% Mizar problem: t54_bilinear,bilinear,2791,63 
fof(t54_bilinear,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(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,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
                     => ( D != k7_hahnban1(A,B)
                       => k13_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k8_vectsp10(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,cc1_vectsp10,cc1_vectsp_1,cc2_vectsp_1,cc3_vectsp10,cc3_vectsp_1,cc4_vectsp_1,cc5_vectsp_1,commutativity_k10_group_1,commutativity_k2_tarski,d10_hahnban1,d10_xboole_0,d11_bilinear,d17_bilinear,d3_tarski,d5_tarski,d9_vectsp10,dt_k10_group_1,dt_k11_bilinear,dt_k13_bilinear,dt_k1_borsuk_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_group_1,dt_k1_rlvect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_pre_topc,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_k7_hahnban1,dt_k8_funct_2,dt_k8_vectsp10,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_m2_relset_1,dt_u1_struct_0,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_m2_relset_1,fc10_bilinear,fc10_vectsp10,fc11_bilinear,fc12_bilinear,fc1_hahnban1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_hahnban1,fc2_subset_1,fc34_bilinear,fc3_hahnban1,fc3_subset_1,fc4_subset_1,fc8_vectsp10,fc9_bilinear,fraenkel_a_3_1_vectsp10,fraenkel_a_3_6_bilinear,fraenkel_a_4_1_bilinear,rc1_bilinear,rc1_hahnban1,rc1_subset_1,rc1_xboole_0,rc2_bilinear,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc4_struct_0,rc5_struct_0,rc5_vectsp10,rc6_vectsp10,rc7_vectsp10,rc8_vectsp_1,rc9_vectsp_1,redefinition_k10_group_1,redefinition_k1_borsuk_1,redefinition_k1_domain_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t113_funct_2,t1_subset,t22_hahnban1,t2_subset,t2_tarski,t3_subset,t44_vectsp_1,t4_subset,t53_bilinear,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(bilinear,t54_bilinear)]).

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

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_vectsp10,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ! [C] : 
          ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
              & v1_hahnban1(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
              & v3_hahnban1(C,A,B) ) ) ) ) ),
    file(vectsp10,cc1_vectsp10),
    []).

fof(cc1_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc1_vectsp_1),
    []).

fof(cc2_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc2_vectsp_1),
    []).

fof(cc3_vectsp10,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ! [C] : 
          ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
              & ~ v5_seqm_3(C) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
              & ~ v1_realset1(C) ) ) ) ) ),
    file(vectsp10,cc3_vectsp10),
    []).

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc5_vectsp_1),
    []).

fof(commutativity_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k10_group_1(A,B,C) = k10_group_1(A,C,B) ) ),
    file(group_1,k10_group_1),
    []).

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

fof(d10_hahnban1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( l4_vectsp_1(B,A)
         => k7_hahnban1(A,B) = k1_borsuk_1(u1_struct_0(A),k2_pre_topc(B),k1_rlvect_1(A)) ) ) ),
    file(hahnban1,d10_hahnban1),
    []).

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

fof(d11_bilinear,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(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,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
                            & m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
                         => ( F = k11_bilinear(A,B,C,D,E)
                          <=> ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(C))
                                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),F,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)) = k1_group_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G),k8_funct_2(u1_struct_0(C),u1_struct_0(A),E,H)) ) ) ) ) ) ) ) ) ) ),
    file(bilinear,d11_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(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

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

fof(d9_vectsp10,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => k8_vectsp10(A,B,C) = a_3_1_vectsp10(A,B,C) ) ) ) ),
    file(vectsp10,d9_vectsp10),
    []).

fof(dt_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k10_group_1),
    []).

fof(dt_k11_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(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,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
     => ( v1_funct_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & m2_relset_1(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ),
    file(bilinear,k11_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_k1_borsuk_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k1_borsuk_1(A,B,C))
        & v1_funct_2(k1_borsuk_1(A,B,C),B,A)
        & m2_relset_1(k1_borsuk_1(A,B,C),B,A) ) ) ),
    file(borsuk_1,k1_borsuk_1),
    []).

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_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k1_group_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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

fof(dt_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k7_hahnban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & l4_vectsp_1(B,A) )
     => ( v1_funct_1(k7_hahnban1(A,B))
        & v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
        & m2_relset_1(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(hahnban1,k7_hahnban1),
    []).

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_k8_vectsp10,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => m1_subset_1(k8_vectsp10(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(vectsp10,k8_vectsp10),
    []).

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_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_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

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_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc10_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_group_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)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
        & v1_hahnban1(D,A,B)
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
     => ( v1_relat_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v2_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ),
    file(bilinear,fc10_bilinear),
    []).

fof(fc10_vectsp10,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)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
        & v3_hahnban1(C,A,B)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ~ v1_xboole_0(k8_vectsp10(A,B,C)) ) ),
    file(vectsp10,fc10_vectsp10),
    []).

fof(fc11_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_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)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
        & v2_hahnban1(E,A,C)
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
     => ( v1_relat_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v3_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ),
    file(bilinear,fc11_bilinear),
    []).

fof(fc12_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_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)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
        & v2_hahnban1(D,A,B)
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
     => ( v1_relat_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v4_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ),
    file(bilinear,fc12_bilinear),
    []).

fof(fc1_hahnban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ( v1_relat_1(k7_hahnban1(A,B))
        & v1_funct_1(k7_hahnban1(A,B))
        & v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
        & v1_hahnban1(k7_hahnban1(A,B),A,B) ) ) ),
    file(hahnban1,fc1_hahnban1),
    []).

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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_hahnban1,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ( v1_relat_1(k7_hahnban1(A,B))
        & v1_funct_1(k7_hahnban1(A,B))
        & v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
        & v1_hahnban1(k7_hahnban1(A,B),A,B)
        & v2_hahnban1(k7_hahnban1(A,B),A,B) ) ) ),
    file(hahnban1,fc2_hahnban1),
    []).

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

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(fc3_hahnban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ( v1_relat_1(k7_hahnban1(A,B))
        & v1_funct_1(k7_hahnban1(A,B))
        & v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
        & v3_hahnban1(k7_hahnban1(A,B),A,B) ) ) ),
    file(hahnban1,fc3_hahnban1),
    []).

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(fc8_vectsp10,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ( v1_relat_1(k7_hahnban1(A,B))
        & v1_funct_1(k7_hahnban1(A,B))
        & v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
        & v5_seqm_3(k7_hahnban1(A,B))
        & v3_hahnban1(k7_hahnban1(A,B),A,B) ) ) ),
    file(vectsp10,fc8_vectsp10),
    []).

fof(fc9_bilinear,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ 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)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
        & v1_hahnban1(E,A,C)
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
     => ( v1_relat_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_1(k11_bilinear(A,B,C,D,E))
        & v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
        & v1_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ),
    file(bilinear,fc9_bilinear),
    []).

fof(fraenkel_a_3_1_vectsp10,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,B)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
        & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_vectsp10(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) = k1_rlvect_1(B) ) ) ) ),
    file(vectsp10,a_3_1_vectsp10),
    []).

fof(fraenkel_a_3_6_bilinear,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & v9_vectsp_1(B)
        & l3_vectsp_1(B)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,B)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
        & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_6_bilinear(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) = k1_rlvect_1(B) ) ) ) ),
    file(bilinear,a_3_6_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(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_hahnban1,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
          & v1_hahnban1(C,A,B)
          & v2_hahnban1(C,A,B)
          & v3_hahnban1(C,A,B) ) ) ),
    file(hahnban1,rc1_hahnban1),
    []).

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_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_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(rc5_vectsp10,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
          & v1_hahnban1(C,A,B)
          & v3_hahnban1(C,A,B) ) ) ),
    file(vectsp10,rc5_vectsp10),
    []).

fof(rc6_vectsp10,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
          & v5_seqm_3(C) ) ) ),
    file(vectsp10,rc6_vectsp10),
    []).

fof(rc7_vectsp10,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
          & v5_seqm_3(C)
          & v1_hahnban1(C,A,B)
          & v3_hahnban1(C,A,B) ) ) ),
    file(vectsp10,rc7_vectsp10),
    []).

fof(rc8_vectsp_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v4_group_1(A)
      & v7_group_1(A) ) ),
    file(vectsp_1,rc8_vectsp_1),
    []).

fof(rc9_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A) ) ),
    file(vectsp_1,rc9_vectsp_1),
    []).

fof(redefinition_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k10_group_1(A,B,C) = k1_group_1(A,B,C) ) ),
    file(group_1,k10_group_1),
    []).

fof(redefinition_k1_borsuk_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k1_borsuk_1(A,B,C) = k2_funcop_1(B,C) ) ),
    file(borsuk_1,k1_borsuk_1),
    []).

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(t113_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( m1_subset_1(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t113_funct_2),
    []).

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

fof(t22_hahnban1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_hahnban1(A,B),C) = k1_rlvect_1(A) ) ) ) ),
    file(hahnban1,t22_hahnban1),
    []).

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

fof(t44_vectsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k10_group_1(A,B,C) = k1_rlvect_1(A)
              <=> ( B = k1_rlvect_1(A)
                  | C = k1_rlvect_1(A) ) ) ) ) ) ),
    file(vectsp_1,t44_vectsp_1),
    []).

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(t53_bilinear,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(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,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
                     => r1_tarski(k8_vectsp10(A,C,E),k13_bilinear(A,B,C,k11_bilinear(A,B,C,D,E))) ) ) ) ) ) ),
    file(bilinear,t53_bilinear),
    []).

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),
    []).