% Mizar problem: t21_topalg_4,topalg_4,879,21 
fof(t21_topalg_4,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] : 
                              ( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                             => ! [H] : 
                                  ( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                                 => ! [I] : 
                                      ( m1_borsuk_2(I,A,C,D)
                                     => ! [J] : 
                                          ( m1_borsuk_2(J,A,C,D)
                                         => ! [K] : 
                                              ( m1_borsuk_2(K,B,E,F)
                                             => ! [L] : 
                                                  ( m1_borsuk_2(L,B,E,F)
                                                 => ! [M] : 
                                                      ( m1_borsuk_6(M,A,C,D,I,J)
                                                     => ! [N] : 
                                                          ( m1_borsuk_6(N,B,E,F,K,L)
                                                         => ( ( I = k4_topalg_4(A,B,k5_topmetr,G)
                                                              & J = k4_topalg_4(A,B,k5_topmetr,H)
                                                              & K = k5_topalg_4(A,B,k5_topmetr,G)
                                                              & L = k5_topalg_4(A,B,k5_topmetr,H)
                                                              & r3_borsuk_2(A,C,D,I,J)
                                                              & r3_borsuk_2(B,E,F,K,L) )
                                                           => m1_borsuk_6(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc1_arytm_3,cc1_borsuk_2,cc1_finseq_1,cc1_relset_1,cc1_tops_1,cc1_xreal_0,cc2_arytm_3,cc2_tops_1,cc2_xreal_0,cc3_arytm_3,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc4_tops_1,cc4_xreal_0,cc5_tops_1,cc5_xreal_0,cc6_tops_1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_tarski,d13_borsuk_6,d1_binop_1,d5_tarski,d7_borsuk_2,dt_g1_pre_topc,dt_k13_funct_3,dt_k15_mcart_1,dt_k16_mcart_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_borsuk_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_topalg_4,dt_k3_topmetr,dt_k4_tarski,dt_k4_topalg_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_topalg_4,dt_k5_topmetr,dt_k6_borsuk_1,dt_k8_borsuk_1,dt_k8_funct_2,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_borsuk_2,dt_m1_borsuk_6,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_borsuk_2,existence_m1_borsuk_6,existence_m1_pre_topc,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,fc2_borsuk_1,fc2_finseq_1,fc4_borsuk_2,fc5_borsuk_1,fc6_borsuk_2,fc7_borsuk_2,free_g1_pre_topc,l27_topalg_4,rc1_arytm_3,rc1_finseq_1,rc1_tops_1,rc1_xreal_0,rc2_finseq_1,rc2_tops_1,rc2_xreal_0,rc3_finseq_1,rc3_struct_0,rc3_tops_1,rc3_xreal_0,rc4_tops_1,rc4_xreal_0,rc5_struct_0,rc5_tops_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k3_topalg_4,redefinition_k4_topalg_4,redefinition_k5_numbers,redefinition_k5_topalg_4,redefinition_k5_topmetr,redefinition_k8_borsuk_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,symmetry_r3_borsuk_2,t1_numerals,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(topalg_4,t21_topalg_4)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    []).

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

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_borsuk_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(borsuk_2,cc1_borsuk_2),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_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_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) ) ) ) ) ),
    file(tops_1,cc1_tops_1),
    []).

fof(cc1_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc2_tops_1),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v3_tops_1(B,A) ) ) ) ),
    file(tops_1,cc3_tops_1),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc4_borsuk_2,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v3_struct_0(A)
       => v2_t_0topsp(A) ) ) ),
    file(borsuk_2,cc4_borsuk_2),
    []).

fof(cc4_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tops_1(B,A)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc4_tops_1),
    []).

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
              & v2_tops_1(B,A) )
           => ( v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc5_tops_1),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc6_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v3_tops_1(B,A) )
           => ( v1_xboole_0(B)
              & v3_pre_topc(B,A)
              & v4_pre_topc(B,A)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc6_tops_1),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

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

fof(d13_borsuk_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] : 
                      ( m1_borsuk_2(E,A,B,C)
                     => ( r3_borsuk_2(A,B,C,D,E)
                       => ! [F] : 
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
                              & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) )
                           => ( m1_borsuk_6(F,A,B,C,D,E)
                            <=> ( v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),A)
                                & ! [G] : 
                                    ( m1_subset_1(G,u1_struct_0(k5_topmetr))
                                   => ( k1_binop_1(F,G,0) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),D,G)
                                      & k1_binop_1(F,G,1) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,G)
                                      & ! [H] : 
                                          ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                         => ( k1_binop_1(F,0,H) = B
                                            & k1_binop_1(F,1,H) = C ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(borsuk_6,d13_borsuk_6),
    []).

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

fof(d7_borsuk_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] : 
                      ( m1_borsuk_2(E,A,B,C)
                     => ( r3_borsuk_2(A,B,C,D,E)
                      <=> ? [F] : 
                            ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
                            & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
                            & v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),A)
                            & ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(k5_topmetr))
                               => ( k1_binop_1(F,G,0) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),D,G)
                                  & k1_binop_1(F,G,1) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,G)
                                  & ! [H] : 
                                      ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                     => ( k1_binop_1(F,0,H) = B
                                        & k1_binop_1(F,1,H) = C ) ) ) ) ) ) ) ) ) ) ) ),
    file(borsuk_2,d7_borsuk_2),
    []).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(dt_k13_funct_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k13_funct_3(A,B))
        & v1_funct_1(k13_funct_3(A,B)) ) ) ),
    file(funct_3,k13_funct_3),
    []).

fof(dt_k15_mcart_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k15_mcart_1(A))
        & v1_funct_1(k15_mcart_1(A)) ) ) ),
    file(mcart_1,k15_mcart_1),
    []).

fof(dt_k16_mcart_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k16_mcart_1(A))
        & v1_funct_1(k16_mcart_1(A)) ) ) ),
    file(mcart_1,k16_mcart_1),
    []).

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

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

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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_k22_borsuk_1,axiom,(
    l1_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,k22_borsuk_1),
    []).

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_topalg_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
        & m1_relset_1(D,u1_struct_0(C),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
     => ( v1_funct_1(k3_topalg_4(A,B,C,D,E))
        & v1_funct_2(k3_topalg_4(A,B,C,D,E),u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
        & m2_relset_1(k3_topalg_4(A,B,C,D,E),u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) ) ) ),
    file(topalg_4,k3_topalg_4),
    []).

fof(dt_k3_topmetr,axiom,
    ( v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & l1_pre_topc(k3_topmetr) ),
    file(topmetr,k3_topmetr),
    []).

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

fof(dt_k4_topalg_4,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
        & m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
     => ( v1_funct_1(k4_topalg_4(A,B,C,D))
        & v1_funct_2(k4_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(A))
        & m2_relset_1(k4_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(A)) ) ) ),
    file(topalg_4,k4_topalg_4),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_topalg_4,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
        & m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
     => ( v1_funct_1(k5_topalg_4(A,B,C,D))
        & v1_funct_2(k5_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(B))
        & m2_relset_1(k5_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(B)) ) ) ),
    file(topalg_4,k5_topalg_4),
    []).

fof(dt_k5_topmetr,axiom,
    ( v1_pre_topc(k5_topmetr)
    & m1_pre_topc(k5_topmetr,k3_topmetr) ),
    file(topmetr,k5_topmetr),
    []).

fof(dt_k6_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B))
        & l1_pre_topc(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,k6_borsuk_1),
    []).

fof(dt_k8_borsuk_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))) ) ),
    file(borsuk_1,k8_borsuk_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(dt_m1_borsuk_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ! [D] : 
          ( m1_borsuk_2(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
            & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) ) ) ) ),
    file(borsuk_2,m1_borsuk_2),
    []).

fof(dt_m1_borsuk_6,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_borsuk_2(D,A,B,C)
        & m1_borsuk_2(E,A,B,C) )
     => ! [F] : 
          ( m1_borsuk_6(F,A,B,C,D,E)
         => ( v1_funct_1(F)
            & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
            & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) ) ) ) ),
    file(borsuk_6,m1_borsuk_6),
    []).

fof(dt_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => l1_pre_topc(B) ) ) ),
    file(pre_topc,m1_pre_topc),
    []).

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_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    []).

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

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(existence_m1_borsuk_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ? [D] : m1_borsuk_2(D,A,B,C) ) ),
    file(borsuk_2,m1_borsuk_2),
    []).

fof(existence_m1_borsuk_6,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_borsuk_2(D,A,B,C)
        & m1_borsuk_2(E,A,B,C) )
     => ? [F] : m1_borsuk_6(F,A,B,C,D,E) ) ),
    file(borsuk_6,m1_borsuk_6),
    []).

fof(existence_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_pre_topc(B,A) ) ),
    file(pre_topc,m1_pre_topc),
    []).

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(fc2_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,fc2_borsuk_1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc4_borsuk_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v2_t_0topsp(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B))
        & v2_t_0topsp(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_2,fc4_borsuk_2),
    []).

fof(fc5_borsuk_1,axiom,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,fc5_borsuk_1),
    []).

fof(fc6_borsuk_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_compts_1(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v3_compts_1(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B))
        & v2_t_0topsp(k6_borsuk_1(A,B))
        & v3_compts_1(k6_borsuk_1(A,B))
        & v3_yellow_8(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_2,fc6_borsuk_2),
    []).

fof(fc7_borsuk_2,axiom,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1)
    & v2_t_0topsp(k22_borsuk_1)
    & v2_compts_1(k22_borsuk_1)
    & v3_compts_1(k22_borsuk_1)
    & v3_yellow_8(k22_borsuk_1) ),
    file(borsuk_2,fc7_borsuk_2),
    []).

fof(free_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(l27_topalg_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] : 
                              ( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                             => ! [H] : 
                                  ( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                                 => ! [I] : 
                                      ( m1_borsuk_2(I,A,C,D)
                                     => ! [J] : 
                                          ( m1_borsuk_2(J,A,C,D)
                                         => ! [K] : 
                                              ( m1_borsuk_2(K,B,E,F)
                                             => ! [L] : 
                                                  ( m1_borsuk_2(L,B,E,F)
                                                 => ! [M] : 
                                                      ( m1_borsuk_6(M,A,C,D,I,J)
                                                     => ! [N] : 
                                                          ( m1_borsuk_6(N,B,E,F,K,L)
                                                         => ( ( I = k4_topalg_4(A,B,k5_topmetr,G)
                                                              & J = k4_topalg_4(A,B,k5_topmetr,H)
                                                              & K = k5_topalg_4(A,B,k5_topmetr,G)
                                                              & L = k5_topalg_4(A,B,k5_topmetr,H)
                                                              & r3_borsuk_2(A,C,D,I,J)
                                                              & r3_borsuk_2(B,E,F,K,L) )
                                                           => ( v5_pre_topc(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),k6_borsuk_1(k5_topmetr,k5_topmetr),k6_borsuk_1(A,B))
                                                              & ! [O] : 
                                                                  ( m1_subset_1(O,u1_struct_0(k22_borsuk_1))
                                                                 => ( k1_binop_1(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),O,0) = k8_funct_2(u1_struct_0(k22_borsuk_1),u1_struct_0(k6_borsuk_1(A,B)),G,O)
                                                                    & k1_binop_1(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),O,1) = k8_funct_2(u1_struct_0(k22_borsuk_1),u1_struct_0(k6_borsuk_1(A,B)),H,O)
                                                                    & ! [P] : 
                                                                        ( m1_subset_1(P,u1_struct_0(k22_borsuk_1))
                                                                       => ( k1_binop_1(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),0,P) = k8_borsuk_1(A,B,C,E)
                                                                          & k1_binop_1(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),1,P) = k8_borsuk_1(A,B,D,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(topalg_4,l27_topalg_4),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A) ) ) ),
    file(tops_1,rc1_tops_1),
    []).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    []).

fof(rc2_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc2_tops_1),
    []).

fof(rc2_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

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

fof(rc3_tops_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc3_tops_1),
    []).

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A) ) ) ),
    file(tops_1,rc4_tops_1),
    []).

fof(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_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(rc5_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A)
          & v3_tops_1(B,A) ) ) ),
    file(tops_1,rc5_tops_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k3_topalg_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
        & m1_relset_1(D,u1_struct_0(C),u1_struct_0(A))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
        & m1_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
     => k3_topalg_4(A,B,C,D,E) = k13_funct_3(D,E) ) ),
    file(topalg_4,k3_topalg_4),
    []).

fof(redefinition_k4_topalg_4,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
        & m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
     => k4_topalg_4(A,B,C,D) = k15_mcart_1(D) ) ),
    file(topalg_4,k4_topalg_4),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k5_topalg_4,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
        & m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
     => k5_topalg_4(A,B,C,D) = k16_mcart_1(D) ) ),
    file(topalg_4,k5_topalg_4),
    []).

fof(redefinition_k5_topmetr,axiom,(
    k5_topmetr = k22_borsuk_1 ),
    file(topmetr,k5_topmetr),
    []).

fof(redefinition_k8_borsuk_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k8_borsuk_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(borsuk_1,k8_borsuk_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_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(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(symmetry_r3_borsuk_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_borsuk_2(D,A,B,C)
        & m1_borsuk_2(E,A,B,C) )
     => ( r3_borsuk_2(A,B,C,D,E)
       => r3_borsuk_2(A,B,C,E,D) ) ) ),
    file(borsuk_2,r3_borsuk_2),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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),
    []).