SET007 Axioms: SET007+313.ax


%------------------------------------------------------------------------------
% File     : SET007+313 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Rings and Modules - Part II
% 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    : mod_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  101 (  18 unit)
%            Number of atoms       : 1574 ( 137 equality)
%            Maximal formula depth :   40 (  12 average)
%            Number of connectives : 1636 ( 163 ~  ;   0  |;1228  &)
%                                         (   7 <=>; 238 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   1 propositional; 0-4 arity)
%            Number of functors    :   52 (  12 constant; 0-6 arity)
%            Number of variables   :  261 (   0 singleton; 249 !;  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_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] :
          ( l1_mod_2(B,A)
          & v2_mod_2(B,A) ) ) )).

fof(rc2_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] :
          ( l1_mod_2(B,A)
          & v2_mod_2(B,A)
          & v3_mod_2(B,A) ) ) )).

fof(fc1_mod_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)
        & 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) )
     => ( v2_mod_2(k5_mod_2(A,B,C),A)
        & v3_mod_2(k5_mod_2(A,B,C),A) ) ) )).

fof(rc3_mod_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)
        & 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) )
     => ? [D] :
          ( m1_mod_2(D,A,B,C)
          & v2_mod_2(D,A)
          & v3_mod_2(D,A) ) ) )).

fof(fc2_mod_2,axiom,(
    ! [A,B,C] : ~ v1_xboole_0(k1_enumset1(A,B,C)) )).

fof(fc3_mod_2,axiom,
    ( ~ v3_struct_0(k18_mod_2)
    & v3_vectsp_1(k18_mod_2) )).

fof(fc4_mod_2,axiom,
    ( ~ v3_struct_0(k18_mod_2)
    & v2_group_1(k18_mod_2)
    & v3_vectsp_1(k18_mod_2)
    & v6_vectsp_1(k18_mod_2)
    & v8_vectsp_1(k18_mod_2) )).

fof(fc5_mod_2,axiom,
    ( ~ v3_struct_0(k18_mod_2)
    & v4_rlvect_1(k18_mod_2)
    & v5_rlvect_1(k18_mod_2)
    & v6_rlvect_1(k18_mod_2)
    & v2_group_1(k18_mod_2)
    & v3_vectsp_1(k18_mod_2)
    & v6_vectsp_1(k18_mod_2)
    & v8_vectsp_1(k18_mod_2)
    & v1_algstr_1(k18_mod_2)
    & v2_algstr_1(k18_mod_2)
    & v3_algstr_1(k18_mod_2)
    & v4_algstr_1(k18_mod_2)
    & v5_algstr_1(k18_mod_2)
    & v6_algstr_1(k18_mod_2) )).

fof(fc6_mod_2,axiom,
    ( ~ v3_struct_0(k18_mod_2)
    & v3_rlvect_1(k18_mod_2)
    & v4_rlvect_1(k18_mod_2)
    & v5_rlvect_1(k18_mod_2)
    & v6_rlvect_1(k18_mod_2)
    & v2_group_1(k18_mod_2)
    & v4_group_1(k18_mod_2)
    & v7_group_1(k18_mod_2)
    & v3_vectsp_1(k18_mod_2)
    & v4_vectsp_1(k18_mod_2)
    & v5_vectsp_1(k18_mod_2)
    & v6_vectsp_1(k18_mod_2)
    & v7_vectsp_1(k18_mod_2)
    & v8_vectsp_1(k18_mod_2)
    & v9_vectsp_1(k18_mod_2)
    & v13_vectsp_1(k18_mod_2)
    & v1_algstr_1(k18_mod_2)
    & v2_algstr_1(k18_mod_2)
    & v3_algstr_1(k18_mod_2)
    & v4_algstr_1(k18_mod_2)
    & v5_algstr_1(k18_mod_2)
    & v6_algstr_1(k18_mod_2) )).

fof(d1_mod_2,axiom,(
    $true )).

fof(d2_mod_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) )
     => k1_mod_2(A) = g4_vectsp_1(A,k1_tarski(k1_xboole_0),k2_midsp_1,k8_vectsp_2,k10_funct_3(u1_struct_0(A),k1_tarski(k1_xboole_0))) ) )).

fof(t1_mod_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(k1_mod_2(A)))
         => B = k1_rlvect_1(k1_mod_2(A)) ) ) )).

fof(d3_mod_2,axiom,(
    $true )).

fof(d4_mod_2,axiom,(
    $true )).

fof(d5_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ( v1_mod_2(D,A,B,C)
                  <=> ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k2_rlvect_1(B,E,F)) = k2_rlvect_1(C,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,E),k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k6_vectsp_1(A,B,E,F)) = k6_vectsp_1(A,C,E,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)) ) ) ) ) ) ) ) ) )).

fof(t2_mod_2,axiom,(
    $true )).

fof(t3_mod_2,axiom,(
    $true )).

fof(t4_mod_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)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ( v1_mod_2(D,A,B,C)
                   => v1_grcat_1(D,B,C) ) ) ) ) ) )).

fof(t5_mod_2,axiom,(
    $true )).

fof(t6_mod_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)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l4_vectsp_1(D,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                         => ( ( v1_mod_2(E,A,B,C)
                              & v1_mod_2(F,A,C,D) )
                           => v1_mod_2(k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),E,F),A,B,D) ) ) ) ) ) ) ) )).

fof(t7_mod_2,axiom,(
    $true )).

fof(t8_mod_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)
            & 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) )
             => v1_mod_2(k8_grcat_1(B,C),A,B,C) ) ) ) )).

fof(d6_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( l1_mod_2(B,A)
         => k2_mod_2(A,B) = u1_mod_2(A,B) ) ) )).

fof(d7_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( l1_mod_2(B,A)
         => k3_mod_2(A,B) = u2_mod_2(A,B) ) ) )).

fof(d8_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( l1_mod_2(B,A)
         => k4_mod_2(A,B) = u3_mod_2(A,B) ) ) )).

fof(t9_mod_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)
            & 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] :
                  ( l1_mod_2(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( D = g1_mod_2(A,B,C,E)
                       => ( k2_mod_2(A,D) = B
                          & k3_mod_2(A,D) = C
                          & k4_mod_2(A,D) = E ) ) ) ) ) ) ) )).

fof(d9_mod_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)
            & 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) )
             => k5_mod_2(A,B,C) = g1_mod_2(A,B,C,k8_grcat_1(B,C)) ) ) ) )).

fof(d10_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( l1_mod_2(B,A)
         => ( v3_mod_2(B,A)
          <=> v1_mod_2(k4_mod_2(A,B),A,k2_mod_2(A,B),k3_mod_2(A,B)) ) ) ) )).

fof(t10_mod_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_mod_2(B,A)
            & l1_mod_2(B,A) )
         => v1_mod_2(u3_mod_2(A,B),A,u1_mod_2(A,B),u2_mod_2(A,B)) ) ) )).

fof(d11_mod_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)
            & 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_mod_2(D,A)
                    & l1_mod_2(D,A) )
                 => ( m1_mod_2(D,A,B,C)
                  <=> ( k2_mod_2(A,D) = B
                      & k3_mod_2(A,D) = C ) ) ) ) ) ) )).

fof(t11_mod_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)
            & 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] :
                  ( l1_mod_2(D,A)
                 => ( ( k2_mod_2(A,D) = B
                      & k3_mod_2(A,D) = C
                      & v1_mod_2(k4_mod_2(A,D),A,k2_mod_2(A,D),k3_mod_2(A,D)) )
                   => m1_mod_2(D,A,B,C) ) ) ) ) ) )).

fof(t12_mod_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)
            & 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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ( v1_mod_2(D,A,B,C)
                   => ( v2_mod_2(g1_mod_2(A,B,C,D),A)
                      & m1_mod_2(g1_mod_2(A,B,C,D),A,B,C) ) ) ) ) ) ) )).

fof(t13_mod_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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => v1_mod_2(k7_grcat_1(B),A,B,B) ) ) )).

fof(d12_mod_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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => k6_mod_2(A,B) = g1_mod_2(A,B,B,k7_grcat_1(B)) ) ) )).

fof(t14_mod_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)
            & 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] :
                  ( m1_mod_2(D,A,B,C)
                 => ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                      & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C))
                      & g1_mod_2(A,u1_mod_2(A,D),u2_mod_2(A,D),u3_mod_2(A,D)) = g1_mod_2(A,B,C,E)
                      & v1_mod_2(E,A,B,C) ) ) ) ) ) )).

fof(t15_mod_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)
            & 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] :
                  ( ( v2_mod_2(D,A)
                    & m1_mod_2(D,A,B,C) )
                 => ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                      & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C))
                      & D = g1_mod_2(A,B,C,E) ) ) ) ) ) )).

fof(t16_mod_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_mod_2(B,A)
            & l1_mod_2(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)
                  & m1_mod_2(B,A,C,D) ) ) ) ) )).

fof(t17_mod_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] :
          ( ( v2_mod_2(B,A)
            & v3_mod_2(B,A)
            & l1_mod_2(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)
                  & ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
                      & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D))
                      & v2_mod_2(B,A)
                      & m1_mod_2(B,A,C,D)
                      & B = g1_mod_2(A,C,D,E)
                      & v1_mod_2(E,A,C,D) ) ) ) ) ) )).

fof(t18_mod_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_mod_2(B,A)
            & l1_mod_2(B,A) )
         => ! [C] :
              ( ( v3_mod_2(C,A)
                & l1_mod_2(C,A) )
             => ~ ( k2_mod_2(A,B) = k3_mod_2(A,C)
                  & ! [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] :
                          ( ( ~ v3_struct_0(E)
                            & v3_rlvect_1(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & v12_vectsp_1(E,A)
                            & l4_vectsp_1(E,A) )
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & v3_rlvect_1(F)
                                & v4_rlvect_1(F)
                                & v5_rlvect_1(F)
                                & v6_rlvect_1(F)
                                & v12_vectsp_1(F,A)
                                & l4_vectsp_1(F,A) )
                             => ~ ( m1_mod_2(B,A,E,F)
                                  & m1_mod_2(C,A,D,E) ) ) ) ) ) ) ) ) )).

fof(d13_mod_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_mod_2(B,A)
            & l1_mod_2(B,A) )
         => ! [C] :
              ( ( v3_mod_2(C,A)
                & l1_mod_2(C,A) )
             => ( k2_mod_2(A,B) = k3_mod_2(A,C)
               => ! [D] :
                    ( ( v2_mod_2(D,A)
                      & v3_mod_2(D,A)
                      & l1_mod_2(D,A) )
                   => ( D = k8_mod_2(A,B,C)
                    <=> ! [E] :
                          ( ( ~ v3_struct_0(E)
                            & v3_rlvect_1(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & v12_vectsp_1(E,A)
                            & l4_vectsp_1(E,A) )
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & v3_rlvect_1(F)
                                & v4_rlvect_1(F)
                                & v5_rlvect_1(F)
                                & v6_rlvect_1(F)
                                & v12_vectsp_1(F,A)
                                & l4_vectsp_1(F,A) )
                             => ! [G] :
                                  ( ( ~ v3_struct_0(G)
                                    & v3_rlvect_1(G)
                                    & v4_rlvect_1(G)
                                    & v5_rlvect_1(G)
                                    & v6_rlvect_1(G)
                                    & v12_vectsp_1(G,A)
                                    & l4_vectsp_1(G,A) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(F),u1_struct_0(G))
                                        & m2_relset_1(H,u1_struct_0(F),u1_struct_0(G)) )
                                     => ! [I] :
                                          ( ( v1_funct_1(I)
                                            & v1_funct_2(I,u1_struct_0(E),u1_struct_0(F))
                                            & m2_relset_1(I,u1_struct_0(E),u1_struct_0(F)) )
                                         => ( ( g1_mod_2(A,u1_mod_2(A,B),u2_mod_2(A,B),u3_mod_2(A,B)) = g1_mod_2(A,F,G,H)
                                              & g1_mod_2(A,u1_mod_2(A,C),u2_mod_2(A,C),u3_mod_2(A,C)) = g1_mod_2(A,E,F,I) )
                                           => D = g1_mod_2(A,E,G,k7_funct_2(u1_struct_0(E),u1_struct_0(F),u1_struct_0(G),I,H)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_mod_2,axiom,(
    $true )).

fof(t20_mod_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)
            & 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) )
                 => ! [E] :
                      ( m1_mod_2(E,A,B,C)
                     => ! [F] :
                          ( m1_mod_2(F,A,D,B)
                         => ( v2_mod_2(k8_mod_2(A,E,F),A)
                            & m1_mod_2(k8_mod_2(A,E,F),A,D,C) ) ) ) ) ) ) ) )).

fof(d14_mod_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)
            & 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) )
                 => ! [E] :
                      ( m1_mod_2(E,A,C,D)
                     => ! [F] :
                          ( m1_mod_2(F,A,B,C)
                         => k9_mod_2(A,B,C,D,E,F) = k8_mod_2(A,E,F) ) ) ) ) ) ) )).

fof(t21_mod_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)
            & 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) )
                 => ! [E] :
                      ( m1_mod_2(E,A,B,C)
                     => ! [F] :
                          ( m1_mod_2(F,A,D,B)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
                                & m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,u1_struct_0(D),u1_struct_0(B))
                                    & m2_relset_1(H,u1_struct_0(D),u1_struct_0(B)) )
                                 => ( ( E = g1_mod_2(A,B,C,G)
                                      & F = g1_mod_2(A,D,B,H) )
                                   => ( k9_mod_2(A,D,B,C,E,F) = g1_mod_2(A,D,C,k7_funct_2(u1_struct_0(D),u1_struct_0(B),u1_struct_0(C),H,G))
                                      & k8_mod_2(A,E,F) = g1_mod_2(A,D,C,k7_funct_2(u1_struct_0(D),u1_struct_0(B),u1_struct_0(C),H,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_mod_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] :
          ( ( v2_mod_2(B,A)
            & v3_mod_2(B,A)
            & l1_mod_2(B,A) )
         => ! [C] :
              ( ( v2_mod_2(C,A)
                & v3_mod_2(C,A)
                & l1_mod_2(C,A) )
             => ~ ( k2_mod_2(A,C) = k3_mod_2(A,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,A)
                        & l4_vectsp_1(D,A) )
                     => ! [E] :
                          ( ( ~ v3_struct_0(E)
                            & v3_rlvect_1(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & v12_vectsp_1(E,A)
                            & l4_vectsp_1(E,A) )
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & v3_rlvect_1(F)
                                & v4_rlvect_1(F)
                                & v5_rlvect_1(F)
                                & v6_rlvect_1(F)
                                & v12_vectsp_1(F,A)
                                & l4_vectsp_1(F,A) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
                                    & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(E),u1_struct_0(F))
                                        & m2_relset_1(H,u1_struct_0(E),u1_struct_0(F)) )
                                     => ~ ( B = g1_mod_2(A,D,E,G)
                                          & C = g1_mod_2(A,E,F,H)
                                          & k8_mod_2(A,C,B) = g1_mod_2(A,D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),G,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_mod_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] :
          ( ( v2_mod_2(B,A)
            & v3_mod_2(B,A)
            & l1_mod_2(B,A) )
         => ! [C] :
              ( ( v2_mod_2(C,A)
                & v3_mod_2(C,A)
                & l1_mod_2(C,A) )
             => ( k2_mod_2(A,C) = k3_mod_2(A,B)
               => ( k2_mod_2(A,k8_mod_2(A,C,B)) = k2_mod_2(A,B)
                  & k3_mod_2(A,k8_mod_2(A,C,B)) = k3_mod_2(A,C) ) ) ) ) ) )).

fof(t24_mod_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)
            & 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) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v3_rlvect_1(E)
                        & v4_rlvect_1(E)
                        & v5_rlvect_1(E)
                        & v6_rlvect_1(E)
                        & v12_vectsp_1(E,A)
                        & l4_vectsp_1(E,A) )
                     => ! [F] :
                          ( ( v2_mod_2(F,A)
                            & m1_mod_2(F,A,B,C) )
                         => ! [G] :
                              ( ( v2_mod_2(G,A)
                                & m1_mod_2(G,A,C,D) )
                             => ! [H] :
                                  ( ( v2_mod_2(H,A)
                                    & m1_mod_2(H,A,D,E) )
                                 => k8_mod_2(A,H,k8_mod_2(A,G,F)) = k8_mod_2(A,k8_mod_2(A,H,G),F) ) ) ) ) ) ) ) ) )).

fof(t25_mod_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] :
          ( ( v2_mod_2(B,A)
            & v3_mod_2(B,A)
            & l1_mod_2(B,A) )
         => ! [C] :
              ( ( v2_mod_2(C,A)
                & v3_mod_2(C,A)
                & l1_mod_2(C,A) )
             => ! [D] :
                  ( ( v2_mod_2(D,A)
                    & v3_mod_2(D,A)
                    & l1_mod_2(D,A) )
                 => ( ( k2_mod_2(A,D) = k3_mod_2(A,C)
                      & k2_mod_2(A,C) = k3_mod_2(A,B) )
                   => k8_mod_2(A,D,k8_mod_2(A,C,B)) = k8_mod_2(A,k8_mod_2(A,D,C),B) ) ) ) ) ) )).

fof(t26_mod_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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ( k2_mod_2(A,k6_mod_2(A,B)) = B
            & k3_mod_2(A,k6_mod_2(A,B)) = B
            & ! [C] :
                ( ( v2_mod_2(C,A)
                  & v3_mod_2(C,A)
                  & l1_mod_2(C,A) )
               => ( k3_mod_2(A,C) = B
                 => k8_mod_2(A,k6_mod_2(A,B),C) = C ) )
            & ! [C] :
                ( ( v2_mod_2(C,A)
                  & v3_mod_2(C,A)
                  & l1_mod_2(C,A) )
               => ( k2_mod_2(A,C) = B
                 => k8_mod_2(A,C,k6_mod_2(A,B)) = C ) ) ) ) ) )).

fof(t27_mod_2,axiom,(
    $true )).

fof(t28_mod_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => m1_subset_1(k1_enumset1(B,C,D),A) ) ) ) ) )).

fof(t29_mod_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,A)
         => m1_subset_1(k1_ordinal1(B),A) ) ) )).

fof(t30_mod_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( m1_subset_1(np__0,A)
        & m1_subset_1(np__1,A)
        & m1_subset_1(np__2,A) ) ) )).

fof(d15_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
     => ( ( A = np__0
         => k10_mod_2(A) = np__0 )
        & ( A = np__1
         => k10_mod_2(A) = np__2 )
        & ( A = np__2
         => k10_mod_2(A) = np__1 ) ) ) )).

fof(d16_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
     => ! [B] :
          ( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
         => ( ( A = np__0
             => k11_mod_2(A,B) = B )
            & ( B = np__0
             => k11_mod_2(A,B) = A )
            & ( ( A = np__1
                & B = np__1 )
             => k11_mod_2(A,B) = np__2 )
            & ( ( A = np__1
                & B = np__2 )
             => k11_mod_2(A,B) = np__0 )
            & ( ( A = np__2
                & B = np__1 )
             => k11_mod_2(A,B) = np__0 )
            & ( ( A = np__2
                & B = np__2 )
             => k11_mod_2(A,B) = np__1 ) ) ) ) )).

fof(d17_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
     => ! [B] :
          ( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
         => ( ( B = np__0
             => k12_mod_2(A,B) = np__0 )
            & ( A = np__0
             => k12_mod_2(A,B) = np__0 )
            & ( B = np__1
             => k12_mod_2(A,B) = A )
            & ( A = np__1
             => k12_mod_2(A,B) = B )
            & ( ( A = np__2
                & B = np__2 )
             => k12_mod_2(A,B) = np__1 ) ) ) ) )).

fof(d18_mod_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
        & m2_relset_1(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) )
     => ( A = k13_mod_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
           => ! [C] :
                ( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
               => k2_binop_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),A,B,C) = k11_mod_2(B,C) ) ) ) ) )).

fof(d19_mod_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
        & m2_relset_1(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) )
     => ( A = k14_mod_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
           => ! [C] :
                ( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
               => k2_binop_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),A,B,C) = k12_mod_2(B,C) ) ) ) ) )).

fof(d20_mod_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2))
        & m2_relset_1(A,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)) )
     => ( A = k15_mod_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
           => k8_funct_2(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),A,B) = k10_mod_2(B) ) ) ) )).

fof(d21_mod_2,axiom,(
    k16_mod_2 = np__1 )).

fof(d22_mod_2,axiom,(
    k17_mod_2 = np__0 )).

fof(d23_mod_2,axiom,(
    k18_mod_2 = g3_vectsp_1(k1_enumset1(np__0,np__1,np__2),k13_mod_2,k14_mod_2,k16_mod_2,k17_mod_2) )).

fof(t31_mod_2,axiom,(
    $true )).

fof(t32_mod_2,axiom,
    ( k1_rlvect_1(k18_mod_2) = np__0
    & k2_group_1(k18_mod_2) = np__1
    & m1_subset_1(k1_rlvect_1(k18_mod_2),k1_enumset1(np__0,np__1,np__2))
    & m1_subset_1(k2_group_1(k18_mod_2),k1_enumset1(np__0,np__1,np__2))
    & u1_rlvect_1(k18_mod_2) = k13_mod_2
    & u1_group_1(k18_mod_2) = k14_mod_2 )).

fof(t33_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k18_mod_2))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k18_mod_2))
         => ! [C] :
              ( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
             => ! [D] :
                  ( m1_subset_1(D,k1_enumset1(np__0,np__1,np__2))
                 => ( ( C = A
                      & D = B )
                   => ( k2_rlvect_1(k18_mod_2,A,B) = k11_mod_2(C,D)
                      & k1_group_1(k18_mod_2,A,B) = k12_mod_2(C,D)
                      & k5_rlvect_1(k18_mod_2,A) = k10_mod_2(C) ) ) ) ) ) ) )).

fof(t34_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k18_mod_2))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k18_mod_2))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k18_mod_2))
             => ! [D] :
                  ( m1_subset_1(D,k1_enumset1(np__0,np__1,np__2))
                 => ! [E] :
                      ( m1_subset_1(E,k1_enumset1(np__0,np__1,np__2))
                     => ! [F] :
                          ( m1_subset_1(F,k1_enumset1(np__0,np__1,np__2))
                         => ( ( D = A
                              & E = B
                              & F = C )
                           => ( k2_rlvect_1(k18_mod_2,k2_rlvect_1(k18_mod_2,A,B),C) = k11_mod_2(k11_mod_2(D,E),F)
                              & k2_rlvect_1(k18_mod_2,A,k2_rlvect_1(k18_mod_2,B,C)) = k11_mod_2(D,k11_mod_2(E,F))
                              & k1_group_1(k18_mod_2,k1_group_1(k18_mod_2,A,B),C) = k12_mod_2(k12_mod_2(D,E),F)
                              & k1_group_1(k18_mod_2,A,k1_group_1(k18_mod_2,B,C)) = k12_mod_2(D,k12_mod_2(E,F)) ) ) ) ) ) ) ) ) )).

fof(t35_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
     => ! [B] :
          ( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
         => ! [C] :
              ( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
             => ! [D] :
                  ( m1_subset_1(D,k1_enumset1(np__0,np__1,np__2))
                 => ! [E] :
                      ( m1_subset_1(E,k1_enumset1(np__0,np__1,np__2))
                     => ( ( D = np__0
                          & E = np__1 )
                       => ( k11_mod_2(A,B) = k11_mod_2(B,A)
                          & k11_mod_2(k11_mod_2(A,B),C) = k11_mod_2(A,k11_mod_2(B,C))
                          & k11_mod_2(A,D) = A
                          & k11_mod_2(A,k10_mod_2(A)) = D
                          & k12_mod_2(A,B) = k12_mod_2(B,A)
                          & k12_mod_2(k12_mod_2(A,B),C) = k12_mod_2(A,k12_mod_2(B,C))
                          & k12_mod_2(E,A) = A
                          & ~ ( A != D
                              & ! [F] :
                                  ( m1_subset_1(F,k1_enumset1(np__0,np__1,np__2))
                                 => k12_mod_2(A,F) != E ) )
                          & D != E
                          & k12_mod_2(A,k11_mod_2(B,C)) = k11_mod_2(k12_mod_2(A,B),k12_mod_2(A,C)) ) ) ) ) ) ) ) )).

fof(t36_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B)
                      & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))
                      & k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
                      & k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
                      & k1_group_1(A,B,C) = k1_group_1(A,C,B)
                      & k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))
                      & k1_group_1(A,k2_group_1(A),B) = B
                      & ~ ( B != k1_rlvect_1(A)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => k1_group_1(A,B,E) != k2_group_1(A) ) )
                      & k1_rlvect_1(A) != k2_group_1(A)
                      & k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) ) ) ) )
       => ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A)
          & v9_vectsp_1(A)
          & ~ v10_vectsp_1(A)
          & l3_vectsp_1(A) ) ) ) )).

fof(t37_mod_2,axiom,
    ( ~ v3_struct_0(k18_mod_2)
    & v3_rlvect_1(k18_mod_2)
    & v4_rlvect_1(k18_mod_2)
    & v5_rlvect_1(k18_mod_2)
    & v6_rlvect_1(k18_mod_2)
    & v4_group_1(k18_mod_2)
    & v7_group_1(k18_mod_2)
    & v7_vectsp_1(k18_mod_2)
    & v8_vectsp_1(k18_mod_2)
    & v9_vectsp_1(k18_mod_2)
    & ~ v10_vectsp_1(k18_mod_2)
    & v13_vectsp_1(k18_mod_2)
    & l3_vectsp_1(k18_mod_2) )).

fof(t38_mod_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_classes2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( ( r2_hidden(A,C)
                      & r2_hidden(B,C) )
                   => r2_hidden(D,C) ) ) ) ) ) )).

fof(t39_mod_2,axiom,(
    $true )).

fof(t40_mod_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( r2_hidden(u1_struct_0(k18_mod_2),A)
        & m1_subset_1(u1_rlvect_1(k18_mod_2),A)
        & m1_subset_1(k7_vectsp_1(k18_mod_2),A)
        & m1_subset_1(u2_struct_0(k18_mod_2),A)
        & m1_subset_1(u1_group_1(k18_mod_2),A)
        & m1_subset_1(u1_vectsp_1(k18_mod_2),A) ) ) )).

fof(dt_m1_mod_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)
        & 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) )
     => ! [D] :
          ( m1_mod_2(D,A,B,C)
         => ( v3_mod_2(D,A)
            & l1_mod_2(D,A) ) ) ) )).

fof(existence_m1_mod_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)
        & 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) )
     => ? [D] : m1_mod_2(D,A,B,C) ) )).

fof(dt_l1_mod_2,axiom,(
    $true )).

fof(existence_l1_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] : l1_mod_2(B,A) ) )).

fof(abstractness_v2_mod_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)
        & l1_mod_2(B,A) )
     => ( v2_mod_2(B,A)
       => B = g1_mod_2(A,u1_mod_2(A,B),u2_mod_2(A,B),u3_mod_2(A,B)) ) ) )).

fof(dt_k1_mod_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_mod_2(A))
        & v3_rlvect_1(k1_mod_2(A))
        & v4_rlvect_1(k1_mod_2(A))
        & v5_rlvect_1(k1_mod_2(A))
        & v6_rlvect_1(k1_mod_2(A))
        & v11_vectsp_1(k1_mod_2(A),A)
        & v12_vectsp_1(k1_mod_2(A),A)
        & l4_vectsp_1(k1_mod_2(A),A) ) ) )).

fof(dt_k2_mod_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)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(k2_mod_2(A,B))
        & v3_rlvect_1(k2_mod_2(A,B))
        & v4_rlvect_1(k2_mod_2(A,B))
        & v5_rlvect_1(k2_mod_2(A,B))
        & v6_rlvect_1(k2_mod_2(A,B))
        & v12_vectsp_1(k2_mod_2(A,B),A)
        & l4_vectsp_1(k2_mod_2(A,B),A) ) ) )).

fof(dt_k3_mod_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)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(k3_mod_2(A,B))
        & v3_rlvect_1(k3_mod_2(A,B))
        & v4_rlvect_1(k3_mod_2(A,B))
        & v5_rlvect_1(k3_mod_2(A,B))
        & v6_rlvect_1(k3_mod_2(A,B))
        & v12_vectsp_1(k3_mod_2(A,B),A)
        & l4_vectsp_1(k3_mod_2(A,B),A) ) ) )).

fof(dt_k4_mod_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)
        & l1_mod_2(B,A) )
     => ( v1_funct_1(k4_mod_2(A,B))
        & v1_funct_2(k4_mod_2(A,B),u1_struct_0(k2_mod_2(A,B)),u1_struct_0(k3_mod_2(A,B)))
        & m2_relset_1(k4_mod_2(A,B),u1_struct_0(k2_mod_2(A,B)),u1_struct_0(k3_mod_2(A,B))) ) ) )).

fof(dt_k5_mod_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)
        & 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) )
     => ( v2_mod_2(k5_mod_2(A,B,C),A)
        & l1_mod_2(k5_mod_2(A,B,C),A) ) ) )).

fof(dt_k6_mod_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)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ( v2_mod_2(k6_mod_2(A,B),A)
        & m1_mod_2(k6_mod_2(A,B),A,B,B) ) ) )).

fof(dt_k7_mod_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)
        & 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) )
     => ( v2_mod_2(k7_mod_2(A,B,C),A)
        & m1_mod_2(k7_mod_2(A,B,C),A,B,C) ) ) )).

fof(redefinition_k7_mod_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)
        & 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) )
     => k7_mod_2(A,B,C) = k5_mod_2(A,B,C) ) )).

fof(dt_k8_mod_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_mod_2(B,A)
        & l1_mod_2(B,A)
        & v3_mod_2(C,A)
        & l1_mod_2(C,A) )
     => ( v2_mod_2(k8_mod_2(A,B,C),A)
        & v3_mod_2(k8_mod_2(A,B,C),A)
        & l1_mod_2(k8_mod_2(A,B,C),A) ) ) )).

fof(dt_k9_mod_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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)
        & ~ 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)
        & m1_mod_2(E,A,C,D)
        & m1_mod_2(F,A,B,C) )
     => ( v2_mod_2(k9_mod_2(A,B,C,D,E,F),A)
        & m1_mod_2(k9_mod_2(A,B,C,D,E,F),A,B,D) ) ) )).

fof(dt_k10_mod_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
     => m1_subset_1(k10_mod_2(A),k1_enumset1(np__0,np__1,np__2)) ) )).

fof(dt_k11_mod_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
        & m1_subset_1(B,k1_enumset1(np__0,np__1,np__2)) )
     => m1_subset_1(k11_mod_2(A,B),k1_enumset1(np__0,np__1,np__2)) ) )).

fof(dt_k12_mod_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
        & m1_subset_1(B,k1_enumset1(np__0,np__1,np__2)) )
     => m1_subset_1(k12_mod_2(A,B),k1_enumset1(np__0,np__1,np__2)) ) )).

fof(dt_k13_mod_2,axiom,
    ( v1_funct_1(k13_mod_2)
    & v1_funct_2(k13_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
    & m2_relset_1(k13_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) )).

fof(dt_k14_mod_2,axiom,
    ( v1_funct_1(k14_mod_2)
    & v1_funct_2(k14_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
    & m2_relset_1(k14_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) )).

fof(dt_k15_mod_2,axiom,
    ( v1_funct_1(k15_mod_2)
    & v1_funct_2(k15_mod_2,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2))
    & m2_relset_1(k15_mod_2,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)) )).

fof(dt_k16_mod_2,axiom,(
    m1_subset_1(k16_mod_2,k1_enumset1(np__0,np__1,np__2)) )).

fof(dt_k17_mod_2,axiom,(
    m1_subset_1(k17_mod_2,k1_enumset1(np__0,np__1,np__2)) )).

fof(dt_k18_mod_2,axiom,
    ( v3_vectsp_1(k18_mod_2)
    & l3_vectsp_1(k18_mod_2) )).

fof(dt_u1_mod_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)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(u1_mod_2(A,B))
        & v3_rlvect_1(u1_mod_2(A,B))
        & v4_rlvect_1(u1_mod_2(A,B))
        & v5_rlvect_1(u1_mod_2(A,B))
        & v6_rlvect_1(u1_mod_2(A,B))
        & v12_vectsp_1(u1_mod_2(A,B),A)
        & l4_vectsp_1(u1_mod_2(A,B),A) ) ) )).

fof(dt_u2_mod_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)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(u2_mod_2(A,B))
        & v3_rlvect_1(u2_mod_2(A,B))
        & v4_rlvect_1(u2_mod_2(A,B))
        & v5_rlvect_1(u2_mod_2(A,B))
        & v6_rlvect_1(u2_mod_2(A,B))
        & v12_vectsp_1(u2_mod_2(A,B),A)
        & l4_vectsp_1(u2_mod_2(A,B),A) ) ) )).

fof(dt_u3_mod_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)
        & l1_mod_2(B,A) )
     => ( v1_funct_1(u3_mod_2(A,B))
        & v1_funct_2(u3_mod_2(A,B),u1_struct_0(u1_mod_2(A,B)),u1_struct_0(u2_mod_2(A,B)))
        & m2_relset_1(u3_mod_2(A,B),u1_struct_0(u1_mod_2(A,B)),u1_struct_0(u2_mod_2(A,B))) ) ) )).

fof(dt_g1_mod_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)
        & 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)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
     => ( v2_mod_2(g1_mod_2(A,B,C,D),A)
        & l1_mod_2(g1_mod_2(A,B,C,D),A) ) ) )).

fof(free_g1_mod_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)
        & 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)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
     => ! [E,F,G,H] :
          ( g1_mod_2(A,B,C,D) = g1_mod_2(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).
%------------------------------------------------------------------------------