SET007 Axioms: SET007+805.ax


%------------------------------------------------------------------------------
% File     : SET007+805 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Witt's Proof of the Wedderburn Theorem
% 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    : weddwitt [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   67 (   0 unit)
%            Number of atoms       :  937 (  67 equality)
%            Maximal formula depth :   21 (  13 average)
%            Number of connectives : 1001 ( 131 ~  ;   3  |; 703  &)
%                                         (  17 <=>; 147 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   52 (   0 propositional; 1-3 arity)
%            Number of functors    :   58 (   4 constant; 0-4 arity)
%            Number of variables   :  156 (   0 singleton; 147 !;   9 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_weddwitt,axiom,(
    ? [A] :
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v3_group_1(A)
      & v4_group_1(A)
      & v6_group_1(A)
      & v11_monoid_0(A)
      & v12_monoid_0(A)
      & v13_monoid_0(A)
      & v14_monoid_0(A)
      & v15_monoid_0(A)
      & v16_monoid_0(A) ) )).

fof(fc1_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k10_group_5(A))
        & v1_group_1(k10_group_5(A))
        & v2_group_1(k10_group_5(A))
        & v3_group_1(k10_group_5(A))
        & v4_group_1(k10_group_5(A))
        & v6_group_1(k10_group_5(A))
        & v11_monoid_0(k10_group_5(A))
        & v12_monoid_0(k10_group_5(A))
        & v13_monoid_0(k10_group_5(A))
        & v14_monoid_0(k10_group_5(A))
        & v15_monoid_0(k10_group_5(A))
        & v16_monoid_0(k10_group_5(A)) ) ) )).

fof(fc2_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_weddwitt(A,B))
        & v1_group_1(k1_weddwitt(A,B))
        & v2_group_1(k1_weddwitt(A,B))
        & v3_group_1(k1_weddwitt(A,B))
        & v4_group_1(k1_weddwitt(A,B))
        & v6_group_1(k1_weddwitt(A,B))
        & v11_monoid_0(k1_weddwitt(A,B))
        & v12_monoid_0(k1_weddwitt(A,B))
        & v13_monoid_0(k1_weddwitt(A,B))
        & v14_monoid_0(k1_weddwitt(A,B))
        & v15_monoid_0(k1_weddwitt(A,B))
        & v16_monoid_0(k1_weddwitt(A,B)) ) ) )).

fof(fc3_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k7_group_3(A,B)) ) )).

fof(fc4_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k4_weddwitt(A))
        & v2_group_1(k4_weddwitt(A))
        & v4_group_1(k4_weddwitt(A))
        & v6_group_1(k4_weddwitt(A))
        & v7_group_1(k4_weddwitt(A))
        & v3_rlvect_1(k4_weddwitt(A))
        & v4_rlvect_1(k4_weddwitt(A))
        & v5_rlvect_1(k4_weddwitt(A))
        & v6_rlvect_1(k4_weddwitt(A))
        & v3_vectsp_1(k4_weddwitt(A))
        & v4_vectsp_1(k4_weddwitt(A))
        & v5_vectsp_1(k4_weddwitt(A))
        & v6_vectsp_1(k4_weddwitt(A))
        & v7_vectsp_1(k4_weddwitt(A))
        & v8_vectsp_1(k4_weddwitt(A))
        & v9_vectsp_1(k4_weddwitt(A))
        & ~ v10_vectsp_1(k4_weddwitt(A))
        & ~ v3_realset2(k4_weddwitt(A)) ) ) )).

fof(fc5_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_weddwitt(A,B))
        & v2_group_1(k5_weddwitt(A,B))
        & v4_group_1(k5_weddwitt(A,B))
        & v6_group_1(k5_weddwitt(A,B))
        & v3_rlvect_1(k5_weddwitt(A,B))
        & v4_rlvect_1(k5_weddwitt(A,B))
        & v5_rlvect_1(k5_weddwitt(A,B))
        & v6_rlvect_1(k5_weddwitt(A,B))
        & v3_vectsp_1(k5_weddwitt(A,B))
        & v4_vectsp_1(k5_weddwitt(A,B))
        & v5_vectsp_1(k5_weddwitt(A,B))
        & v6_vectsp_1(k5_weddwitt(A,B))
        & v7_vectsp_1(k5_weddwitt(A,B))
        & v8_vectsp_1(k5_weddwitt(A,B))
        & v9_vectsp_1(k5_weddwitt(A,B))
        & ~ v10_vectsp_1(k5_weddwitt(A,B))
        & ~ v3_realset2(k5_weddwitt(A,B)) ) ) )).

fof(t1_weddwitt,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( k3_prepower(B,A) = np__1
           => ( r1_xreal_0(B,np__1)
              | A = np__0 ) ) ) ) )).

fof(t2_weddwitt,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( ~ r1_xreal_0(D,np__1)
                      & ~ r1_xreal_0(B,np__0)
                      & k3_prepower(D,k1_nat_1(k2_nat_1(A,B),C)) != k4_real_1(k3_prepower(D,A),k3_prepower(D,k1_nat_1(k2_nat_1(A,k5_binarith(B,np__1)),C))) ) ) ) ) ) )).

fof(t3_weddwitt,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_nat_1(k5_binarith(k3_euler_2(A,B),np__1),k5_binarith(k3_euler_2(A,C),np__1))
               => ( r1_xreal_0(B,np__0)
                  | r1_xreal_0(A,np__1)
                  | r1_nat_1(B,C) ) ) ) ) ) )).

fof(t4_weddwitt,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,np__0)
           => k1_card_1(k1_funct_2(A,B)) = k3_euler_2(B,A) ) ) ) )).

fof(t5_weddwitt,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,k4_finseq_1(A))
                 => r1_nat_1(B,k4_finseq_4(k5_numbers,k5_numbers,A,C)) ) )
           => r1_nat_1(B,k9_wsierp_1(A)) ) ) ) )).

fof(t6_weddwitt,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ( ( v2_funct_1(C)
                  & k2_relat_1(C) = B )
               => ! [D] :
                    ( m2_finseq_1(D,k5_numbers)
                   => ( ( k3_finseq_1(D) = k3_finseq_1(C)
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(E,k4_finseq_1(D))
                             => k3_wsierp_1(D,E) = k1_card_1(k1_funct_1(C,E)) ) ) )
                     => k4_card_1(A) = k9_wsierp_1(D) ) ) ) ) ) ) )).

fof(t7_weddwitt,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] :
              ( r1_rlvect_1(k1_weddwitt(A,B),C)
             => r1_rlvect_1(A,C) ) ) ) )).

fof(t8_weddwitt,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,B,C) = k1_group_1(A,C,B)
              <=> m1_subset_1(C,u1_struct_0(k1_weddwitt(A,B))) ) ) ) ) )).

fof(d2_weddwitt,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_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),k7_group_3(A,B))
                & m2_relset_1(C,u1_struct_0(A),k7_group_3(A,B)) )
             => ( C = k2_weddwitt(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),k7_group_3(A,B),C,D) = k2_group_3(A,B,D) ) ) ) ) ) )).

fof(t9_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_struct_0(C,A,k7_group_3(A,B))
             => k4_card_1(k3_funct_2(u1_struct_0(A),k7_group_3(A,B),k2_weddwitt(A,B),k18_group_2(k7_group_3(A,B),C))) = k9_group_1(k1_weddwitt(A,B)) ) ) ) )).

fof(t10_weddwitt,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_struct_0(C,A,k7_group_3(A,B))
             => ! [D] :
                  ( m1_struct_0(D,A,k7_group_3(A,B))
                 => ( C != D
                   => r1_xboole_0(k3_funct_2(u1_struct_0(A),k7_group_3(A,B),k2_weddwitt(A,B),k18_group_2(k7_group_3(A,B),C)),k3_funct_2(u1_struct_0(A),k7_group_3(A,B),k2_weddwitt(A,B),k18_group_2(k7_group_3(A,B),D))) ) ) ) ) ) )).

fof(t13_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_group_1(A) = k2_nat_1(k4_card_1(k7_group_3(A,B)),k9_group_1(k1_weddwitt(A,B))) ) ) )).

fof(t14_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( r2_hidden(B,k3_weddwitt(A))
        <=> ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & k7_group_3(A,C) = B ) ) ) )).

fof(t15_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_weddwitt(A))
         => ( ( v2_funct_1(B)
              & k2_relat_1(B) = k3_weddwitt(A) )
           => ! [C] :
                ( m2_finseq_1(C,k5_numbers)
               => ( ( k3_finseq_1(C) = k3_finseq_1(B)
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( r2_hidden(D,k4_finseq_1(C))
                         => k3_wsierp_1(C,D) = k1_card_1(k1_funct_1(B,D)) ) ) )
                 => k9_group_1(A) = k9_wsierp_1(C) ) ) ) ) ) )).

fof(t16_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v7_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( v2_matrlin(B,A)
                      & C = k1_vectsp_9(A,B)
                      & D = k1_card_1(u1_struct_0(A)) )
                   => k1_card_1(u1_struct_0(B)) = k3_euler_2(D,C) ) ) ) ) ) )).

fof(t17_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => r1_tarski(u1_struct_0(k4_weddwitt(A)),u1_struct_0(A)) ) )).

fof(t18_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r1_rlvect_1(k4_weddwitt(A),B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_group_1(A,B,C) = k1_group_1(A,C,B) ) ) ) ) )).

fof(t19_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => r1_rlvect_1(k4_weddwitt(A),k1_rlvect_1(A)) ) )).

fof(t20_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => r1_rlvect_1(k4_weddwitt(A),k2_group_1(A)) ) )).

fof(t21_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ~ r1_xreal_0(k4_card_1(u1_struct_0(k4_weddwitt(A))),np__1) ) )).

fof(t22_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( k4_card_1(u1_struct_0(k4_weddwitt(A))) = k4_card_1(u1_struct_0(A))
      <=> v7_group_1(A) ) ) )).

fof(t23_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => u1_struct_0(k4_weddwitt(A)) = k2_xboole_0(u1_struct_0(k10_group_5(k1_uniroots(A))),k18_group_2(u1_struct_0(A),k1_rlvect_1(A))) ) )).

fof(t24_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(u1_struct_0(k5_weddwitt(A,B)),u1_struct_0(A)) ) ) )).

fof(t25_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,u1_struct_0(k5_weddwitt(A,B)))
              <=> k1_group_1(A,C,B) = k1_group_1(A,B,C) ) ) ) ) )).

fof(t26_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(u1_struct_0(k4_weddwitt(A)),u1_struct_0(k5_weddwitt(A,B))) ) ) )).

fof(t27_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_hidden(C,u1_struct_0(k4_weddwitt(A)))
                      & r2_hidden(D,u1_struct_0(k5_weddwitt(A,B))) )
                   => r2_hidden(k1_group_1(A,C,D),u1_struct_0(k5_weddwitt(A,B))) ) ) ) ) ) )).

fof(t28_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( m1_subset_1(k1_rlvect_1(A),u1_struct_0(k5_weddwitt(A,B)))
            & m1_subset_1(k2_group_1(A),u1_struct_0(k5_weddwitt(A,B))) ) ) ) )).

fof(t29_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ r1_xreal_0(k4_card_1(u1_struct_0(k5_weddwitt(A,B))),np__1) ) ) )).

fof(t30_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k1_uniroots(A)))
             => ( C = B
               => u1_struct_0(k5_weddwitt(A,B)) = k2_xboole_0(u1_struct_0(k1_weddwitt(k1_uniroots(A),C)),k18_group_2(u1_struct_0(A),k1_rlvect_1(A))) ) ) ) ) )).

fof(t31_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k1_uniroots(A)))
             => ( C = B
               => k9_group_1(k1_weddwitt(k1_uniroots(A),C)) = k5_real_1(k4_card_1(u1_struct_0(k5_weddwitt(A,B))),np__1) ) ) ) ) )).

fof(d6_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v11_vectsp_1(B,k4_weddwitt(A))
            & v12_vectsp_1(B,k4_weddwitt(A))
            & l4_vectsp_1(B,k4_weddwitt(A)) )
         => ( B = k6_weddwitt(A)
          <=> ( g1_rlvect_1(u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B)) = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))
              & u2_vectsp_1(k4_weddwitt(A),B) = k7_relat_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(k4_weddwitt(A)),u1_struct_0(A))) ) ) ) ) )).

fof(t32_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => k4_card_1(u1_struct_0(A)) = k3_euler_2(k4_card_1(u1_struct_0(k4_weddwitt(A))),k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A))) ) )).

fof(t33_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ~ r1_xreal_0(k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A)),np__0) ) )).

fof(d7_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v11_vectsp_1(C,k4_weddwitt(A))
                & v12_vectsp_1(C,k4_weddwitt(A))
                & l4_vectsp_1(C,k4_weddwitt(A)) )
             => ( C = k7_weddwitt(A,B)
              <=> ( g1_rlvect_1(u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C)) = g1_rlvect_1(u1_struct_0(k5_weddwitt(A,B)),u1_rlvect_1(k5_weddwitt(A,B)),u2_struct_0(k5_weddwitt(A,B)))
                  & u2_vectsp_1(k4_weddwitt(A),C) = k7_relat_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(k4_weddwitt(A)),u1_struct_0(k5_weddwitt(A,B)))) ) ) ) ) ) )).

fof(t34_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_card_1(u1_struct_0(k5_weddwitt(A,B))) = k3_euler_2(k4_card_1(u1_struct_0(k4_weddwitt(A))),k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B))) ) ) )).

fof(t35_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ r1_xreal_0(k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B)),np__0) ) ) )).

fof(t36_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( m1_subset_1(B,u1_struct_0(k1_uniroots(A)))
           => r2_int_1(k5_real_1(k3_euler_2(k4_card_1(u1_struct_0(k4_weddwitt(A))),k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B))),np__1),k5_real_1(k3_euler_2(k4_card_1(u1_struct_0(k4_weddwitt(A))),k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A))),np__1)) ) ) ) )).

fof(t37_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( m1_subset_1(B,u1_struct_0(k1_uniroots(A)))
           => r1_nat_1(k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B)),k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A))) ) ) ) )).

fof(t38_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => k4_card_1(u1_struct_0(k10_group_5(k1_uniroots(A)))) = k5_real_1(k4_card_1(u1_struct_0(k4_weddwitt(A))),np__1) ) )).

fof(t39_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => v7_group_1(A) ) )).

fof(t40_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => k2_group_1(k4_weddwitt(A)) = k2_group_1(A) ) )).

fof(t41_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_group_1(k5_weddwitt(A,B)) = k2_group_1(A) ) ) )).

fof(dt_k1_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_group_1(k1_weddwitt(A,B))
        & m1_group_2(k1_weddwitt(A,B),A) ) ) )).

fof(dt_k2_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k2_weddwitt(A,B))
        & v1_funct_2(k2_weddwitt(A,B),u1_struct_0(A),k7_group_3(A,B))
        & m2_relset_1(k2_weddwitt(A,B),u1_struct_0(A),k7_group_3(A,B)) ) ) )).

fof(dt_k3_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m1_eqrel_1(k3_weddwitt(A),u1_struct_0(A)) ) )).

fof(dt_k4_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k4_weddwitt(A))
        & v4_group_1(k4_weddwitt(A))
        & v7_group_1(k4_weddwitt(A))
        & v3_rlvect_1(k4_weddwitt(A))
        & v4_rlvect_1(k4_weddwitt(A))
        & v5_rlvect_1(k4_weddwitt(A))
        & v6_rlvect_1(k4_weddwitt(A))
        & v3_vectsp_1(k4_weddwitt(A))
        & v7_vectsp_1(k4_weddwitt(A))
        & v8_vectsp_1(k4_weddwitt(A))
        & v9_vectsp_1(k4_weddwitt(A))
        & ~ v10_vectsp_1(k4_weddwitt(A))
        & l3_vectsp_1(k4_weddwitt(A)) ) ) )).

fof(dt_k5_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_weddwitt(A,B))
        & v4_group_1(k5_weddwitt(A,B))
        & v3_rlvect_1(k5_weddwitt(A,B))
        & v4_rlvect_1(k5_weddwitt(A,B))
        & v5_rlvect_1(k5_weddwitt(A,B))
        & v6_rlvect_1(k5_weddwitt(A,B))
        & v3_vectsp_1(k5_weddwitt(A,B))
        & v6_vectsp_1(k5_weddwitt(A,B))
        & v7_vectsp_1(k5_weddwitt(A,B))
        & v8_vectsp_1(k5_weddwitt(A,B))
        & v9_vectsp_1(k5_weddwitt(A,B))
        & ~ v10_vectsp_1(k5_weddwitt(A,B))
        & l3_vectsp_1(k5_weddwitt(A,B)) ) ) )).

fof(dt_k6_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k6_weddwitt(A))
        & v3_rlvect_1(k6_weddwitt(A))
        & v4_rlvect_1(k6_weddwitt(A))
        & v5_rlvect_1(k6_weddwitt(A))
        & v6_rlvect_1(k6_weddwitt(A))
        & v11_vectsp_1(k6_weddwitt(A),k4_weddwitt(A))
        & v12_vectsp_1(k6_weddwitt(A),k4_weddwitt(A))
        & l4_vectsp_1(k6_weddwitt(A),k4_weddwitt(A)) ) ) )).

fof(dt_k7_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k7_weddwitt(A,B))
        & v3_rlvect_1(k7_weddwitt(A,B))
        & v4_rlvect_1(k7_weddwitt(A,B))
        & v5_rlvect_1(k7_weddwitt(A,B))
        & v6_rlvect_1(k7_weddwitt(A,B))
        & v11_vectsp_1(k7_weddwitt(A,B),k4_weddwitt(A))
        & v12_vectsp_1(k7_weddwitt(A,B),k4_weddwitt(A))
        & l4_vectsp_1(k7_weddwitt(A,B),k4_weddwitt(A)) ) ) )).

fof(d1_weddwitt,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_1(C)
                & m1_group_2(C,A) )
             => ( C = k1_weddwitt(A,B)
              <=> u1_struct_0(C) = a_2_0_weddwitt(A,B) ) ) ) ) )).

fof(t11_weddwitt,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))
         => m1_eqrel_1(a_2_1_weddwitt(A,B),u1_struct_0(A)) ) ) )).

fof(t12_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v6_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_card_1(a_2_2_weddwitt(A,B)) = k4_card_1(k7_group_3(A,B)) ) ) )).

fof(d3_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k3_weddwitt(A) = a_1_0_weddwitt(A) ) )).

fof(d4_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v3_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & v9_vectsp_1(B)
            & ~ v10_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ( B = k4_weddwitt(A)
          <=> ( u1_struct_0(B) = a_1_1_weddwitt(A)
              & u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B))
              & u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B))
              & u2_struct_0(B) = u2_struct_0(A)
              & u1_vectsp_1(B) = k2_group_1(A) ) ) ) ) )).

fof(d5_weddwitt,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v3_vectsp_1(C)
                & v6_vectsp_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ( C = k5_weddwitt(A,B)
              <=> ( u1_struct_0(C) = a_2_3_weddwitt(A,B)
                  & u1_rlvect_1(C) = k1_realset1(u1_rlvect_1(A),u1_struct_0(C))
                  & u1_group_1(C) = k1_realset1(u1_group_1(A),u1_struct_0(C))
                  & u2_struct_0(C) = u2_struct_0(A)
                  & u1_vectsp_1(C) = k2_group_1(A) ) ) ) ) ) )).

fof(fraenkel_a_2_0_weddwitt,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_weddwitt(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & k1_group_1(B,C,D) = k1_group_1(B,D,C) ) ) ) )).

fof(fraenkel_a_2_1_weddwitt,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_1_weddwitt(B,C))
      <=> ? [D] :
            ( m1_struct_0(D,B,k7_group_3(B,C))
            & A = k3_funct_2(u1_struct_0(B),k7_group_3(B,C),k2_weddwitt(B,C),k18_group_2(k7_group_3(B,C),D)) ) ) ) )).

fof(fraenkel_a_2_2_weddwitt,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & v6_group_1(B)
        & l1_group_1(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_2_weddwitt(B,C))
      <=> ? [D] :
            ( m1_struct_0(D,B,k7_group_3(B,C))
            & A = k3_funct_2(u1_struct_0(B),k7_group_3(B,C),k2_weddwitt(B,C),k18_group_2(k7_group_3(B,C),D)) ) ) ) )).

fof(fraenkel_a_1_0_weddwitt,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_weddwitt(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & ? [D] :
                ( m1_subset_1(D,u1_struct_0(B))
                & C = k7_group_3(B,D) ) ) ) ) )).

fof(fraenkel_a_1_1_weddwitt,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v4_group_1(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & v9_vectsp_1(B)
        & ~ v10_vectsp_1(B)
        & l3_vectsp_1(B) )
     => ( r2_hidden(A,a_1_1_weddwitt(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ! [D] :
                ( m1_subset_1(D,u1_struct_0(B))
               => k1_group_1(B,C,D) = k1_group_1(B,D,C) ) ) ) ) )).

fof(fraenkel_a_2_3_weddwitt,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v4_group_1(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & v9_vectsp_1(B)
        & ~ v10_vectsp_1(B)
        & l3_vectsp_1(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_weddwitt(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & k1_group_1(B,D,C) = k1_group_1(B,C,D) ) ) ) )).
%------------------------------------------------------------------------------