% Mizar problem: t3_realset2,realset2,833,63 
fof(t3_realset2,conjecture,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] : 
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] : 
                  ( m1_subset_1(D,k2_realset2(A))
                 => ( k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k3_realset2(A),k4_tarski(C,D)))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k5_realset2(A),k4_tarski(B,D))))
                    & k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_rlvect_1,abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc1_realset1,cc1_relset_1,commutativity_k2_tarski,d10_realset2,d11_realset2,d12_realset2,d3_realset1,d5_tarski,d8_realset2,d9_realset1,d9_realset2,dt_g1_rlvect_1,dt_g3_vectsp_1,dt_k1_funct_1,dt_k1_realset1,dt_k1_realset2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_realset2,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_realset2,dt_k4_realset1,dt_k4_realset2,dt_k4_tarski,dt_k4_xboole_0,dt_k5_realset1,dt_k5_realset2,dt_k7_relat_1,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_m3_realset1,dt_m4_realset1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_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_m3_realset1,existence_m4_realset1,fc1_realset1,fc1_subset_1,fc1_xboole_0,fc2_group_1,fc2_realset1,fc2_subset_1,fc3_realset1,fc3_subset_1,fc4_realset1,fc4_subset_1,free_g1_rlvect_1,free_g3_vectsp_1,rc1_realset1,rc1_realset2,rc1_rlvect_1,rc1_subset_1,rc1_xboole_0,rc2_realset1,rc2_realset2,rc2_subset_1,rc2_xboole_0,rc3_realset1,rc3_realset2,rc4_realset2,rc4_rlvect_1,redefinition_k5_realset1,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(realset2,t3_realset2)]).

fof(abstractness_v1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_rlvect_1(A)
       => A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ) ),
    file(rlvect_1,v1_rlvect_1),
    []).

fof(abstractness_v3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( v3_vectsp_1(A)
       => A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) ),
    file(vectsp_1,v3_vectsp_1),
    []).

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

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d10_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A))
            & m2_relset_1(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) )
         => ( B = k3_realset2(A)
          <=> ? [C] : 
                ( m1_subset_1(C,k2_realset2(A))
                & ? [D] : 
                    ( m3_realset1(D,k2_realset2(A),C)
                    & ? [E] : 
                        ( m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),C)))
                        & A = k1_realset2(k2_realset2(A),B,D,C,E) ) ) ) ) ) ) ),
    file(realset2,d10_realset2),
    []).

fof(d11_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_realset2(A))
         => ( B = k4_realset2(A)
          <=> ? [C] : 
                ( m3_realset1(C,k2_realset2(A),B)
                & ? [D] : 
                    ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),B)))
                    & A = k1_realset2(k2_realset2(A),k3_realset2(A),C,B,D) ) ) ) ) ) ),
    file(realset2,d11_realset2),
    []).

fof(d12_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m3_realset1(B,k2_realset2(A),k4_realset2(A))
         => ( B = k5_realset2(A)
          <=> ? [C] : 
                ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                & A = k1_realset2(k2_realset2(A),k3_realset2(A),B,k4_realset2(A),C) ) ) ) ) ),
    file(realset2,d12_realset2),
    []).

fof(d3_realset1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B)) ) ),
    file(realset1,d3_realset1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d8_realset2,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( v4_realset2(A)
      <=> ? [B] : 
            ( ~ v1_realset1(B)
            & ? [C] : 
                ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B)
                & ? [D] : 
                    ( m1_subset_1(D,B)
                    & ? [E] : 
                        ( m3_realset1(E,B,D)
                        & ? [F] : 
                            ( m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D)))
                            & A = k1_realset2(B,C,E,D,F)
                            & ~ v3_struct_0(g1_rlvect_1(B,C,D))
                            & v3_rlvect_1(g1_rlvect_1(B,C,D))
                            & v4_rlvect_1(g1_rlvect_1(B,C,D))
                            & v1_realset2(g1_rlvect_1(B,C,D))
                            & v2_realset2(g1_rlvect_1(B,C,D))
                            & l1_rlvect_1(g1_rlvect_1(B,C,D))
                            & ! [G] : 
                                ( ~ v1_xboole_0(G)
                               => ! [H] : 
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,k2_zfmisc_1(G,G),G)
                                      & m2_relset_1(H,k2_zfmisc_1(G,G),G) )
                                   => ! [I] : 
                                        ( m1_subset_1(I,G)
                                       => ( ( G = k4_xboole_0(B,k5_realset1(B,D))
                                            & I = F
                                            & H = k4_realset1(B,D,E) )
                                         => ( ~ v3_struct_0(g1_rlvect_1(G,H,I))
                                            & v3_rlvect_1(g1_rlvect_1(G,H,I))
                                            & v4_rlvect_1(g1_rlvect_1(G,H,I))
                                            & v1_realset2(g1_rlvect_1(G,H,I))
                                            & v2_realset2(g1_rlvect_1(G,H,I))
                                            & l1_rlvect_1(g1_rlvect_1(G,H,I)) ) ) ) ) )
                            & ! [G] : 
                                ( m1_subset_1(G,B)
                               => ! [H] : 
                                    ( m1_subset_1(H,B)
                                   => ! [I] : 
                                        ( m1_subset_1(I,B)
                                       => ( k1_funct_1(E,k4_tarski(G,k1_funct_1(C,k4_tarski(H,I)))) = k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,H)),k1_funct_1(E,k4_tarski(G,I))))
                                          & k1_funct_1(E,k4_tarski(k1_funct_1(C,k4_tarski(G,H)),I)) = k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,I)),k1_funct_1(E,k4_tarski(H,I)))) ) ) ) ) ) ) ) ) ) ) ) ),
    file(realset2,d8_realset2),
    []).

fof(d9_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m3_realset1(C,A,B)
             => k4_realset1(A,B,C) = k1_realset1(C,k4_xboole_0(A,k1_tarski(B))) ) ) ) ),
    file(realset1,d9_realset1),
    []).

fof(d9_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ~ v1_realset1(B)
         => ( B = k2_realset2(A)
          <=> ? [C] : 
                ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B)
                & ? [D] : 
                    ( m1_subset_1(D,B)
                    & ? [E] : 
                        ( m3_realset1(E,B,D)
                        & ? [F] : 
                            ( m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D)))
                            & A = k1_realset2(B,C,E,D,F) ) ) ) ) ) ) ) ),
    file(realset2,d9_realset2),
    []).

fof(dt_g1_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( v1_rlvect_1(g1_rlvect_1(A,B,C))
        & l1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ),
    file(rlvect_1,g1_rlvect_1),
    []).

fof(dt_g3_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ( v3_vectsp_1(g3_vectsp_1(A,B,C,D,E))
        & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ),
    file(vectsp_1,g3_vectsp_1),
    []).

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

fof(dt_k1_realset1,axiom,(
    $true ),
    file(realset1,k1_realset1),
    []).

fof(dt_k1_realset2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_realset1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,k4_xboole_0(A,k5_realset1(A,D))) )
     => ( v3_vectsp_1(k1_realset2(A,B,C,D,E))
        & ~ v3_realset2(k1_realset2(A,B,C,D,E))
        & l3_vectsp_1(k1_realset2(A,B,C,D,E)) ) ) ),
    file(realset2,k1_realset2),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ~ v1_realset1(k2_realset2(A)) ) ),
    file(realset2,k2_realset2),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k3_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k3_realset2(A))
        & v1_funct_2(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A))
        & m2_relset_1(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) ) ) ),
    file(realset2,k3_realset2),
    []).

fof(dt_k4_realset1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_realset1(A)
        & m1_subset_1(B,A)
        & m3_realset1(C,A,B) )
     => ( v1_funct_1(k4_realset1(A,B,C))
        & v1_funct_2(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B)))
        & m2_relset_1(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) ) ) ),
    file(realset1,k4_realset1),
    []).

fof(dt_k4_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m1_subset_1(k4_realset2(A),k2_realset2(A)) ) ),
    file(realset2,k4_realset2),
    []).

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

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_realset1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_realset1(A)
        & m1_subset_1(B,A) )
     => m4_realset1(k5_realset1(A,B),A) ) ),
    file(realset1,k5_realset1),
    []).

fof(dt_k5_realset2,axiom,(
    ! [A] : 
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m3_realset1(k5_realset2(A),k2_realset2(A),k4_realset2(A)) ) ),
    file(realset2,k5_realset2),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

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_m3_realset1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m3_realset1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,k2_zfmisc_1(A,A),A)
            & m2_relset_1(C,k2_zfmisc_1(A,A),A) ) ) ) ),
    file(realset1,m3_realset1),
    []).

fof(dt_m4_realset1,axiom,(
    $true ),
    file(realset1,m4_realset1),
    []).

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_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    []).

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

fof(dt_u1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)) ) ),
    file(vectsp_1,u1_vectsp_1),
    []).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_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_m3_realset1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ? [C] : m3_realset1(C,A,B) ) ),
    file(realset1,m3_realset1),
    []).

fof(existence_m4_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ? [B] : m4_realset1(B,A) ) ),
    file(realset1,m4_realset1),
    []).

fof(fc1_realset1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k1_realset1(A,B)) ) ),
    file(realset1,fc1_realset1),
    []).

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_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(g1_rlvect_1(A,B,C))
        & v1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ),
    file(group_1,fc2_group_1),
    []).

fof(fc2_realset1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_realset1(A,B))
        & v1_funct_1(k1_realset1(A,B)) ) ) ),
    file(realset1,fc2_realset1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_realset1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_realset1(A)
        & m4_realset1(B,A) )
     => ~ v1_xboole_0(k4_xboole_0(A,B)) ) ),
    file(realset1,fc4_realset1),
    []).

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_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ! [D,E,F] : 
          ( g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(rlvect_1,g1_rlvect_1),
    []).

fof(free_g3_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ! [F,G,H,I,J] : 
          ( g3_vectsp_1(A,B,C,D,E) = g3_vectsp_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) ),
    file(vectsp_1,g3_vectsp_1),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

fof(rc1_realset2,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v1_realset2(A)
      & v2_realset2(A) ) ),
    file(realset2,rc1_realset2),
    []).

fof(rc1_rlvect_1,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & v1_rlvect_1(A) ) ),
    file(rlvect_1,rc1_rlvect_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_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_realset2,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & v3_realset2(A) ) ),
    file(realset2,rc2_realset2),
    []).

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_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ? [B] : 
          ( m4_realset1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(realset1,rc3_realset1),
    []).

fof(rc3_realset2,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & v3_vectsp_1(A)
      & ~ v3_realset2(A) ) ),
    file(realset2,rc3_realset2),
    []).

fof(rc4_realset2,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & v3_vectsp_1(A)
      & v4_realset2(A) ) ),
    file(realset2,rc4_realset2),
    []).

fof(rc4_rlvect_1,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A) ) ),
    file(rlvect_1,rc4_rlvect_1),
    []).

fof(redefinition_k5_realset1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_realset1(A)
        & m1_subset_1(B,A) )
     => k5_realset1(A,B) = k1_tarski(B) ) ),
    file(realset1,k5_realset1),
    []).

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(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_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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),
    []).