SET007 Axioms: SET007+278.ax


%------------------------------------------------------------------------------
% File     : SET007+278 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Submodules and Cosets of Submodules
% Version  : [Urb08] axioms.
% English  : Submodules and Cosets of Submodules in Right Module over
%            Associative Ring,

% 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    : rmod_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  110 (  16 unit)
%            Number of atoms       : 2072 (  68 equality)
%            Maximal formula depth :   25 (  12 average)
%            Number of connectives : 2169 ( 207 ~  ;   1  |;1533  &)
%                                         (  24 <=>; 404 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-4 arity)
%            Number of functors    :   21 (   1 constant; 0-5 arity)
%            Number of variables   :  402 (   0 singleton; 390 !;  12 ?)
%            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(rc1_rmod_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)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A) )
     => ? [C] :
          ( m1_rmod_2(C,A,B)
          & ~ v3_struct_0(C)
          & v3_rlvect_1(C)
          & v4_rlvect_1(C)
          & v5_rlvect_1(C)
          & v6_rlvect_1(C)
          & v3_vectsp_2(C,A)
          & v5_vectsp_2(C,A) ) ) )).

fof(d1_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v1_rmod_2(C,A,B)
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ( ( r2_hidden(D,C)
                              & r2_hidden(E,C) )
                           => r2_hidden(k4_rlvect_1(B,D,E),C) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ( r2_hidden(E,C)
                           => r2_hidden(k6_vectsp_2(A,B,D,E),C) ) ) ) ) ) ) ) ) )).

fof(t1_rmod_2,axiom,(
    $true )).

fof(t2_rmod_2,axiom,(
    $true )).

fof(t3_rmod_2,axiom,(
    $true )).

fof(t4_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v1_rmod_2(C,A,B)
               => ( C = k1_xboole_0
                  | r2_hidden(k1_rlvect_1(B),C) ) ) ) ) ) )).

fof(t5_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v1_rmod_2(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( r2_hidden(D,C)
                     => r2_hidden(k5_rlvect_1(B,D),C) ) ) ) ) ) ) )).

fof(t6_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v1_rmod_2(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( ( r2_hidden(D,C)
                            & r2_hidden(E,C) )
                         => r2_hidden(k6_rlvect_1(B,D,E),C) ) ) ) ) ) ) ) )).

fof(t7_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => v1_rmod_2(k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)),A,B) ) ) )).

fof(t8_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( u1_struct_0(B) = C
               => v1_rmod_2(C,A,B) ) ) ) ) )).

fof(t10_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(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)))
                 => ( ( v1_rmod_2(C,A,B)
                      & v1_rmod_2(D,A,B) )
                   => v1_rmod_2(k5_subset_1(u1_struct_0(B),C,D),A,B) ) ) ) ) ) )).

fof(d2_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ( m1_rmod_2(C,A,B)
              <=> ( r1_tarski(u1_struct_0(C),u1_struct_0(B))
                  & u2_struct_0(C) = u2_struct_0(B)
                  & u1_rlvect_1(C) = k7_relat_1(u1_rlvect_1(B),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)))
                  & u1_vectsp_2(A,C) = k7_relat_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(A))) ) ) ) ) ) )).

fof(t11_rmod_2,axiom,(
    $true )).

fof(t12_rmod_2,axiom,(
    $true )).

fof(t13_rmod_2,axiom,(
    $true )).

fof(t14_rmod_2,axiom,(
    $true )).

fof(t15_rmod_2,axiom,(
    $true )).

fof(t16_rmod_2,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)
            & v5_vectsp_2(C,B)
            & l1_vectsp_2(C,B) )
         => ! [D] :
              ( m1_rmod_2(D,B,C)
             => ! [E] :
                  ( m1_rmod_2(E,B,C)
                 => ( ( r1_rlvect_1(D,A)
                      & m1_rmod_2(D,B,E) )
                   => r1_rlvect_1(E,A) ) ) ) ) ) )).

fof(t17_rmod_2,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)
            & v5_vectsp_2(C,B)
            & l1_vectsp_2(C,B) )
         => ! [D] :
              ( m1_rmod_2(D,B,C)
             => ( r1_rlvect_1(D,A)
               => r1_rlvect_1(C,A) ) ) ) ) )).

fof(t18_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => m1_subset_1(D,u1_struct_0(B)) ) ) ) ) )).

fof(t19_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => k1_rlvect_1(C) = k1_rlvect_1(B) ) ) ) )).

fof(t20_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => k1_rlvect_1(C) = k1_rlvect_1(D) ) ) ) ) )).

fof(t21_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(E))
                             => ( ( F = C
                                  & G = D )
                               => k4_rlvect_1(E,F,G) = k4_rlvect_1(B,C,D) ) ) ) ) ) ) ) ) )).

fof(t22_rmod_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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_rmod_2(E,A,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ( F = D
                           => k6_vectsp_2(A,E,B,F) = k6_vectsp_2(A,C,B,D) ) ) ) ) ) ) ) )).

fof(t23_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ( E = C
                       => k5_rlvect_1(B,C) = k5_rlvect_1(D,E) ) ) ) ) ) ) )).

fof(t24_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(E))
                             => ( ( F = C
                                  & G = D )
                               => k6_rlvect_1(E,F,G) = k6_rlvect_1(B,C,D) ) ) ) ) ) ) ) ) )).

fof(t25_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) )).

fof(t26_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => r1_rlvect_1(D,k1_rlvect_1(C)) ) ) ) ) )).

fof(t27_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => r1_rlvect_1(B,k1_rlvect_1(C)) ) ) ) )).

fof(t28_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( ( r1_rlvect_1(E,C)
                          & r1_rlvect_1(E,D) )
                       => r1_rlvect_1(E,k4_rlvect_1(B,C,D)) ) ) ) ) ) ) )).

fof(t29_rmod_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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_rmod_2(E,A,C)
                     => ( r1_rlvect_1(E,D)
                       => r1_rlvect_1(E,k6_vectsp_2(A,C,B,D)) ) ) ) ) ) ) )).

fof(t30_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( r1_rlvect_1(D,C)
                   => r1_rlvect_1(D,k5_rlvect_1(B,C)) ) ) ) ) ) )).

fof(t31_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( ( r1_rlvect_1(E,C)
                          & r1_rlvect_1(E,D) )
                       => r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) )).

fof(t32_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => m1_rmod_2(B,A,B) ) ) )).

fof(t33_rmod_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)
            & v3_vectsp_2(B,A)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v3_vectsp_2(C,A)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ( ( m1_rmod_2(C,A,B)
                  & m1_rmod_2(B,A,C) )
               => C = B ) ) ) ) )).

fof(t34_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v5_vectsp_2(D,A)
                    & l1_vectsp_2(D,A) )
                 => ( ( m1_rmod_2(B,A,C)
                      & m1_rmod_2(C,A,D) )
                   => m1_rmod_2(B,A,D) ) ) ) ) ) )).

fof(t35_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( r1_tarski(u1_struct_0(C),u1_struct_0(D))
                   => m1_rmod_2(C,A,D) ) ) ) ) ) )).

fof(t36_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r1_rlvect_1(C,E)
                         => r1_rlvect_1(D,E) ) )
                   => m1_rmod_2(C,A,D) ) ) ) ) ) )).

fof(t37_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( v3_vectsp_2(C,A)
                & m1_rmod_2(C,A,B) )
             => ! [D] :
                  ( ( v3_vectsp_2(D,A)
                    & m1_rmod_2(D,A,B) )
                 => ( u1_struct_0(C) = u1_struct_0(D)
                   => C = D ) ) ) ) ) )).

fof(t38_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( v3_vectsp_2(C,A)
                & m1_rmod_2(C,A,B) )
             => ! [D] :
                  ( ( v3_vectsp_2(D,A)
                    & m1_rmod_2(D,A,B) )
                 => ( ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r1_rlvect_1(C,E)
                        <=> r1_rlvect_1(D,E) ) )
                   => C = D ) ) ) ) ) )).

fof(t39_rmod_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)
            & v3_vectsp_2(B,A)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( v3_vectsp_2(C,A)
                & m1_rmod_2(C,A,B) )
             => ( u1_struct_0(C) = u1_struct_0(B)
               => C = B ) ) ) ) )).

fof(t40_rmod_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)
            & v3_vectsp_2(B,A)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( v3_vectsp_2(C,A)
                & m1_rmod_2(C,A,B) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => r1_rlvect_1(C,D) )
               => C = B ) ) ) ) )).

fof(t41_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( u1_struct_0(D) = C
                   => v1_rmod_2(C,A,B) ) ) ) ) ) )).

fof(t42_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ~ ( C != k1_xboole_0
                  & v1_rmod_2(C,A,B)
                  & ! [D] :
                      ( ( v3_vectsp_2(D,A)
                        & m1_rmod_2(D,A,B) )
                     => C != u1_struct_0(D) ) ) ) ) ) )).

fof(d3_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( v3_vectsp_2(C,A)
                & m1_rmod_2(C,A,B) )
             => ( C = k1_rmod_2(A,B)
              <=> u1_struct_0(C) = k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)) ) ) ) ) )).

fof(d4_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => k2_rmod_2(A,B) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) )).

fof(t43_rmod_2,axiom,(
    $true )).

fof(t44_rmod_2,axiom,(
    $true )).

fof(t45_rmod_2,axiom,(
    $true )).

fof(t46_rmod_2,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)
            & v5_vectsp_2(C,B)
            & l1_vectsp_2(C,B) )
         => ( r1_rlvect_1(k1_rmod_2(B,C),A)
          <=> A = k1_rlvect_1(C) ) ) ) )).

fof(t47_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => k1_rmod_2(A,C) = k1_rmod_2(A,B) ) ) ) )).

fof(t48_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => k1_rmod_2(A,C) = k1_rmod_2(A,D) ) ) ) ) )).

fof(t49_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => m1_rmod_2(k1_rmod_2(A,C),A,B) ) ) ) )).

fof(t50_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => m1_rmod_2(k1_rmod_2(A,B),A,C) ) ) ) )).

fof(t51_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => m1_rmod_2(k1_rmod_2(A,C),A,D) ) ) ) ) )).

fof(t52_rmod_2,axiom,(
    $true )).

fof(t53_rmod_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)
            & v3_vectsp_2(B,A)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => m1_rmod_2(B,A,k2_rmod_2(A,B)) ) ) )).

fof(d6_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( m2_rmod_2(D,A,B,C)
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                        & D = k3_rmod_2(A,B,E,C) ) ) ) ) ) ) )).

fof(t54_rmod_2,axiom,(
    $true )).

fof(t55_rmod_2,axiom,(
    $true )).

fof(t56_rmod_2,axiom,(
    $true )).

fof(t57_rmod_2,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)
            & v5_vectsp_2(C,B)
            & l1_vectsp_2(C,B) )
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(C))
             => ! [E] :
                  ( m1_rmod_2(E,B,C)
                 => ( r2_hidden(A,k3_rmod_2(B,C,D,E))
                  <=> ? [F] :
                        ( m1_subset_1(F,u1_struct_0(C))
                        & r1_rlvect_1(E,F)
                        & A = k4_rlvect_1(C,D,F) ) ) ) ) ) ) )).

fof(t58_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( r2_hidden(k1_rlvect_1(B),k3_rmod_2(A,B,C,D))
                  <=> r1_rlvect_1(D,C) ) ) ) ) ) )).

fof(t59_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => r2_hidden(C,k3_rmod_2(A,B,C,D)) ) ) ) ) )).

fof(t60_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => k3_rmod_2(A,B,k1_rlvect_1(B),C) = u1_struct_0(C) ) ) ) )).

fof(t61_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rmod_2(A,B,C,k1_rmod_2(A,B)) = k6_domain_1(u1_struct_0(B),C) ) ) ) )).

fof(t62_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rmod_2(A,B,C,k2_rmod_2(A,B)) = u1_struct_0(B) ) ) ) )).

fof(t63_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( r2_hidden(k1_rlvect_1(B),k3_rmod_2(A,B,C,D))
                  <=> k3_rmod_2(A,B,C,D) = u1_struct_0(D) ) ) ) ) ) )).

fof(t64_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( r1_rlvect_1(D,C)
                  <=> k3_rmod_2(A,B,C,D) = u1_struct_0(D) ) ) ) ) ) )).

fof(t65_rmod_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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_rmod_2(E,A,C)
                     => ( r1_rlvect_1(E,D)
                       => k3_rmod_2(A,C,k6_vectsp_2(A,C,B,D),E) = u1_struct_0(E) ) ) ) ) ) ) )).

fof(t66_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( r1_rlvect_1(E,C)
                      <=> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,k4_rlvect_1(B,D,C),E) ) ) ) ) ) ) )).

fof(t67_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( r1_rlvect_1(E,C)
                      <=> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,k6_rlvect_1(B,D,C),E) ) ) ) ) ) ) )).

fof(t68_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( r2_hidden(C,k3_rmod_2(A,B,D,E))
                      <=> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,E) ) ) ) ) ) ) )).

fof(t69_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_rmod_2(F,A,B)
                         => ( ( r2_hidden(C,k3_rmod_2(A,B,D,F))
                              & r2_hidden(C,k3_rmod_2(A,B,E,F)) )
                           => k3_rmod_2(A,B,D,F) = k3_rmod_2(A,B,E,F) ) ) ) ) ) ) ) )).

fof(t70_rmod_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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v5_vectsp_2(C,A)
                & l1_vectsp_2(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_rmod_2(E,A,C)
                     => ( r1_rlvect_1(E,D)
                       => r2_hidden(k6_vectsp_2(A,C,B,D),k3_rmod_2(A,C,D,E)) ) ) ) ) ) ) )).

fof(t71_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ( r1_rlvect_1(D,C)
                   => r2_hidden(k5_rlvect_1(B,C),k3_rmod_2(A,B,C,D)) ) ) ) ) ) )).

fof(t72_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( r2_hidden(k4_rlvect_1(B,C,D),k3_rmod_2(A,B,D,E))
                      <=> r1_rlvect_1(E,C) ) ) ) ) ) ) )).

fof(t73_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( r2_hidden(k6_rlvect_1(B,C,D),k3_rmod_2(A,B,C,E))
                      <=> r1_rlvect_1(E,D) ) ) ) ) ) ) )).

fof(t74_rmod_2,axiom,(
    $true )).

fof(t75_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( r2_hidden(C,k3_rmod_2(A,B,D,E))
                      <=> ? [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                            & r1_rlvect_1(E,F)
                            & C = k6_rlvect_1(B,D,F) ) ) ) ) ) ) ) )).

fof(t76_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( ? [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                            & r2_hidden(C,k3_rmod_2(A,B,F,E))
                            & r2_hidden(D,k3_rmod_2(A,B,F,E)) )
                      <=> r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) )).

fof(t77_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ~ ( k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ~ ( r1_rlvect_1(E,F)
                                  & k4_rlvect_1(B,C,F) = D ) ) ) ) ) ) ) ) )).

fof(t78_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ~ ( k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ~ ( r1_rlvect_1(E,F)
                                  & k6_rlvect_1(B,C,F) = D ) ) ) ) ) ) ) ) )).

fof(t79_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( ( v3_vectsp_2(D,A)
                    & m1_rmod_2(D,A,B) )
                 => ! [E] :
                      ( ( v3_vectsp_2(E,A)
                        & m1_rmod_2(E,A,B) )
                     => ( k3_rmod_2(A,B,C,D) = k3_rmod_2(A,B,C,E)
                      <=> D = E ) ) ) ) ) ) )).

fof(t80_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( ( v3_vectsp_2(E,A)
                        & m1_rmod_2(E,A,B) )
                     => ! [F] :
                          ( ( v3_vectsp_2(F,A)
                            & m1_rmod_2(F,A,B) )
                         => ( k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,F)
                           => E = F ) ) ) ) ) ) ) )).

fof(t81_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ? [E] :
                      ( m2_rmod_2(E,A,B,D)
                      & r2_hidden(C,E) ) ) ) ) ) )).

fof(t82_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m2_rmod_2(D,A,B,C)
                 => ( v1_rmod_2(D,A,B)
                  <=> D = u1_struct_0(C) ) ) ) ) ) )).

fof(t83_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( ( v3_vectsp_2(C,A)
                & m1_rmod_2(C,A,B) )
             => ! [D] :
                  ( ( v3_vectsp_2(D,A)
                    & m1_rmod_2(D,A,B) )
                 => ! [E] :
                      ( m2_rmod_2(E,A,B,C)
                     => ! [F] :
                          ( m2_rmod_2(F,A,B,D)
                         => ( E = F
                           => C = D ) ) ) ) ) ) ) )).

fof(t84_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m2_rmod_2(k6_domain_1(u1_struct_0(B),C),A,B,k1_rmod_2(A,B)) ) ) ) )).

fof(t85_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ~ ( m2_rmod_2(C,A,B,k1_rmod_2(A,B))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => C != k6_domain_1(u1_struct_0(B),D) ) ) ) ) ) )).

fof(t86_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => m2_rmod_2(u1_struct_0(C),A,B,C) ) ) ) )).

fof(t87_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => m2_rmod_2(u1_struct_0(B),A,B,k2_rmod_2(A,B)) ) ) )).

fof(t88_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( m2_rmod_2(C,A,B,k2_rmod_2(A,B))
               => C = u1_struct_0(B) ) ) ) ) )).

fof(t89_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_rmod_2(C,A,B)
             => ! [D] :
                  ( m2_rmod_2(D,A,B,C)
                 => ( r2_hidden(k1_rlvect_1(B),D)
                  <=> D = u1_struct_0(C) ) ) ) ) ) )).

fof(t90_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ! [E] :
                      ( m2_rmod_2(E,A,B,D)
                     => ( r2_hidden(C,E)
                      <=> E = k3_rmod_2(A,B,C,D) ) ) ) ) ) ) )).

fof(t91_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ! [F] :
                          ( m2_rmod_2(F,A,B,E)
                         => ~ ( r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ~ ( r1_rlvect_1(E,G)
                                      & k4_rlvect_1(B,C,G) = D ) ) ) ) ) ) ) ) ) )).

fof(t92_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ! [F] :
                          ( m2_rmod_2(F,A,B,E)
                         => ~ ( r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ~ ( r1_rlvect_1(E,G)
                                      & k6_rlvect_1(B,C,G) = D ) ) ) ) ) ) ) ) ) )).

fof(t93_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_rmod_2(E,A,B)
                     => ( ? [F] :
                            ( m2_rmod_2(F,A,B,E)
                            & r2_hidden(C,F)
                            & r2_hidden(D,F) )
                      <=> r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) )).

fof(t94_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => ! [E] :
                      ( m2_rmod_2(E,A,B,D)
                     => ! [F] :
                          ( m2_rmod_2(F,A,B,D)
                         => ( ( r2_hidden(C,E)
                              & r2_hidden(C,F) )
                           => E = F ) ) ) ) ) ) ) )).

fof(dt_m1_rmod_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)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A) )
     => ! [C] :
          ( m1_rmod_2(C,A,B)
         => ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v5_vectsp_2(C,A)
            & l1_vectsp_2(C,A) ) ) ) )).

fof(existence_m1_rmod_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)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A) )
     => ? [C] : m1_rmod_2(C,A,B) ) )).

fof(dt_m2_rmod_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)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A)
        & m1_rmod_2(C,A,B) )
     => ! [D] :
          ( m2_rmod_2(D,A,B,C)
         => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) ) )).

fof(existence_m2_rmod_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)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A)
        & m1_rmod_2(C,A,B) )
     => ? [D] : m2_rmod_2(D,A,B,C) ) )).

fof(dt_k1_rmod_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)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A) )
     => ( v3_vectsp_2(k1_rmod_2(A,B),A)
        & m1_rmod_2(k1_rmod_2(A,B),A,B) ) ) )).

fof(dt_k2_rmod_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)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A) )
     => ( v3_vectsp_2(k2_rmod_2(A,B),A)
        & m1_rmod_2(k2_rmod_2(A,B),A,B) ) ) )).

fof(dt_k3_rmod_2,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)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_rmod_2(D,A,B) )
     => m1_subset_1(k3_rmod_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(t9_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(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)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v1_rmod_2(C,A,B)
                          & v1_rmod_2(D,A,B)
                          & E = a_4_0_rmod_2(A,B,C,D) )
                       => v1_rmod_2(E,A,B) ) ) ) ) ) ) )).

fof(d5_rmod_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)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_rmod_2(D,A,B)
                 => k3_rmod_2(A,B,C,D) = a_4_1_rmod_2(A,B,C,D) ) ) ) ) )).

fof(fraenkel_a_4_0_rmod_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ 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(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v5_vectsp_2(C,B)
        & l1_vectsp_2(C,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) )
     => ( r2_hidden(A,a_4_0_rmod_2(B,C,D,E))
      <=> ? [F,G] :
            ( m1_subset_1(F,u1_struct_0(C))
            & m1_subset_1(G,u1_struct_0(C))
            & A = k4_rlvect_1(C,F,G)
            & r2_hidden(F,D)
            & r2_hidden(G,E) ) ) ) )).

fof(fraenkel_a_4_1_rmod_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ 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(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v5_vectsp_2(C,B)
        & l1_vectsp_2(C,B)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_rmod_2(E,B,C) )
     => ( r2_hidden(A,a_4_1_rmod_2(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(C))
            & A = k4_rlvect_1(C,D,F)
            & r1_rlvect_1(E,F) ) ) ) )).
%------------------------------------------------------------------------------