SET007 Axioms: SET007+547.ax


%------------------------------------------------------------------------------
% File     : SET007+547 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Field of Quotients Over an Integral Domain
% 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    : quofield [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  142 (   6 unit)
%            Number of atoms       : 2095 ( 124 equality)
%            Maximal formula depth :   26 (  13 average)
%            Number of connectives : 2271 ( 318 ~  ;   0  |;1588  &)
%                                         (  31 <=>; 334 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   50 (   1 propositional; 0-3 arity)
%            Number of functors    :   51 (   0 constant; 1-6 arity)
%            Number of variables   :  363 (   0 singleton; 348 !;  15 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ( ~ v1_xboole_0(k1_quofield(A))
        & v1_relat_1(k1_quofield(A)) ) ) )).

fof(fc2_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => ~ v1_xboole_0(k8_quofield(A,B)) ) )).

fof(fc3_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ~ v1_xboole_0(k9_quofield(A)) ) )).

fof(fc4_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v3_vectsp_1(k21_quofield(A)) ) ) )).

fof(fc5_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v4_rlvect_1(k21_quofield(A))
        & v5_rlvect_1(k21_quofield(A))
        & v6_rlvect_1(k21_quofield(A))
        & v3_vectsp_1(k21_quofield(A))
        & v1_algstr_1(k21_quofield(A))
        & v2_algstr_1(k21_quofield(A))
        & v3_algstr_1(k21_quofield(A))
        & v4_algstr_1(k21_quofield(A))
        & v5_algstr_1(k21_quofield(A))
        & v6_algstr_1(k21_quofield(A)) ) ) )).

fof(fc6_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v4_rlvect_1(k21_quofield(A))
        & v5_rlvect_1(k21_quofield(A))
        & v6_rlvect_1(k21_quofield(A))
        & v7_group_1(k21_quofield(A))
        & v3_vectsp_1(k21_quofield(A))
        & v1_algstr_1(k21_quofield(A))
        & v2_algstr_1(k21_quofield(A))
        & v3_algstr_1(k21_quofield(A))
        & v4_algstr_1(k21_quofield(A))
        & v5_algstr_1(k21_quofield(A))
        & v6_algstr_1(k21_quofield(A)) ) ) )).

fof(fc7_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v4_rlvect_1(k21_quofield(A))
        & v5_rlvect_1(k21_quofield(A))
        & v6_rlvect_1(k21_quofield(A))
        & v2_group_1(k21_quofield(A))
        & v7_group_1(k21_quofield(A))
        & v3_vectsp_1(k21_quofield(A))
        & v6_vectsp_1(k21_quofield(A))
        & v8_vectsp_1(k21_quofield(A))
        & v1_algstr_1(k21_quofield(A))
        & v2_algstr_1(k21_quofield(A))
        & v3_algstr_1(k21_quofield(A))
        & v4_algstr_1(k21_quofield(A))
        & v5_algstr_1(k21_quofield(A))
        & v6_algstr_1(k21_quofield(A)) ) ) )).

fof(fc8_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v3_rlvect_1(k21_quofield(A))
        & v4_rlvect_1(k21_quofield(A))
        & v5_rlvect_1(k21_quofield(A))
        & v6_rlvect_1(k21_quofield(A))
        & v2_group_1(k21_quofield(A))
        & v4_group_1(k21_quofield(A))
        & v7_group_1(k21_quofield(A))
        & v3_vectsp_1(k21_quofield(A))
        & v4_vectsp_1(k21_quofield(A))
        & v5_vectsp_1(k21_quofield(A))
        & v6_vectsp_1(k21_quofield(A))
        & v7_vectsp_1(k21_quofield(A))
        & v8_vectsp_1(k21_quofield(A))
        & v9_vectsp_1(k21_quofield(A))
        & ~ v10_vectsp_1(k21_quofield(A))
        & v3_gcd_1(k21_quofield(A))
        & v1_algstr_1(k21_quofield(A))
        & v2_algstr_1(k21_quofield(A))
        & v3_algstr_1(k21_quofield(A))
        & v4_algstr_1(k21_quofield(A))
        & v5_algstr_1(k21_quofield(A))
        & v6_algstr_1(k21_quofield(A)) ) ) )).

fof(cc1_quofield,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A)
          & v9_vectsp_1(A)
          & ~ v10_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v2_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A)
          & v9_vectsp_1(A)
          & ~ v10_vectsp_1(A)
          & v2_vectsp_2(A)
          & v3_gcd_1(A)
          & v1_algstr_1(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A)
          & v6_algstr_1(A) ) ) ) )).

fof(rc1_quofield,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A)
      & v3_gcd_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A) ) )).

fof(cc2_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v1_quofield(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v1_grcat_1(C,A,B)
              & v1_endalg(C,A,B)
              & v1_group_6(C,A,B) ) ) ) ) )).

fof(cc3_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v1_grcat_1(C,A,B)
              & v1_endalg(C,A,B)
              & v1_group_6(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v1_quofield(C,A,B) ) ) ) ) )).

fof(cc4_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v4_quofield(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v2_quofield(C,A,B)
              & v3_quofield(C,A,B) ) ) ) ) )).

fof(cc5_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l3_vectsp_1(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v2_quofield(C,A,B)
              & v3_quofield(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v4_quofield(C,A,B) ) ) ) ) )).

fof(fc9_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ( v1_relat_1(k7_grcat_1(A))
        & v1_funct_1(k7_grcat_1(A))
        & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
        & v1_grcat_1(k7_grcat_1(A),A,A)
        & v1_endalg(k7_grcat_1(A),A,A)
        & v1_group_6(k7_grcat_1(A),A,A)
        & v1_quofield(k7_grcat_1(A),A,A) ) ) )).

fof(fc10_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v3_rlvect_1(k21_quofield(A))
        & v4_rlvect_1(k21_quofield(A))
        & v5_rlvect_1(k21_quofield(A))
        & v6_rlvect_1(k21_quofield(A))
        & v2_group_1(k21_quofield(A))
        & v4_group_1(k21_quofield(A))
        & v7_group_1(k21_quofield(A))
        & v3_vectsp_1(k21_quofield(A))
        & v4_vectsp_1(k21_quofield(A))
        & v5_vectsp_1(k21_quofield(A))
        & v6_vectsp_1(k21_quofield(A))
        & v7_vectsp_1(k21_quofield(A))
        & v8_vectsp_1(k21_quofield(A))
        & v9_vectsp_1(k21_quofield(A))
        & ~ v10_vectsp_1(k21_quofield(A))
        & v2_vectsp_2(k21_quofield(A))
        & v3_gcd_1(k21_quofield(A))
        & v1_algstr_1(k21_quofield(A))
        & v2_algstr_1(k21_quofield(A))
        & v3_algstr_1(k21_quofield(A))
        & v4_algstr_1(k21_quofield(A))
        & v5_algstr_1(k21_quofield(A))
        & v6_algstr_1(k21_quofield(A)) ) ) )).

fof(d1_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))))
         => ( B = k1_quofield(A)
          <=> ! [C] :
                ( r2_hidden(C,B)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & C = k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)
                        & E != k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(t1_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ~ v1_xboole_0(k1_quofield(A)) ) )).

fof(t2_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => k3_domain_1(u1_struct_0(A),u1_struct_0(A),B) != k1_rlvect_1(A) ) ) )).

fof(d2_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => k4_quofield(A,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),k2_rlvect_1(A,k1_group_1(A,k2_quofield(A,B),k3_quofield(A,C)),k1_group_1(A,k2_quofield(A,C),k3_quofield(A,B))),k1_group_1(A,k3_quofield(A,B),k3_quofield(A,C))) ) ) ) )).

fof(d3_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => k5_quofield(A,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),k1_group_1(A,k2_quofield(A,B),k2_quofield(A,C)),k1_group_1(A,k3_quofield(A,B),k3_quofield(A,C))) ) ) ) )).

fof(t3_quofield,axiom,(
    $true )).

fof(t4_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                 => ( k4_quofield(A,B,k4_quofield(A,C,D)) = k4_quofield(A,k4_quofield(A,B,C),D)
                    & k4_quofield(A,B,C) = k4_quofield(A,C,B) ) ) ) ) ) )).

fof(t5_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                 => ( k5_quofield(A,B,k5_quofield(A,C,D)) = k5_quofield(A,k5_quofield(A,B,C),D)
                    & k5_quofield(A,B,C) = k5_quofield(A,C,B) ) ) ) ) ) )).

fof(d4_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_quofield(A)))
             => ( C = k8_quofield(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                   => ( r2_hidden(D,C)
                    <=> k1_group_1(A,k2_quofield(A,D),k3_quofield(A,B)) = k1_group_1(A,k3_quofield(A,D),k2_quofield(A,B)) ) ) ) ) ) ) )).

fof(t6_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => r2_hidden(B,k8_quofield(A,B)) ) ) )).

fof(d5_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k1_quofield(A))))
         => ( B = k9_quofield(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_quofield(A)))
               => ( r2_hidden(C,B)
                <=> ? [D] :
                      ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                      & C = k8_quofield(A,D) ) ) ) ) ) ) )).

fof(t7_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => ~ v1_xboole_0(k9_quofield(A)) ) )).

fof(t8_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => ( ? [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                    & r2_hidden(B,D)
                    & r2_hidden(C,D) )
               => k10_group_1(A,k2_quofield(A,B),k3_quofield(A,C)) = k10_group_1(A,k2_quofield(A,C),k3_quofield(A,B)) ) ) ) ) )).

fof(t9_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ( ~ r1_xboole_0(B,C)
               => B = C ) ) ) ) )).

fof(d6_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => ( D = k10_quofield(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                       => ( r2_hidden(E,D)
                        <=> ? [F] :
                              ( m2_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                              & ? [G] :
                                  ( m2_subset_1(G,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                                  & r2_hidden(F,B)
                                  & r2_hidden(G,C)
                                  & k10_group_1(A,k2_quofield(A,E),k10_group_1(A,k3_quofield(A,F),k3_quofield(A,G))) = k10_group_1(A,k3_quofield(A,E),k4_rlvect_1(A,k10_group_1(A,k2_quofield(A,F),k3_quofield(A,G)),k10_group_1(A,k2_quofield(A,G),k3_quofield(A,F)))) ) ) ) ) ) ) ) ) ) )).

fof(d7_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => ( D = k11_quofield(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                       => ( r2_hidden(E,D)
                        <=> ? [F] :
                              ( m2_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                              & ? [G] :
                                  ( m2_subset_1(G,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                                  & r2_hidden(F,B)
                                  & r2_hidden(G,C)
                                  & k10_group_1(A,k2_quofield(A,E),k10_group_1(A,k3_quofield(A,F),k3_quofield(A,G))) = k10_group_1(A,k3_quofield(A,E),k10_group_1(A,k2_quofield(A,F),k2_quofield(A,G))) ) ) ) ) ) ) ) ) ) )).

fof(t10_quofield,axiom,(
    $true )).

fof(t11_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => k10_quofield(A,k12_quofield(A,B),k12_quofield(A,C)) = k12_quofield(A,k6_quofield(A,B,C)) ) ) ) )).

fof(t12_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
             => k11_quofield(A,k12_quofield(A,B),k12_quofield(A,C)) = k12_quofield(A,k7_quofield(A,B,C)) ) ) ) )).

fof(d8_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( B = k13_quofield(A)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
               => ( r2_hidden(C,B)
                <=> k2_quofield(A,C) = k1_rlvect_1(A) ) ) ) ) ) )).

fof(d9_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( B = k14_quofield(A)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
               => ( r2_hidden(C,B)
                <=> k2_quofield(A,C) = k3_quofield(A,C) ) ) ) ) ) )).

fof(d10_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ( C = k15_quofield(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                          & r2_hidden(E,B)
                          & k10_group_1(A,k2_quofield(A,D),k3_quofield(A,E)) = k10_group_1(A,k3_quofield(A,D),k5_rlvect_1(A,k2_quofield(A,E))) ) ) ) ) ) ) ) )).

fof(d11_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( B != k13_quofield(A)
           => ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
               => ( C = k16_quofield(A,B)
                <=> ! [D] :
                      ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                     => ( r2_hidden(D,C)
                      <=> ? [E] :
                            ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                            & r2_hidden(E,B)
                            & k10_group_1(A,k2_quofield(A,D),k2_quofield(A,E)) = k10_group_1(A,k3_quofield(A,D),k3_quofield(A,E)) ) ) ) ) ) ) ) ) )).

fof(t13_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => ( k10_quofield(A,B,k10_quofield(A,C,D)) = k10_quofield(A,k10_quofield(A,B,C),D)
                    & k10_quofield(A,B,C) = k10_quofield(A,C,B) ) ) ) ) ) )).

fof(t14_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( k10_quofield(A,B,k13_quofield(A)) = B
            & k10_quofield(A,k13_quofield(A),B) = B ) ) ) )).

fof(t15_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => ( k11_quofield(A,B,k11_quofield(A,C,D)) = k11_quofield(A,k11_quofield(A,B,C),D)
                    & k11_quofield(A,B,C) = k11_quofield(A,C,B) ) ) ) ) ) )).

fof(t16_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( k11_quofield(A,B,k14_quofield(A)) = B
            & k11_quofield(A,k14_quofield(A),B) = B ) ) ) )).

fof(t17_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => k11_quofield(A,k10_quofield(A,B,C),D) = k10_quofield(A,k11_quofield(A,B,D),k11_quofield(A,C,D)) ) ) ) ) )).

fof(t18_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => k11_quofield(A,B,k10_quofield(A,C,D)) = k10_quofield(A,k11_quofield(A,B,C),k11_quofield(A,B,D)) ) ) ) ) )).

fof(t19_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( k10_quofield(A,B,k15_quofield(A,B)) = k13_quofield(A)
            & k10_quofield(A,k15_quofield(A,B),B) = k13_quofield(A) ) ) ) )).

fof(t20_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( B != k13_quofield(A)
           => ( k11_quofield(A,B,k16_quofield(A,B)) = k14_quofield(A)
              & k11_quofield(A,k16_quofield(A,B),B) = k14_quofield(A) ) ) ) ) )).

fof(t21_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => k14_quofield(A) != k13_quofield(A) ) )).

fof(d12_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A)) )
         => ( B = k17_quofield(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                   => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),B,C,D) = k10_quofield(A,C,D) ) ) ) ) ) )).

fof(d13_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A)) )
         => ( B = k18_quofield(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                   => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),B,C,D) = k11_quofield(A,C,D) ) ) ) ) ) )).

fof(d14_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k9_quofield(A),k9_quofield(A))
            & m2_relset_1(B,k9_quofield(A),k9_quofield(A)) )
         => ( B = k19_quofield(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
               => k8_funct_2(k9_quofield(A),k9_quofield(A),B,C) = k15_quofield(A,C) ) ) ) ) )).

fof(d15_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k9_quofield(A),k9_quofield(A))
            & m2_relset_1(B,k9_quofield(A),k9_quofield(A)) )
         => ( B = k20_quofield(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
               => k8_funct_2(k9_quofield(A),k9_quofield(A),B,C) = k16_quofield(A,C) ) ) ) ) )).

fof(t22_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),B,C),D) = k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),B,k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),C,D)) ) ) ) ) )).

fof(t23_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),B,C) = k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),C,B) ) ) ) )).

fof(t24_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),B,k13_quofield(A)) = B
            & k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),k13_quofield(A),B) = B ) ) ) )).

fof(t25_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,C),D) = k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),C,D)) ) ) ) ) )).

fof(t26_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,C) = k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),C,B) ) ) ) )).

fof(t27_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,k14_quofield(A)) = B
            & k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),k14_quofield(A),B) = B ) ) ) )).

fof(t28_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),B,C),D) = k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,D),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),C,D)) ) ) ) ) )).

fof(t29_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
                 => k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),C,D)) = k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,C),k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,D)) ) ) ) ) )).

fof(t30_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),B,k8_funct_2(k9_quofield(A),k9_quofield(A),k19_quofield(A),B)) = k13_quofield(A)
            & k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k17_quofield(A),k8_funct_2(k9_quofield(A),k9_quofield(A),k19_quofield(A),B),B) = k13_quofield(A) ) ) ) )).

fof(t31_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k9_quofield(A))
         => ( B != k13_quofield(A)
           => ( k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),B,k8_funct_2(k9_quofield(A),k9_quofield(A),k20_quofield(A),B)) = k14_quofield(A)
              & k2_binop_1(k9_quofield(A),k9_quofield(A),k9_quofield(A),k18_quofield(A),k8_funct_2(k9_quofield(A),k9_quofield(A),k20_quofield(A),B),B) = k14_quofield(A) ) ) ) ) )).

fof(d16_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => k21_quofield(A) = g3_vectsp_1(k9_quofield(A),k17_quofield(A),k18_quofield(A),k14_quofield(A),k13_quofield(A)) ) )).

fof(t32_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( u1_struct_0(k21_quofield(A)) = k9_quofield(A)
        & u1_rlvect_1(k21_quofield(A)) = k17_quofield(A)
        & u1_group_1(k21_quofield(A)) = k18_quofield(A)
        & u2_struct_0(k21_quofield(A)) = k13_quofield(A)
        & u1_vectsp_1(k21_quofield(A)) = k14_quofield(A) ) ) )).

fof(t33_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => m1_subset_1(k1_binop_1(k17_quofield(A),B,C),u1_struct_0(k21_quofield(A))) ) ) ) )).

fof(t34_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => m1_subset_1(k1_funct_1(k19_quofield(A),B),u1_struct_0(k21_quofield(A))) ) ) )).

fof(t35_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => m1_subset_1(k1_binop_1(k18_quofield(A),B,C),u1_struct_0(k21_quofield(A))) ) ) ) )).

fof(t36_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => m1_subset_1(k1_funct_1(k20_quofield(A),B),u1_struct_0(k21_quofield(A))) ) ) )).

fof(t37_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => k2_rlvect_1(k21_quofield(A),B,C) = k1_binop_1(k17_quofield(A),B,C) ) ) ) )).

fof(t38_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => k5_rlvect_1(k21_quofield(A),B) = k1_funct_1(k19_quofield(A),B) ) ) )).

fof(t39_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => k1_group_1(k21_quofield(A),B,C) = k1_binop_1(k18_quofield(A),B,C) ) ) ) )).

fof(t40_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( k2_group_1(k21_quofield(A)) = k14_quofield(A)
        & k1_rlvect_1(k21_quofield(A)) = k13_quofield(A) ) ) )).

fof(t41_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k21_quofield(A)))
                 => k2_rlvect_1(k21_quofield(A),k2_rlvect_1(k21_quofield(A),B,C),D) = k2_rlvect_1(k21_quofield(A),B,k2_rlvect_1(k21_quofield(A),C,D)) ) ) ) ) )).

fof(t42_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => k2_rlvect_1(k21_quofield(A),B,C) = k2_rlvect_1(k21_quofield(A),C,B) ) ) ) )).

fof(t43_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => k2_rlvect_1(k21_quofield(A),B,k1_rlvect_1(k21_quofield(A))) = B ) ) )).

fof(t44_quofield,axiom,(
    $true )).

fof(t45_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => k10_group_1(k21_quofield(A),k2_group_1(k21_quofield(A)),B) = B ) ) )).

fof(t46_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => k10_group_1(k21_quofield(A),B,C) = k10_group_1(k21_quofield(A),C,B) ) ) ) )).

fof(t47_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k21_quofield(A)))
                 => k10_group_1(k21_quofield(A),k10_group_1(k21_quofield(A),B,C),D) = k10_group_1(k21_quofield(A),B,k10_group_1(k21_quofield(A),C,D)) ) ) ) ) )).

fof(t48_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ~ ( B != k1_rlvect_1(k21_quofield(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k21_quofield(A)))
                 => k10_group_1(k21_quofield(A),B,C) != k2_group_1(k21_quofield(A)) ) ) ) ) )).

fof(t49_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k21_quofield(A))
        & v3_rlvect_1(k21_quofield(A))
        & v4_rlvect_1(k21_quofield(A))
        & v5_rlvect_1(k21_quofield(A))
        & v6_rlvect_1(k21_quofield(A))
        & v2_group_1(k21_quofield(A))
        & v4_group_1(k21_quofield(A))
        & v7_vectsp_1(k21_quofield(A))
        & v9_vectsp_1(k21_quofield(A))
        & ~ v10_vectsp_1(k21_quofield(A))
        & l3_vectsp_1(k21_quofield(A)) ) ) )).

fof(t50_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k21_quofield(A)))
         => ( B != k1_rlvect_1(k21_quofield(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C != k1_rlvect_1(A)
                 => ! [D] :
                      ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                     => ( ( B = k12_quofield(A,D)
                          & D = k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,k2_group_1(A)) )
                       => ! [E] :
                            ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A))
                           => ( E = k1_domain_1(u1_struct_0(A),u1_struct_0(A),k2_group_1(A),C)
                             => k4_vectsp_1(k21_quofield(A),B) = k12_quofield(A,E) ) ) ) ) ) ) ) ) ) )).

fof(d17_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_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))
             => k22_quofield(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)) ) ) ) )).

fof(t51_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( C != k1_rlvect_1(A)
                          & E != k1_rlvect_1(A)
                          & k10_group_1(A,k22_quofield(A,B,C),k22_quofield(A,D,E)) != k22_quofield(A,k10_group_1(A,B,D),k10_group_1(A,C,E)) ) ) ) ) ) ) )).

fof(t52_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( C != k1_rlvect_1(A)
                          & E != k1_rlvect_1(A)
                          & k4_rlvect_1(A,k22_quofield(A,B,C),k22_quofield(A,D,E)) != k22_quofield(A,k4_rlvect_1(A,k10_group_1(A,B,E),k10_group_1(A,D,C)),k10_group_1(A,C,E)) ) ) ) ) ) ) )).

fof(d18_quofield,axiom,(
    $true )).

fof(d19_quofield,axiom,(
    $true )).

fof(d20_quofield,axiom,(
    $true )).

fof(d21_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_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_quofield(C,A,B)
              <=> ( v1_grcat_1(C,A,B)
                  & v1_group_6(C,A,B)
                  & v1_endalg(C,A,B) ) ) ) ) ) )).

fof(d22_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_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)) )
             => ( v2_quofield(C,A,B)
              <=> ( v1_quofield(C,A,B)
                  & k2_relat_1(C) = u1_struct_0(B) ) ) ) ) ) )).

fof(d23_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_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)) )
             => ( v3_quofield(C,A,B)
              <=> ( v1_quofield(C,A,B)
                  & v2_funct_1(C) ) ) ) ) ) )).

fof(d24_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_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)) )
             => ( v4_quofield(C,A,B)
              <=> ( v3_quofield(C,A,B)
                  & v2_quofield(C,A,B) ) ) ) ) ) )).

fof(t53_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_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_quofield(C,A,B)
               => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_rlvect_1(A)) = k1_rlvect_1(B) ) ) ) ) )).

fof(t54_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_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)) )
             => ( v3_quofield(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k1_rlvect_1(B)
                    <=> D = k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(t55_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_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)
            & v4_group_1(B)
            & v7_group_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) )
         => ! [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_quofield(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( D != k1_rlvect_1(A)
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_vectsp_1(A,D)) = k4_vectsp_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ) )).

fof(t56_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_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)
            & v4_group_1(B)
            & v7_group_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) )
         => ! [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_quofield(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( E != k1_rlvect_1(A)
                         => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k10_group_1(A,D,k4_vectsp_1(A,E))) = k10_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_vectsp_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))) ) ) ) ) ) ) ) )).

fof(t57_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v4_group_1(B)
            & v6_vectsp_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v4_group_1(C)
                & v6_vectsp_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( v1_quofield(D,A,B)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                          & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                       => ( v1_quofield(E,B,C)
                         => v1_quofield(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ) )).

fof(t58_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => v1_quofield(k7_grcat_1(A),A,A) ) )).

fof(d25_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_1(B) )
         => ( r1_quofield(A,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))
                & v3_quofield(C,A,B) ) ) ) ) )).

fof(d26_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_1(B) )
         => ( r2_quofield(A,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))
                & v4_quofield(C,A,B) ) ) ) ) )).

fof(d27_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( C != k1_rlvect_1(A)
               => k23_quofield(A,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) )).

fof(d28_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k21_quofield(A)))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k21_quofield(A))) )
         => ( B = k24_quofield(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(k21_quofield(A)),B,C) = k12_quofield(A,k23_quofield(A,C,k2_group_1(A))) ) ) ) ) )).

fof(t59_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => v1_quofield(k24_quofield(A),A,k21_quofield(A)) ) )).

fof(t60_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => v3_quofield(k24_quofield(A),A,k21_quofield(A)) ) )).

fof(t61_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => r1_quofield(A,k21_quofield(A)) ) )).

fof(t62_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => r2_quofield(A,k21_quofield(A)) ) )).

fof(t63_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => r2_quofield(k21_quofield(k21_quofield(A)),k21_quofield(A)) ) )).

fof(d29_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_vectsp_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)) )
             => ( r3_quofield(A,B,C)
              <=> ( v3_quofield(C,A,B)
                  & ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & v3_rlvect_1(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & v4_group_1(D)
                        & v7_group_1(D)
                        & v7_vectsp_1(D)
                        & v8_vectsp_1(D)
                        & v9_vectsp_1(D)
                        & ~ v10_vectsp_1(D)
                        & l3_vectsp_1(D) )
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(D))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) )
                         => ~ ( v3_quofield(E,A,D)
                              & ! [F] :
                                  ( ( v1_funct_1(F)
                                    & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                                    & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                                 => ~ ( v1_quofield(F,B,D)
                                      & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(D),C,F) = E
                                      & ! [G] :
                                          ( ( v1_funct_1(G)
                                            & v1_funct_2(G,u1_struct_0(B),u1_struct_0(D))
                                            & m2_relset_1(G,u1_struct_0(B),u1_struct_0(D)) )
                                         => ( ( v1_quofield(G,B,D)
                                              & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(D),C,G) = E )
                                           => G = F ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t64_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(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)
          & v4_group_1(B)
          & v7_group_1(B)
          & v7_vectsp_1(B)
          & v8_vectsp_1(B)
          & v9_vectsp_1(B)
          & ~ v10_vectsp_1(B)
          & l3_vectsp_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))
              & r3_quofield(A,B,C) ) ) ) )).

fof(t65_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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)
            & v4_group_1(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & v9_vectsp_1(B)
            & ~ v10_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(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(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ( ( r3_quofield(A,B,D)
                          & r3_quofield(A,C,E) )
                       => r2_quofield(B,C) ) ) ) ) ) ) )).

fof(symmetry_r2_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & l3_vectsp_1(B) )
     => ( r2_quofield(A,B)
       => r2_quofield(B,A) ) ) )).

fof(dt_k1_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => m1_subset_1(k1_quofield(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) )).

fof(dt_k2_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => m1_subset_1(k2_quofield(A,B),u1_struct_0(A)) ) )).

fof(redefinition_k2_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => k2_quofield(A,B) = k1_mcart_1(B) ) )).

fof(dt_k3_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => m1_subset_1(k3_quofield(A,B),u1_struct_0(A)) ) )).

fof(redefinition_k3_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => k3_quofield(A,B) = k2_mcart_1(B) ) )).

fof(dt_k4_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => m2_subset_1(k4_quofield(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) ) )).

fof(dt_k5_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => m2_subset_1(k5_quofield(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) ) )).

fof(dt_k6_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => m2_subset_1(k6_quofield(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) ) )).

fof(commutativity_k6_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => k6_quofield(A,B,C) = k6_quofield(A,C,B) ) )).

fof(redefinition_k6_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => k6_quofield(A,B,C) = k4_quofield(A,B,C) ) )).

fof(dt_k7_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => m2_subset_1(k7_quofield(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) ) )).

fof(commutativity_k7_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => k7_quofield(A,B,C) = k7_quofield(A,C,B) ) )).

fof(redefinition_k7_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A))
        & m1_subset_1(C,k1_quofield(A)) )
     => k7_quofield(A,B,C) = k5_quofield(A,B,C) ) )).

fof(dt_k8_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => m1_subset_1(k8_quofield(A,B),k1_zfmisc_1(k1_quofield(A))) ) )).

fof(dt_k9_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A) )
     => m1_subset_1(k9_quofield(A),k1_zfmisc_1(k1_zfmisc_1(k1_quofield(A)))) ) )).

fof(dt_k10_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k9_quofield(A))
        & m1_subset_1(C,k9_quofield(A)) )
     => m2_subset_1(k10_quofield(A,B,C),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(dt_k11_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k9_quofield(A))
        & m1_subset_1(C,k9_quofield(A)) )
     => m2_subset_1(k11_quofield(A,B,C),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(dt_k12_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => m2_subset_1(k12_quofield(A,B),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(redefinition_k12_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v10_vectsp_1(A)
        & l2_vectsp_1(A)
        & m1_subset_1(B,k1_quofield(A)) )
     => k12_quofield(A,B) = k8_quofield(A,B) ) )).

fof(dt_k13_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => m2_subset_1(k13_quofield(A),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(dt_k14_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => m2_subset_1(k14_quofield(A),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(dt_k15_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k9_quofield(A)) )
     => m2_subset_1(k15_quofield(A,B),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(dt_k16_quofield,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k9_quofield(A)) )
     => m2_subset_1(k16_quofield(A,B),k1_zfmisc_1(k1_quofield(A)),k9_quofield(A)) ) )).

fof(dt_k17_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k17_quofield(A))
        & v1_funct_2(k17_quofield(A),k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A))
        & m2_relset_1(k17_quofield(A),k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A)) ) ) )).

fof(dt_k18_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k18_quofield(A))
        & v1_funct_2(k18_quofield(A),k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A))
        & m2_relset_1(k18_quofield(A),k2_zfmisc_1(k9_quofield(A),k9_quofield(A)),k9_quofield(A)) ) ) )).

fof(dt_k19_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k19_quofield(A))
        & v1_funct_2(k19_quofield(A),k9_quofield(A),k9_quofield(A))
        & m2_relset_1(k19_quofield(A),k9_quofield(A),k9_quofield(A)) ) ) )).

fof(dt_k20_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k20_quofield(A))
        & v1_funct_2(k20_quofield(A),k9_quofield(A),k9_quofield(A))
        & m2_relset_1(k20_quofield(A),k9_quofield(A),k9_quofield(A)) ) ) )).

fof(dt_k21_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( v3_vectsp_1(k21_quofield(A))
        & l3_vectsp_1(k21_quofield(A)) ) ) )).

fof(dt_k22_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k22_quofield(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k23_quofield,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k23_quofield(A,B,C),k1_quofield(A)) ) )).

fof(dt_k24_quofield,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k24_quofield(A))
        & v1_funct_2(k24_quofield(A),u1_struct_0(A),u1_struct_0(k21_quofield(A)))
        & m2_relset_1(k24_quofield(A),u1_struct_0(A),u1_struct_0(k21_quofield(A))) ) ) )).
%------------------------------------------------------------------------------