SET007 Axioms: SET007+246.ax


%------------------------------------------------------------------------------
% File     : SET007+246 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subgroup and Cosets of Subgroups
% 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    : group_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  236 (  27 unit)
%            Number of atoms       : 1659 ( 182 equality)
%            Maximal formula depth :   19 (   8 average)
%            Number of connectives : 1667 ( 244 ~  ;   2  |; 772  &)
%                                         (  33 <=>; 616 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   1 propositional; 0-3 arity)
%            Number of functors    :   54 (   5 constant; 0-5 arity)
%            Number of variables   :  629 (   0 singleton; 605 !;  24 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => v4_group_1(B) ) ) )).

fof(rc1_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ? [B] :
          ( m1_group_2(B,A)
          & ~ v3_struct_0(B)
          & v1_group_1(B)
          & v2_group_1(B)
          & v3_group_1(B)
          & v4_group_1(B) ) ) )).

fof(cc2_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v4_group_1(B)
            & v7_group_1(B) ) ) ) )).

fof(t1_group_2,axiom,(
    $true )).

fof(t2_group_2,axiom,(
    $true )).

fof(t3_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_group_1(A)
           => v1_finset_1(B) ) ) ) )).

fof(t4_group_2,axiom,(
    $true )).

fof(t5_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ( r2_hidden(A,k1_group_2(B,C))
          <=> ? [D] :
                ( m1_subset_1(D,u1_struct_0(B))
                & A = k3_group_1(B,D)
                & r2_hidden(D,C) ) ) ) ) )).

fof(t6_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_group_2(A,k6_domain_1(u1_struct_0(A),B)) = k6_domain_1(u1_struct_0(A),k3_group_1(A,B)) ) ) )).

fof(t7_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_2(A,k7_domain_1(u1_struct_0(A),B,C)) = k7_domain_1(u1_struct_0(A),k3_group_1(A,B),k3_group_1(A,C)) ) ) ) )).

fof(t8_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k1_group_2(A,k1_subset_1(u1_struct_0(A))) = k1_xboole_0 ) )).

fof(t9_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k1_group_2(A,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A) ) )).

fof(t10_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ ( B != k1_xboole_0
                & k1_group_2(A,B) = k1_xboole_0 )
            & ~ ( k1_group_2(A,B) != k1_xboole_0
                & B = k1_xboole_0 ) ) ) ) )).

fof(t11_group_2,axiom,(
    $true )).

fof(t12_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(A,k2_group_2(B,C,D))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k1_group_1(B,E,F)
                        & r2_hidden(E,C)
                        & r2_hidden(F,D) ) ) ) ) ) ) )).

fof(t13_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( B != k1_xboole_0
                  & C != k1_xboole_0 )
              <=> k2_group_2(A,B,C) != k1_xboole_0 ) ) ) ) )).

fof(t14_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v4_group_1(A)
                   => k2_group_2(A,k2_group_2(A,B,C),D) = k2_group_2(A,B,k2_group_2(A,C,D)) ) ) ) ) ) )).

fof(t15_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k1_group_2(A,k2_group_2(A,B,C)) = k2_group_2(A,k1_group_2(A,C),k1_group_2(A,B)) ) ) ) )).

fof(t16_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k2_group_2(A,B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),C,D)) = k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,C),k2_group_2(A,B,D)) ) ) ) ) )).

fof(t17_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k2_group_2(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C),D) = k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,D),k2_group_2(A,C,D)) ) ) ) ) )).

fof(t18_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k2_group_2(A,B,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),C,D)),k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,C),k2_group_2(A,B,D))) ) ) ) ) )).

fof(t19_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k2_group_2(A,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C),D),k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,D),k2_group_2(A,C,D))) ) ) ) ) )).

fof(t20_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( k2_group_2(A,k1_subset_1(u1_struct_0(A)),B) = k1_xboole_0
            & k2_group_2(A,B,k1_subset_1(u1_struct_0(A))) = k1_xboole_0 ) ) ) )).

fof(t21_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B != k1_xboole_0
           => ( k2_group_2(A,k2_subset_1(u1_struct_0(A)),B) = u1_struct_0(A)
              & k2_group_2(A,B,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A) ) ) ) ) )).

fof(t22_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_2(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)) = k6_domain_1(u1_struct_0(A),k1_group_1(A,B,C)) ) ) ) )).

fof(t23_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_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_group_2(A,k6_domain_1(u1_struct_0(A),B),k7_domain_1(u1_struct_0(A),C,D)) = k7_domain_1(u1_struct_0(A),k1_group_1(A,B,C),k1_group_1(A,B,D)) ) ) ) ) )).

fof(t24_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_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_group_2(A,k7_domain_1(u1_struct_0(A),B,C),k6_domain_1(u1_struct_0(A),D)) = k7_domain_1(u1_struct_0(A),k1_group_1(A,B,D),k1_group_1(A,C,D)) ) ) ) ) )).

fof(t25_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k2_group_2(A,k7_domain_1(u1_struct_0(A),B,C),k7_domain_1(u1_struct_0(A),D,E)) = k9_domain_1(u1_struct_0(A),k1_group_1(A,B,D),k1_group_1(A,B,E),k1_group_1(A,C,D),k1_group_1(A,C,E)) ) ) ) ) ) )).

fof(t26_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r2_hidden(D,B) )
                       => r2_hidden(k1_group_1(A,C,D),B) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r2_hidden(C,B)
                   => r2_hidden(k3_group_1(A,C),B) ) ) )
           => k2_group_2(A,B,B) = B ) ) ) )).

fof(t27_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => r2_hidden(k3_group_1(A,C),B) ) )
           => k1_group_2(A,B) = B ) ) ) )).

fof(t28_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r2_hidden(D,B)
                            & r2_hidden(E,C) )
                         => k1_group_1(A,D,E) = k1_group_1(A,E,D) ) ) )
               => k2_group_2(A,B,C) = k2_group_2(A,C,B) ) ) ) ) )).

fof(t29_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( ~ v3_struct_0(A)
                  & v3_group_1(A)
                  & v4_group_1(A)
                  & v7_group_1(A)
                  & l1_group_1(A) )
               => k2_group_2(A,B,C) = k2_group_2(A,C,B) ) ) ) ) )).

fof(t30_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k1_group_2(A,k2_group_2(A,B,C)) = k2_group_2(A,k1_group_2(A,B),k1_group_2(A,C)) ) ) ) )).

fof(d3_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k3_group_2(A,B,C) = k2_group_2(A,k6_domain_1(u1_struct_0(A),B),C) ) ) ) )).

fof(d4_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_group_2(A,B,C) = k2_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) )).

fof(t31_group_2,axiom,(
    $true )).

fof(t32_group_2,axiom,(
    $true )).

fof(t33_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k3_group_2(B,D,C))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,D,E)
                    & r2_hidden(E,C) ) ) ) ) ) )).

fof(t34_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k4_group_2(B,D,C))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,E,D)
                    & r2_hidden(E,C) ) ) ) ) ) )).

fof(t35_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k2_group_2(A,k3_group_2(A,D,B),C) = k3_group_2(A,D,k2_group_2(A,B,C)) ) ) ) ) ) )).

fof(t36_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k2_group_2(A,k4_group_2(A,D,B),C) = k2_group_2(A,B,k3_group_2(A,D,C)) ) ) ) ) ) )).

fof(t37_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k4_group_2(A,D,k2_group_2(A,B,C)) = k2_group_2(A,B,k4_group_2(A,D,C)) ) ) ) ) ) )).

fof(t38_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k3_group_2(A,k1_group_1(A,C,D),B) = k3_group_2(A,C,k3_group_2(A,D,B)) ) ) ) ) ) )).

fof(t39_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k4_group_2(A,D,k3_group_2(A,C,B)) = k3_group_2(A,C,k4_group_2(A,D,B)) ) ) ) ) ) )).

fof(t40_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k4_group_2(A,D,k4_group_2(A,C,B)) = k4_group_2(A,k1_group_1(A,C,D),B) ) ) ) ) ) )).

fof(t41_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k4_group_2(A,B,k1_subset_1(u1_struct_0(A))) = k1_xboole_0
            & k3_group_2(A,B,k1_subset_1(u1_struct_0(A))) = k1_xboole_0 ) ) ) )).

fof(t42_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k4_group_2(A,B,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A)
            & k3_group_2(A,B,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A) ) ) ) )).

fof(t43_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( k3_group_2(A,k2_group_1(A),B) = B
            & k4_group_2(A,k2_group_1(A),B) = B ) ) ) )).

fof(t44_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( ~ v3_struct_0(A)
                  & v3_group_1(A)
                  & v4_group_1(A)
                  & v7_group_1(A)
                  & l1_group_1(A) )
               => k3_group_2(A,B,C) = k4_group_2(A,B,C) ) ) ) ) )).

fof(d5_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => ( m1_group_2(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B)) ) ) ) ) )).

fof(t45_group_2,axiom,(
    $true )).

fof(t46_group_2,axiom,(
    $true )).

fof(t47_group_2,axiom,(
    $true )).

fof(t48_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v6_group_1(A)
           => v6_group_1(B) ) ) ) )).

fof(t49_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ( r1_rlvect_1(C,A)
           => r1_rlvect_1(B,A) ) ) ) )).

fof(t50_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => r1_rlvect_1(A,C) ) ) ) )).

fof(t51_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).

fof(t52_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( ( E = B
                              & F = C )
                           => k1_group_1(D,E,F) = k1_group_1(A,B,C) ) ) ) ) ) ) ) )).

fof(t53_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k2_group_1(B) = k2_group_1(A) ) ) )).

fof(t54_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => k2_group_1(B) = k2_group_1(C) ) ) ) )).

fof(t55_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => r1_rlvect_1(B,k2_group_1(A)) ) ) )).

fof(t56_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => r1_rlvect_1(C,k2_group_1(B)) ) ) ) )).

fof(t57_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( D = B
                   => k3_group_1(C,D) = k3_group_1(A,B) ) ) ) ) ) )).

fof(t58_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k4_group_1(B) = k8_relset_1(u1_struct_0(A),u1_struct_0(A),k4_group_1(A),u1_struct_0(B)) ) ) )).

fof(t59_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k1_group_1(A,B,C)) ) ) ) ) ) )).

fof(t60_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r1_rlvect_1(C,B)
               => r1_rlvect_1(C,k3_group_1(A,B)) ) ) ) ) )).

fof(t61_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( B != k1_xboole_0
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r2_hidden(D,B) )
                       => r2_hidden(k1_group_1(A,C,D),B) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r2_hidden(C,B)
                   => r2_hidden(k3_group_1(A,C),B) ) )
              & ! [C] :
                  ( ( v1_group_1(C)
                    & m1_group_2(C,A) )
                 => u1_struct_0(C) != B ) ) ) ) )).

fof(t62_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( ( ~ v3_struct_0(A)
              & v3_group_1(A)
              & v4_group_1(A)
              & v7_group_1(A)
              & l1_group_1(A) )
           => v7_group_1(B) ) ) ) )).

fof(t63_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m1_group_2(A,A) ) )).

fof(t64_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( ( m1_group_2(A,B)
              & m1_group_2(B,A) )
           => g1_group_1(u1_struct_0(A),u1_group_1(A)) = g1_group_1(u1_struct_0(B),u1_group_1(B)) ) ) ) )).

fof(t65_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ( ( m1_group_2(A,B)
                  & m1_group_2(B,C) )
               => m1_group_2(A,C) ) ) ) ) )).

fof(t66_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m1_group_2(B,C) ) ) ) ) )).

fof(t67_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                     => r1_rlvect_1(C,D) ) )
               => m1_group_2(B,C) ) ) ) ) )).

fof(t68_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( u1_struct_0(B) = u1_struct_0(C)
               => g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(C),u1_group_1(C)) ) ) ) ) )).

fof(t69_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                    <=> r1_rlvect_1(C,D) ) )
               => g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(C),u1_group_1(C)) ) ) ) ) )).

fof(d6_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & m1_group_2(C,A) )
             => ( r1_group_2(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                    <=> r1_rlvect_1(C,D) ) ) ) ) ) ) )).

fof(t70_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( u1_struct_0(B) = u1_struct_0(A)
           => B = A ) ) ) )).

fof(t71_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_rlvect_1(B,C) )
           => g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) )).

fof(d7_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( B = k5_group_2(A)
          <=> u1_struct_0(B) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) )).

fof(d8_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_group_2(A) = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) )).

fof(t72_group_2,axiom,(
    $true )).

fof(t73_group_2,axiom,(
    $true )).

fof(t74_group_2,axiom,(
    $true )).

fof(t75_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k5_group_2(B) = k5_group_2(A) ) ) )).

fof(t76_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => k5_group_2(B) = k5_group_2(C) ) ) ) )).

fof(t77_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => m1_group_2(k5_group_2(A),B) ) ) )).

fof(t78_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => m1_group_2(B,k6_group_2(A)) ) ) )).

fof(t79_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m1_group_2(A,k6_group_2(A)) ) )).

fof(t80_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => v6_group_1(k5_group_2(A)) ) )).

fof(t81_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k9_group_1(k5_group_2(A)) = np__1 ) )).

fof(t82_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( v6_group_1(B)
              & k9_group_1(B) = np__1 )
           => r1_group_2(A,B,k5_group_2(A)) ) ) ) )).

fof(t83_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => r1_tarski(k8_group_1(B),k8_group_1(A)) ) ) )).

fof(t84_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v6_group_1(A)
           => r1_xreal_0(k9_group_1(B),k9_group_1(A)) ) ) ) )).

fof(t85_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( v6_group_1(A)
              & k9_group_1(A) = k9_group_1(B) )
           => B = A ) ) ) )).

fof(d9_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k7_group_2(A,B) = u1_struct_0(B) ) ) )).

fof(t86_group_2,axiom,(
    $true )).

fof(t87_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k7_group_2(A,B) != k1_xboole_0 ) ) )).

fof(t88_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ( r2_hidden(A,k7_group_2(B,C))
          <=> r1_rlvect_1(C,A) ) ) ) )).

fof(t89_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( ( r2_hidden(B,k7_group_2(A,D))
                      & r2_hidden(C,k7_group_2(A,D)) )
                   => r2_hidden(k1_group_1(A,B,C),k7_group_2(A,D)) ) ) ) ) ) )).

fof(t90_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r2_hidden(B,k7_group_2(A,C))
               => r2_hidden(k3_group_1(A,B),k7_group_2(A,C)) ) ) ) ) )).

fof(t91_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k2_group_2(A,k7_group_2(A,B),k7_group_2(A,B)) = k7_group_2(A,B) ) ) )).

fof(t92_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k1_group_2(A,k7_group_2(A,B)) = k7_group_2(A,B) ) ) )).

fof(t93_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ~ ( k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = k2_group_2(A,k7_group_2(A,C),k7_group_2(A,B))
                    & ! [D] :
                        ( ( v1_group_1(D)
                          & m1_group_2(D,A) )
                       => u1_struct_0(D) != k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) ) )
                & ( ? [D] :
                      ( m1_group_2(D,A)
                      & u1_struct_0(D) = k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) )
                 => k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = k2_group_2(A,k7_group_2(A,C),k7_group_2(A,B)) ) ) ) ) ) )).

fof(t94_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ~ ( ~ v3_struct_0(A)
                  & v3_group_1(A)
                  & v4_group_1(A)
                  & v7_group_1(A)
                  & l1_group_1(A)
                  & ! [D] :
                      ( ( v1_group_1(D)
                        & m1_group_2(D,A) )
                     => u1_struct_0(D) != k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ) ) )).

fof(d10_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( ( v1_group_1(D)
                    & m1_group_2(D,A) )
                 => ( D = k8_group_2(A,B,C)
                  <=> u1_struct_0(D) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ) ) )).

fof(t95_group_2,axiom,(
    $true )).

fof(t96_group_2,axiom,(
    $true )).

fof(t97_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ! [D] :
                    ( m1_group_2(D,A)
                   => ( D = k8_group_2(A,B,C)
                     => u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) )
                & ! [D] :
                    ( ( v1_group_1(D)
                      & m1_group_2(D,A) )
                   => ( u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C))
                     => r1_group_2(A,D,k8_group_2(A,B,C)) ) ) ) ) ) ) )).

fof(t98_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => k7_group_2(A,k8_group_2(A,B,C)) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k7_group_2(A,B),k7_group_2(A,C)) ) ) ) )).

fof(t99_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r1_rlvect_1(k8_group_2(B,C,D),A)
              <=> ( r1_rlvect_1(C,A)
                  & r1_rlvect_1(D,A) ) ) ) ) ) )).

fof(t100_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => r1_group_2(A,k8_group_2(A,B,B),B) ) ) )).

fof(t101_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => r1_group_2(A,k8_group_2(A,B,C),k8_group_2(A,C,B)) ) ) ) )).

fof(t102_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => r1_group_2(A,k9_group_2(A,k9_group_2(A,B,C),D),k9_group_2(A,B,k9_group_2(A,C,D))) ) ) ) ) )).

fof(t103_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( r1_group_2(A,k9_group_2(A,k5_group_2(A),B),k5_group_2(A))
            & r1_group_2(A,k9_group_2(A,B,k5_group_2(A)),k5_group_2(A)) ) ) ) )).

fof(t104_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( r1_group_2(A,k9_group_2(A,B,k6_group_2(A)),B)
            & r1_group_2(A,k9_group_2(A,k6_group_2(A),B),B) ) ) ) )).

fof(t105_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k9_group_2(A,k6_group_2(A),k6_group_2(A)) = A ) )).

fof(t106_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( m1_group_2(k9_group_2(A,B,C),B)
                & m1_group_2(k9_group_2(A,B,C),C) ) ) ) ) )).

fof(t107_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( ( v1_group_1(C)
                & m1_group_2(C,A) )
             => ( m1_group_2(C,B)
              <=> r1_group_2(A,k9_group_2(A,C,B),C) ) ) ) ) )).

fof(t108_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( m1_group_2(B,C)
                   => m1_group_2(k9_group_2(A,B,D),C) ) ) ) ) ) )).

fof(t109_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( ( m1_group_2(B,C)
                      & m1_group_2(B,D) )
                   => m1_group_2(B,k9_group_2(A,C,D)) ) ) ) ) ) )).

fof(t110_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( m1_group_2(B,C)
                   => m1_group_2(k9_group_2(A,B,D),k9_group_2(A,C,D)) ) ) ) ) ) )).

fof(t111_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ( v6_group_1(B)
                  | v6_group_1(C) )
               => v6_group_1(k9_group_2(A,B,C)) ) ) ) ) )).

fof(d11_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k10_group_2(A,B,C) = k2_group_2(A,C,k7_group_2(A,B)) ) ) ) )).

fof(d12_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k11_group_2(A,B,C) = k2_group_2(A,k7_group_2(A,B),C) ) ) ) )).

fof(t112_group_2,axiom,(
    $true )).

fof(t113_group_2,axiom,(
    $true )).

fof(t114_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k10_group_2(B,D,C))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k1_group_1(B,E,F)
                        & r2_hidden(E,C)
                        & r1_rlvect_1(D,F) ) ) ) ) ) ) )).

fof(t115_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k11_group_2(B,D,C))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k1_group_1(B,E,F)
                        & r1_rlvect_1(D,E)
                        & r2_hidden(F,C) ) ) ) ) ) ) )).

fof(t116_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k10_group_2(A,D,k2_group_2(A,B,C)) = k2_group_2(A,B,k10_group_2(A,D,C)) ) ) ) ) )).

fof(t117_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k2_group_2(A,k10_group_2(A,D,B),C) = k2_group_2(A,B,k11_group_2(A,D,C)) ) ) ) ) )).

fof(t118_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k2_group_2(A,k11_group_2(A,D,B),C) = k11_group_2(A,D,k2_group_2(A,B,C)) ) ) ) ) )).

fof(t119_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k10_group_2(A,D,k10_group_2(A,C,B)) = k2_group_2(A,B,k11_group_2(A,C,k7_group_2(A,D))) ) ) ) ) )).

fof(t120_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k10_group_2(A,D,k11_group_2(A,C,B)) = k11_group_2(A,C,k10_group_2(A,D,B)) ) ) ) ) )).

fof(t121_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k2_group_2(A,k11_group_2(A,C,k7_group_2(A,D)),B) = k11_group_2(A,C,k11_group_2(A,D,B)) ) ) ) ) )).

fof(t122_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ( ~ v3_struct_0(A)
                  & v3_group_1(A)
                  & v4_group_1(A)
                  & v7_group_1(A)
                  & l1_group_1(A) )
               => k10_group_2(A,C,B) = k11_group_2(A,C,B) ) ) ) ) )).

fof(d13_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_group_2(A,B,C) = k3_group_2(A,C,k7_group_2(A,B)) ) ) ) )).

fof(d14_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k13_group_2(A,B,C) = k4_group_2(A,C,k7_group_2(A,B)) ) ) ) )).

fof(t123_group_2,axiom,(
    $true )).

fof(t124_group_2,axiom,(
    $true )).

fof(t125_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k12_group_2(B,D,C))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,C,E)
                    & r1_rlvect_1(D,E) ) ) ) ) ) )).

fof(t126_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k13_group_2(B,D,C))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,E,C)
                    & r1_rlvect_1(D,E) ) ) ) ) ) )).

fof(t127_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k12_group_2(A,D,k1_group_1(A,B,C)) = k3_group_2(A,B,k12_group_2(A,D,C)) ) ) ) ) )).

fof(t128_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k4_group_2(A,C,k12_group_2(A,D,B)) = k3_group_2(A,B,k13_group_2(A,D,C)) ) ) ) ) )).

fof(t129_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k4_group_2(A,C,k13_group_2(A,D,B)) = k13_group_2(A,D,k1_group_1(A,B,C)) ) ) ) ) )).

fof(t130_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r2_hidden(B,k12_group_2(A,C,B))
                & r2_hidden(B,k13_group_2(A,C,B)) ) ) ) ) )).

fof(t131_group_2,axiom,(
    $true )).

fof(t132_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( k12_group_2(A,B,k2_group_1(A)) = k7_group_2(A,B)
            & k13_group_2(A,B,k2_group_1(A)) = k7_group_2(A,B) ) ) ) )).

fof(t133_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k13_group_2(A,k5_group_2(A),B) = k6_domain_1(u1_struct_0(A),B)
            & k12_group_2(A,k5_group_2(A),B) = k6_domain_1(u1_struct_0(A),B) ) ) ) )).

fof(t134_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k12_group_2(A,k6_group_2(A),B) = u1_struct_0(A)
            & k13_group_2(A,k6_group_2(A),B) = u1_struct_0(A) ) ) ) )).

fof(t135_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( ( ~ v3_struct_0(A)
                  & v3_group_1(A)
                  & v4_group_1(A)
                  & v7_group_1(A)
                  & l1_group_1(A) )
               => k12_group_2(A,C,B) = k13_group_2(A,C,B) ) ) ) ) )).

fof(t136_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k12_group_2(A,C,B) = k7_group_2(A,C) ) ) ) ) )).

fof(t137_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( k12_group_2(A,D,B) = k12_group_2(A,D,C)
                  <=> r1_rlvect_1(D,k1_group_1(A,k3_group_1(A,C),B)) ) ) ) ) ) )).

fof(t138_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( k12_group_2(A,D,B) = k12_group_2(A,D,C)
                  <=> ~ r1_xboole_0(k12_group_2(A,D,B),k12_group_2(A,D,C)) ) ) ) ) ) )).

fof(t139_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => r1_tarski(k12_group_2(A,D,k1_group_1(A,B,C)),k2_group_2(A,k12_group_2(A,D,B),k12_group_2(A,D,C))) ) ) ) ) )).

fof(t140_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r1_tarski(k7_group_2(A,C),k2_group_2(A,k12_group_2(A,C,B),k12_group_2(A,C,k3_group_1(A,B))))
                & r1_tarski(k7_group_2(A,C),k2_group_2(A,k12_group_2(A,C,k3_group_1(A,B)),k12_group_2(A,C,B))) ) ) ) ) )).

fof(t141_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => r1_tarski(k12_group_2(A,C,k6_group_1(A,np__2,B)),k2_group_2(A,k12_group_2(A,C,B),k12_group_2(A,C,B))) ) ) ) )).

fof(t142_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k13_group_2(A,C,B) = k7_group_2(A,C) ) ) ) ) )).

fof(t143_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( k13_group_2(A,D,B) = k13_group_2(A,D,C)
                  <=> r1_rlvect_1(D,k1_group_1(A,C,k3_group_1(A,B))) ) ) ) ) ) )).

fof(t144_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( k13_group_2(A,D,B) = k13_group_2(A,D,C)
                  <=> ~ r1_xboole_0(k13_group_2(A,D,B),k13_group_2(A,D,C)) ) ) ) ) ) )).

fof(t145_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => r1_tarski(k4_group_2(A,C,k13_group_2(A,D,B)),k2_group_2(A,k13_group_2(A,D,B),k13_group_2(A,D,C))) ) ) ) ) )).

fof(t146_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r1_tarski(k7_group_2(A,C),k2_group_2(A,k13_group_2(A,C,B),k13_group_2(A,C,k3_group_1(A,B))))
                & r1_tarski(k7_group_2(A,C),k2_group_2(A,k13_group_2(A,C,k3_group_1(A,B)),k13_group_2(A,C,B))) ) ) ) ) )).

fof(t147_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => r1_tarski(k13_group_2(A,C,k6_group_1(A,np__2,B)),k2_group_2(A,k13_group_2(A,C,B),k13_group_2(A,C,B))) ) ) ) )).

fof(t148_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k12_group_2(A,k9_group_2(A,C,D),B) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k12_group_2(A,C,B),k12_group_2(A,D,B)) ) ) ) ) )).

fof(t149_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => k13_group_2(A,k9_group_2(A,C,D),B) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k13_group_2(A,C,B),k13_group_2(A,D,B)) ) ) ) ) )).

fof(t150_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ? [D] :
                  ( v1_group_1(D)
                  & m1_group_2(D,A)
                  & u1_struct_0(D) = k4_group_2(A,k3_group_1(A,B),k12_group_2(A,C,B)) ) ) ) ) )).

fof(t151_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => r2_wellord2(k12_group_2(A,D,B),k12_group_2(A,D,C)) ) ) ) ) )).

fof(t152_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => r2_wellord2(k12_group_2(A,D,B),k13_group_2(A,D,C)) ) ) ) ) )).

fof(t153_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => r2_wellord2(k13_group_2(A,D,B),k13_group_2(A,D,C)) ) ) ) ) )).

fof(t154_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( r2_wellord2(k7_group_2(A,C),k12_group_2(A,C,B))
                & r2_wellord2(k7_group_2(A,C),k13_group_2(A,C,B)) ) ) ) ) )).

fof(t155_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ( k8_group_1(C) = k1_card_1(k12_group_2(A,C,B))
                & k8_group_1(C) = k1_card_1(k13_group_2(A,C,B)) ) ) ) ) )).

fof(t156_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ~ ( v6_group_1(C)
                  & ! [D] :
                      ( v1_finset_1(D)
                     => ! [E] :
                          ( v1_finset_1(E)
                         => ~ ( D = k12_group_2(A,C,B)
                              & E = k13_group_2(A,C,B)
                              & k9_group_1(C) = k4_card_1(D)
                              & k9_group_1(C) = k4_card_1(E) ) ) ) ) ) ) ) )).

fof(d15_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( C = k14_group_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & D = k12_group_2(A,B,E) ) ) ) ) ) ) ) )).

fof(d16_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( C = k15_group_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & D = k13_group_2(A,B,E) ) ) ) ) ) ) ) )).

fof(t157_group_2,axiom,(
    $true )).

fof(t158_group_2,axiom,(
    $true )).

fof(t159_group_2,axiom,(
    $true )).

fof(t160_group_2,axiom,(
    $true )).

fof(t161_group_2,axiom,(
    $true )).

fof(t162_group_2,axiom,(
    $true )).

fof(t163_group_2,axiom,(
    $true )).

fof(t164_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v6_group_1(A)
           => ( v1_finset_1(k15_group_2(A,B))
              & v1_finset_1(k14_group_2(A,B)) ) ) ) ) )).

fof(t165_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( r2_hidden(k7_group_2(A,B),k14_group_2(A,B))
            & r2_hidden(k7_group_2(A,B),k15_group_2(A,B)) ) ) ) )).

fof(t166_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => r2_wellord2(k14_group_2(A,B),k15_group_2(A,B)) ) ) )).

fof(t167_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( k5_setfam_1(u1_struct_0(A),k14_group_2(A,B)) = u1_struct_0(A)
            & k5_setfam_1(u1_struct_0(A),k15_group_2(A,B)) = u1_struct_0(A) ) ) ) )).

fof(t172_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( k14_group_2(A,k6_group_2(A)) = k1_tarski(u1_struct_0(A))
        & k15_group_2(A,k6_group_2(A)) = k1_tarski(u1_struct_0(A)) ) ) )).

fof(t173_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( k14_group_2(A,B) = k1_tarski(u1_struct_0(A))
           => B = A ) ) ) )).

fof(t174_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( k15_group_2(A,B) = k1_tarski(u1_struct_0(A))
           => B = A ) ) ) )).

fof(d17_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => k16_group_2(A,B) = k1_card_1(k14_group_2(A,B)) ) ) )).

fof(t175_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( k16_group_2(A,B) = k1_card_1(k14_group_2(A,B))
            & k16_group_2(A,B) = k1_card_1(k15_group_2(A,B)) ) ) ) )).

fof(d18_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v1_finset_1(k14_group_2(A,B))
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( C = k17_group_2(A,B)
                <=> ? [D] :
                      ( v1_finset_1(D)
                      & D = k14_group_2(A,B)
                      & C = k4_card_1(D) ) ) ) ) ) ) )).

fof(t176_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v1_finset_1(k14_group_2(A,B))
           => ( ? [C] :
                  ( v1_finset_1(C)
                  & C = k14_group_2(A,B)
                  & k17_group_2(A,B) = k4_card_1(C) )
              & ? [C] :
                  ( v1_finset_1(C)
                  & C = k15_group_2(A,B)
                  & k17_group_2(A,B) = k4_card_1(C) ) ) ) ) ) )).

fof(t177_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v6_group_1(A)
           => k9_group_1(A) = k2_nat_1(k9_group_1(B),k17_group_2(A,B)) ) ) ) )).

fof(t178_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( v6_group_1(A)
           => r1_nat_1(k9_group_1(B),k9_group_1(A)) ) ) ) )).

fof(t179_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,C)
                 => ( ( v6_group_1(A)
                      & B = D )
                   => k17_group_2(A,B) = k2_nat_1(k17_group_2(C,D),k17_group_2(A,C)) ) ) ) ) ) )).

fof(t180_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k17_group_2(A,k6_group_2(A)) = np__1 ) )).

fof(t181_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( v1_finset_1(k14_group_2(A,B))
              & k17_group_2(A,B) = np__1 )
           => B = A ) ) ) )).

fof(t182_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k16_group_2(A,k5_group_2(A)) = k8_group_1(A) ) )).

fof(t183_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v6_group_1(A)
       => k17_group_2(A,k5_group_2(A)) = k9_group_1(A) ) ) )).

fof(t184_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( v6_group_1(A)
              & k17_group_2(A,B) = k9_group_1(A) )
           => r1_group_2(A,B,k5_group_2(A)) ) ) ) )).

fof(t185_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( v1_finset_1(k14_group_2(A,B))
              & k16_group_2(A,B) = k8_group_1(A) )
           => ( v6_group_1(A)
              & r1_group_2(A,B,k5_group_2(A)) ) ) ) ) )).

fof(t186_group_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_finset_1(B)
         => ~ ( ! [C] :
                  ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( v1_finset_1(D)
                       => ~ ( D = C
                            & k4_card_1(D) = A
                            & ! [E] :
                                ( r2_hidden(E,B)
                               => ( C = E
                                  | ( r2_wellord2(C,E)
                                    & r1_xboole_0(C,E) ) ) ) ) ) )
              & ! [C] :
                  ( v1_finset_1(C)
                 => ~ ( C = k3_tarski(B)
                      & k4_card_1(C) = k2_nat_1(A,k4_card_1(B)) ) ) ) ) ) )).

fof(dt_m1_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) ) ) ) )).

fof(existence_m1_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ? [B] : m1_group_2(B,A) ) )).

fof(symmetry_r1_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
       => r1_group_2(A,C,B) ) ) )).

fof(reflexivity_r1_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => r1_group_2(A,B,B) ) )).

fof(redefinition_r1_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
      <=> B = C ) ) )).

fof(dt_k1_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k2_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k3_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k5_group_2(A))
        & m1_group_2(k5_group_2(A),A) ) ) )).

fof(dt_k6_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k6_group_2(A))
        & m1_group_2(k6_group_2(A),A) ) ) )).

fof(dt_k7_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => m1_subset_1(k7_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k8_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k8_group_2(A,B,C))
        & m1_group_2(k8_group_2(A,B,C),A) ) ) )).

fof(dt_k9_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k9_group_2(A,B,C))
        & m1_group_2(k9_group_2(A,B,C),A) ) ) )).

fof(commutativity_k9_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => k9_group_2(A,B,C) = k9_group_2(A,C,B) ) )).

fof(redefinition_k9_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => k9_group_2(A,B,C) = k8_group_2(A,B,C) ) )).

fof(dt_k10_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k10_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k11_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k11_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k12_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k12_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k13_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k13_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k14_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => m1_subset_1(k14_group_2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k15_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => m1_subset_1(k15_group_2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k16_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => v1_card_1(k16_group_2(A,B)) ) )).

fof(dt_k17_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => m2_subset_1(k17_group_2(A,B),k1_numbers,k5_numbers) ) )).

fof(dt_k18_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k18_group_2(A,B),k5_finsub_1(A)) ) )).

fof(redefinition_k18_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k18_group_2(A,B) = k1_tarski(B) ) )).

fof(d1_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_group_2(A,B) = a_2_0_group_2(A,B) ) ) )).

fof(d2_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k2_group_2(A,B,C) = a_3_0_group_2(A,B,C) ) ) ) )).

fof(t168_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k14_group_2(A,k5_group_2(A)) = a_1_0_group_2(A) ) )).

fof(t169_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k15_group_2(A,k5_group_2(A)) = a_1_0_group_2(A) ) )).

fof(t170_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( k14_group_2(A,B) = a_1_0_group_2(A)
           => r1_group_2(A,B,k5_group_2(A)) ) ) ) )).

fof(t171_group_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( k15_group_2(A,B) = a_1_0_group_2(A)
           => r1_group_2(A,B,k5_group_2(A)) ) ) ) )).

fof(fraenkel_a_2_0_group_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_group_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k3_group_1(B,D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_3_0_group_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_group_2(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k1_group_1(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).

fof(fraenkel_a_1_0_group_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_hidden(A,a_1_0_group_2(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = k6_domain_1(u1_struct_0(B),C) ) ) ) )).
%------------------------------------------------------------------------------