% Mizar problem: t22_vectsp_9,vectsp_9,980,66 
fof(t22_vectsp_9,conjecture,(
    ! [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_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_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] : 
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
             => ! [D] : 
                  ( ( v1_finset_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ~ ( r1_rlvect_1(k1_vectsp_7(A,B,k4_subset_1(u1_struct_0(B),C,D)),E)
                          & ~ r1_rlvect_1(k1_vectsp_7(A,B,D),E)
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ~ ( r2_hidden(F,C)
                                  & r1_rlvect_1(k1_vectsp_7(A,B,k4_subset_1(u1_struct_0(B),k6_subset_1(u1_struct_0(B),k4_subset_1(u1_struct_0(B),C,D),k1_struct_0(B,F)),k1_struct_0(B,E))),F) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v11_vectsp_1,antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_funct_2,cc1_nat_1,cc1_relset_1,cc1_vectsp_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc2_vectsp_1,cc2_xreal_0,cc3_nat_1,cc3_vectsp_1,cc3_xreal_0,cc4_vectsp_1,cc4_xreal_0,cc5_funct_2,cc5_vectsp_1,cc5_xreal_0,cc6_funct_2,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_rlvect_1,commutativity_k4_subset_1,d11_rlvect_1,d1_tarski,d26_vectsp_1,d7_vectsp_6,d9_vectsp_6,dt_g4_vectsp_1,dt_k12_finseq_1,dt_k1_finseq_3,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_group_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_vectsp_6,dt_k1_vectsp_7,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_group_1,dt_k2_relat_1,dt_k2_rlvect_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_vectsp_6,dt_k3_xboole_0,dt_k4_rlvect_1,dt_k4_subset_1,dt_k4_vectsp_1,dt_k4_vectsp_6,dt_k4_xboole_0,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_rlvect_1,dt_k5_vectsp_6,dt_k6_finseq_4,dt_k6_rlvect_1,dt_k6_subset_1,dt_k6_vectsp_1,dt_k6_vectsp_6,dt_k7_finseq_1,dt_k7_finseq_4,dt_k7_vectsp_6,dt_k8_finseq_1,dt_k8_funct_2,dt_k9_finseq_1,dt_k9_rlvect_1,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_finseq_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m1_vectsp_4,dt_m1_vectsp_6,dt_m2_finseq_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_vectsp_6,dt_u1_rlvect_1,dt_u1_struct_0,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_finseq_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m1_vectsp_4,existence_m1_vectsp_6,existence_m2_finseq_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_vectsp_6,fc10_finset_1,fc11_finseq_1,fc11_finset_1,fc12_finseq_1,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_finset_1,fc1_funct_2,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_funct_2,fc2_subset_1,fc3_finseq_1,fc4_finseq_1,fc4_subset_1,fc6_vectsp_1,fc9_finset_1,free_g4_vectsp_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,involutiveness_k7_vectsp_6,rc11_vectsp_1,rc12_vectsp_1,rc13_vectsp_1,rc1_finseq_1,rc1_finset_1,rc1_funct_2,rc1_nat_1,rc1_subset_1,rc1_vectsp_9,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc3_struct_0,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_struct_0,rc4_xreal_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rc8_vectsp_1,rc9_vectsp_1,redefinition_k12_finseq_1,redefinition_k1_fraenkel,redefinition_k1_struct_0,redefinition_k4_rlvect_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k6_subset_1,redefinition_k8_finseq_1,redefinition_k8_funct_2,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,t10_finseq_4,t12_vectsp_7,t13_vectsp_7,t13_xboole_1,t19_vectsp_6,t1_boole,t1_subset,t1_xboole_1,t22_vectsp_2,t28_xboole_1,t2_boole,t2_subset,t33_xboole_1,t34_vectsp_6,t36_xboole_1,t37_vectsp_6,t3_boole,t3_subset,t3_xboole_0,t45_finseq_1,t4_boole,t4_subset,t51_vectsp_6,t53_finseq_4,t58_rlvect_1,t58_vectsp_6,t5_subset,t61_rlvect_1,t65_finseq_4,t66_finseq_4,t67_finseq_4,t67_vectsp_1,t68_finseq_4,t69_finseq_4,t69_vectsp_6,t6_boole,t70_vectsp_1,t72_finseq_3,t72_finseq_4,t73_xboole_1,t77_vectsp_6,t78_vectsp_6,t79_vectsp_6,t7_boole,t7_vectsp_1,t8_boole,t8_vectsp_9,t98_finseq_3]),
    [file(vectsp_9,t22_vectsp_9)]).

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

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

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

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

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

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_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(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

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_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(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_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(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_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

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(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_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(d11_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) ) ) ) ),
    file(rlvect_1,d11_rlvect_1),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d26_vectsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ( v12_vectsp_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ( k6_vectsp_1(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,C,F))
                              & k6_vectsp_1(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E))
                              & k6_vectsp_1(A,B,k1_group_1(A,C,D),E) = k6_vectsp_1(A,B,C,k6_vectsp_1(A,B,D,E))
                              & k6_vectsp_1(A,B,k2_group_1(A),E) = E ) ) ) ) ) ) ) ) ),
    file(vectsp_1,d26_vectsp_1),
    []).

fof(d7_vectsp_6,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,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => ( m2_vectsp_6(D,A,B,C)
                  <=> r1_tarski(k1_vectsp_6(A,B,D),C) ) ) ) ) ) ),
    file(vectsp_6,d7_vectsp_6),
    []).

fof(d9_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_6(C,A,B)
             => ( ( v3_rlvect_1(B)
                  & v4_rlvect_1(B)
                  & v5_rlvect_1(B)
                  & v6_rlvect_1(B) )
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( D = k4_vectsp_6(A,B,C)
                    <=> ? [E] : 
                          ( m2_finseq_1(E,u1_struct_0(B))
                          & v2_funct_1(E)
                          & k2_relat_1(E) = k1_vectsp_6(A,B,C)
                          & D = k9_rlvect_1(B,k3_vectsp_6(A,B,E,C)) ) ) ) ) ) ) ) ),
    file(vectsp_6,d9_vectsp_6),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_1(k12_finseq_1(A,B),A) ) ),
    file(finseq_1,k12_finseq_1),
    []).

fof(dt_k1_finseq_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k1_finseq_3(A,B))
        & v1_funct_1(k1_finseq_3(A,B))
        & v1_finseq_1(k1_finseq_3(A,B)) ) ) ),
    file(finseq_3,k1_finseq_3),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

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

fof(dt_k1_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B) )
     => ( v1_finset_1(k1_vectsp_6(A,B,C))
        & m1_subset_1(k1_vectsp_6(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ) ),
    file(vectsp_6,k1_vectsp_6),
    []).

fof(dt_k1_vectsp_7,axiom,(
    ! [A,B,C] : 
      ( ( ~ 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_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_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)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( v11_vectsp_1(k1_vectsp_7(A,B,C),A)
        & m1_vectsp_4(k1_vectsp_7(A,B,C),A,B) ) ) ),
    file(vectsp_7,k1_vectsp_7),
    []).

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_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ),
    file(group_1,k2_group_1),
    []).

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

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_vectsp_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_finseq_1(C,u1_struct_0(B))
        & 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)) )
     => m2_finseq_1(k3_vectsp_6(A,B,C,D),u1_struct_0(B)) ) ),
    file(vectsp_6,k3_vectsp_6),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_vectsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(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)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)) ) ),
    file(vectsp_1,k4_vectsp_1),
    []).

fof(dt_k4_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B) )
     => m1_subset_1(k4_vectsp_6(A,B,C),u1_struct_0(B)) ) ),
    file(vectsp_6,k4_vectsp_6),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

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

fof(dt_k5_rlvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ),
    file(rlvect_1,k5_rlvect_1),
    []).

fof(dt_k5_vectsp_6,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)
        & m1_vectsp_6(C,A,B)
        & m1_vectsp_6(D,A,B) )
     => m1_vectsp_6(k5_vectsp_6(A,B,C,D),A,B) ) ),
    file(vectsp_6,k5_vectsp_6),
    []).

fof(dt_k6_finseq_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k6_finseq_4(A,B))
        & v1_funct_1(k6_finseq_4(A,B))
        & v1_finseq_1(k6_finseq_4(A,B)) ) ) ),
    file(finseq_4,k6_finseq_4),
    []).

fof(dt_k6_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k6_rlvect_1),
    []).

fof(dt_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(dt_k6_vectsp_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)) ) ),
    file(vectsp_1,k6_vectsp_1),
    []).

fof(dt_k6_vectsp_6,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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_vectsp_6(D,A,B) )
     => m1_vectsp_6(k6_vectsp_6(A,B,C,D),A,B) ) ),
    file(vectsp_6,k6_vectsp_6),
    []).

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    []).

fof(dt_k7_finseq_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k7_finseq_4(A,B))
        & v1_funct_1(k7_finseq_4(A,B))
        & v1_finseq_1(k7_finseq_4(A,B)) ) ) ),
    file(finseq_4,k7_finseq_4),
    []).

fof(dt_k7_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ 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)
        & m1_vectsp_6(C,A,B) )
     => m1_vectsp_6(k7_vectsp_6(A,B,C),A,B) ) ),
    file(vectsp_6,k7_vectsp_6),
    []).

fof(dt_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ),
    file(finseq_1,k8_finseq_1),
    []).

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_k9_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k9_finseq_1(A))
      & v1_funct_1(k9_finseq_1(A)) ) ),
    file(finseq_1,k9_finseq_1),
    []).

fof(dt_k9_rlvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_finseq_1(B,u1_struct_0(A)) )
     => m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)) ) ),
    file(rlvect_1,k9_rlvect_1),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

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_m1_vectsp_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ! [C] : 
          ( m1_vectsp_6(C,A,B)
         => m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))) ) ) ),
    file(vectsp_6,m1_vectsp_6),
    []).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_m2_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ! [D] : 
          ( m2_vectsp_6(D,A,B,C)
         => m1_vectsp_6(D,A,B) ) ) ),
    file(vectsp_6,m2_vectsp_6),
    []).

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_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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

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_m1_vectsp_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ? [C] : m1_vectsp_6(C,A,B) ) ),
    file(vectsp_6,m1_vectsp_6),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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

fof(existence_m2_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ? [D] : m2_vectsp_6(D,A,B,C) ) ),
    file(vectsp_6,m2_vectsp_6),
    []).

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc12_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    []).

fof(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

fof(fc13_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(A,B))
        & v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,fc13_finseq_1),
    []).

fof(fc14_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(B,A))
        & v1_relat_1(k7_finseq_1(B,A))
        & v1_funct_1(k7_finseq_1(B,A))
        & v1_finset_1(k7_finseq_1(B,A))
        & v1_finseq_1(k7_finseq_1(B,A)) ) ) ),
    file(finseq_1,fc14_finseq_1),
    []).

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

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

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(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

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

fof(fc3_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    []).

fof(fc4_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_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_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & 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) )
     => ( ~ v3_struct_0(g4_vectsp_1(A,B,C,D,E))
        & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) ),
    file(vectsp_1,fc6_vectsp_1),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_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(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(involutiveness_k7_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ 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)
        & m1_vectsp_6(C,A,B) )
     => k7_vectsp_6(A,B,k7_vectsp_6(A,B,C)) = C ) ),
    file(vectsp_6,k7_vectsp_6),
    []).

fof(rc11_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & v11_vectsp_1(B,A) ) ) ),
    file(vectsp_1,rc11_vectsp_1),
    []).

fof(rc12_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v11_vectsp_1(B,A) ) ) ),
    file(vectsp_1,rc12_vectsp_1),
    []).

fof(rc13_vectsp_1,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] : 
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v11_vectsp_1(B,A)
          & v12_vectsp_1(B,A) ) ) ),
    file(vectsp_1,rc13_vectsp_1),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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_vectsp_9,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(vectsp_9,rc1_vectsp_9),
    []).

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

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

fof(rc2_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

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_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_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

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

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

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_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k12_finseq_1(A,B) = k5_finseq_1(B) ) ),
    file(finseq_1,k12_finseq_1),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

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

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(redefinition_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ),
    file(finseq_1,k8_finseq_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_k9_finseq_1,axiom,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_1),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t10_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k2_relat_1(A))
           => r2_finseq_4(A,B) ) ) ) ),
    file(finseq_4,t10_finseq_4),
    []).

fof(t12_vectsp_7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(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)
        & ~ v10_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [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,B)
            & l4_vectsp_1(C,B) )
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
             => ( r1_rlvect_1(k1_vectsp_7(B,C,D),A)
              <=> ? [E] : 
                    ( m2_vectsp_6(E,B,C,D)
                    & A = k4_vectsp_6(B,C,E) ) ) ) ) ) ),
    file(vectsp_7,t12_vectsp_7),
    []).

fof(t13_vectsp_7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(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)
        & ~ v10_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [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,B)
            & l4_vectsp_1(C,B) )
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
             => ( r2_hidden(A,D)
               => r1_rlvect_1(k1_vectsp_7(B,C,D),A) ) ) ) ) ),
    file(vectsp_7,t13_vectsp_7),
    []).

fof(t13_xboole_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    []).

fof(t19_vectsp_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [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,B)
            & l4_vectsp_1(C,B) )
         => ! [D] : 
              ( m1_vectsp_6(D,B,C)
             => ( r2_hidden(A,k1_vectsp_6(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(vectsp_6,t19_vectsp_6),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t22_vectsp_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( k4_rlvect_1(A,B,C) = D
                     => B = k6_rlvect_1(A,D,C) )
                    & ( B = k6_rlvect_1(A,D,C)
                     => k4_rlvect_1(A,B,C) = D )
                    & ( k4_rlvect_1(A,B,C) = D
                     => C = k6_rlvect_1(A,D,B) )
                    & ( C = k6_rlvect_1(A,D,B)
                     => k4_rlvect_1(A,B,C) = D ) ) ) ) ) ) ),
    file(vectsp_2,t22_vectsp_2),
    []).

fof(t28_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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

fof(t33_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ),
    file(xboole_1,t33_xboole_1),
    []).

fof(t34_vectsp_6,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] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [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)) )
                 => k3_vectsp_6(A,B,k12_finseq_1(u1_struct_0(B),C),D) = k12_finseq_1(u1_struct_0(B),k6_vectsp_1(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C)) ) ) ) ) ),
    file(vectsp_6,t34_vectsp_6),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t37_vectsp_6,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] : 
              ( m2_finseq_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
                     => k3_vectsp_6(A,B,k8_finseq_1(u1_struct_0(B),C,D),E) = k8_finseq_1(u1_struct_0(B),k3_vectsp_6(A,B,C,E),k3_vectsp_6(A,B,D,E)) ) ) ) ) ) ),
    file(vectsp_6,t37_vectsp_6),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t45_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ),
    file(finseq_1,t45_finseq_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t51_vectsp_6,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] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => r1_tarski(k1_vectsp_6(A,B,k5_vectsp_6(A,B,C,D)),k4_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,C),k1_vectsp_6(A,B,D))) ) ) ) ) ),
    file(vectsp_6,t51_vectsp_6),
    []).

fof(t53_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B,C] : 
          ( ~ v1_xboole_0(C)
         => ( ( r2_hidden(B,k2_relat_1(A))
              & m2_finseq_1(A,C) )
           => m2_finseq_1(k6_finseq_4(A,B),C) ) ) ) ),
    file(finseq_4,t53_finseq_4),
    []).

fof(t58_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) ) ) ) ),
    file(rlvect_1,t58_rlvect_1),
    []).

fof(t58_vectsp_6,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] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => r1_tarski(k1_vectsp_6(A,B,k6_vectsp_6(A,B,C,D)),k1_vectsp_6(A,B,D)) ) ) ) ) ),
    file(vectsp_6,t58_vectsp_6),
    []).

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(t61_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) ),
    file(rlvect_1,t61_rlvect_1),
    []).

fof(t65_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B,C] : 
          ( ~ v1_xboole_0(C)
         => ( ( r2_hidden(B,k2_relat_1(A))
              & m2_finseq_1(A,C) )
           => m2_finseq_1(k7_finseq_4(A,B),C) ) ) ) ),
    file(finseq_4,t65_finseq_4),
    []).

fof(t66_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k2_relat_1(A))
         => A = k7_finseq_1(k7_finseq_1(k6_finseq_4(A,B),k9_finseq_1(B)),k7_finseq_4(A,B)) ) ) ),
    file(finseq_4,t66_finseq_4),
    []).

fof(t67_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( r2_hidden(B,k2_relat_1(A))
            & v2_funct_1(A) )
         => v2_funct_1(k6_finseq_4(A,B)) ) ) ),
    file(finseq_4,t67_finseq_4),
    []).

fof(t67_vectsp_1,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_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ~ 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) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( B != k1_rlvect_1(A)
                   => k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D ) ) ) ) ) ),
    file(vectsp_1,t67_vectsp_1),
    []).

fof(t68_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( r2_hidden(B,k2_relat_1(A))
            & v2_funct_1(A) )
         => v2_funct_1(k7_finseq_4(A,B)) ) ) ),
    file(finseq_4,t68_finseq_4),
    []).

fof(t69_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( r2_finseq_4(A,B)
        <=> ( r2_hidden(B,k2_relat_1(A))
            & k1_finseq_3(A,k1_tarski(B)) = k7_finseq_1(k6_finseq_4(A,B),k7_finseq_4(A,B)) ) ) ) ),
    file(finseq_4,t69_finseq_4),
    []).

fof(t69_vectsp_6,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] : 
              ( m1_vectsp_6(C,A,B)
             => k1_vectsp_6(A,B,k7_vectsp_6(A,B,C)) = k1_vectsp_6(A,B,C) ) ) ) ),
    file(vectsp_6,t69_vectsp_6),
    []).

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

fof(t70_vectsp_1,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ 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) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)) = k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)) ) ) ) ) ) ),
    file(vectsp_1,t70_vectsp_1),
    []).

fof(t72_finseq_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : k2_relat_1(k1_finseq_3(A,B)) = k4_xboole_0(k2_relat_1(A),B) ) ),
    file(finseq_3,t72_finseq_3),
    []).

fof(t72_finseq_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( r2_hidden(B,k2_relat_1(A))
            & v2_funct_1(A) )
         => r1_xboole_0(k2_relat_1(k6_finseq_4(A,B)),k2_relat_1(k7_finseq_4(A,B))) ) ) ),
    file(finseq_4,t72_finseq_4),
    []).

fof(t73_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,k2_xboole_0(B,C))
        & r1_xboole_0(A,C) )
     => r1_tarski(A,B) ) ),
    file(xboole_1,t73_xboole_1),
    []).

fof(t77_vectsp_6,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] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => k4_vectsp_6(A,B,k5_vectsp_6(A,B,C,D)) = k4_rlvect_1(B,k4_vectsp_6(A,B,C),k4_vectsp_6(A,B,D)) ) ) ) ) ),
    file(vectsp_6,t77_vectsp_6),
    []).

fof(t78_vectsp_6,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_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_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] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k4_vectsp_6(A,B,k6_vectsp_6(A,B,D,C)) = k6_vectsp_1(A,B,D,k4_vectsp_6(A,B,C)) ) ) ) ) ),
    file(vectsp_6,t78_vectsp_6),
    []).

fof(t79_vectsp_6,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] : 
              ( m1_vectsp_6(C,A,B)
             => k4_vectsp_6(A,B,k7_vectsp_6(A,B,C)) = k5_rlvect_1(B,k4_vectsp_6(A,B,C)) ) ) ) ),
    file(vectsp_6,t79_vectsp_6),
    []).

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

fof(t7_vectsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B)
                      & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))
                      & k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
                      & ? [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                          & k2_rlvect_1(A,B,E) = k1_rlvect_1(A) ) ) ) ) )
      <=> ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & l1_rlvect_1(A) ) ) ) ),
    file(vectsp_1,t7_vectsp_1),
    []).

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

fof(t8_vectsp_9,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_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_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] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ? [E] : 
                      ( m1_vectsp_6(E,A,B)
                      & k1_vectsp_6(A,B,E) = k3_xboole_0(k2_relat_1(D),k1_vectsp_6(A,B,C))
                      & k3_vectsp_6(A,B,D,C) = k3_vectsp_6(A,B,D,E) ) ) ) ) ) ),
    file(vectsp_9,t8_vectsp_9),
    []).

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