% Mizar problem: t15_quofield,quofield,1359,62 
fof(t15_quofield,conjecture,(
    ! [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) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_algstr_1,cc1_gcd_1,cc1_relset_1,cc1_vectsp_1,cc2_algstr_1,cc2_gcd_1,cc2_vectsp_1,cc3_algstr_1,cc3_gcd_1,cc3_vectsp_1,cc4_algstr_1,cc4_gcd_1,cc4_vectsp_1,cc5_vectsp_1,commutativity_k7_quofield,d1_binop_1,d1_group_1,d3_quofield,d5_quofield,dt_k11_quofield,dt_k12_quofield,dt_k1_binop_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_group_1,dt_k1_mcart_1,dt_k1_quofield,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_mcart_1,dt_k2_quofield,dt_k2_zfmisc_1,dt_k3_quofield,dt_k4_tarski,dt_k5_quofield,dt_k7_quofield,dt_k8_quofield,dt_k9_quofield,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_group_1,dt_u1_struct_0,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc1_quofield,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_quofield,fc3_quofield,fc4_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc4_struct_0,rc5_struct_0,rc8_vectsp_1,rc9_vectsp_1,redefinition_k12_quofield,redefinition_k1_domain_1,redefinition_k2_binop_1,redefinition_k2_quofield,redefinition_k3_quofield,redefinition_k7_quofield,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t12_quofield,t1_subset,t2_subset,t3_subset,t4_subset,t5_quofield,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(quofield,t15_quofield)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) ) ) ) ),
    file(algstr_1,cc1_algstr_1),
    []).

fof(cc1_gcd_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v6_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(gcd_1,cc1_gcd_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc1_vectsp_1),
    []).

fof(cc2_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc2_algstr_1),
    []).

fof(cc2_gcd_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v4_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(gcd_1,cc2_gcd_1),
    []).

fof(cc2_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc2_vectsp_1),
    []).

fof(cc3_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_rlvect_1(A) ) ) ) ),
    file(algstr_1,cc3_algstr_1),
    []).

fof(cc3_gcd_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(gcd_1,cc3_gcd_1),
    []).

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

fof(cc4_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(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) ) ) ) ),
    file(algstr_1,cc4_algstr_1),
    []).

fof(cc4_gcd_1,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)
          & v4_group_1(A)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_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)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(gcd_1,cc4_gcd_1),
    []).

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc5_vectsp_1),
    []).

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) ) ),
    file(quofield,k7_quofield),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d1_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) ) ) ) ),
    file(group_1,d1_group_1),
    []).

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))) ) ) ) ),
    file(quofield,d3_quofield),
    []).

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) ) ) ) ) ) ) ),
    file(quofield,d5_quofield),
    []).

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)) ) ),
    file(quofield,k11_quofield),
    []).

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)) ) ),
    file(quofield,k12_quofield),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k1_group_1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

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)))) ) ),
    file(quofield,k1_quofield),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

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)) ) ),
    file(quofield,k2_quofield),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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)) ) ),
    file(quofield,k3_quofield),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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)) ) ),
    file(quofield,k5_quofield),
    []).

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)) ) ),
    file(quofield,k7_quofield),
    []).

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))) ) ),
    file(quofield,k8_quofield),
    []).

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)))) ) ),
    file(quofield,k9_quofield),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

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)) ) ) ),
    file(quofield,fc1_quofield),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

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)) ) ),
    file(quofield,fc2_quofield),
    []).

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

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc8_vectsp_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v4_group_1(A)
      & v7_group_1(A) ) ),
    file(vectsp_1,rc8_vectsp_1),
    []).

fof(rc9_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A) ) ),
    file(vectsp_1,rc9_vectsp_1),
    []).

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) ) ),
    file(quofield,k12_quofield),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

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) ) ),
    file(quofield,k2_quofield),
    []).

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) ) ),
    file(quofield,k3_quofield),
    []).

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) ) ),
    file(quofield,k7_quofield),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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)) ) ) ) ),
    file(quofield,t12_quofield),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

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) ) ) ) ) ) ),
    file(quofield,t5_quofield),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).