SET007 Axioms: SET007+312.ax


%------------------------------------------------------------------------------
% File     : SET007+312 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Homomorphisms and Isomorphisms of Groups. Quotient Group
% 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_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  142 (  10 unit)
%            Number of atoms       : 1561 (  84 equality)
%            Maximal formula depth :   26 (  10 average)
%            Number of connectives : 1636 ( 217 ~  ;   0  |;1027  &)
%                                         (  25 <=>; 367 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-3 arity)
%            Number of functors    :   63 (   3 constant; 0-6 arity)
%            Number of variables   :  398 (   0 singleton; 385 !;  13 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k5_group_2(A))
        & v1_group_1(k5_group_2(A))
        & v2_group_1(k5_group_2(A))
        & v3_group_1(k5_group_2(A))
        & v4_group_1(k5_group_2(A))
        & v1_group_3(k5_group_2(A),A) ) ) )).

fof(fc2_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k6_group_2(A))
        & v1_group_1(k6_group_2(A))
        & v2_group_1(k6_group_2(A))
        & v3_group_1(k6_group_2(A))
        & v4_group_1(k6_group_2(A))
        & v1_group_3(k6_group_2(A),A) ) ) )).

fof(rc1_group_6,axiom,(
    ? [A] :
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v3_group_1(A)
      & v4_group_1(A)
      & v3_realset2(A) ) )).

fof(fc3_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A) )
     => ~ v1_xboole_0(k4_group_6(A,B)) ) )).

fof(fc4_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A) )
     => ( ~ v3_struct_0(k6_group_6(A,B))
        & v1_group_1(k6_group_6(A,B)) ) ) )).

fof(fc5_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A) )
     => ( ~ v3_struct_0(k6_group_6(A,B))
        & v1_group_1(k6_group_6(A,B))
        & v2_group_1(k6_group_6(A,B))
        & v3_group_1(k6_group_6(A,B))
        & v4_group_1(k6_group_6(A,B)) ) ) )).

fof(rc2_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ? [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
          & v1_group_6(C,A,B) ) ) )).

fof(fc6_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( ~ v3_struct_0(k12_group_6(A,B,C))
        & v1_group_1(k12_group_6(A,B,C))
        & v2_group_1(k12_group_6(A,B,C))
        & v3_group_1(k12_group_6(A,B,C))
        & v4_group_1(k12_group_6(A,B,C))
        & v1_group_3(k12_group_6(A,B,C),A) ) ) )).

fof(t1_group_6,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_funct_1(C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ( k8_funct_2(A,B,C,D) = k8_funct_2(A,B,C,E)
                         => D = E ) ) ) ) ) ) ) )).

fof(t2_group_6,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))
             => ! [D] :
                  ( m1_group_6(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( E = C
                       => ( k12_group_2(B,D,E) = k12_group_2(A,D,C)
                          & k13_group_2(B,D,E) = k13_group_2(A,D,C) ) ) ) ) ) ) ) )).

fof(t3_group_6,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_6(C,A,B)
             => ! [D] :
                  ( m1_group_6(D,A,B)
                 => k9_group_2(A,C,D) = k9_group_2(B,C,D) ) ) ) ) )).

fof(t4_group_6,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_1(A,k1_group_1(A,B,C),k3_group_1(A,B)) = k2_group_3(A,C,k3_group_1(A,B))
                & k1_group_1(A,B,k1_group_1(A,C,k3_group_1(A,B))) = k2_group_3(A,C,k3_group_1(A,B)) ) ) ) ) )).

fof(t5_group_6,axiom,(
    $true )).

fof(t6_group_6,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))
             => ( k10_group_2(A,B,k12_group_2(A,B,C)) = k12_group_2(A,B,C)
                & k3_group_2(A,C,k7_group_4(A,B,B)) = k12_group_2(A,B,C)
                & k4_group_2(A,C,k7_group_4(A,B,B)) = k13_group_2(A,B,C)
                & k11_group_2(A,B,k13_group_2(A,B,C)) = k13_group_2(A,B,C) ) ) ) ) )).

fof(t8_group_6,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) )
         => ( m1_group_6(k9_group_5(A),A,B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_rlvect_1(B,k2_group_5(A,C,D)) ) ) ) ) ) )).

fof(t9_group_6,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_3(C,A)
                & m1_group_2(C,A) )
             => ( m1_group_6(C,A,B)
               => ( v1_group_3(C,B)
                  & m1_group_6(C,A,B) ) ) ) ) ) )).

fof(d1_group_6,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_3(C,A)
                & m1_group_2(C,A) )
             => ( m1_group_6(g1_group_1(u1_struct_0(C),u1_group_1(C)),A,B)
               => k1_group_6(A,B,C) = g1_group_1(u1_struct_0(C),u1_group_1(C)) ) ) ) ) )).

fof(t10_group_6,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_3(C,A)
                & m1_group_2(C,A) )
             => ( v1_group_3(k9_group_2(A,B,C),B)
                & m1_group_6(k9_group_2(A,B,C),A,B)
                & v1_group_3(k9_group_2(A,C,B),B)
                & m1_group_6(k9_group_2(A,C,B),A,B) ) ) ) ) )).

fof(d2_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ( v3_realset2(A)
      <=> ? [B] : u1_struct_0(A) = k1_tarski(B) ) ) )).

fof(t11_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => v3_realset2(k5_group_2(A)) ) )).

fof(t12_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v3_realset2(A)
      <=> ( k9_group_1(A) = np__1
          & v6_group_1(A) ) ) ) )).

fof(t13_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v3_realset2(A)
       => k5_group_2(A) = A ) ) )).

fof(d3_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => k4_group_6(A,B) = k14_group_2(A,B) ) ) )).

fof(t14_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ( k4_group_6(A,B) = k14_group_2(A,B)
            & k4_group_6(A,B) = k15_group_2(A,B) ) ) ) )).

fof(t15_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B,C] :
          ( ( v1_group_3(C,A)
            & m1_group_2(C,A) )
         => ~ ( r2_hidden(B,k4_group_6(A,C))
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( B = k12_group_2(A,C,D)
                      & B = k13_group_2(A,C,D) ) ) ) ) ) )).

fof(t16_group_6,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] :
              ( ( v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( r2_hidden(k12_group_2(A,C,B),k4_group_6(A,C))
                & r2_hidden(k13_group_2(A,C,B),k4_group_6(A,C)) ) ) ) ) )).

fof(t17_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B,C] :
          ( ( v1_group_3(C,A)
            & m1_group_2(C,A) )
         => ( r2_hidden(B,k4_group_6(A,C))
           => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t18_group_6,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] :
                  ( ( v1_group_3(D,A)
                    & m1_group_2(D,A) )
                 => ( ( r2_hidden(B,k4_group_6(A,D))
                      & r2_hidden(C,k4_group_6(A,D)) )
                   => r2_hidden(k2_group_2(A,B,C),k4_group_6(A,D)) ) ) ) ) ) )).

fof(d4_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B))
                & m2_relset_1(C,k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) )
             => ( C = k5_group_6(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_group_6(A,B))
                   => ! [E] :
                        ( m1_subset_1(E,k4_group_6(A,B))
                       => ! [F] :
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                           => ! [G] :
                                ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                               => ( ( D = F
                                    & E = G )
                                 => k2_binop_1(k4_group_6(A,B),k4_group_6(A,B),k4_group_6(A,B),C,D,E) = k2_group_2(A,F,G) ) ) ) ) ) ) ) ) ) )).

fof(d5_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => k6_group_6(A,B) = g1_group_1(k4_group_6(A,B),k5_group_6(A,B)) ) ) )).

fof(t19_group_6,axiom,(
    $true )).

fof(t20_group_6,axiom,(
    $true )).

fof(t21_group_6,axiom,(
    $true )).

fof(t22_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => u1_struct_0(k6_group_6(A,B)) = k4_group_6(A,B) ) ) )).

fof(t23_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => u1_group_1(k6_group_6(A,B)) = k5_group_6(A,B) ) ) )).

fof(d6_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
             => k7_group_6(A,B,C) = C ) ) ) )).

fof(t24_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_group_6(A,B)))
                 => k2_group_2(A,k7_group_6(A,B,C),k7_group_6(A,B,D)) = k1_group_1(k6_group_6(A,B),C,D) ) ) ) ) )).

fof(t25_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_group_6(A,B)))
                 => k7_group_6(A,B,k1_group_1(k6_group_6(A,B),C,D)) = k2_group_2(A,k7_group_6(A,B,C),k7_group_6(A,B,D)) ) ) ) ) )).

fof(t26_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & C = k12_group_2(A,B,D)
                  & C = k13_group_2(A,B,D) ) ) ) ) )).

fof(t27_group_6,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] :
              ( ( v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( m1_subset_1(k13_group_2(A,C,B),u1_struct_0(k6_group_6(A,C)))
                & m1_subset_1(k12_group_2(A,C,B),u1_struct_0(k6_group_6(A,C)))
                & m1_subset_1(k7_group_2(A,C),u1_struct_0(k6_group_6(A,C))) ) ) ) ) )).

fof(t28_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B,C] :
          ( ( v1_group_3(C,A)
            & m1_group_2(C,A) )
         => ( r1_rlvect_1(k6_group_6(A,C),B)
          <=> ? [D] :
                ( m1_subset_1(D,u1_struct_0(A))
                & B = k12_group_2(A,C,D)
                & B = k13_group_2(A,C,D) ) ) ) ) )).

fof(t29_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => k2_group_1(k6_group_6(A,B)) = k7_group_2(A,B) ) ) )).

fof(t30_group_6,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] :
              ( ( v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_group_6(A,C)))
                 => ( D = k12_group_2(A,C,B)
                   => k3_group_1(k6_group_6(A,C),D) = k12_group_2(A,C,k3_group_1(A,B)) ) ) ) ) ) )).

fof(t31_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ( v1_finset_1(k14_group_2(A,B))
           => v6_group_1(k6_group_6(A,B)) ) ) ) )).

fof(t32_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => k8_group_1(k6_group_6(A,B)) = k16_group_2(A,B) ) ) )).

fof(t33_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ( v1_finset_1(k14_group_2(A,B))
           => k9_group_1(k6_group_6(A,B)) = k17_group_2(A,B) ) ) ) )).

fof(t34_group_6,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)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( m1_group_6(C,A,B)
               => m1_group_2(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C)) ) ) ) ) )).

fof(t35_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( m1_group_6(C,A,B)
               => ( v1_group_3(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C))
                  & m1_group_2(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C)) ) ) ) ) ) )).

fof(t36_group_6,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)
            & v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ( ( ~ v3_struct_0(k6_group_6(A,B))
              & v3_group_1(k6_group_6(A,B))
              & v4_group_1(k6_group_6(A,B))
              & v7_group_1(k6_group_6(A,B))
              & l1_group_1(k6_group_6(A,B)) )
          <=> m1_group_6(k9_group_5(A),A,B) ) ) ) )).

fof(d7_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_group_6(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_group_1(A,D,E)) = k1_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) )).

fof(t37_group_6,axiom,(
    $true )).

fof(t38_group_6,axiom,(
    $true )).

fof(t39_group_6,axiom,(
    $true )).

fof(t40_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_group_1(A)) = k2_group_1(B) ) ) ) )).

fof(t41_group_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,k3_group_1(A,C)) = k3_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) )).

fof(t42_group_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & v1_group_6(E,A,B)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,k2_group_3(A,C,D)) = k2_group_3(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) )).

fof(t43_group_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & v1_group_6(E,A,B)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,k2_group_5(A,C,D)) = k2_group_5(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) )).

fof(t44_group_6,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] :
              ( 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))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
                            & v1_group_6(F,A,B)
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
                         => k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,k3_group_5(A,C,D,E)) = k3_group_5(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,E)) ) ) ) ) ) ) )).

fof(t45_group_6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_group_6(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,k6_group_1(B,A,D)) = k6_group_1(C,A,k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,D)) ) ) ) ) ) )).

fof(t46_group_6,axiom,(
    ! [A] :
      ( v1_int_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) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_group_6(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,k6_group_1(B,A,D)) = k6_group_1(C,A,k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,D)) ) ) ) ) ) )).

fof(t47_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_funct_1(k6_partfun1(u1_struct_0(A)))
        & v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A))
        & v1_group_6(k6_partfun1(u1_struct_0(A)),A,A)
        & m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(t48_group_6,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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & v1_group_6(D,B,A)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & v1_group_6(E,A,C)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ( v1_funct_1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E))
                        & v1_funct_2(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),u1_struct_0(B),u1_struct_0(C))
                        & v1_group_6(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),B,C)
                        & m2_relset_1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) )).

fof(d8_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( C = k10_group_6(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k2_group_1(B) ) ) ) ) ) )).

fof(t49_group_6,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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_group_6(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( k8_group_6(A,B,C,k10_group_6(A,B),E) = k10_group_6(A,C)
                        & k8_group_6(A,B,C,D,k10_group_6(B,C)) = k10_group_6(A,C) ) ) ) ) ) ) )).

fof(d9_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k6_group_6(A,B)))
                & v1_group_6(C,A,k6_group_6(A,B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) )
             => ( C = k11_group_6(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k6_group_6(A,B)),C,D) = k12_group_2(A,B,D) ) ) ) ) ) )).

fof(t50_group_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r1_rlvect_1(k12_group_6(A,B,D),C)
                  <=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C) = k2_group_1(B) ) ) ) ) ) )).

fof(t51_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => k12_group_6(A,B,k10_group_6(A,B)) = A ) ) )).

fof(t52_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & v1_group_3(B,A)
            & m1_group_2(B,A) )
         => r1_group_2(A,k12_group_6(A,k6_group_6(A,B),k11_group_6(A,B)),B) ) ) )).

fof(d11_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_group_1(D)
                    & m1_group_2(D,B) )
                 => ( D = k13_group_6(A,B,C)
                  <=> u1_struct_0(D) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(A)) ) ) ) ) ) )).

fof(t53_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => k9_group_6(A,B,C) = u1_struct_0(k13_group_6(A,B,C)) ) ) ) )).

fof(t54_group_6,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,D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(D,B,A)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
             => ( r1_rlvect_1(k13_group_6(B,A,D),C)
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & C = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) ) ) ) ) ) )).

fof(t55_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => r1_group_2(B,k13_group_6(A,B,C),k5_group_4(B,k9_group_6(A,B,C))) ) ) ) )).

fof(t56_group_6,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) )
         => r1_group_2(B,k13_group_6(A,B,k10_group_6(A,B)),k5_group_2(B)) ) ) )).

fof(t57_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => k13_group_6(A,k6_group_6(A,B),k11_group_6(A,B)) = k6_group_6(A,B) ) ) )).

fof(t58_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(k13_group_6(B,A,C)))
                & v1_group_6(C,B,k13_group_6(B,A,C))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(k13_group_6(B,A,C))) ) ) ) ) )).

fof(t59_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v6_group_1(B)
               => v6_group_1(k13_group_6(B,A,C)) ) ) ) ) )).

fof(t60_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( ( ~ v3_struct_0(B)
                  & v3_group_1(B)
                  & v4_group_1(B)
                  & v7_group_1(B)
                  & l1_group_1(B) )
               => v7_group_1(k13_group_6(B,A,C)) ) ) ) ) )).

fof(t61_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => r1_tarski(k8_group_1(k13_group_6(B,A,C)),k8_group_1(B)) ) ) ) )).

fof(t62_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v6_group_1(B)
               => r1_xreal_0(k9_group_1(k13_group_6(B,A,C)),k9_group_1(B)) ) ) ) ) )).

fof(d12_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v2_group_6(C,A,B)
              <=> v2_funct_1(C) ) ) ) ) )).

fof(d13_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_group_6(C,A,B)
              <=> k9_group_6(A,B,C) = u1_struct_0(B) ) ) ) ) )).

fof(t63_group_6,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] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( ( v2_group_6(D,A,B)
                      & r1_rlvect_1(k13_group_6(A,B,D),C) )
                   => k1_funct_1(D,k1_funct_1(k2_funct_1(D),C)) = C ) ) ) ) ) )).

fof(t64_group_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( v2_group_6(D,A,B)
                   => k1_funct_1(k2_funct_1(D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C)) = C ) ) ) ) ) )).

fof(t65_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v2_group_6(C,B,A)
               => ( v1_funct_1(k2_funct_1(C))
                  & v1_funct_2(k2_funct_1(C),u1_struct_0(k13_group_6(B,A,C)),u1_struct_0(B))
                  & v1_group_6(k2_funct_1(C),k13_group_6(B,A,C),B)
                  & m2_relset_1(k2_funct_1(C),u1_struct_0(k13_group_6(B,A,C)),u1_struct_0(B)) ) ) ) ) ) )).

fof(t66_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v2_group_6(C,B,A)
              <=> r1_group_2(B,k12_group_6(B,A,C),k5_group_2(B)) ) ) ) ) )).

fof(t67_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_group_6(C,A,B)
              <=> k13_group_6(A,B,C) = B ) ) ) ) )).

fof(t68_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_group_6(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) = D ) ) ) ) ) ) )).

fof(t69_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => v3_group_6(k11_group_6(A,B),A,k6_group_6(A,B)) ) ) )).

fof(d14_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
              <=> ( v3_group_6(C,A,B)
                  & v2_group_6(C,A,B) ) ) ) ) ) )).

fof(t70_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
              <=> ( k9_group_6(A,B,C) = u1_struct_0(B)
                  & v2_funct_1(C) ) ) ) ) ) )).

fof(t71_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
               => ( k1_relat_1(C) = u1_struct_0(A)
                  & k9_group_6(A,B,C) = u1_struct_0(B) ) ) ) ) ) )).

fof(t72_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
               => ( v1_funct_1(k2_funct_1(C))
                  & v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
                  & v1_group_6(k2_funct_1(C),B,A)
                  & m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) )).

fof(t73_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( ( v4_group_6(C,B,A)
                      & D = k2_funct_1(C) )
                   => v4_group_6(D,A,B) ) ) ) ) ) )).

fof(t74_group_6,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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_group_6(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v4_group_6(D,A,B)
                          & v4_group_6(E,B,C) )
                       => v4_group_6(k8_group_6(A,B,C,D,E),A,C) ) ) ) ) ) ) )).

fof(t75_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => v4_group_6(k11_group_6(A,k5_group_2(A)),A,k6_group_6(A,k5_group_2(A))) ) )).

fof(d15_group_6,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) )
         => ( r1_group_6(A,B)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                & v4_group_6(C,A,B) ) ) ) ) )).

fof(t76_group_6,axiom,(
    $true )).

fof(t77_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( r1_group_6(A,B)
           => r1_group_6(B,A) ) ) ) )).

fof(t78_group_6,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) )
             => ( ( r1_group_6(A,B)
                  & r1_group_6(B,C) )
               => r1_group_6(A,C) ) ) ) ) )).

fof(t79_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( v2_group_6(C,B,A)
               => r1_group_6(B,k13_group_6(B,A,C)) ) ) ) ) )).

fof(t80_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( ( v3_realset2(A)
              & v3_realset2(B) )
           => r2_group_6(A,B) ) ) ) )).

fof(t81_group_6,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) )
         => r2_group_6(k5_group_2(A),k5_group_2(B)) ) ) )).

fof(t82_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r2_group_6(A,k6_group_6(A,k5_group_2(A))) ) )).

fof(t83_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => v3_realset2(k6_group_6(A,k6_group_2(A))) ) )).

fof(t84_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( r2_group_6(A,B)
           => k8_group_1(A) = k8_group_1(B) ) ) ) )).

fof(t85_group_6,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) )
         => ( ( r1_group_6(A,B)
              & v6_group_1(A) )
           => v6_group_1(B) ) ) ) )).

fof(t86_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( ( r2_group_6(A,B)
              & v6_group_1(A) )
           => k9_group_1(A) = k9_group_1(B) ) ) ) )).

fof(t87_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( ( r2_group_6(A,B)
              & v3_realset2(A) )
           => v3_realset2(B) ) ) ) )).

fof(t88_group_6,axiom,(
    $true )).

fof(t89_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( ( r1_group_6(A,B)
              & ~ v3_struct_0(A)
              & v3_group_1(A)
              & v4_group_1(A)
              & v7_group_1(A)
              & l1_group_1(A) )
           => ( ~ v3_struct_0(B)
              & v3_group_1(B)
              & v4_group_1(B)
              & v7_group_1(B)
              & l1_group_1(B) ) ) ) ) )).

fof(t90_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => r2_group_6(k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C)) ) ) ) )).

fof(t91_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ? [D] :
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(k6_group_6(B,k12_group_6(B,A,C))),u1_struct_0(k13_group_6(B,A,C)))
                  & v1_group_6(D,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C))
                  & m2_relset_1(D,u1_struct_0(k6_group_6(B,k12_group_6(B,A,C))),u1_struct_0(k13_group_6(B,A,C)))
                  & v4_group_6(D,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C))
                  & C = k8_group_6(B,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C),k11_group_6(B,k12_group_6(B,A,C)),D) ) ) ) ) )).

fof(t92_group_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ! [D] :
                  ( ( v1_group_1(D)
                    & v1_group_3(D,k6_group_6(A,C))
                    & m1_group_2(D,k6_group_6(A,C)) )
                 => ( ( D = k6_group_6(B,k1_group_6(A,B,C))
                      & m1_group_6(C,A,B) )
                   => r2_group_6(k6_group_6(k6_group_6(A,C),D),k6_group_6(A,B)) ) ) ) ) ) )).

fof(t93_group_6,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)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => r2_group_6(k6_group_6(k8_group_4(A,B,C),k1_group_6(A,k8_group_4(A,B,C),C)),k6_group_6(B,k2_group_6(A,B,C))) ) ) ) )).

fof(dt_m1_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ! [C] :
          ( m1_group_6(C,A,B)
         => m1_group_2(C,A) ) ) )).

fof(existence_m1_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ? [C] : m1_group_6(C,A,B) ) )).

fof(redefinition_m1_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ! [C] :
          ( m1_group_6(C,A,B)
        <=> m1_group_2(C,B) ) ) )).

fof(reflexivity_r1_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => r1_group_6(A,A) ) )).

fof(symmetry_r2_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v1_group_1(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_group_6(A,B)
       => r2_group_6(B,A) ) ) )).

fof(reflexivity_r2_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v1_group_1(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => r2_group_6(A,A) ) )).

fof(redefinition_r2_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v1_group_1(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_group_6(A,B)
      <=> r1_group_6(A,B) ) ) )).

fof(dt_k1_group_6,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)
        & v1_group_3(C,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k1_group_6(A,B,C))
        & v1_group_3(k1_group_6(A,B,C),B)
        & m1_group_6(k1_group_6(A,B,C),A,B) ) ) )).

fof(dt_k2_group_6,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)
        & v1_group_3(C,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k2_group_6(A,B,C))
        & v1_group_3(k2_group_6(A,B,C),B)
        & m1_group_6(k2_group_6(A,B,C),A,B) ) ) )).

fof(redefinition_k2_group_6,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)
        & v1_group_3(C,A)
        & m1_group_2(C,A) )
     => k2_group_6(A,B,C) = k8_group_2(A,B,C) ) )).

fof(dt_k3_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k3_group_6(A,B,C))
        & v1_group_3(k3_group_6(A,B,C),C)
        & m1_group_6(k3_group_6(A,B,C),A,C) ) ) )).

fof(redefinition_k3_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => k3_group_6(A,B,C) = k8_group_2(A,B,C) ) )).

fof(dt_k4_group_6,axiom,(
    $true )).

fof(dt_k5_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A) )
     => ( v1_funct_1(k5_group_6(A,B))
        & v1_funct_2(k5_group_6(A,B),k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B))
        & m2_relset_1(k5_group_6(A,B),k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) ) ) )).

fof(dt_k6_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A) )
     => l1_group_1(k6_group_6(A,B)) ) )).

fof(dt_k7_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A)
        & m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) )
     => m1_subset_1(k7_group_6(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k8_group_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v1_group_6(E,B,C)
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => ( v1_funct_1(k8_group_6(A,B,C,D,E))
        & v1_funct_2(k8_group_6(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
        & v1_group_6(k8_group_6(A,B,C,D,E),A,C)
        & m2_relset_1(k8_group_6(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) ) ) )).

fof(redefinition_k8_group_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v1_group_6(E,B,C)
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => k8_group_6(A,B,C,D,E) = k5_relat_1(D,E) ) )).

fof(dt_k9_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k9_group_6(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(redefinition_k9_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => k9_group_6(A,B,C) = k2_relat_1(C) ) )).

fof(dt_k10_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( v1_funct_1(k10_group_6(A,B))
        & v1_funct_2(k10_group_6(A,B),u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(k10_group_6(A,B),A,B)
        & m2_relset_1(k10_group_6(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(dt_k11_group_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_3(B,A)
        & m1_group_2(B,A) )
     => ( v1_funct_1(k11_group_6(A,B))
        & v1_funct_2(k11_group_6(A,B),u1_struct_0(A),u1_struct_0(k6_group_6(A,B)))
        & v1_group_6(k11_group_6(A,B),A,k6_group_6(A,B))
        & m2_relset_1(k11_group_6(A,B),u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) ) ) )).

fof(dt_k12_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_group_1(k12_group_6(A,B,C))
        & m1_group_2(k12_group_6(A,B,C),A) ) ) )).

fof(dt_k13_group_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v1_group_6(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_group_1(k13_group_6(A,B,C))
        & m1_group_2(k13_group_6(A,B,C),B) ) ) )).

fof(t7_group_6,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 = a_1_0_group_6(A)
           => r1_group_2(A,k9_group_5(A),k5_group_4(A,B)) ) ) ) )).

fof(d10_group_6,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_group_1(D)
                    & m1_group_2(D,A) )
                 => ( D = k12_group_6(A,B,C)
                  <=> u1_struct_0(D) = a_3_0_group_6(A,B,C) ) ) ) ) ) )).

fof(fraenkel_a_1_0_group_6,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_6(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,u1_struct_0(B))
            & m1_subset_1(D,u1_struct_0(B))
            & A = k2_group_5(B,C,D) ) ) ) )).

fof(fraenkel_a_3_0_group_6,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & v1_group_6(D,B,C)
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_group_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) = k2_group_1(C) ) ) ) )).
%------------------------------------------------------------------------------