cc18_membered,axiom,(
    ! [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),
    []).

fof(cc19_membered,axiom,(
    ! [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),
    []).

fof(cc1_complfld,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k1_complfld))
     => v1_xcmplx_0(A) ) ),
    file(complfld,cc1_complfld),
    []).

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

fof(cc1_relset_1,axiom,(
    ! [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),
    []).

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

fof(cc20_membered,axiom,(
    ! [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),
    []).

fof(cc2_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v3_hermitan(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v4_hermitan(B,A) ) ) ) ) ),
    file(hermitan,cc2_hermitan),
    []).

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

fof(cc2_xcmplx_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc2_xcmplx_0),
    []).

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

fof(cc3_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v1_bilinear(B,k1_complfld,A,A)
              & v3_hermitan(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v2_bilinear(B,k1_complfld,A,A) ) ) ) ) ),
    file(hermitan,cc3_hermitan),
    []).

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

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

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

fof(cc4_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v2_bilinear(B,k1_complfld,A,A)
              & v3_hermitan(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v1_bilinear(B,k1_complfld,A,A) ) ) ) ) ),
    file(hermitan,cc4_hermitan),
    []).

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

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

fof(cc5_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v4_bilinear(B,k1_complfld,A,A)
              & v3_hermitan(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v2_hermitan(B,A,A) ) ) ) ) ),
    file(hermitan,cc5_hermitan),
    []).

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

fof(cc6_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v2_hermitan(B,A,A)
              & v3_hermitan(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
              & v4_bilinear(B,k1_complfld,A,A) ) ) ) ) ),
    file(hermitan,cc6_hermitan),
    []).

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

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

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

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d16_bilinear,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
                    & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
                 => k12_bilinear(A,B,C,D) = a_4_0_bilinear(A,B,C,D) ) ) ) ) ),
    file(bilinear,d16_bilinear),
    []).

fof(d17_bilinear,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
                    & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
                 => k13_bilinear(A,B,C,D) = a_4_1_bilinear(A,B,C,D) ) ) ) ) ),
    file(bilinear,d17_bilinear),
    []).

fof(d18_bilinear,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
             => k14_bilinear(A,B,C) = a_3_0_bilinear(A,B,C) ) ) ) ),
    file(bilinear,d18_bilinear),
    []).

fof(d19_bilinear,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
                    & v2_bilinear(D,A,B,C)
                    & v4_bilinear(D,A,B,C)
                    & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
                 => ! [E] : 
                      ( ( ~ v3_struct_0(E)
                        & v11_vectsp_1(E,A)
                        & m1_vectsp_4(E,A,B) )
                     => ( E = k15_bilinear(A,B,C,D)
                      <=> u1_struct_0(E) = k12_bilinear(A,B,C,D) ) ) ) ) ) ) ),
    file(bilinear,d19_bilinear),
    []).

fof(d20_bilinear,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
                    & v1_bilinear(D,A,B,C)
                    & v3_bilinear(D,A,B,C)
                    & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
                 => ! [E] : 
                      ( ( ~ v3_struct_0(E)
                        & v11_vectsp_1(E,A)
                        & m1_vectsp_4(E,A,C) )
                     => ( E = k16_bilinear(A,B,C,D)
                      <=> u1_struct_0(E) = k13_bilinear(A,B,C,D) ) ) ) ) ) ) ),
    file(bilinear,d20_bilinear),
    []).

fof(d2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => k1_rlvect_1(A) = u2_struct_0(A) ) ),
    file(rlvect_1,d2_rlvect_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_g3_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ( v3_vectsp_1(g3_vectsp_1(A,B,C,D,E))
        & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ),
    file(vectsp_1,g3_vectsp_1),
    []).

fof(dt_g4_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B)
        & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) )
     => ( v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A)
        & l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) ),
    file(vectsp_1,g4_vectsp_1),
    []).

fof(dt_k12_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => m1_subset_1(k12_bilinear(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(bilinear,k12_bilinear),
    []).

fof(dt_k13_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => m1_subset_1(k13_bilinear(A,B,C,D),k1_zfmisc_1(u1_struct_0(C))) ) ),
    file(bilinear,k13_bilinear),
    []).

fof(dt_k14_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
     => m1_subset_1(k14_bilinear(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(bilinear,k14_bilinear),
    []).

fof(dt_k15_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v2_bilinear(D,A,B,C)
        & v4_bilinear(D,A,B,C)
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k15_bilinear(A,B,C,D))
        & v11_vectsp_1(k15_bilinear(A,B,C,D),A)
        & m1_vectsp_4(k15_bilinear(A,B,C,D),A,B) ) ) ),
    file(bilinear,k15_bilinear),
    []).

fof(dt_k16_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v1_bilinear(D,A,B,C)
        & v3_bilinear(D,A,B,C)
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k16_bilinear(A,B,C,D))
        & v11_vectsp_1(k16_bilinear(A,B,C,D),A)
        & m1_vectsp_4(k16_bilinear(A,B,C,D),A,C) ) ) ),
    file(bilinear,k16_bilinear),
    []).

fof(dt_k1_complfld,axiom,
    ( v3_vectsp_1(k1_complfld)
    & l3_vectsp_1(k1_complfld) ),
    file(complfld,k1_complfld),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

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

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_hermitan,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,k1_complfld)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
     => ( v1_funct_1(k3_hermitan(A,B,C))
        & v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & m2_relset_1(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) ) ) ),
    file(hermitan,k3_hermitan),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

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

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

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

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

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_l4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l4_vectsp_1(B,A)
         => l1_rlvect_1(B) ) ) ),
    file(vectsp_1,l4_vectsp_1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m1_vectsp_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ! [C] : 
          ( m1_vectsp_4(C,A,B)
         => ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,A)
            & l4_vectsp_1(C,A) ) ) ) ),
    file(vectsp_4,m1_vectsp_4),
    []).

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),
    []).

fof(dt_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    []).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    []).

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

fof(dt_u1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)) ) ),
    file(vectsp_1,u1_vectsp_1),
    []).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    []).

fof(dt_u2_vectsp_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l4_vectsp_1(B,A) )
     => ( v1_funct_1(u2_vectsp_1(A,B))
        & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B))
        & m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) ) ) ),
    file(vectsp_1,u2_vectsp_1),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

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

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

fof(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

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

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(existence_l4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l4_vectsp_1(B,A) ) ),
    file(vectsp_1,l4_vectsp_1),
    []).

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

fof(existence_m1_vectsp_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ? [C] : m1_vectsp_4(C,A,B) ) ),
    file(vectsp_4,m1_vectsp_4),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc12_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    []).

fof(fc13_membered,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    []).

fof(fc14_membered,axiom,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    []).

fof(fc15_membered,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    []).

fof(fc16_membered,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    []).

fof(fc1_complfld,axiom,
    ( ~ v3_struct_0(k1_complfld)
    & v3_vectsp_1(k1_complfld) ),
    file(complfld,fc1_complfld),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc21_hermitan,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,k1_complfld)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v1_bilinear(C,k1_complfld,A,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
     => ( v1_relat_1(k3_hermitan(A,B,C))
        & v1_funct_1(k3_hermitan(A,B,C))
        & v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v1_bilinear(k3_hermitan(A,B,C),k1_complfld,A,B) ) ) ),
    file(hermitan,fc21_hermitan),
    []).

fof(fc22_hermitan,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,k1_complfld)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v2_bilinear(C,k1_complfld,A,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
     => ( v1_relat_1(k3_hermitan(A,B,C))
        & v1_funct_1(k3_hermitan(A,B,C))
        & v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v2_bilinear(k3_hermitan(A,B,C),k1_complfld,A,B) ) ) ),
    file(hermitan,fc22_hermitan),
    []).

fof(fc23_hermitan,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,k1_complfld)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v3_bilinear(C,k1_complfld,A,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
     => ( v1_relat_1(k3_hermitan(A,B,C))
        & v1_funct_1(k3_hermitan(A,B,C))
        & v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v2_hermitan(k3_hermitan(A,B,C),A,B) ) ) ),
    file(hermitan,fc23_hermitan),
    []).

fof(fc24_hermitan,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,k1_complfld)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v2_hermitan(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
     => ( v1_relat_1(k3_hermitan(A,B,C))
        & v1_funct_1(k3_hermitan(A,B,C))
        & v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
        & v3_bilinear(k3_hermitan(A,B,C),k1_complfld,A,B) ) ) ),
    file(hermitan,fc24_hermitan),
    []).

fof(fc27_hermitan,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v12_vectsp_1(A,k1_complfld)
        & l4_vectsp_1(A,k1_complfld)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
        & v2_hermitan(B,A,A)
        & m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
     => ~ v1_xboole_0(k14_bilinear(k1_complfld,A,B)) ) ),
    file(hermitan,fc27_hermitan),
    []).

fof(fc2_complfld,axiom,
    ( ~ v3_struct_0(k1_complfld)
    & v2_group_1(k1_complfld)
    & v3_vectsp_1(k1_complfld)
    & v6_vectsp_1(k1_complfld)
    & v8_vectsp_1(k1_complfld) ),
    file(complfld,fc2_complfld),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc32_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v2_bilinear(D,A,B,C)
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k12_bilinear(A,B,C,D)) ) ),
    file(bilinear,fc32_bilinear),
    []).

fof(fc33_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v4_bilinear(D,A,B,C)
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k12_bilinear(A,B,C,D)) ) ),
    file(bilinear,fc33_bilinear),
    []).

fof(fc34_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v5_rlvect_1(C)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v1_bilinear(D,A,B,C)
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k13_bilinear(A,B,C,D)) ) ),
    file(bilinear,fc34_bilinear),
    []).

fof(fc35_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v3_bilinear(D,A,B,C)
        & m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k13_bilinear(A,B,C,D)) ) ),
    file(bilinear,fc35_bilinear),
    []).

fof(fc36_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
        & v1_bilinear(C,A,B,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ),
    file(bilinear,fc36_bilinear),
    []).

fof(fc37_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
        & v2_bilinear(C,A,B,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ),
    file(bilinear,fc37_bilinear),
    []).

fof(fc38_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
        & v3_bilinear(C,A,B,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ),
    file(bilinear,fc38_bilinear),
    []).

fof(fc39_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
        & v4_bilinear(C,A,B,B)
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
     => ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ),
    file(bilinear,fc39_bilinear),
    []).

fof(fc3_complfld,axiom,
    ( ~ v3_struct_0(k1_complfld)
    & v3_rlvect_1(k1_complfld)
    & v4_rlvect_1(k1_complfld)
    & v5_rlvect_1(k1_complfld)
    & v6_rlvect_1(k1_complfld)
    & v2_group_1(k1_complfld)
    & v4_group_1(k1_complfld)
    & v7_group_1(k1_complfld)
    & v3_vectsp_1(k1_complfld)
    & v4_vectsp_1(k1_complfld)
    & v5_vectsp_1(k1_complfld)
    & v6_vectsp_1(k1_complfld)
    & v7_vectsp_1(k1_complfld)
    & v8_vectsp_1(k1_complfld)
    & v9_vectsp_1(k1_complfld)
    & ~ v10_vectsp_1(k1_complfld) ),
    file(complfld,fc3_complfld),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc6_membered,axiom,
    ( 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),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

fof(fc8_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

fof(fraenkel_a_3_0_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( l2_struct_0(B)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B))
        & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_bilinear(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & k8_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B),D,k1_domain_1(u1_struct_0(C),u1_struct_0(C),E,E)) = k1_rlvect_1(B) ) ) ) ),
    file(bilinear,a_3_0_bilinear),
    []).

fof(fraenkel_a_4_0_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l2_struct_0(B)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,B)
        & ~ v3_struct_0(D)
        & l4_vectsp_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B))
        & m2_relset_1(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)) )
     => ( r2_hidden(A,a_4_0_bilinear(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,u1_struct_0(C))
            & A = F
            & ! [G] : 
                ( m1_subset_1(G,u1_struct_0(D))
               => k8_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B),E,k1_domain_1(u1_struct_0(C),u1_struct_0(D),F,G)) = k1_rlvect_1(B) ) ) ) ) ),
    file(bilinear,a_4_0_bilinear),
    []).

fof(fraenkel_a_4_1_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l2_struct_0(B)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,B)
        & ~ v3_struct_0(D)
        & l4_vectsp_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B))
        & m2_relset_1(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)) )
     => ( r2_hidden(A,a_4_1_bilinear(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,u1_struct_0(D))
            & A = F
            & ! [G] : 
                ( m1_subset_1(G,u1_struct_0(C))
               => k8_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B),E,k1_domain_1(u1_struct_0(C),u1_struct_0(D),G,F)) = k1_rlvect_1(B) ) ) ) ) ),
    file(bilinear,a_4_1_bilinear),
    []).

fof(free_g3_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ! [F,G,H,I,J] : 
          ( g3_vectsp_1(A,B,C,D,E) = g3_vectsp_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) ),
    file(vectsp_1,g3_vectsp_1),
    []).

fof(free_g4_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B)
        & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) )
     => ! [F,G,H,I,J] : 
          ( g4_vectsp_1(A,B,C,D,E) = g4_vectsp_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) ),
    file(vectsp_1,g4_vectsp_1),
    []).

fof(rc1_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A) )
     => ? [D] : 
          ( m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
          & v1_relat_1(D)
          & v1_funct_1(D)
          & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
          & v1_bilinear(D,A,B,C)
          & v2_bilinear(D,A,B,C) ) ) ),
    file(bilinear,rc1_bilinear),
    []).

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

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

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

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

fof(rc2_bilinear,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,A) )
     => ? [D] : 
          ( m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
          & v1_relat_1(D)
          & v1_funct_1(D)
          & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
          & v1_bilinear(D,A,B,C)
          & v2_bilinear(D,A,B,C)
          & v3_bilinear(D,A,B,C)
          & v4_bilinear(D,A,B,C) ) ) ),
    file(bilinear,rc2_bilinear),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_vectsp10,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l3_vectsp_1(A) )
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v11_vectsp_1(B,A) ) ) ),
    file(vectsp10,rc2_vectsp10),
    []).

fof(rc2_xcmplx_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_0),
    []).

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

fof(rc3_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ? [B] : 
          ( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
          & v1_bilinear(B,k1_complfld,A,A)
          & v2_bilinear(B,k1_complfld,A,A)
          & v4_bilinear(B,k1_complfld,A,A)
          & v2_hermitan(B,A,A)
          & v3_hermitan(B,A)
          & v4_hermitan(B,A)
          & v5_hermitan(B,A) ) ) ),
    file(hermitan,rc3_hermitan),
    []).

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

fof(rc3_vectsp10,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v11_vectsp_1(B,A)
          & v12_vectsp_1(B,A) ) ) ),
    file(vectsp10,rc3_vectsp10),
    []).

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

fof(rc4_hermitan,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,k1_complfld) )
     => ? [C] : 
          ( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
          & v1_bilinear(C,k1_complfld,A,B)
          & v2_bilinear(C,k1_complfld,A,B)
          & v4_bilinear(C,k1_complfld,A,B)
          & v2_hermitan(C,A,B) ) ) ),
    file(hermitan,rc4_hermitan),
    []).

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

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

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

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

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

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

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

fof(t37_vectsp_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( v11_vectsp_1(C,A)
                & m1_vectsp_4(C,A,B) )
             => ! [D] : 
                  ( ( v11_vectsp_1(D,A)
                    & m1_vectsp_4(D,A,B) )
                 => ( u1_struct_0(C) = u1_struct_0(D)
                   => C = D ) ) ) ) ) ),
    file(vectsp_4,t37_vectsp_4),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

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

fof(t55_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v12_vectsp_1(A,k1_complfld)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
            & v2_bilinear(B,k1_complfld,A,A)
            & v4_bilinear(B,k1_complfld,A,A)
            & v3_hermitan(B,A)
            & v5_hermitan(B,A)
            & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
         => k14_bilinear(k1_complfld,A,B) = k12_bilinear(k1_complfld,A,A,B) ) ) ),
    file(hermitan,t55_hermitan),
    []).

fof(t56_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v12_vectsp_1(A,k1_complfld)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
            & v2_bilinear(B,k1_complfld,A,A)
            & v4_bilinear(B,k1_complfld,A,A)
            & v3_hermitan(B,A)
            & v5_hermitan(B,A)
            & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
         => k14_bilinear(k1_complfld,A,B) = k13_bilinear(k1_complfld,A,A,B) ) ) ),
    file(hermitan,t56_hermitan),
    []).

fof(t58_hermitan,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_vectsp_1(A,k1_complfld) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,k1_complfld) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
             => ( k12_bilinear(k1_complfld,A,B,C) = k12_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))
                & k13_bilinear(k1_complfld,A,B,C) = k13_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)) ) ) ) ) ),
    file(hermitan,t58_hermitan),
    []).

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

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

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

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