SET007 Axioms: SET007+747.ax


%------------------------------------------------------------------------------
% File     : SET007+747 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Quotient Vector Spaces and Functionals
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : vectsp10 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   88 (   1 unit)
%            Number of atoms       : 1735 (  96 equality)
%            Maximal formula depth :   30 (  15 average)
%            Number of connectives : 1885 ( 238 ~  ;   9  |;1287  &)
%                                         (  12 <=>; 339 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   44 (   1 propositional; 0-4 arity)
%            Number of functors    :   41 (   0 constant; 1-6 arity)
%            Number of variables   :  360 (   0 singleton; 342 !;  18 ?)
%            Maximal term depth    :    7 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(fc2_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v3_rlvect_1(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(fc3_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v4_rlvect_1(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(fc4_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v5_rlvect_1(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(fc5_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_rlvect_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v6_rlvect_1(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(fc6_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A)
        & v12_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(fc7_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_vectsp10(A))
        & v11_vectsp_1(k1_vectsp10(A),A)
        & ~ v3_realset2(k1_vectsp10(A)) ) ) )).

fof(rc1_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] :
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & ~ v3_realset2(B) ) ) )).

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

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

fof(rc4_vectsp10,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)
        & ~ v10_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)
          & ~ v3_realset2(B) ) ) )).

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) ) ) )).

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) ) ) ) ) )).

fof(cc2_vectsp10,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ! [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))
              & v2_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) ) ) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) ) ) )).

fof(rc8_vectsp10,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_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)
        & ~ v3_realset2(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)
          & v2_hahnban1(C,A,B)
          & v3_hahnban1(C,A,B)
          & ~ v1_realset1(C) ) ) )).

fof(cc4_vectsp10,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_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)
        & ~ v3_realset2(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_realset1(C) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
              & v5_seqm_3(C) ) ) ) ) )).

fof(fc9_vectsp10,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_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)
        & ~ v3_realset2(B)
        & l4_vectsp_1(B,A) )
     => ( ~ v3_struct_0(k8_hahnban1(A,B))
        & v3_rlvect_1(k8_hahnban1(A,B))
        & v4_rlvect_1(k8_hahnban1(A,B))
        & v5_rlvect_1(k8_hahnban1(A,B))
        & v6_rlvect_1(k8_hahnban1(A,B))
        & v11_vectsp_1(k8_hahnban1(A,B),A)
        & v12_vectsp_1(k8_hahnban1(A,B),A)
        & ~ v3_realset2(k8_hahnban1(A,B)) ) ) )).

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)) ) )).

fof(cc5_vectsp10,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & ~ v3_realset2(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))
              & v3_hahnban1(C,A,B)
              & ~ v2_vectsp10(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
              & ~ v5_seqm_3(C)
              & ~ v1_realset1(C) ) ) ) ) )).

fof(fc11_vectsp10,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)
        & ~ v3_realset2(B)
        & l4_vectsp_1(B,A)
        & 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)
        & v2_hahnban1(C,A,B)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( v1_relat_1(k11_vectsp10(A,B,C))
        & v1_funct_1(k11_vectsp10(A,B,C))
        & v1_funct_2(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A))
        & ~ v5_seqm_3(k11_vectsp10(A,B,C))
        & v1_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & v2_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & v3_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & ~ v1_realset1(k11_vectsp10(A,B,C)) ) ) )).

fof(fc12_vectsp10,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)
        & 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)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( v1_relat_1(k11_vectsp10(A,B,C))
        & v1_funct_1(k11_vectsp10(A,B,C))
        & v1_funct_2(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A))
        & v1_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & v2_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & v3_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & ~ v2_vectsp10(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C))) ) ) )).

fof(d1_vectsp10,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => k1_vectsp10(A) = g4_vectsp_1(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) ) )).

fof(t1_vectsp10,axiom,(
    $true )).

fof(t2_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( 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))
                 => ( k6_vectsp_1(A,C,k1_rlvect_1(A),D) = k1_rlvect_1(C)
                    & k6_vectsp_1(A,C,B,k1_rlvect_1(C)) = k1_rlvect_1(C) ) ) ) ) ) )).

fof(t3_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( ( k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B)
                          & r1_rlvect_1(C,E)
                          & r1_rlvect_1(D,E) )
                       => E = k1_rlvect_1(B) ) ) ) ) ) ) )).

fof(t4_vectsp10,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,D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r1_rlvect_1(k1_vectsp_7(A,B,k7_rlvect_2(B,D)),C)
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(A))
                    & C = k6_vectsp_1(A,B,E,D) ) ) ) ) ) )).

fof(t5_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k6_vectsp_1(A,B,D,C) = k6_vectsp_1(A,B,E,C)
                       => ( C = k1_rlvect_1(B)
                          | D = E ) ) ) ) ) ) ) )).

fof(t6_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_vectsp_5(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ( ( r1_rlvect_1(C,F)
                                    & r1_rlvect_1(D,G)
                                    & E = k4_rlvect_1(B,F,G) )
                                 => k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) ) ) ) ) ) ) ) ) ) )).

fof(t7_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_vectsp_5(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G)
                                 => E = k4_rlvect_1(B,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t8_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_vectsp_5(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G)
                                 => ( r1_rlvect_1(C,F)
                                    & r1_rlvect_1(D,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t9_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_vectsp_5(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G)
                                 => k4_vectsp_5(A,B,E,D,C) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),G,F) ) ) ) ) ) ) ) ) ) )).

fof(t10_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_vectsp_5(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r1_rlvect_1(C,E)
                         => k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,k1_rlvect_1(B)) ) ) ) ) ) ) ) )).

fof(t11_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_vectsp_5(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r1_rlvect_1(D,E)
                         => k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),k1_rlvect_1(B),E) ) ) ) ) ) ) ) )).

fof(t12_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r1_rlvect_1(D,E)
                       => m1_subset_1(E,u1_struct_0(C)) ) ) ) ) ) ) )).

fof(t13_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ! [F] :
                          ( m1_vectsp_4(F,A,E)
                         => ! [G] :
                              ( m1_vectsp_4(G,A,E)
                             => ( ( F = C
                                  & G = D )
                               => k1_vectsp_5(A,E,F,G) = k1_vectsp_5(A,B,C,D) ) ) ) ) ) ) ) ) )).

fof(t14_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( D = E
                       => k1_vectsp_7(A,C,k7_rlvect_2(C,E)) = k1_vectsp_7(A,B,k7_rlvect_2(B,D)) ) ) ) ) ) ) )).

fof(t15_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( ~ r1_rlvect_1(D,C)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                       => ! [F] :
                            ( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
                           => ( ( C = E
                                & F = D )
                             => r1_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) ) ) ) ) ) ) ) ) )).

fof(t16_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                     => ! [F] :
                          ( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
                         => ( ( C = E
                              & D = F )
                           => ( r1_rlvect_1(D,C)
                              | k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(F),u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))),k1_rlvect_1(F),E) ) ) ) ) ) ) ) ) )).

fof(t17_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                     => ! [F] :
                          ( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
                         => ( ( C = E
                              & D = F )
                           => ( r1_rlvect_1(D,C)
                              | ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                                 => ( r1_rlvect_1(D,G)
                                   => k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))),u1_struct_0(B),G,k1_rlvect_1(B)) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_vectsp10,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] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ? [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                          & ? [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                              & k4_vectsp_5(A,B,C,D,E) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) ) ) ) ) ) ) ) )).

fof(t19_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                     => ! [F] :
                          ( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
                         => ( ( C = E
                              & D = F )
                           => ( r1_rlvect_1(D,C)
                              | ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                                 => ? [H] :
                                      ( m1_subset_1(H,u1_struct_0(D))
                                      & ? [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                          & k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),H,k6_vectsp_1(A,B,I,C)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                     => ! [F] :
                          ( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
                         => ( ( C = E
                              & D = F )
                           => ( r1_rlvect_1(D,C)
                              | ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(D))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(D))
                                             => ! [K] :
                                                  ( m1_subset_1(K,u1_struct_0(A))
                                                 => ! [L] :
                                                      ( m1_subset_1(L,u1_struct_0(A))
                                                     => ( ( k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),I,k6_vectsp_1(A,B,K,C))
                                                          & k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),H,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),J,k6_vectsp_1(A,B,L,C)) )
                                                       => k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k4_rlvect_1(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,H),F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),k4_rlvect_1(D,I,J),k6_vectsp_1(A,B,k4_rlvect_1(A,K,L),C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_vectsp10,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_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                     => ! [F] :
                          ( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
                         => ( ( C = E
                              & D = F )
                           => ( r1_rlvect_1(D,C)
                              | ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(D))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ( k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),H,k6_vectsp_1(A,B,J,C))
                                               => k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k6_vectsp_1(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),I,G),F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),k6_vectsp_1(A,D,I,H),k6_vectsp_1(A,B,k10_group_1(A,I,J),C)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
                    & m2_relset_1(D,k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) )
                 => ( D = k3_vectsp10(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C))
                       => ! [F] :
                            ( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(B))
                                   => ( ( E = k3_vectsp_4(A,B,G,C)
                                        & F = k3_vectsp_4(A,B,H,C) )
                                     => k2_binop_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C),k2_vectsp10(A,B,C),D,E,F) = k3_vectsp_4(A,B,k4_rlvect_1(B,G,H),C) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_vectsp10,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_4(C,A,B)
             => k4_vectsp10(A,B,C) = u1_struct_0(C) ) ) ) )).

fof(d5_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
                    & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) )
                 => ( D = k5_vectsp10(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ( F = k3_vectsp_4(A,B,G,C)
                                 => k2_binop_1(u1_struct_0(A),k2_vectsp10(A,B,C),k2_vectsp10(A,B,C),D,E,F) = k3_vectsp_4(A,B,k6_vectsp_1(A,B,E,G),C) ) ) ) ) ) ) ) ) ) )).

fof(d6_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v11_vectsp_1(D,A)
                    & v12_vectsp_1(D,A)
                    & l4_vectsp_1(D,A) )
                 => ( D = k6_vectsp10(A,B,C)
                  <=> ( u1_struct_0(D) = k2_vectsp10(A,B,C)
                      & u1_rlvect_1(D) = k3_vectsp10(A,B,C)
                      & u2_struct_0(D) = k4_vectsp10(A,B,C)
                      & u2_vectsp_1(A,D) = k5_vectsp10(A,B,C) ) ) ) ) ) ) )).

fof(t22_vectsp10,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_4(C,A,B)
             => ( k4_vectsp10(A,B,C) = k3_vectsp_4(A,B,k1_rlvect_1(B),C)
                & k1_rlvect_1(k6_vectsp10(A,B,C)) = k4_vectsp10(A,B,C) ) ) ) ) )).

fof(t23_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C)))
                 => ( m2_vectsp_4(D,A,B,C)
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                        & D = k3_vectsp_4(A,B,E,C) ) ) ) ) ) ) )).

fof(t24_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( m2_vectsp_4(k3_vectsp_4(A,B,D,C),A,B,C)
                    & m1_subset_1(k3_vectsp_4(A,B,D,C),u1_struct_0(k6_vectsp10(A,B,C))) ) ) ) ) ) )).

fof(t25_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m2_vectsp_4(D,A,B,C)
                 => m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C))) ) ) ) ) )).

fof(t26_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( D = k3_vectsp_4(A,B,E,C)
                           => k6_vectsp_1(A,k6_vectsp10(A,B,C),F,D) = k3_vectsp_4(A,B,k6_vectsp_1(A,B,F,E),C) ) ) ) ) ) ) ) )).

fof(t27_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k6_vectsp10(A,B,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ( ( D = k3_vectsp_4(A,B,F,C)
                                  & E = k3_vectsp_4(A,B,G,C) )
                               => k4_rlvect_1(k6_vectsp10(A,B,C),D,E) = k3_vectsp_4(A,B,k4_rlvect_1(B,F,G),C) ) ) ) ) ) ) ) ) )).

fof(t28_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
                    & v1_hahnban1(D,A,C)
                    & v2_hahnban1(D,A,C)
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))))
                         => ( E = F
                           => ( r1_rlvect_1(C,E)
                              | ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ? [H] :
                                      ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A))
                                      & v1_hahnban1(H,A,k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E))))
                                      & v2_hahnban1(H,A,k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E))))
                                      & m2_relset_1(H,u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A))
                                      & k8_relset_1(u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A),H,u1_struct_0(C)) = D
                                      & k8_funct_2(u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A),H,F) = G ) ) ) ) ) ) ) ) ) ) )).

fof(d7_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_rlvect_1(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v3_hahnban1(C,A,B)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v5_seqm_3(C)
              <=> C = k7_hahnban1(A,B) ) ) ) ) )).

fof(d8_vectsp10,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)
            & ~ v3_realset2(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_5(D,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
                 => ( C != k1_rlvect_1(B)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
                          & ~ v5_seqm_3(E)
                          & v1_hahnban1(E,A,B)
                          & v2_hahnban1(E,A,B)
                          & ~ v1_realset1(E)
                          & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
                       => ( E = k7_vectsp10(A,B,C,D)
                        <=> ( k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C) = k2_group_1(A)
                            & k8_relset_1(u1_struct_0(B),u1_struct_0(A),E,u1_struct_0(D)) = k7_hahnban1(A,D) ) ) ) ) ) ) ) ) )).

fof(t29_vectsp10,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)
            & ~ v3_realset2(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & ~ v5_seqm_3(C)
                & v3_hahnban1(C,A,B)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                  & D != k1_rlvect_1(B)
                  & k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D) != k1_rlvect_1(A) ) ) ) ) )).

fof(t30_vectsp10,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)
            & ~ v3_realset2(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_vectsp_5(E,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
                     => ( C != k1_rlvect_1(B)
                       => k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_vectsp10(A,B,C,E),k6_vectsp_1(A,B,D,C)) = D ) ) ) ) ) ) )).

fof(t31_vectsp10,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)
            & ~ v3_realset2(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_vectsp_5(E,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
                     => ( r1_rlvect_1(E,D)
                       => ( C = k1_rlvect_1(B)
                          | k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_vectsp10(A,B,C,E),D) = k1_rlvect_1(A) ) ) ) ) ) ) ) )).

fof(t32_vectsp10,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)
            & ~ v3_realset2(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_vectsp_5(F,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
                         => ( r1_rlvect_1(F,D)
                           => ( C = k1_rlvect_1(B)
                              | k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_vectsp10(A,B,C,F),k4_rlvect_1(B,k6_vectsp_1(A,B,E,C),D)) = E ) ) ) ) ) ) ) ) )).

fof(t33_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(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)) )
             => ! [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] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => k8_funct_2(u1_struct_0(B),u1_struct_0(A),k5_hahnban1(A,B,C,D),E) = k6_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E)) ) ) ) ) ) )).

fof(t34_vectsp10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ 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] :
              ( ( 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)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => v1_vectsp_4(k8_vectsp10(A,B,C),A,B) ) ) ) )).

fof(d10_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)) )
             => ( v2_vectsp10(C,A,B)
              <=> k8_vectsp10(A,B,C) != k7_rlvect_2(B,k1_rlvect_1(B)) ) ) ) ) )).

fof(d11_vectsp10,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] :
              ( ( 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)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v11_vectsp_1(D,A)
                    & m1_vectsp_4(D,A,B) )
                 => ( D = k9_vectsp10(A,B,C)
                  <=> u1_struct_0(D) = k8_vectsp10(A,B,C) ) ) ) ) ) )).

fof(d12_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & v1_hahnban1(D,A,B)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ( r1_tarski(u1_struct_0(C),k8_vectsp10(A,B,D))
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A))
                          & v1_hahnban1(E,A,k6_vectsp10(A,B,C))
                          & m2_relset_1(E,u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A)) )
                       => ( E = k10_vectsp10(A,B,C,D)
                        <=> ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,C)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( F = k3_vectsp_4(A,B,G,C)
                                   => k8_funct_2(u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A),E,F) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_vectsp10,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_4(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & v1_hahnban1(D,A,B)
                    & v2_hahnban1(D,A,B)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ( r1_tarski(u1_struct_0(C),k8_vectsp10(A,B,D))
                   => v2_hahnban1(k10_vectsp10(A,B,C,D),A,k6_vectsp10(A,B,C)) ) ) ) ) ) )).

fof(d13_vectsp10,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] :
              ( ( 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)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => k11_vectsp10(A,B,C) = k10_vectsp10(A,B,k9_vectsp10(A,B,C),C) ) ) ) )).

fof(t36_vectsp10,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] :
              ( ( 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)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( D = k3_vectsp_4(A,B,E,k9_vectsp10(A,B,C))
                       => k8_funct_2(u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A),k11_vectsp10(A,B,C),D) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E) ) ) ) ) ) ) )).

fof(redefinition_v1_vectsp10,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & l4_vectsp_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,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_vectsp10(C,A,B)
      <=> v5_seqm_3(C) ) ) )).

fof(dt_k1_vectsp10,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => ( v11_vectsp_1(k1_vectsp10(A),A)
        & l4_vectsp_1(k1_vectsp10(A),A) ) ) )).

fof(dt_k2_vectsp10,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_4(C,A,B) )
     => ( ~ v1_xboole_0(k2_vectsp10(A,B,C))
        & m1_subset_1(k2_vectsp10(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) ) )).

fof(dt_k3_vectsp10,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_4(C,A,B) )
     => ( v1_funct_1(k3_vectsp10(A,B,C))
        & v1_funct_2(k3_vectsp10(A,B,C),k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
        & m2_relset_1(k3_vectsp10(A,B,C),k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) ) ) )).

fof(dt_k4_vectsp10,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_4(C,A,B) )
     => m2_subset_1(k4_vectsp10(A,B,C),k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C)) ) )).

fof(dt_k5_vectsp10,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_4(C,A,B) )
     => ( v1_funct_1(k5_vectsp10(A,B,C))
        & v1_funct_2(k5_vectsp10(A,B,C),k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
        & m2_relset_1(k5_vectsp10(A,B,C),k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) ) ) )).

fof(dt_k6_vectsp10,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_4(C,A,B) )
     => ( ~ v3_struct_0(k6_vectsp10(A,B,C))
        & v3_rlvect_1(k6_vectsp10(A,B,C))
        & v4_rlvect_1(k6_vectsp10(A,B,C))
        & v5_rlvect_1(k6_vectsp10(A,B,C))
        & v6_rlvect_1(k6_vectsp10(A,B,C))
        & v11_vectsp_1(k6_vectsp10(A,B,C),A)
        & v12_vectsp_1(k6_vectsp10(A,B,C),A)
        & l4_vectsp_1(k6_vectsp10(A,B,C),A) ) ) )).

fof(dt_k7_vectsp10,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_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)
        & ~ v3_realset2(B)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_vectsp_5(D,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C))) )
     => ( v1_funct_1(k7_vectsp10(A,B,C,D))
        & v1_funct_2(k7_vectsp10(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
        & ~ v5_seqm_3(k7_vectsp10(A,B,C,D))
        & v1_hahnban1(k7_vectsp10(A,B,C,D),A,B)
        & v2_hahnban1(k7_vectsp10(A,B,C,D),A,B)
        & ~ v1_realset1(k7_vectsp10(A,B,C,D))
        & m2_relset_1(k7_vectsp10(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) )).

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))) ) )).

fof(dt_k9_vectsp10,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)
        & 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)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k9_vectsp10(A,B,C))
        & v11_vectsp_1(k9_vectsp10(A,B,C),A)
        & m1_vectsp_4(k9_vectsp10(A,B,C),A,B) ) ) )).

fof(dt_k10_vectsp10,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_4(C,A,B)
        & 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(k10_vectsp10(A,B,C,D))
        & v1_funct_2(k10_vectsp10(A,B,C,D),u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A))
        & v1_hahnban1(k10_vectsp10(A,B,C,D),A,k6_vectsp10(A,B,C))
        & m2_relset_1(k10_vectsp10(A,B,C,D),u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A)) ) ) )).

fof(dt_k11_vectsp10,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)
        & 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)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( v1_funct_1(k11_vectsp10(A,B,C))
        & v1_funct_2(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A))
        & v1_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & v2_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
        & m2_relset_1(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A)) ) ) )).

fof(d2_vectsp10,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_4(C,A,B)
             => k2_vectsp10(A,B,C) = a_3_0_vectsp10(A,B,C) ) ) ) )).

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) ) ) ) )).

fof(fraenkel_a_3_0_vectsp10,axiom,(
    ! [A,B,C,D] :
      ( ( ~ 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)
        & ~ 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)
        & m1_vectsp_4(D,B,C) )
     => ( r2_hidden(A,a_3_0_vectsp10(B,C,D))
      <=> ? [E] :
            ( m2_vectsp_4(E,B,C,D)
            & A = E ) ) ) )).

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) ) ) ) )).
%------------------------------------------------------------------------------