SET007 Axioms: SET007+241.ax


%------------------------------------------------------------------------------
% File     : SET007+241 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Rings and Left-, Right-, and Bi-Modules over a Ring
% 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    : vectsp_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  154 (  68 unit)
%            Number of atoms       : 1283 ( 127 equality)
%            Maximal formula depth :   28 (   8 average)
%            Number of connectives : 1300 ( 171 ~  ;   1  |; 931  &)
%                                         (   8 <=>; 189 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   41 (   1 propositional; 0-3 arity)
%            Number of functors    :   35 (   4 constant; 0-7 arity)
%            Number of variables   :  243 (   0 singleton; 223 !;  20 ?)
%            Maximal term depth    :    4 (   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(cc1_vectsp_2,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_vectsp_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) )).

fof(rc1_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A) ) )).

fof(rc2_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A) ) )).

fof(rc3_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A) ) )).

fof(rc4_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A) ) )).

fof(rc5_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A) ) )).

fof(rc6_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A) ) )).

fof(rc7_vectsp_2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A) ) )).

fof(cc2_vectsp_2,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) )).

fof(cc3_vectsp_2,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v6_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) )).

fof(rc8_vectsp_2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] :
          ( l1_vectsp_2(B,A)
          & v3_vectsp_2(B,A) ) ) )).

fof(rc9_vectsp_2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] :
          ( l1_vectsp_2(B,A)
          & ~ v3_struct_0(B) ) ) )).

fof(fc1_vectsp_2,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(B,u1_struct_0(A)),B)
        & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) )
     => ( ~ v3_struct_0(g1_vectsp_2(A,B,C,D,E))
        & v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) ) ) )).

fof(rc10_vectsp_2,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ? [C] :
          ( l2_vectsp_2(C,A,B)
          & v4_vectsp_2(C,A,B) ) ) )).

fof(rc11_vectsp_2,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ? [C] :
          ( l2_vectsp_2(C,A,B)
          & ~ v3_struct_0(C) ) ) )).

fof(fc2_vectsp_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,C),C)
        & m1_relset_1(D,k2_zfmisc_1(C,C),C)
        & m1_subset_1(E,C)
        & v1_funct_1(F)
        & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C)
        & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C)
        & v1_funct_1(G)
        & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C)
        & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) )
     => ( ~ v3_struct_0(g2_vectsp_2(A,B,C,D,E,F,G))
        & v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) ) ) )).

fof(rc12_vectsp_2,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] :
          ( 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) ) ) )).

fof(rc13_vectsp_2,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] :
          ( l1_vectsp_2(B,A)
          & ~ v3_struct_0(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v3_vectsp_2(B,A) ) ) )).

fof(rc14_vectsp_2,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)
        & v6_vectsp_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)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ? [C] :
          ( l2_vectsp_2(C,A,B)
          & ~ v3_struct_0(C)
          & v3_rlvect_1(C)
          & v4_rlvect_1(C)
          & v5_rlvect_1(C)
          & v6_rlvect_1(C)
          & v4_vectsp_2(C,A,B) ) ) )).

fof(rc15_vectsp_2,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] :
          ( 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) ) ) )).

fof(fc3_vectsp_2,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) )
     => ( ~ v3_struct_0(k4_vectsp_2(A))
        & v3_rlvect_1(k4_vectsp_2(A))
        & v4_rlvect_1(k4_vectsp_2(A))
        & v5_rlvect_1(k4_vectsp_2(A))
        & v6_rlvect_1(k4_vectsp_2(A))
        & v11_vectsp_1(k4_vectsp_2(A),A)
        & v12_vectsp_1(k4_vectsp_2(A),A) ) ) )).

fof(rc16_vectsp_2,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] :
          ( l1_vectsp_2(B,A)
          & ~ v3_struct_0(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v3_vectsp_2(B,A)
          & v5_vectsp_2(B,A) ) ) )).

fof(fc4_vectsp_2,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) )
     => ( ~ v3_struct_0(k5_vectsp_2(A))
        & v3_rlvect_1(k5_vectsp_2(A))
        & v4_rlvect_1(k5_vectsp_2(A))
        & v5_rlvect_1(k5_vectsp_2(A))
        & v6_rlvect_1(k5_vectsp_2(A))
        & v3_vectsp_2(k5_vectsp_2(A),A)
        & v5_vectsp_2(k5_vectsp_2(A),A) ) ) )).

fof(rc17_vectsp_2,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)
        & v6_vectsp_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)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ? [C] :
          ( l2_vectsp_2(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)
          & v4_vectsp_2(C,A,B)
          & v5_vectsp_2(C,B)
          & v6_vectsp_2(C,A,B) ) ) )).

fof(fc5_vectsp_2,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)
        & v6_vectsp_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)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k9_vectsp_2(A,B))
        & v3_rlvect_1(k9_vectsp_2(A,B))
        & v4_rlvect_1(k9_vectsp_2(A,B))
        & v5_rlvect_1(k9_vectsp_2(A,B))
        & v6_rlvect_1(k9_vectsp_2(A,B))
        & v12_vectsp_1(k9_vectsp_2(A,B),A)
        & v4_vectsp_2(k9_vectsp_2(A,B),A,B)
        & v5_vectsp_2(k9_vectsp_2(A,B),B)
        & v6_vectsp_2(k9_vectsp_2(A,B),A,B) ) ) )).

fof(d1_vectsp_2,axiom,(
    $true )).

fof(d2_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ( v1_vectsp_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( k1_group_1(A,B,k2_vectsp_1(A)) = B
              & k1_group_1(A,k2_vectsp_1(A),B) = B ) ) ) ) )).

fof(t1_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_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
                      & k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
                      & k1_group_1(A,B,k2_group_1(A)) = B
                      & k1_group_1(A,k2_group_1(A),B) = B
                      & k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))
                      & k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
                      & k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,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)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A)
          & l3_vectsp_1(A) ) ) ) )).

fof(d3_vectsp_2,axiom,(
    $true )).

fof(d4_vectsp_2,axiom,(
    $true )).

fof(d5_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_vectsp_1(A) )
     => ( v2_vectsp_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( k1_group_1(A,B,C) = k1_rlvect_1(A)
                    & B != k1_rlvect_1(A)
                    & C != k1_rlvect_1(A) ) ) ) ) ) )).

fof(t2_vectsp_2,axiom,(
    $true )).

fof(t3_vectsp_2,axiom,(
    $true )).

fof(t4_vectsp_2,axiom,(
    $true )).

fof(t5_vectsp_2,axiom,(
    $true )).

fof(t6_vectsp_2,axiom,(
    $true )).

fof(t7_vectsp_2,axiom,(
    $true )).

fof(t8_vectsp_2,axiom,(
    $true )).

fof(t9_vectsp_2,axiom,(
    $true )).

fof(t10_vectsp_2,axiom,(
    $true )).

fof(t11_vectsp_2,axiom,(
    $true )).

fof(t12_vectsp_2,axiom,(
    $true )).

fof(t13_vectsp_2,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) )
     => ( ~ 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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) ) ) )).

fof(t14_vectsp_2,axiom,(
    $true )).

fof(t15_vectsp_2,axiom,(
    $true )).

fof(t16_vectsp_2,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] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( ~ ( B != k1_rlvect_1(A)
                  & ! [C] :
                      ( m1_subset_1(C,u1_struct_0(A))
                     => k1_group_1(A,B,C) != k2_group_1(A) ) )
              & k1_rlvect_1(A) != k2_group_1(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)
          & v9_vectsp_1(A)
          & ~ v10_vectsp_1(A)
          & l3_vectsp_1(A) ) ) ) )).

fof(t17_vectsp_2,axiom,(
    $true )).

fof(t18_vectsp_2,axiom,(
    $true )).

fof(t19_vectsp_2,axiom,(
    $true )).

fof(t20_vectsp_2,axiom,(
    $true )).

fof(t21_vectsp_2,axiom,(
    $true )).

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 ) ) ) ) ) ) )).

fof(t23_vectsp_2,axiom,(
    $true )).

fof(t24_vectsp_2,axiom,(
    $true )).

fof(t25_vectsp_2,axiom,(
    $true )).

fof(t26_vectsp_2,axiom,(
    $true )).

fof(t27_vectsp_2,axiom,(
    $true )).

fof(t28_vectsp_2,axiom,(
    $true )).

fof(t29_vectsp_2,axiom,(
    $true )).

fof(t30_vectsp_2,axiom,(
    $true )).

fof(t31_vectsp_2,axiom,(
    $true )).

fof(t32_vectsp_2,axiom,(
    $true )).

fof(t33_vectsp_2,axiom,(
    $true )).

fof(t34_vectsp_2,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))
         => ( B = k1_rlvect_1(A)
          <=> k5_rlvect_1(A,B) = k1_rlvect_1(A) ) ) ) )).

fof(t35_vectsp_2,axiom,(
    $true )).

fof(t36_vectsp_2,axiom,(
    $true )).

fof(t37_vectsp_2,axiom,(
    $true )).

fof(t38_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))
                  & B = k4_rlvect_1(A,C,D)
                  & B = k4_rlvect_1(A,D,C) ) ) ) ) )).

fof(t39_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_group_1(A,B,C) = k2_group_1(A)
               => ( B != k1_rlvect_1(A)
                  & C != k1_rlvect_1(A) ) ) ) ) ) )).

fof(t40_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ( B != k1_rlvect_1(A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k1_group_1(A,C,B) != k2_group_1(A) ) ) ) ) )).

fof(t41_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_group_1(A,B,C) = k2_group_1(A)
               => k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) )).

fof(t42_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v7_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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k1_group_1(A,B,C) = k1_group_1(A,B,D)
                   => ( B = k1_rlvect_1(A)
                      | C = D ) ) ) ) ) ) )).

fof(d6_vectsp_2,axiom,(
    $true )).

fof(d7_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k1_vectsp_2(A,B)
                <=> k1_group_1(A,B,C) = k2_group_1(A) ) ) ) ) ) )).

fof(d8_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_vectsp_2(A,B,C) = k1_group_1(A,B,k1_vectsp_2(A,C)) ) ) ) )).

fof(t43_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => ( k1_group_1(A,B,k1_vectsp_2(A,B)) = k2_group_1(A)
              & k1_group_1(A,k1_vectsp_2(A,B),B) = k2_group_1(A) ) ) ) ) )).

fof(t44_vectsp_2,axiom,(
    $true )).

fof(t45_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_group_1(A,B,C) = k2_group_1(A)
               => ( B = k1_vectsp_2(A,C)
                  & C = k1_vectsp_2(A,B) ) ) ) ) ) )).

fof(t46_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != k1_rlvect_1(A)
                  & C != k1_rlvect_1(A)
                  & k1_group_1(A,k1_vectsp_2(A,B),k1_vectsp_2(A,C)) != k1_vectsp_2(A,k1_group_1(A,C,B)) ) ) ) ) )).

fof(t47_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( k1_group_1(A,B,C) = k1_rlvect_1(A)
                  & B != k1_rlvect_1(A)
                  & C != k1_rlvect_1(A) ) ) ) ) )).

fof(t48_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ( B != k1_rlvect_1(A)
              & k1_vectsp_2(A,B) = k1_rlvect_1(A) ) ) ) )).

fof(t49_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => k1_vectsp_2(A,k1_vectsp_2(A,B)) = B ) ) ) )).

fof(t50_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => ( k2_vectsp_2(A,k2_group_1(A),B) = k1_vectsp_2(A,B)
              & k2_vectsp_2(A,k2_group_1(A),k1_vectsp_2(A,B)) = B ) ) ) ) )).

fof(t51_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => ( k1_group_1(A,B,k2_vectsp_2(A,k2_group_1(A),B)) = k2_group_1(A)
              & k1_group_1(A,k2_vectsp_2(A,k2_group_1(A),B),B) = k2_group_1(A) ) ) ) ) )).

fof(t52_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => k2_vectsp_2(A,B,B) = k2_group_1(A) ) ) ) )).

fof(t53_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( B != k1_rlvect_1(A)
                      & C != k1_rlvect_1(A)
                      & k2_vectsp_2(A,D,B) != k2_vectsp_2(A,k1_group_1(A,D,C),k1_group_1(A,B,C)) ) ) ) ) ) )).

fof(t54_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B != k1_rlvect_1(A)
               => ( k5_rlvect_1(A,k2_vectsp_2(A,C,B)) = k2_vectsp_2(A,k5_rlvect_1(A,C),B)
                  & k2_vectsp_2(A,C,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k2_vectsp_2(A,C,B)) ) ) ) ) ) )).

fof(t55_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( B != k1_rlvect_1(A)
                   => ( k4_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B)) = k2_vectsp_2(A,k4_rlvect_1(A,C,D),B)
                      & k6_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B)) = k2_vectsp_2(A,k6_rlvect_1(A,C,D),B) ) ) ) ) ) ) )).

fof(t56_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( B != k1_rlvect_1(A)
                      & C != k1_rlvect_1(A)
                      & k2_vectsp_2(A,D,k2_vectsp_2(A,B,C)) != k2_vectsp_2(A,k1_group_1(A,D,C),B) ) ) ) ) ) )).

fof(t57_vectsp_2,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)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B != k1_rlvect_1(A)
               => k1_group_1(A,k2_vectsp_2(A,C,B),B) = C ) ) ) ) )).

fof(d9_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) )
     => k3_vectsp_2(A) = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) )).

fof(d10_vectsp_2,axiom,(
    $true )).

fof(d11_vectsp_2,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) )
     => k4_vectsp_2(A) = g4_vectsp_1(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) ) )).

fof(d12_vectsp_2,axiom,(
    $true )).

fof(d13_vectsp_2,axiom,(
    $true )).

fof(d14_vectsp_2,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) )
     => k5_vectsp_2(A) = g1_vectsp_2(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) ) )).

fof(d15_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k6_vectsp_2(A,B,C,D) = k2_binop_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_vectsp_2(A,B),D,C) ) ) ) ) )).

fof(d16_vectsp_2,axiom,(
    $true )).

fof(d17_vectsp_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))
        & m2_relset_1(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) )
     => A = k7_vectsp_2 ) )).

fof(d18_vectsp_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_tarski(k1_xboole_0))
     => A = k8_vectsp_2 ) )).

fof(d19_vectsp_2,axiom,(
    $true )).

fof(d20_vectsp_2,axiom,(
    $true )).

fof(d21_vectsp_2,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)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => k9_vectsp_2(A,B) = g2_vectsp_2(A,B,k1_tarski(k1_xboole_0),k2_midsp_1,k8_vectsp_2,k10_funct_3(u1_struct_0(A),k1_tarski(k1_xboole_0)),k9_funct_3(k1_tarski(k1_xboole_0),u1_struct_0(B))) ) ) )).

fof(t58_vectsp_2,axiom,(
    $true )).

fof(t59_vectsp_2,axiom,(
    $true )).

fof(t60_vectsp_2,axiom,(
    $true )).

fof(t61_vectsp_2,axiom,(
    $true )).

fof(t62_vectsp_2,axiom,(
    $true )).

fof(t63_vectsp_2,axiom,(
    $true )).

fof(t64_vectsp_2,axiom,(
    $true )).

fof(t65_vectsp_2,axiom,(
    $true )).

fof(t66_vectsp_2,axiom,(
    $true )).

fof(t67_vectsp_2,axiom,(
    $true )).

fof(t68_vectsp_2,axiom,(
    $true )).

fof(t69_vectsp_2,axiom,(
    $true )).

fof(t70_vectsp_2,axiom,(
    $true )).

fof(t71_vectsp_2,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] :
          ( 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(k4_vectsp_2(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k4_vectsp_2(A)))
                     => ( k6_vectsp_1(A,k4_vectsp_2(A),B,k4_rlvect_1(k4_vectsp_2(A),D,E)) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),B,E))
                        & k6_vectsp_1(A,k4_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),C,D))
                        & k6_vectsp_1(A,k4_vectsp_2(A),k1_group_1(A,B,C),D) = k6_vectsp_1(A,k4_vectsp_2(A),B,k6_vectsp_1(A,k4_vectsp_2(A),C,D))
                        & k6_vectsp_1(A,k4_vectsp_2(A),k2_group_1(A),D) = D ) ) ) ) ) ) )).

fof(t72_vectsp_2,axiom,(
    $true )).

fof(t73_vectsp_2,axiom,(
    $true )).

fof(t74_vectsp_2,axiom,(
    $true )).

fof(t75_vectsp_2,axiom,(
    $true )).

fof(t76_vectsp_2,axiom,(
    $true )).

fof(t77_vectsp_2,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] :
          ( 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(k5_vectsp_2(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_vectsp_2(A)))
                     => ( k6_vectsp_2(A,k5_vectsp_2(A),B,k4_rlvect_1(k5_vectsp_2(A),D,E)) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),B,E))
                        & k6_vectsp_2(A,k5_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),C,D))
                        & k6_vectsp_2(A,k5_vectsp_2(A),k1_group_1(A,C,B),D) = k6_vectsp_2(A,k5_vectsp_2(A),B,k6_vectsp_2(A,k5_vectsp_2(A),C,D))
                        & k6_vectsp_2(A,k5_vectsp_2(A),k2_group_1(A),D) = D ) ) ) ) ) ) )).

fof(d22_vectsp_2,axiom,(
    $true )).

fof(d23_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_vectsp_2(B,A) )
         => ( v5_vectsp_2(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_2(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,C,F))
                              & k6_vectsp_2(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,D,E))
                              & k6_vectsp_2(A,B,k1_group_1(A,D,C),E) = k6_vectsp_2(A,B,C,k6_vectsp_2(A,B,D,E))
                              & k6_vectsp_2(A,B,k2_group_1(A),E) = E ) ) ) ) ) ) ) ) )).

fof(d24_vectsp_2,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)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_vectsp_2(C,A,B) )
             => ( v6_vectsp_2(C,A,B)
              <=> ! [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(C))
                           => k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,E,F)) = k6_vectsp_2(B,C,E,k6_vectsp_1(A,C,D,F)) ) ) ) ) ) ) ) )).

fof(t78_vectsp_2,axiom,(
    $true )).

fof(t79_vectsp_2,axiom,(
    $true )).

fof(t80_vectsp_2,axiom,(
    $true )).

fof(t81_vectsp_2,axiom,(
    $true )).

fof(t82_vectsp_2,axiom,(
    $true )).

fof(t83_vectsp_2,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)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_vectsp_2(C,A,B) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(C))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(C))
                                       => ( k6_vectsp_1(A,C,D,k2_rlvect_1(C,H,I)) = k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,D,I))
                                          & k6_vectsp_1(A,C,k4_rlvect_1(A,D,E),H) = k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,E,H))
                                          & k6_vectsp_1(A,C,k1_group_1(A,D,E),H) = k6_vectsp_1(A,C,D,k6_vectsp_1(A,C,E,H))
                                          & k6_vectsp_1(A,C,k2_group_1(A),H) = H
                                          & k6_vectsp_2(B,C,F,k2_rlvect_1(C,H,I)) = k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,F,I))
                                          & k6_vectsp_2(B,C,k4_rlvect_1(B,F,G),H) = k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,G,H))
                                          & k6_vectsp_2(B,C,k1_group_1(B,G,F),H) = k6_vectsp_2(B,C,F,k6_vectsp_2(B,C,G,H))
                                          & k6_vectsp_2(B,C,k2_group_1(B),H) = H
                                          & k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,F,H)) = k6_vectsp_2(B,C,F,k6_vectsp_1(A,C,D,H)) ) ) ) ) ) ) )
              <=> ( v5_vectsp_2(C,B)
                  & v12_vectsp_1(C,A)
                  & v6_vectsp_2(C,A,B) ) ) ) ) ) )).

fof(t84_vectsp_2,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)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ( ~ v3_struct_0(k9_vectsp_2(A,B))
            & v3_rlvect_1(k9_vectsp_2(A,B))
            & v4_rlvect_1(k9_vectsp_2(A,B))
            & v5_rlvect_1(k9_vectsp_2(A,B))
            & v6_rlvect_1(k9_vectsp_2(A,B))
            & v12_vectsp_1(k9_vectsp_2(A,B),A)
            & v5_vectsp_2(k9_vectsp_2(A,B),B)
            & v6_vectsp_2(k9_vectsp_2(A,B),A,B)
            & l2_vectsp_2(k9_vectsp_2(A,B),A,B) ) ) ) )).

fof(t85_vectsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ( v1_vectsp_2(A)
       => k2_vectsp_1(A) = k2_group_1(A) ) ) )).

fof(dt_l1_vectsp_2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_vectsp_2(B,A)
         => l1_rlvect_1(B) ) ) )).

fof(existence_l1_vectsp_2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] : l1_vectsp_2(B,A) ) )).

fof(dt_l2_vectsp_2,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ! [C] :
          ( l2_vectsp_2(C,A,B)
         => ( l4_vectsp_1(C,A)
            & l1_vectsp_2(C,B) ) ) ) )).

fof(existence_l2_vectsp_2,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ? [C] : l2_vectsp_2(C,A,B) ) )).

fof(abstractness_v3_vectsp_2,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_vectsp_2(B,A) )
     => ( v3_vectsp_2(B,A)
       => B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) )).

fof(abstractness_v4_vectsp_2,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & l2_vectsp_2(C,A,B) )
     => ( v4_vectsp_2(C,A,B)
       => C = g2_vectsp_2(A,B,u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C),u2_vectsp_1(B,C),u1_vectsp_2(B,C)) ) ) )).

fof(dt_k1_vectsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_vectsp_2(A,B),u1_struct_0(A)) ) )).

fof(dt_k2_vectsp_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_vectsp_2(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_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) )
     => ( ~ v3_struct_0(k3_vectsp_2(A))
        & v1_rlvect_1(k3_vectsp_2(A))
        & v3_rlvect_1(k3_vectsp_2(A))
        & v4_rlvect_1(k3_vectsp_2(A))
        & v5_rlvect_1(k3_vectsp_2(A))
        & v6_rlvect_1(k3_vectsp_2(A))
        & l1_rlvect_1(k3_vectsp_2(A)) ) ) )).

fof(dt_k4_vectsp_2,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) )
     => ( ~ v3_struct_0(k4_vectsp_2(A))
        & v3_rlvect_1(k4_vectsp_2(A))
        & v4_rlvect_1(k4_vectsp_2(A))
        & v5_rlvect_1(k4_vectsp_2(A))
        & v6_rlvect_1(k4_vectsp_2(A))
        & v11_vectsp_1(k4_vectsp_2(A),A)
        & l4_vectsp_1(k4_vectsp_2(A),A) ) ) )).

fof(dt_k5_vectsp_2,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) )
     => ( ~ v3_struct_0(k5_vectsp_2(A))
        & v3_rlvect_1(k5_vectsp_2(A))
        & v4_rlvect_1(k5_vectsp_2(A))
        & v5_rlvect_1(k5_vectsp_2(A))
        & v6_rlvect_1(k5_vectsp_2(A))
        & v3_vectsp_2(k5_vectsp_2(A),A)
        & l1_vectsp_2(k5_vectsp_2(A),A) ) ) )).

fof(dt_k6_vectsp_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_vectsp_2(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k6_vectsp_2(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k7_vectsp_2,axiom,
    ( v1_funct_1(k7_vectsp_2)
    & v1_funct_2(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))
    & m2_relset_1(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) )).

fof(dt_k8_vectsp_2,axiom,(
    m1_subset_1(k8_vectsp_2,k1_tarski(k1_xboole_0)) )).

fof(dt_k9_vectsp_2,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)
        & v6_vectsp_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)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k9_vectsp_2(A,B))
        & v3_rlvect_1(k9_vectsp_2(A,B))
        & v4_rlvect_1(k9_vectsp_2(A,B))
        & v5_rlvect_1(k9_vectsp_2(A,B))
        & v6_rlvect_1(k9_vectsp_2(A,B))
        & v4_vectsp_2(k9_vectsp_2(A,B),A,B)
        & l2_vectsp_2(k9_vectsp_2(A,B),A,B) ) ) )).

fof(dt_u1_vectsp_2,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_vectsp_2(B,A) )
     => ( v1_funct_1(u1_vectsp_2(A,B))
        & v1_funct_2(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B))
        & m2_relset_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B)) ) ) )).

fof(dt_g1_vectsp_2,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(B,u1_struct_0(A)),B)
        & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) )
     => ( v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A)
        & l1_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) ) ) )).

fof(free_g1_vectsp_2,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(B,u1_struct_0(A)),B)
        & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) )
     => ! [F,G,H,I,J] :
          ( g1_vectsp_2(A,B,C,D,E) = g1_vectsp_2(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(dt_g2_vectsp_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,C),C)
        & m1_relset_1(D,k2_zfmisc_1(C,C),C)
        & m1_subset_1(E,C)
        & v1_funct_1(F)
        & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C)
        & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C)
        & v1_funct_1(G)
        & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C)
        & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) )
     => ( v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B)
        & l2_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) ) ) )).

fof(free_g2_vectsp_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,C),C)
        & m1_relset_1(D,k2_zfmisc_1(C,C),C)
        & m1_subset_1(E,C)
        & v1_funct_1(F)
        & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C)
        & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C)
        & v1_funct_1(G)
        & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C)
        & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) )
     => ! [H,I,J,K,L,M,N] :
          ( g2_vectsp_2(A,B,C,D,E,F,G) = g2_vectsp_2(H,I,J,K,L,M,N)
         => ( A = H
            & B = I
            & C = J
            & D = K
            & E = L
            & F = M
            & G = N ) ) ) )).
%------------------------------------------------------------------------------