% Mizar problem: t20_mod_2,mod_2,462,34 
fof(t20_mod_2,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)
        & 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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,A)
                    & l4_vectsp_1(D,A) )
                 => ! [E] : 
                      ( m1_mod_2(E,A,B,C)
                     => ! [F] : 
                          ( m1_mod_2(F,A,D,B)
                         => ( v2_mod_2(k8_mod_2(A,E,F),A)
                            & m1_mod_2(k8_mod_2(A,E,F),A,D,C) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v2_mod_2,antisymmetry_r2_hidden,cc1_algstr_1,cc1_relset_1,cc1_vectsp_1,cc2_algstr_1,cc2_vectsp_1,cc3_algstr_1,cc3_vectsp_1,cc4_algstr_1,cc4_vectsp_1,d11_mod_2,d13_mod_2,d6_mod_2,d7_mod_2,dt_g1_mod_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mod_2,dt_k2_zfmisc_1,dt_k3_mod_2,dt_k5_relat_1,dt_k7_funct_2,dt_k8_mod_2,dt_l1_group_1,dt_l1_mod_2,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_l4_vectsp_1,dt_m1_mod_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_mod_2,dt_u1_struct_0,dt_u2_mod_2,dt_u3_mod_2,existence_l1_group_1,existence_l1_mod_2,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_l4_vectsp_1,existence_m1_mod_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc4_subset_1,free_g1_mod_2,rc1_mod_2,rc1_subset_1,rc1_xboole_0,rc2_mod_2,rc2_subset_1,rc2_xboole_0,rc3_mod_2,rc3_struct_0,rc4_struct_0,rc5_struct_0,redefinition_k7_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t14_mod_2,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(mod_2,t20_mod_2)]).

fof(abstractness_v2_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & l1_mod_2(B,A) )
     => ( v2_mod_2(B,A)
       => B = g1_mod_2(A,u1_mod_2(A,B),u2_mod_2(A,B),u3_mod_2(A,B)) ) ) ),
    file(mod_2,v2_mod_2),
    []).

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_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_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_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_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(d11_mod_2,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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( ( v3_mod_2(D,A)
                    & l1_mod_2(D,A) )
                 => ( m1_mod_2(D,A,B,C)
                  <=> ( k2_mod_2(A,D) = B
                      & k3_mod_2(A,D) = C ) ) ) ) ) ) ),
    file(mod_2,d11_mod_2),
    []).

fof(d13_mod_2,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_mod_2(B,A)
            & l1_mod_2(B,A) )
         => ! [C] : 
              ( ( v3_mod_2(C,A)
                & l1_mod_2(C,A) )
             => ( k2_mod_2(A,B) = k3_mod_2(A,C)
               => ! [D] : 
                    ( ( v2_mod_2(D,A)
                      & v3_mod_2(D,A)
                      & l1_mod_2(D,A) )
                   => ( D = k8_mod_2(A,B,C)
                    <=> ! [E] : 
                          ( ( ~ v3_struct_0(E)
                            & v3_rlvect_1(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & v12_vectsp_1(E,A)
                            & l4_vectsp_1(E,A) )
                         => ! [F] : 
                              ( ( ~ v3_struct_0(F)
                                & v3_rlvect_1(F)
                                & v4_rlvect_1(F)
                                & v5_rlvect_1(F)
                                & v6_rlvect_1(F)
                                & v12_vectsp_1(F,A)
                                & l4_vectsp_1(F,A) )
                             => ! [G] : 
                                  ( ( ~ v3_struct_0(G)
                                    & v3_rlvect_1(G)
                                    & v4_rlvect_1(G)
                                    & v5_rlvect_1(G)
                                    & v6_rlvect_1(G)
                                    & v12_vectsp_1(G,A)
                                    & l4_vectsp_1(G,A) )
                                 => ! [H] : 
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(F),u1_struct_0(G))
                                        & m2_relset_1(H,u1_struct_0(F),u1_struct_0(G)) )
                                     => ! [I] : 
                                          ( ( v1_funct_1(I)
                                            & v1_funct_2(I,u1_struct_0(E),u1_struct_0(F))
                                            & m2_relset_1(I,u1_struct_0(E),u1_struct_0(F)) )
                                         => ( ( g1_mod_2(A,u1_mod_2(A,B),u2_mod_2(A,B),u3_mod_2(A,B)) = g1_mod_2(A,F,G,H)
                                              & g1_mod_2(A,u1_mod_2(A,C),u2_mod_2(A,C),u3_mod_2(A,C)) = g1_mod_2(A,E,F,I) )
                                           => D = g1_mod_2(A,E,G,k7_funct_2(u1_struct_0(E),u1_struct_0(F),u1_struct_0(G),I,H)) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(mod_2,d13_mod_2),
    []).

fof(d6_mod_2,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] : 
          ( l1_mod_2(B,A)
         => k2_mod_2(A,B) = u1_mod_2(A,B) ) ) ),
    file(mod_2,d6_mod_2),
    []).

fof(d7_mod_2,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] : 
          ( l1_mod_2(B,A)
         => k3_mod_2(A,B) = u2_mod_2(A,B) ) ) ),
    file(mod_2,d7_mod_2),
    []).

fof(dt_g1_mod_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ 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)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
     => ( v2_mod_2(g1_mod_2(A,B,C,D),A)
        & l1_mod_2(g1_mod_2(A,B,C,D),A) ) ) ),
    file(mod_2,g1_mod_2),
    []).

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_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(k2_mod_2(A,B))
        & v3_rlvect_1(k2_mod_2(A,B))
        & v4_rlvect_1(k2_mod_2(A,B))
        & v5_rlvect_1(k2_mod_2(A,B))
        & v6_rlvect_1(k2_mod_2(A,B))
        & v12_vectsp_1(k2_mod_2(A,B),A)
        & l4_vectsp_1(k2_mod_2(A,B),A) ) ) ),
    file(mod_2,k2_mod_2),
    []).

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

fof(dt_k3_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(k3_mod_2(A,B))
        & v3_rlvect_1(k3_mod_2(A,B))
        & v4_rlvect_1(k3_mod_2(A,B))
        & v5_rlvect_1(k3_mod_2(A,B))
        & v6_rlvect_1(k3_mod_2(A,B))
        & v12_vectsp_1(k3_mod_2(A,B),A)
        & l4_vectsp_1(k3_mod_2(A,B),A) ) ) ),
    file(mod_2,k3_mod_2),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(dt_k8_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & v3_mod_2(B,A)
        & l1_mod_2(B,A)
        & v3_mod_2(C,A)
        & l1_mod_2(C,A) )
     => ( v2_mod_2(k8_mod_2(A,B,C),A)
        & v3_mod_2(k8_mod_2(A,B,C),A)
        & l1_mod_2(k8_mod_2(A,B,C),A) ) ) ),
    file(mod_2,k8_mod_2),
    []).

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

fof(dt_l1_mod_2,axiom,(
    $true ),
    file(mod_2,l1_mod_2),
    []).

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_l4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l4_vectsp_1(B,A)
         => l1_rlvect_1(B) ) ) ),
    file(vectsp_1,l4_vectsp_1),
    []).

fof(dt_m1_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A) )
     => ! [D] : 
          ( m1_mod_2(D,A,B,C)
         => ( v3_mod_2(D,A)
            & l1_mod_2(D,A) ) ) ) ),
    file(mod_2,m1_mod_2),
    []).

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_u1_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(u1_mod_2(A,B))
        & v3_rlvect_1(u1_mod_2(A,B))
        & v4_rlvect_1(u1_mod_2(A,B))
        & v5_rlvect_1(u1_mod_2(A,B))
        & v6_rlvect_1(u1_mod_2(A,B))
        & v12_vectsp_1(u1_mod_2(A,B),A)
        & l4_vectsp_1(u1_mod_2(A,B),A) ) ) ),
    file(mod_2,u1_mod_2),
    []).

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

fof(dt_u2_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & l1_mod_2(B,A) )
     => ( ~ v3_struct_0(u2_mod_2(A,B))
        & v3_rlvect_1(u2_mod_2(A,B))
        & v4_rlvect_1(u2_mod_2(A,B))
        & v5_rlvect_1(u2_mod_2(A,B))
        & v6_rlvect_1(u2_mod_2(A,B))
        & v12_vectsp_1(u2_mod_2(A,B),A)
        & l4_vectsp_1(u2_mod_2(A,B),A) ) ) ),
    file(mod_2,u2_mod_2),
    []).

fof(dt_u3_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & l1_mod_2(B,A) )
     => ( v1_funct_1(u3_mod_2(A,B))
        & v1_funct_2(u3_mod_2(A,B),u1_struct_0(u1_mod_2(A,B)),u1_struct_0(u2_mod_2(A,B)))
        & m2_relset_1(u3_mod_2(A,B),u1_struct_0(u1_mod_2(A,B)),u1_struct_0(u2_mod_2(A,B))) ) ) ),
    file(mod_2,u3_mod_2),
    []).

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

fof(existence_l1_mod_2,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] : l1_mod_2(B,A) ) ),
    file(mod_2,l1_mod_2),
    []).

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_l4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l4_vectsp_1(B,A) ) ),
    file(vectsp_1,l4_vectsp_1),
    []).

fof(existence_m1_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A) )
     => ? [D] : m1_mod_2(D,A,B,C) ) ),
    file(mod_2,m1_mod_2),
    []).

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(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(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(free_g1_mod_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ 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)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
     => ! [E,F,G,H] : 
          ( g1_mod_2(A,B,C,D) = g1_mod_2(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(mod_2,g1_mod_2),
    []).

fof(rc1_mod_2,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] : 
          ( l1_mod_2(B,A)
          & v2_mod_2(B,A) ) ) ),
    file(mod_2,rc1_mod_2),
    []).

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_mod_2,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] : 
          ( l1_mod_2(B,A)
          & v2_mod_2(B,A)
          & v3_mod_2(B,A) ) ) ),
    file(mod_2,rc2_mod_2),
    []).

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_mod_2,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)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A) )
     => ? [D] : 
          ( m1_mod_2(D,A,B,C)
          & v2_mod_2(D,A)
          & v3_mod_2(D,A) ) ) ),
    file(mod_2,rc3_mod_2),
    []).

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(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

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

fof(t14_mod_2,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)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] : 
                  ( m1_mod_2(D,A,B,C)
                 => ? [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))
                      & g1_mod_2(A,u1_mod_2(A,D),u2_mod_2(A,D),u3_mod_2(A,D)) = g1_mod_2(A,B,C,E)
                      & v1_mod_2(E,A,B,C) ) ) ) ) ) ),
    file(mod_2,t14_mod_2),
    []).

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_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),
    []).