SET007 Axioms: SET007+213.ax


%------------------------------------------------------------------------------
% File     : SET007+213 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Abelian Groups, Fields and Vector Spaces
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  178 (  76 unit)
%            Number of atoms       :  945 ( 140 equality)
%            Maximal formula depth :   20 (   5 average)
%            Number of connectives :  885 ( 118 ~  ;   5  |; 524  &)
%                                         (  17 <=>; 221 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-3 arity)
%            Number of functors    :   35 (   7 constant; 0-6 arity)
%            Number of variables   :  268 (   0 singleton; 248 !;  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(fc1_vectsp_1,axiom,
    ( ~ v3_struct_0(k1_vectsp_1)
    & v1_rlvect_1(k1_vectsp_1) )).

fof(fc2_vectsp_1,axiom,
    ( ~ v3_struct_0(k1_vectsp_1)
    & v1_rlvect_1(k1_vectsp_1)
    & v3_rlvect_1(k1_vectsp_1)
    & v4_rlvect_1(k1_vectsp_1)
    & v5_rlvect_1(k1_vectsp_1)
    & v6_rlvect_1(k1_vectsp_1) )).

fof(rc1_vectsp_1,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A) ) )).

fof(rc2_vectsp_1,axiom,(
    ? [A] :
      ( l1_vectsp_1(A)
      & v1_vectsp_1(A) ) )).

fof(rc3_vectsp_1,axiom,(
    ? [A] :
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v1_vectsp_1(A) ) )).

fof(rc4_vectsp_1,axiom,(
    ? [A] :
      ( l2_vectsp_1(A)
      & v2_vectsp_1(A) ) )).

fof(rc5_vectsp_1,axiom,(
    ? [A] :
      ( l2_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_vectsp_1(A) ) )).

fof(rc6_vectsp_1,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & v3_vectsp_1(A) ) )).

fof(rc7_vectsp_1,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_vectsp_1(A) ) )).

fof(fc3_vectsp_1,axiom,
    ( ~ v3_struct_0(k3_vectsp_1)
    & v3_vectsp_1(k3_vectsp_1) )).

fof(fc4_vectsp_1,axiom,
    ( ~ v3_struct_0(k3_vectsp_1)
    & v2_group_1(k3_vectsp_1)
    & v3_vectsp_1(k3_vectsp_1) )).

fof(fc5_vectsp_1,axiom,
    ( ~ v3_struct_0(k3_vectsp_1)
    & v3_rlvect_1(k3_vectsp_1)
    & v4_rlvect_1(k3_vectsp_1)
    & v5_rlvect_1(k3_vectsp_1)
    & v6_rlvect_1(k3_vectsp_1)
    & v2_group_1(k3_vectsp_1)
    & v4_group_1(k3_vectsp_1)
    & v7_group_1(k3_vectsp_1)
    & v3_vectsp_1(k3_vectsp_1)
    & v6_vectsp_1(k3_vectsp_1)
    & v7_vectsp_1(k3_vectsp_1)
    & v8_vectsp_1(k3_vectsp_1)
    & v9_vectsp_1(k3_vectsp_1)
    & ~ v10_vectsp_1(k3_vectsp_1) )).

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

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

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

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

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

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

fof(rc10_vectsp_1,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)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A) ) )).

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

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

fof(fc6_vectsp_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B)
        & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) )
     => ( ~ v3_struct_0(g4_vectsp_1(A,B,C,D,E))
        & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) )).

fof(rc13_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] :
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v11_vectsp_1(B,A)
          & v12_vectsp_1(B,A) ) ) )).

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

fof(rc14_vectsp_1,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v13_vectsp_1(A) ) )).

fof(rc15_vectsp_1,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)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v13_vectsp_1(A) ) )).

fof(d1_vectsp_1,axiom,(
    $true )).

fof(d2_vectsp_1,axiom,(
    $true )).

fof(d3_vectsp_1,axiom,(
    $true )).

fof(d4_vectsp_1,axiom,(
    $true )).

fof(d5_vectsp_1,axiom,(
    $true )).

fof(d6_vectsp_1,axiom,(
    k1_vectsp_1 = g1_rlvect_1(k1_numbers,k33_binop_2,np__0) )).

fof(t1_vectsp_1,axiom,(
    $true )).

fof(t2_vectsp_1,axiom,(
    $true )).

fof(t3_vectsp_1,axiom,(
    $true )).

fof(t4_vectsp_1,axiom,(
    $true )).

fof(t5_vectsp_1,axiom,(
    $true )).

fof(t6_vectsp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k1_vectsp_1))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k1_vectsp_1))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k1_vectsp_1))
             => ( k4_rlvect_1(k1_vectsp_1,A,B) = k4_rlvect_1(k1_vectsp_1,B,A)
                & k4_rlvect_1(k1_vectsp_1,k4_rlvect_1(k1_vectsp_1,A,B),C) = k4_rlvect_1(k1_vectsp_1,A,k4_rlvect_1(k1_vectsp_1,B,C))
                & k4_rlvect_1(k1_vectsp_1,A,k1_rlvect_1(k1_vectsp_1)) = A
                & k4_rlvect_1(k1_vectsp_1,A,k5_rlvect_1(k1_vectsp_1,A)) = k1_rlvect_1(k1_vectsp_1) ) ) ) ) )).

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

fof(d7_vectsp_1,axiom,(
    $true )).

fof(d8_vectsp_1,axiom,(
    $true )).

fof(d9_vectsp_1,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => k2_vectsp_1(A) = u1_vectsp_1(A) ) )).

fof(d10_vectsp_1,axiom,(
    $true )).

fof(d11_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ( v4_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,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) ) ) ) ) ) )).

fof(d12_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ( v5_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,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) ) ) ) ) ) )).

fof(d13_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ( v6_vectsp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k1_group_1(A,B,k2_group_1(A)) = B ) ) ) )).

fof(d14_vectsp_1,axiom,(
    $true )).

fof(d15_vectsp_1,axiom,(
    k3_vectsp_1 = g3_vectsp_1(k1_numbers,k33_binop_2,k35_binop_2,np__1,np__0) )).

fof(d16_vectsp_1,axiom,(
    $true )).

fof(d17_vectsp_1,axiom,(
    $true )).

fof(d18_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ( v7_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,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)) ) ) ) ) ) ) )).

fof(d19_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ( v8_vectsp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k1_group_1(A,k2_group_1(A),B) = B ) ) ) )).

fof(d20_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_vectsp_1(A) )
     => ( v9_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) ) ) ) ) ) )).

fof(d21_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_vectsp_1(A) )
     => ( v10_vectsp_1(A)
      <=> k1_rlvect_1(A) = k2_group_1(A) ) ) )).

fof(t8_vectsp_1,axiom,(
    $true )).

fof(t9_vectsp_1,axiom,(
    $true )).

fof(t10_vectsp_1,axiom,(
    $true )).

fof(t11_vectsp_1,axiom,(
    $true )).

fof(t12_vectsp_1,axiom,(
    $true )).

fof(t13_vectsp_1,axiom,(
    $true )).

fof(t14_vectsp_1,axiom,(
    $true )).

fof(t15_vectsp_1,axiom,(
    $true )).

fof(t16_vectsp_1,axiom,(
    $true )).

fof(t17_vectsp_1,axiom,(
    $true )).

fof(t18_vectsp_1,axiom,(
    $true )).

fof(t19_vectsp_1,axiom,(
    $true )).

fof(t20_vectsp_1,axiom,(
    k2_group_1(k3_vectsp_1) = np__1 )).

fof(t21_vectsp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_vectsp_1))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_vectsp_1))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_vectsp_1))
             => ( k4_rlvect_1(k3_vectsp_1,A,B) = k4_rlvect_1(k3_vectsp_1,B,A)
                & k4_rlvect_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,A,B),C) = k4_rlvect_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C))
                & k4_rlvect_1(k3_vectsp_1,A,k1_rlvect_1(k3_vectsp_1)) = A
                & k4_rlvect_1(k3_vectsp_1,A,k5_rlvect_1(k3_vectsp_1,A)) = k1_rlvect_1(k3_vectsp_1)
                & k10_group_1(k3_vectsp_1,A,B) = k10_group_1(k3_vectsp_1,B,A)
                & k10_group_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),C) = k10_group_1(k3_vectsp_1,A,k10_group_1(k3_vectsp_1,B,C))
                & k10_group_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),A) = A
                & ~ ( A != k1_rlvect_1(k3_vectsp_1)
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(k3_vectsp_1))
                       => k10_group_1(k3_vectsp_1,A,D) != k2_group_1(k3_vectsp_1) ) )
                & k10_group_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),k10_group_1(k3_vectsp_1,A,C))
                & k10_group_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,B,C),A) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,B,A),k10_group_1(k3_vectsp_1,C,A)) ) ) ) ) )).

fof(t22_vectsp_1,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))
                   => ( ~ ( B != k1_rlvect_1(A)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => k1_group_1(A,B,E) != k2_group_1(A) ) )
                      & 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)
          & v7_vectsp_1(A)
          & v9_vectsp_1(A)
          & l3_vectsp_1(A) ) ) ) )).

fof(t23_vectsp_1,axiom,(
    $true )).

fof(t24_vectsp_1,axiom,(
    $true )).

fof(t25_vectsp_1,axiom,(
    $true )).

fof(t26_vectsp_1,axiom,(
    $true )).

fof(t27_vectsp_1,axiom,(
    $true )).

fof(t28_vectsp_1,axiom,(
    $true )).

fof(t29_vectsp_1,axiom,(
    $true )).

fof(t30_vectsp_1,axiom,(
    $true )).

fof(t31_vectsp_1,axiom,(
    $true )).

fof(t32_vectsp_1,axiom,(
    $true )).

fof(t33_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [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))
                 => ( k10_group_1(A,B,C) = k10_group_1(A,B,D)
                   => ( B = k1_rlvect_1(A)
                      | C = D ) ) ) ) ) ) )).

fof(d22_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k4_vectsp_1(A,B)
                <=> k10_group_1(A,B,C) = k2_group_1(A) ) ) ) ) ) )).

fof(d23_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_vectsp_1(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)) ) ) ) )).

fof(t34_vectsp_1,axiom,(
    $true )).

fof(t35_vectsp_1,axiom,(
    $true )).

fof(t36_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_group_1(A,B,k1_rlvect_1(A)) = k1_rlvect_1(A) ) ) )).

fof(t37_vectsp_1,axiom,(
    $true )).

fof(t38_vectsp_1,axiom,(
    $true )).

fof(t39_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v5_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_group_1(A,k1_rlvect_1(A),B) = k1_rlvect_1(A) ) ) )).

fof(t40_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_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,k5_rlvect_1(A,C)) = k5_rlvect_1(A,k1_group_1(A,B,C)) ) ) ) )).

fof(t41_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v5_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,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k1_group_1(A,B,C)) ) ) ) )).

fof(t42_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) = k1_group_1(A,B,C) ) ) ) )).

fof(t43_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_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,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) ) ) ) ) )).

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

fof(t45_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v5_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,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k1_group_1(A,B,D),k1_group_1(A,C,D)) ) ) ) ) )).

fof(d24_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k6_vectsp_1(A,B,C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) ) ) ) ) )).

fof(d25_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k7_vectsp_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k5_rlvect_1(A,C) ) ) ) ) )).

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

fof(t46_vectsp_1,axiom,(
    $true )).

fof(t47_vectsp_1,axiom,(
    $true )).

fof(t48_vectsp_1,axiom,(
    $true )).

fof(t49_vectsp_1,axiom,(
    $true )).

fof(t50_vectsp_1,axiom,(
    $true )).

fof(t51_vectsp_1,axiom,(
    $true )).

fof(t52_vectsp_1,axiom,(
    $true )).

fof(t53_vectsp_1,axiom,(
    $true )).

fof(t54_vectsp_1,axiom,(
    $true )).

fof(t55_vectsp_1,axiom,(
    $true )).

fof(t56_vectsp_1,axiom,(
    $true )).

fof(t57_vectsp_1,axiom,(
    $true )).

fof(t58_vectsp_1,axiom,(
    $true )).

fof(t59_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( 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,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(C,D)
                    & k6_vectsp_1(A,C,B,k1_rlvect_1(C)) = k1_rlvect_1(C) ) ) ) ) ) )).

fof(t60_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( k6_vectsp_1(A,C,B,D) = k1_rlvect_1(C)
                  <=> ( B = k1_rlvect_1(A)
                      | D = k1_rlvect_1(C) ) ) ) ) ) ) )).

fof(t61_vectsp_1,axiom,(
    $true )).

fof(t62_vectsp_1,axiom,(
    $true )).

fof(t63_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_rlvect_1(A,B,C) = k1_rlvect_1(A)
              <=> k5_rlvect_1(A,B) = C ) ) ) ) )).

fof(t64_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k5_rlvect_1(A,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k5_rlvect_1(A,D),C)
                    & k5_rlvect_1(A,k2_rlvect_1(A,D,k5_rlvect_1(A,C))) = k6_rlvect_1(A,C,D)
                    & k5_rlvect_1(A,k6_rlvect_1(A,C,D)) = k2_rlvect_1(A,D,k5_rlvect_1(A,C))
                    & k5_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,C),D)) = k2_rlvect_1(A,D,C)
                    & k6_rlvect_1(A,B,k2_rlvect_1(A,D,C)) = k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) ) ) ) ) ) )).

fof(t65_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B)
            & k6_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) )).

fof(t66_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k1_rlvect_1(A)
                 => B = C )
                & ( B = C
                 => k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k1_rlvect_1(A) )
                & ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
                 => B = C )
                & ( B = C
                 => k6_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) )).

fof(t67_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( B != k1_rlvect_1(A)
                   => k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D ) ) ) ) ) )).

fof(t68_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) = k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)
                        & k6_rlvect_1(B,E,k6_vectsp_1(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)) ) ) ) ) ) ) )).

fof(t69_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k6_vectsp_1(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) ) ) ) ) )).

fof(t70_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)) = k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)) ) ) ) ) ) )).

fof(t71_vectsp_1,axiom,(
    $true )).

fof(t72_vectsp_1,axiom,(
    $true )).

fof(t73_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => k4_vectsp_1(A,k4_vectsp_1(A,B)) = B ) ) ) )).

fof(t74_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => ( k4_vectsp_1(A,B) != k1_rlvect_1(A)
              & k5_rlvect_1(A,k4_vectsp_1(A,B)) != k1_rlvect_1(A) ) ) ) ) )).

fof(t75_vectsp_1,axiom,(
    $true )).

fof(t76_vectsp_1,axiom,(
    $true )).

fof(t77_vectsp_1,axiom,(
    $true )).

fof(t78_vectsp_1,axiom,(
    k4_rlvect_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),k2_group_1(k3_vectsp_1)) != k1_rlvect_1(k3_vectsp_1) )).

fof(d27_vectsp_1,axiom,(
    $true )).

fof(d28_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v13_vectsp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( k2_rlvect_1(A,B,B) = k1_rlvect_1(A)
             => B = k1_rlvect_1(A) ) ) ) ) )).

fof(d29_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( v13_vectsp_1(A)
      <=> k2_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A) ) ) )).

fof(t79_vectsp_1,axiom,(
    $true )).

fof(t80_vectsp_1,axiom,(
    $true )).

fof(t81_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k6_rlvect_1(A,C,B) ) ) ) )).

fof(t82_vectsp_1,axiom,(
    $true )).

fof(t83_vectsp_1,axiom,(
    $true )).

fof(t84_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => B = C ) ) ) ) )).

fof(t85_vectsp_1,axiom,(
    $true )).

fof(t86_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k5_rlvect_1(A,B) = k1_rlvect_1(A)
           => B = k1_rlvect_1(A) ) ) ) )).

fof(t87_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => k6_rlvect_1(A,C,B) = k1_rlvect_1(A) ) ) ) ) )).

fof(t88_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( k6_rlvect_1(A,k10_group_1(A,B,D),C) = k1_rlvect_1(A)
                     => ( B = k1_rlvect_1(A)
                        | D = k10_group_1(A,C,k4_vectsp_1(A,B)) ) )
                    & ( k6_rlvect_1(A,C,k10_group_1(A,D,B)) = k1_rlvect_1(A)
                     => ( B = k1_rlvect_1(A)
                        | D = k10_group_1(A,C,k4_vectsp_1(A,B)) ) ) ) ) ) ) ) )).

fof(t89_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B))) ) ) ) )).

fof(t90_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,k2_rlvect_1(A,C,B),k2_rlvect_1(A,D,B)) = k6_rlvect_1(A,C,D) ) ) ) ) )).

fof(t91_vectsp_1,axiom,(
    $true )).

fof(t92_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,B),C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),B) ) ) ) )).

fof(t93_vectsp_1,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))
                 => k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) )).

fof(t94_vectsp_1,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(g1_group_1(u1_struct_0(A),u1_rlvect_1(A)))
        & v3_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A)))
        & v4_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A)))
        & v7_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A)))
        & l1_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) ) ) )).

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

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

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

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

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

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

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

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

fof(abstractness_v1_vectsp_1,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => ( v1_vectsp_1(A)
       => A = g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A)) ) ) )).

fof(abstractness_v2_vectsp_1,axiom,(
    ! [A] :
      ( l2_vectsp_1(A)
     => ( v2_vectsp_1(A)
       => A = g2_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) )).

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

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

fof(dt_k1_vectsp_1,axiom,
    ( v1_rlvect_1(k1_vectsp_1)
    & l1_rlvect_1(k1_vectsp_1) )).

fof(dt_k2_vectsp_1,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)) ) )).

fof(dt_k3_vectsp_1,axiom,
    ( v3_vectsp_1(k3_vectsp_1)
    & l3_vectsp_1(k3_vectsp_1) )).

fof(dt_k4_vectsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)) ) )).

fof(dt_k5_vectsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k5_vectsp_1(A,B,C),u1_struct_0(A)) ) )).

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

fof(dt_k7_vectsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_funct_1(k7_vectsp_1(A))
        & v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

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

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

fof(dt_g1_vectsp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( v1_vectsp_1(g1_vectsp_1(A,B,C))
        & l1_vectsp_1(g1_vectsp_1(A,B,C)) ) ) )).

fof(free_g1_vectsp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ! [D,E,F] :
          ( g1_vectsp_1(A,B,C) = g1_vectsp_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).

fof(dt_g2_vectsp_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => ( v2_vectsp_1(g2_vectsp_1(A,B,C,D))
        & l2_vectsp_1(g2_vectsp_1(A,B,C,D)) ) ) )).

fof(free_g2_vectsp_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => ! [E,F,G,H] :
          ( g2_vectsp_1(A,B,C,D) = g2_vectsp_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).

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

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

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

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