SET007 Axioms: SET007+341.ax


%------------------------------------------------------------------------------
% File     : SET007+341 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Submodules
% 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    : lmod_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   58 (   6 unit)
%            Number of atoms       : 1200 (  30 equality)
%            Maximal formula depth :   34 (  13 average)
%            Number of connectives : 1261 ( 119 ~  ;   1  |; 914  &)
%                                         (   9 <=>; 218 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   1 propositional; 0-4 arity)
%            Number of functors    :   27 (   1 constant; 0-5 arity)
%            Number of variables   :  200 (   0 singleton; 200 !;   0 ?)
%            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_lmod_6,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_vectsp_4(C,A,B)
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) )
     => ~ v1_xboole_0(k2_lmod_6(A,B,C,D)) ) )).

fof(t1_lmod_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,B)
            & l4_vectsp_1(C,B) )
         => ! [D] :
              ( ( ~ v3_struct_0(D)
                & v3_rlvect_1(D)
                & v4_rlvect_1(D)
                & v5_rlvect_1(D)
                & v6_rlvect_1(D)
                & v12_vectsp_1(D,B)
                & l4_vectsp_1(D,B) )
             => ( C = g4_vectsp_1(B,u1_struct_0(D),u1_rlvect_1(D),u2_struct_0(D),u2_vectsp_1(B,D))
               => ( r1_rlvect_1(C,A)
                <=> r1_rlvect_1(D,A) ) ) ) ) ) )).

fof(t2_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(g4_vectsp_1(A,u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C),u2_vectsp_1(A,C))))
                     => ( D = E
                       => k6_vectsp_1(A,C,B,D) = k6_vectsp_1(A,g4_vectsp_1(A,u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C),u2_vectsp_1(A,C)),B,E) ) ) ) ) ) ) )).

fof(t3_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ( v11_vectsp_1(g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)),A)
            & m1_vectsp_4(g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)),A,B) ) ) ) )).

fof(t4_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => m1_vectsp_4(B,A,k2_vectsp_4(A,B)) ) ) )).

fof(d1_lmod_6,axiom,(
    $true )).

fof(d2_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( v3_realset2(A)
      <=> k1_rlvect_1(A) = k2_group_1(A) ) ) )).

fof(t5_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ( v3_realset2(A)
           => ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => C = k1_rlvect_1(A) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => C = k1_rlvect_1(B) ) ) ) ) ) )).

fof(t6_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ( v3_realset2(A)
           => v3_realset2(B) ) ) ) )).

fof(t7_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ( v3_realset2(B)
          <=> g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = k1_vectsp_4(A,B) ) ) ) )).

fof(d3_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v11_vectsp_1(C,A)
                & m1_vectsp_4(C,A,B) )
             => k1_lmod_6(A,B,C) = C ) ) ) )).

fof(t8_lmod_6,axiom,(
    $true )).

fof(t9_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
                 => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) )).

fof(d4_lmod_6,axiom,(
    $true )).

fof(d5_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
                 => k2_lmod_6(A,B,C,D) = D ) ) ) ) )).

fof(t10_lmod_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,B)
            & l4_vectsp_1(C,B) )
         => ( r2_hidden(A,k2_pre_topc(C))
          <=> r1_rlvect_1(C,A) ) ) ) )).

fof(t11_lmod_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,B)
            & l4_vectsp_1(C,B) )
         => ! [D] :
              ( m1_vectsp_4(D,B,C)
             => ( r2_hidden(A,k2_lmod_6(B,C,D,k2_pre_topc(D)))
              <=> r1_rlvect_1(D,A) ) ) ) ) )).

fof(t12_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => r1_tarski(C,k2_pre_topc(k1_mod_3(A,B,C))) ) ) ) )).

fof(t13_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] :
                  ( m2_vectsp_6(D,A,B,C)
                 => ( v1_vectsp_4(C,A,B)
                   => ( C = k1_xboole_0
                      | r2_hidden(k4_vectsp_6(A,B,D),C) ) ) ) ) ) ) )).

fof(t14_lmod_6,axiom,(
    $true )).

fof(t15_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( ( r2_hidden(k1_rlvect_1(B),C)
                  & v1_vectsp_4(C,A,B) )
               => C = k2_pre_topc(k1_mod_3(A,B,C)) ) ) ) ) )).

fof(d6_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k4_lmod_6(A,B,C) = k1_mod_3(A,B,k3_lmod_6(A,B,C)) ) ) ) )).

fof(d7_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( r1_lmod_6(A,B,C)
              <=> m1_vectsp_4(B,A,C) ) ) ) ) )).

fof(t16_lmod_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,B)
            & l4_vectsp_1(C,B) )
         => ! [D] :
              ( ( ~ v3_struct_0(D)
                & v3_rlvect_1(D)
                & v4_rlvect_1(D)
                & v5_rlvect_1(D)
                & v6_rlvect_1(D)
                & v12_vectsp_1(D,B)
                & l4_vectsp_1(D,B) )
             => ( r1_lmod_6(B,C,D)
               => ( ( r1_rlvect_1(C,A)
                   => r1_rlvect_1(D,A) )
                  & ( m1_subset_1(A,u1_struct_0(C))
                   => m1_subset_1(A,u1_struct_0(D)) ) ) ) ) ) ) )).

fof(t17_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,A)
                    & l4_vectsp_1(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(C))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(D))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(D))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(D))
                                         => ( r1_lmod_6(A,C,D)
                                           => ( k1_rlvect_1(C) = k1_rlvect_1(D)
                                              & ( ( E = H
                                                  & F = I )
                                               => k4_rlvect_1(C,E,F) = k4_rlvect_1(D,H,I) )
                                              & ( G = J
                                               => k6_vectsp_1(A,C,B,G) = k6_vectsp_1(A,D,B,J) )
                                              & ( G = J
                                               => k5_rlvect_1(D,J) = k5_rlvect_1(C,G) )
                                              & ( ( E = H
                                                  & F = I )
                                               => k6_rlvect_1(C,E,F) = k6_rlvect_1(D,H,I) )
                                              & r1_rlvect_1(C,k1_rlvect_1(D))
                                              & r1_rlvect_1(D,k1_rlvect_1(C))
                                              & ( ( r1_rlvect_1(C,H)
                                                  & r1_rlvect_1(C,I) )
                                               => r1_rlvect_1(C,k4_rlvect_1(D,H,I)) )
                                              & ( r1_rlvect_1(C,J)
                                               => r1_rlvect_1(C,k6_vectsp_1(A,D,B,J)) )
                                              & ( r1_rlvect_1(C,J)
                                               => r1_rlvect_1(C,k5_rlvect_1(D,J)) )
                                              & ( ( r1_rlvect_1(C,H)
                                                  & r1_rlvect_1(C,I) )
                                               => r1_rlvect_1(C,k6_rlvect_1(D,H,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,A)
                    & l4_vectsp_1(D,A) )
                 => ( ( r1_lmod_6(A,B,C)
                      & r1_lmod_6(A,D,C) )
                   => ( k1_rlvect_1(B) = k1_rlvect_1(D)
                      & r1_rlvect_1(D,k1_rlvect_1(B))
                      & ( r1_tarski(u1_struct_0(B),u1_struct_0(D))
                       => r1_lmod_6(A,B,D) )
                      & ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(C))
                           => ( r1_rlvect_1(B,E)
                             => r1_rlvect_1(D,E) ) )
                       => r1_lmod_6(A,B,D) )
                      & ( ( u1_struct_0(B) = u1_struct_0(D)
                          & v11_vectsp_1(B,A)
                          & v11_vectsp_1(D,A) )
                       => B = D )
                      & r1_lmod_6(A,k1_vectsp_4(A,B),D) ) ) ) ) ) ) )).

fof(t19_lmod_6,axiom,(
    $true )).

fof(t20_lmod_6,axiom,(
    $true )).

fof(t21_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v11_vectsp_1(B,A)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v11_vectsp_1(C,A)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( ( r1_lmod_6(A,B,C)
                  & r1_lmod_6(A,C,B) )
               => B = C ) ) ) ) )).

fof(t22_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,A)
                    & l4_vectsp_1(D,A) )
                 => ( ( r1_lmod_6(A,B,C)
                      & r1_lmod_6(A,C,D) )
                   => r1_lmod_6(A,B,D) ) ) ) ) ) )).

fof(t23_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( r1_lmod_6(A,B,C)
               => r1_lmod_6(A,k1_vectsp_4(A,B),C) ) ) ) ) )).

fof(t24_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( r1_lmod_6(A,B,C)
               => r1_lmod_6(A,k1_vectsp_4(A,C),B) ) ) ) ) )).

fof(t25_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( r1_lmod_6(A,B,C)
               => r1_lmod_6(A,B,k2_vectsp_4(A,C)) ) ) ) ) )).

fof(t26_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_lmod_6(A,C,k1_vectsp_5(A,B,C,D))
                    & r1_lmod_6(A,D,k1_vectsp_5(A,B,C,D)) ) ) ) ) ) )).

fof(t27_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_lmod_6(A,k2_vectsp_5(A,B,C,D),C)
                    & r1_lmod_6(A,k2_vectsp_5(A,B,C,D),D) ) ) ) ) ) )).

fof(t28_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( r1_lmod_6(A,C,D)
                       => r1_lmod_6(A,k2_vectsp_5(A,B,C,E),k2_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).

fof(t29_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( r1_lmod_6(A,C,D)
                       => r1_lmod_6(A,k2_vectsp_5(A,B,C,E),D) ) ) ) ) ) ) )).

fof(t30_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( ( r1_lmod_6(A,C,D)
                          & r1_lmod_6(A,C,E) )
                       => r1_lmod_6(A,C,k2_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).

fof(t31_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => r1_lmod_6(A,k2_vectsp_5(A,B,C,D),k1_vectsp_5(A,B,C,D)) ) ) ) ) )).

fof(t32_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => r1_lmod_6(A,k1_vectsp_5(A,B,k2_vectsp_5(A,B,C,D),k2_vectsp_5(A,B,D,E)),k2_vectsp_5(A,B,D,k1_vectsp_5(A,B,C,E))) ) ) ) ) ) )).

fof(t33_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( r1_lmod_6(A,C,D)
                       => k2_vectsp_5(A,B,D,k1_vectsp_5(A,B,C,E)) = k1_vectsp_5(A,B,k2_vectsp_5(A,B,C,D),k2_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).

fof(t34_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => r1_lmod_6(A,k1_vectsp_5(A,B,C,k2_vectsp_5(A,B,D,E)),k2_vectsp_5(A,B,k1_vectsp_5(A,B,D,C),k1_vectsp_5(A,B,C,E))) ) ) ) ) ) )).

fof(t35_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( r1_lmod_6(A,C,D)
                       => k1_vectsp_5(A,B,D,k2_vectsp_5(A,B,C,E)) = k2_vectsp_5(A,B,k1_vectsp_5(A,B,C,D),k1_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).

fof(t36_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( r1_lmod_6(A,C,D)
                       => r1_lmod_6(A,C,k1_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).

fof(t37_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( ( r1_lmod_6(A,C,D)
                          & r1_lmod_6(A,E,D) )
                       => r1_lmod_6(A,k1_vectsp_5(A,B,C,E),D) ) ) ) ) ) ) )).

fof(t38_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( r1_tarski(C,D)
                   => r1_lmod_6(A,k1_mod_3(A,B,C),k1_mod_3(A,B,D)) ) ) ) ) ) )).

fof(t39_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => r1_lmod_6(A,k1_mod_3(A,B,k5_subset_1(u1_struct_0(B),C,D)),k2_vectsp_5(A,B,k1_mod_3(A,B,C),k1_mod_3(A,B,D))) ) ) ) ) )).

fof(t40_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( r1_lmod_6(A,B,C)
               => r1_tarski(k2_pre_topc(B),k2_pre_topc(C)) ) ) ) ) )).

fof(t41_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_lmod_6(A,C,D)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r1_rlvect_1(C,E)
                         => r1_rlvect_1(D,E) ) ) ) ) ) ) ) )).

fof(t42_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_lmod_6(A,C,D)
                  <=> r1_tarski(k2_pre_topc(C),k2_pre_topc(D)) ) ) ) ) ) )).

fof(t43_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ( r1_lmod_6(A,C,D)
                  <=> r1_tarski(k2_lmod_6(A,B,C,k2_pre_topc(C)),k2_lmod_6(A,B,D,k2_pre_topc(D))) ) ) ) ) ) )).

fof(t44_lmod_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_4(C,A,B)
             => ! [D] :
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_4(E,A,B)
                     => ( r1_lmod_6(A,k1_vectsp_4(A,C),B)
                        & r1_lmod_6(A,k1_vectsp_4(A,B),C)
                        & r1_lmod_6(A,k1_vectsp_4(A,D),E) ) ) ) ) ) ) )).

fof(reflexivity_r1_lmod_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A) )
     => r1_lmod_6(A,B,B) ) )).

fof(dt_k1_lmod_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & v11_vectsp_1(C,A)
        & m1_vectsp_4(C,A,B) )
     => m1_subset_1(k1_lmod_6(A,B,C),k3_vectsp_5(A,B)) ) )).

fof(dt_k2_lmod_6,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_vectsp_4(C,A,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) )
     => m1_subset_1(k2_lmod_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(dt_k3_lmod_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => m1_subset_1(k3_lmod_6(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(redefinition_k3_lmod_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => k3_lmod_6(A,B,C) = k1_tarski(C) ) )).

fof(dt_k4_lmod_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & 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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v11_vectsp_1(k4_lmod_6(A,B,C),A)
        & m1_vectsp_4(k4_lmod_6(A,B,C),A,B) ) ) )).
%------------------------------------------------------------------------------