SET007 Axioms: SET007+833.ax


%------------------------------------------------------------------------------
% File     : SET007+833 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Fundamental Group
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : topalg_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   2 unit)
%            Number of atoms       :  822 (  56 equality)
%            Maximal formula depth :   43 (  13 average)
%            Number of connectives :  814 (  74 ~  ;   0  |; 288  &)
%                                         (  10 <=>; 442 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-6 arity)
%            Number of functors    :   50 (   6 constant; 0-6 arity)
%            Number of variables   :  446 (   0 singleton; 443 !;   3 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_topalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_topalg_1(A,B)) ) )).

fof(fc2_topalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k2_topalg_1(A,B))
        & ~ v1_xboole_0(k2_topalg_1(A,B))
        & v1_relat_2(k2_topalg_1(A,B))
        & v3_relat_2(k2_topalg_1(A,B))
        & v8_relat_2(k2_topalg_1(A,B))
        & v1_partfun1(k2_topalg_1(A,B),k1_topalg_1(A,B),k1_topalg_1(A,B)) ) ) )).

fof(fc3_topalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_topalg_1(A,B))
        & v1_group_1(k3_topalg_1(A,B)) ) ) )).

fof(fc4_topalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_topalg_1(A,B))
        & v1_group_1(k3_topalg_1(A,B))
        & v2_group_1(k3_topalg_1(A,B))
        & v3_group_1(k3_topalg_1(A,B))
        & v4_group_1(k3_topalg_1(A,B)) ) ) )).

fof(fc5_topalg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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) )
     => ( v1_relat_1(k4_topalg_1(A,B,C,D))
        & v1_funct_1(k4_topalg_1(A,B,C,D))
        & v2_funct_1(k4_topalg_1(A,B,C,D))
        & v1_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
        & v2_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) )).

fof(cc1_topalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A)))
        & m1_borsuk_2(D,k15_euclid(A),B,C)
        & m1_borsuk_2(E,k15_euclid(A),B,C) )
     => ! [F] :
          ( m1_borsuk_6(F,k15_euclid(A),B,C,D,E)
         => ( v1_relat_1(F)
            & v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),k15_euclid(A)) ) ) ) )).

fof(fc6_topalg_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A))) )
     => ( ~ v3_struct_0(k3_topalg_1(k15_euclid(A),B))
        & v1_group_1(k3_topalg_1(k15_euclid(A),B))
        & v2_group_1(k3_topalg_1(k15_euclid(A),B))
        & v3_group_1(k3_topalg_1(k15_euclid(A),B))
        & v4_group_1(k3_topalg_1(k15_euclid(A),B))
        & v3_realset2(k3_topalg_1(k15_euclid(A),B)) ) ) )).

fof(t1_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),k2_tops_2(A,B,C),C) = k7_grcat_1(B)
                  & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,k2_tops_2(A,B,C)) = k7_grcat_1(A) )
               => v4_group_6(C,A,B) ) ) ) ) )).

fof(t2_topalg_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
         => ( A = k2_rcomp_2(B,np__1)
           => k3_subset_1(u1_struct_0(k22_borsuk_1),A) = k1_rcomp_1(np__0,B) ) ) ) )).

fof(t3_topalg_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
         => ( A = k1_rcomp_2(np__0,B)
           => k3_subset_1(u1_struct_0(k22_borsuk_1),A) = k1_rcomp_1(B,np__1) ) ) ) )).

fof(t4_topalg_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
         => ( A = k2_rcomp_2(B,np__1)
           => v3_pre_topc(A,k22_borsuk_1) ) ) ) )).

fof(t5_topalg_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
         => ( A = k1_rcomp_2(np__0,B)
           => v3_pre_topc(A,k22_borsuk_1) ) ) ) )).

fof(t6_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_finseq_2(B,k1_numbers))
             => k10_rvsum_1(B,A,k6_rvsum_1(B,C)) = k6_rvsum_1(B,k10_rvsum_1(B,A,C)) ) ) ) )).

fof(t7_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_finseq_2(B,k1_numbers))
             => ! [D] :
                  ( m1_subset_1(D,k4_finseq_2(B,k1_numbers))
                 => k10_rvsum_1(B,A,k8_rvsum_1(B,C,D)) = k8_rvsum_1(B,k10_rvsum_1(B,A,C),k10_rvsum_1(B,A,D)) ) ) ) ) )).

fof(t8_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k4_finseq_2(C,k1_numbers))
                 => k10_rvsum_1(C,k6_xcmplx_0(A,B),D) = k8_rvsum_1(C,k10_rvsum_1(C,A,D),k10_rvsum_1(C,B,D)) ) ) ) ) )).

fof(t9_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k4_finseq_2(A,k1_numbers))
         => ! [C] :
              ( m1_subset_1(C,k4_finseq_2(A,k1_numbers))
             => ! [D] :
                  ( m1_subset_1(D,k4_finseq_2(A,k1_numbers))
                 => ! [E] :
                      ( m1_subset_1(E,k4_finseq_2(A,k1_numbers))
                     => k8_rvsum_1(A,k4_rvsum_1(A,B,C),k4_rvsum_1(A,D,E)) = k4_rvsum_1(A,k8_rvsum_1(A,B,D),k8_rvsum_1(A,C,E)) ) ) ) ) ) )).

fof(t10_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k1_euclid(B))
             => ( ( r1_xreal_0(np__0,A)
                  & r1_xreal_0(A,np__1) )
               => r1_xreal_0(k12_euclid(k9_euclid(B,A,C)),k12_euclid(C)) ) ) ) ) )).

fof(t11_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k22_borsuk_1))
             => r1_xreal_0(k12_euclid(k9_euclid(A,C,B)),k12_euclid(B)) ) ) ) )).

fof(t12_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k14_euclid(C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k14_euclid(C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k14_euclid(C)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k14_euclid(C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k14_euclid(C)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k15_euclid(C)))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(k15_euclid(C)))
                                             => ! [L] :
                                                  ( m1_subset_1(L,u1_struct_0(k15_euclid(C)))
                                                 => ! [M] :
                                                      ( m1_subset_1(M,u1_struct_0(k15_euclid(C)))
                                                     => ~ ( D = J
                                                          & E = K
                                                          & F = L
                                                          & G = M
                                                          & H = k17_euclid(C,J,L)
                                                          & I = k17_euclid(C,K,M)
                                                          & ~ r1_xreal_0(A,k4_metric_1(k14_euclid(C),D,E))
                                                          & ~ r1_xreal_0(B,k4_metric_1(k14_euclid(C),F,G))
                                                          & r1_xreal_0(k2_xcmplx_0(A,B),k4_metric_1(k14_euclid(C),H,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(C)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k14_euclid(C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k14_euclid(C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k14_euclid(C)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k15_euclid(C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k15_euclid(C)))
                                     => ~ ( D = H
                                          & E = I
                                          & F = k18_euclid(A,C,H)
                                          & G = k18_euclid(A,C,I)
                                          & ~ r1_xreal_0(B,k4_metric_1(k14_euclid(C),D,E))
                                          & A != np__0
                                          & r1_xreal_0(k3_xcmplx_0(k18_complex1(A),B),k4_metric_1(k14_euclid(C),F,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k14_euclid(E)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k14_euclid(E)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k14_euclid(E)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k14_euclid(E)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k14_euclid(E)))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(k14_euclid(E)))
                                             => ! [L] :
                                                  ( m1_subset_1(L,u1_struct_0(k15_euclid(E)))
                                                 => ! [M] :
                                                      ( m1_subset_1(M,u1_struct_0(k15_euclid(E)))
                                                     => ! [N] :
                                                          ( m1_subset_1(N,u1_struct_0(k15_euclid(E)))
                                                         => ! [O] :
                                                              ( m1_subset_1(O,u1_struct_0(k15_euclid(E)))
                                                             => ~ ( F = L
                                                                  & G = M
                                                                  & H = N
                                                                  & I = O
                                                                  & J = k17_euclid(E,k18_euclid(A,E,L),k18_euclid(B,E,N))
                                                                  & K = k17_euclid(E,k18_euclid(A,E,M),k18_euclid(B,E,O))
                                                                  & ~ r1_xreal_0(C,k4_metric_1(k14_euclid(E),F,G))
                                                                  & ~ r1_xreal_0(D,k4_metric_1(k14_euclid(E),H,I))
                                                                  & A != np__0
                                                                  & B != np__0
                                                                  & r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k18_complex1(A),C),k3_xcmplx_0(k18_complex1(B),D)),k4_metric_1(k14_euclid(E),J,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_topalg_1,axiom,(
    $true )).

fof(t16_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k15_euclid(B)))
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(k15_euclid(B))) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(k15_euclid(B)))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(k15_euclid(B))) )
                     => ( ( v5_pre_topc(D,C,k15_euclid(B))
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(C))
                             => k7_yellow_2(u1_struct_0(C),k15_euclid(B),E,F) = k18_euclid(A,B,k7_yellow_2(u1_struct_0(C),k15_euclid(B),D,F)) ) )
                       => v5_pre_topc(E,C,k15_euclid(B)) ) ) ) ) ) ) )).

fof(t17_topalg_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(D),u1_struct_0(k15_euclid(C)))
                        & m2_relset_1(E,u1_struct_0(D),u1_struct_0(k15_euclid(C))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(D),u1_struct_0(k15_euclid(C)))
                            & m2_relset_1(F,u1_struct_0(D),u1_struct_0(k15_euclid(C))) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(D),u1_struct_0(k15_euclid(C)))
                                & m2_relset_1(G,u1_struct_0(D),u1_struct_0(k15_euclid(C))) )
                             => ( ( v5_pre_topc(E,D,k15_euclid(C))
                                  & v5_pre_topc(F,D,k15_euclid(C))
                                  & ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(D))
                                     => k7_yellow_2(u1_struct_0(D),k15_euclid(C),G,H) = k17_euclid(C,k18_euclid(A,C,k7_yellow_2(u1_struct_0(D),k15_euclid(C),E,H)),k18_euclid(B,C,k7_yellow_2(u1_struct_0(D),k15_euclid(C),F,H))) ) )
                               => v5_pre_topc(G,D,k15_euclid(C)) ) ) ) ) ) ) ) ) )).

fof(t18_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A))) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k22_borsuk_1))
                   => k1_binop_1(B,C,D) = k18_euclid(k6_xcmplx_0(np__1,D),A,C) ) )
           => v5_pre_topc(B,k6_borsuk_1(k15_euclid(A),k22_borsuk_1),k15_euclid(A)) ) ) ) )).

fof(t19_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A))) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k22_borsuk_1))
                   => k1_binop_1(B,C,D) = k18_euclid(D,A,C) ) )
           => v5_pre_topc(B,k6_borsuk_1(k15_euclid(A),k22_borsuk_1),k15_euclid(A)) ) ) ) )).

fof(t20_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,C,D) )
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,C)
                       => ! [F] :
                            ( m1_borsuk_2(F,A,C,D)
                           => r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,F),k2_borsuk_2(A,C,D,F))) ) ) ) ) ) ) ) )).

fof(t21_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,C,D)
                         => r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,F),k2_borsuk_2(A,C,D,F))) ) ) ) ) ) ) )).

fof(t22_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,D,C) )
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,C)
                       => ! [F] :
                            ( m1_borsuk_2(F,A,D,C)
                           => r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,k2_borsuk_2(A,D,C,F)),F)) ) ) ) ) ) ) ) )).

fof(t23_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,D,C)
                         => r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,k2_borsuk_2(A,D,C,F)),F)) ) ) ) ) ) ) )).

fof(t24_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,D,B) )
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,C)
                       => ! [F] :
                            ( m1_borsuk_2(F,A,D,B)
                           => r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,k2_borsuk_2(A,D,B,F),F),E)) ) ) ) ) ) ) ) )).

fof(t25_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,D,B)
                         => r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,k2_borsuk_2(A,D,B,F),F),E)) ) ) ) ) ) ) )).

fof(t26_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,B,D) )
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,C)
                       => ! [F] :
                            ( m1_borsuk_2(F,A,B,D)
                           => r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,F,k2_borsuk_2(A,B,D,F)),E)) ) ) ) ) ) ) ) )).

fof(t27_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,D)
                         => r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,F,k2_borsuk_2(A,B,D,F)),E)) ) ) ) ) ) ) )).

fof(t28_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,D,C) )
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,C)
                       => ! [F] :
                            ( m1_borsuk_2(F,A,B,C)
                           => ! [G] :
                                ( m1_borsuk_2(G,A,C,D)
                               => ( r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,G))
                                 => r3_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t29_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,C,D)
                             => ( r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,G))
                               => r4_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) )).

fof(t30_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,B,D) )
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,C)
                       => ! [F] :
                            ( m1_borsuk_2(F,A,B,C)
                           => ! [G] :
                                ( m1_borsuk_2(G,A,D,B)
                               => ( r3_borsuk_2(A,D,C,k1_borsuk_2(A,D,B,C,G,E),k1_borsuk_2(A,D,B,C,G,F))
                                 => r3_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t31_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,D,B)
                             => ( r4_borsuk_2(A,D,C,k1_borsuk_2(A,D,B,C,G,E),k1_borsuk_2(A,D,B,C,G,F))
                               => r4_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) )).

fof(t32_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_borsuk_6(A,B,C)
                              & r1_borsuk_6(A,C,D)
                              & r1_borsuk_6(A,D,E)
                              & r1_borsuk_6(A,E,F) )
                           => ! [G] :
                                ( m1_borsuk_2(G,A,B,C)
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,C,D)
                                   => ! [I] :
                                        ( m1_borsuk_2(I,A,D,E)
                                       => ! [J] :
                                            ( m1_borsuk_2(J,A,E,F)
                                           => r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t33_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_borsuk_2(G,A,B,C)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,C,D)
                                 => ! [I] :
                                      ( m1_borsuk_2(I,A,D,E)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,A,E,F)
                                         => r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J)) ) ) ) ) ) ) ) ) ) ) )).

fof(t34_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_borsuk_6(A,B,C)
                              & r1_borsuk_6(A,C,D)
                              & r1_borsuk_6(A,D,E)
                              & r1_borsuk_6(A,E,F) )
                           => ! [G] :
                                ( m1_borsuk_2(G,A,B,C)
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,C,D)
                                   => ! [I] :
                                        ( m1_borsuk_2(I,A,D,E)
                                       => ! [J] :
                                            ( m1_borsuk_2(J,A,E,F)
                                           => r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,C,F,G,k1_borsuk_2(A,C,E,F,k1_borsuk_2(A,C,D,E,H,I),J))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_borsuk_2(G,A,B,C)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,C,D)
                                 => ! [I] :
                                      ( m1_borsuk_2(I,A,D,E)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,A,E,F)
                                         => r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,C,F,G,k1_borsuk_2(A,C,E,F,k1_borsuk_2(A,C,D,E,H,I),J))) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_borsuk_6(A,B,C)
                              & r1_borsuk_6(A,C,D)
                              & r1_borsuk_6(A,D,E)
                              & r1_borsuk_6(A,E,F) )
                           => ! [G] :
                                ( m1_borsuk_2(G,A,B,C)
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,C,D)
                                   => ! [I] :
                                        ( m1_borsuk_2(I,A,D,E)
                                       => ! [J] :
                                            ( m1_borsuk_2(J,A,E,F)
                                           => r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J),k1_borsuk_2(A,B,D,F,k1_borsuk_2(A,B,C,D,G,H),k1_borsuk_2(A,D,E,F,I,J))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_borsuk_2(G,A,B,C)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,C,D)
                                 => ! [I] :
                                      ( m1_borsuk_2(I,A,D,E)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,A,E,F)
                                         => r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J),k1_borsuk_2(A,B,D,F,k1_borsuk_2(A,B,C,D,G,H),k1_borsuk_2(A,D,E,F,I,J))) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_borsuk_6(A,B,C)
                          & r1_borsuk_6(A,C,D)
                          & r1_borsuk_6(A,C,E) )
                       => ! [F] :
                            ( m1_borsuk_2(F,A,B,C)
                           => ! [G] :
                                ( m1_borsuk_2(G,A,E,C)
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,C,D)
                                   => r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,k1_borsuk_2(A,B,E,C,k1_borsuk_2(A,B,C,E,F,k2_borsuk_2(A,E,C,G)),G),H),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t39_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,D,C)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,C,E)
                                 => r4_borsuk_2(A,B,E,k1_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,F,k2_borsuk_2(A,D,C,G)),G),H),k1_borsuk_2(A,B,C,E,F,H)) ) ) ) ) ) ) ) ) )).

fof(t40_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_borsuk_6(A,B,C)
                          & r1_borsuk_6(A,B,D)
                          & r1_borsuk_6(A,D,E) )
                       => ! [F] :
                            ( m1_borsuk_2(F,A,B,C)
                           => ! [G] :
                                ( m1_borsuk_2(G,A,D,E)
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,B,D)
                                   => r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,B,D,k1_borsuk_2(A,B,C,B,F,k2_borsuk_2(A,B,C,F)),H),G),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) ) )).

fof(t41_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,D,E)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,B,D)
                                 => r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,B,D,k1_borsuk_2(A,B,C,B,F,k2_borsuk_2(A,B,C,F)),H),G),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) )).

fof(t42_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_borsuk_6(A,B,C)
                          & r1_borsuk_6(A,B,D)
                          & r1_borsuk_6(A,E,D) )
                       => ! [F] :
                            ( m1_borsuk_2(F,A,B,C)
                           => ! [G] :
                                ( m1_borsuk_2(G,A,D,E)
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,B,D)
                                   => r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,k1_borsuk_2(A,C,B,D,k2_borsuk_2(A,B,C,F),H),G)),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) ) )).

fof(t43_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,D,E)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,B,D)
                                 => r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,k1_borsuk_2(A,C,B,D,k2_borsuk_2(A,B,C,F),H),G)),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) )).

fof(t44_topalg_1,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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_borsuk_6(A,B,C)
                                  & r1_borsuk_6(A,C,D)
                                  & r1_borsuk_6(A,D,E)
                                  & r1_borsuk_6(A,E,F)
                                  & r1_borsuk_6(A,B,G) )
                               => ! [H] :
                                    ( m1_borsuk_2(H,A,B,C)
                                   => ! [I] :
                                        ( m1_borsuk_2(I,A,C,D)
                                       => ! [J] :
                                            ( m1_borsuk_2(J,A,D,E)
                                           => ! [K] :
                                                ( m1_borsuk_2(K,A,E,F)
                                               => ! [L] :
                                                    ( m1_borsuk_2(L,A,G,D)
                                                   => r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,H,k1_borsuk_2(A,C,D,E,I,J)),K),k1_borsuk_2(A,B,G,F,k1_borsuk_2(A,B,D,G,k1_borsuk_2(A,B,C,D,H,I),k2_borsuk_2(A,G,D,L)),k1_borsuk_2(A,G,E,F,k1_borsuk_2(A,G,D,E,L,J),K))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t45_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,B,C)
                                 => ! [I] :
                                      ( m1_borsuk_2(I,A,C,D)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,A,D,E)
                                         => ! [K] :
                                              ( m1_borsuk_2(K,A,E,F)
                                             => ! [L] :
                                                  ( m1_borsuk_2(L,A,G,D)
                                                 => r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,H,k1_borsuk_2(A,C,D,E,I,J)),K),k1_borsuk_2(A,B,G,F,k1_borsuk_2(A,B,D,G,k1_borsuk_2(A,B,C,D,H,I),k2_borsuk_2(A,G,D,L)),k1_borsuk_2(A,G,E,F,k1_borsuk_2(A,G,D,E,L,J),K))) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( C = k1_topalg_1(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> m1_borsuk_2(D,A,B,B) ) ) ) ) )).

fof(d2_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_relset_1(C,k1_topalg_1(A,B),k1_topalg_1(A,B))
             => ( C = k2_topalg_1(A,B)
              <=> ! [D] :
                    ( m1_borsuk_2(D,A,B,B)
                   => ! [E] :
                        ( m1_borsuk_2(E,A,B,B)
                       => ( r2_hidden(k4_tarski(D,E),C)
                        <=> r3_borsuk_2(A,B,B,D,E) ) ) ) ) ) ) ) )).

fof(t46_topalg_1,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_borsuk_2(C,A,B,B)
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,B)
                 => ( r2_hidden(D,k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),C))
                  <=> r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) )).

fof(t47_topalg_1,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_borsuk_2(C,A,B,B)
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,B)
                 => ( k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),C) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),D)
                  <=> r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) )).

fof(d3_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_group_1(C)
                & l1_group_1(C) )
             => ( C = k3_topalg_1(A,B)
              <=> ( u1_struct_0(C) = k8_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(C))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(C))
                         => ? [F] :
                              ( m1_borsuk_2(F,A,B,B)
                              & ? [G] :
                                  ( m1_borsuk_2(G,A,B,B)
                                  & D = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),F)
                                  & E = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),G)
                                  & k1_binop_1(u1_group_1(C),D,E) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),k1_borsuk_2(A,B,B,B,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t48_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r2_hidden(C,u1_struct_0(k3_topalg_1(A,B)))
            <=> ? [D] :
                  ( m1_borsuk_2(D,A,B,B)
                  & C = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),D) ) ) ) ) )).

fof(d4_topalg_1,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)
                 => ( r1_borsuk_6(A,B,C)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
                          & m2_relset_1(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) )
                       => ( E = k4_topalg_1(A,B,C,D)
                        <=> ! [F] :
                              ( m1_borsuk_2(F,A,C,C)
                             => k1_funct_1(E,k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),F)) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),k1_borsuk_2(A,B,C,B,k1_borsuk_2(A,B,C,C,D,F),k2_borsuk_2(A,B,C,D))) ) ) ) ) ) ) ) ) )).

fof(t49_topalg_1,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)
                     => ( ( r1_borsuk_6(A,B,C)
                          & r3_borsuk_2(A,B,C,D,E) )
                       => k4_topalg_1(A,B,C,D) = k4_topalg_1(A,B,C,E) ) ) ) ) ) ) )).

fof(t50_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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)
                     => ( r4_borsuk_2(A,B,C,D,E)
                       => k4_topalg_1(A,B,C,D) = k4_topalg_1(A,B,C,E) ) ) ) ) ) ) )).

fof(t51_topalg_1,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)
                 => ( r1_borsuk_6(A,B,C)
                   => ( v1_funct_1(k4_topalg_1(A,B,C,D))
                      & v1_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
                      & v1_group_6(k4_topalg_1(A,B,C,D),k3_topalg_1(A,C),k3_topalg_1(A,B))
                      & m2_relset_1(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ) ) ) ) )).

fof(t52_topalg_1,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)
                 => ( r1_borsuk_6(A,B,C)
                   => v2_funct_1(k4_topalg_1(A,B,C,D)) ) ) ) ) ) )).

fof(t53_topalg_1,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)
                 => ( r1_borsuk_6(A,B,C)
                   => v2_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ) ) ) )).

fof(t54_topalg_1,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)
                 => ( r1_borsuk_6(A,B,C)
                   => k2_tops_2(k3_topalg_1(A,C),k3_topalg_1(A,B),k4_topalg_1(A,B,C,D)) = k4_topalg_1(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) ) )).

fof(t55_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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)
                 => k2_tops_2(k3_topalg_1(A,C),k3_topalg_1(A,B),k5_topalg_1(A,B,C,D)) = k5_topalg_1(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) )).

fof(t56_topalg_1,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)
                 => ( r1_borsuk_6(A,B,C)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
                          & v1_group_6(E,k3_topalg_1(A,C),k3_topalg_1(A,B))
                          & m2_relset_1(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) )
                       => ( E = k4_topalg_1(A,B,C,D)
                         => v4_group_6(E,k3_topalg_1(A,C),k3_topalg_1(A,B)) ) ) ) ) ) ) ) )).

fof(t57_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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)
                 => v4_group_6(k5_topalg_1(A,B,C,D),k3_topalg_1(A,C),k3_topalg_1(A,B)) ) ) ) ) )).

fof(t58_topalg_1,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))
             => ( r1_borsuk_6(A,B,C)
               => r2_group_6(k3_topalg_1(A,B),k3_topalg_1(A,C)) ) ) ) ) )).

fof(t59_topalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_group_6(k3_topalg_1(A,B),k3_topalg_1(A,C)) ) ) ) )).

fof(d5_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_borsuk_2(D,k15_euclid(A),B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,k15_euclid(A),B,C)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
                            & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A))) )
                         => ( F = k6_topalg_1(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_subset_1(G,u1_struct_0(k22_borsuk_1))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k22_borsuk_1))
                                   => k1_binop_1(F,G,H) = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,H),A,k7_yellow_2(u1_struct_0(k22_borsuk_1),k15_euclid(A),D,G)),k18_euclid(H,A,k7_yellow_2(u1_struct_0(k22_borsuk_1),k15_euclid(A),E,G))) ) ) ) ) ) ) ) ) ) )).

fof(t60_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_borsuk_2(D,k15_euclid(A),B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,k15_euclid(A),B,C)
                     => r4_borsuk_2(k15_euclid(A),B,C,D,E) ) ) ) ) ) )).

fof(t61_topalg_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_borsuk_2(C,k15_euclid(A),B,B)
             => u1_struct_0(k3_topalg_1(k15_euclid(A),B)) = k1_tarski(k6_eqrel_1(k1_topalg_1(k15_euclid(A),B),k2_topalg_1(k15_euclid(A),B),C)) ) ) ) )).

fof(dt_k1_topalg_1,axiom,(
    $true )).

fof(dt_k2_topalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m2_relset_1(k2_topalg_1(A,B),k1_topalg_1(A,B),k1_topalg_1(A,B)) ) )).

fof(dt_k3_topalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_group_1(k3_topalg_1(A,B))
        & l1_group_1(k3_topalg_1(A,B)) ) ) )).

fof(dt_k4_topalg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ 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) )
     => ( v1_funct_1(k4_topalg_1(A,B,C,D))
        & v1_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
        & m2_relset_1(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) )).

fof(dt_k5_topalg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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) )
     => ( v1_funct_1(k5_topalg_1(A,B,C,D))
        & v1_funct_2(k5_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
        & v1_group_6(k5_topalg_1(A,B,C,D),k3_topalg_1(A,C),k3_topalg_1(A,B))
        & m2_relset_1(k5_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) )).

fof(redefinition_k5_topalg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(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) )
     => k5_topalg_1(A,B,C,D) = k4_topalg_1(A,B,C,D) ) )).

fof(dt_k6_topalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A)))
        & m1_borsuk_2(D,k15_euclid(A),B,C)
        & m1_borsuk_2(E,k15_euclid(A),B,C) )
     => ( v1_funct_1(k6_topalg_1(A,B,C,D,E))
        & v1_funct_2(k6_topalg_1(A,B,C,D,E),u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
        & m2_relset_1(k6_topalg_1(A,B,C,D,E),u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A))) ) ) )).

fof(dt_k7_topalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A)))
        & m1_borsuk_2(D,k15_euclid(A),B,C)
        & m1_borsuk_2(E,k15_euclid(A),B,C) )
     => m1_borsuk_6(k7_topalg_1(A,B,C,D,E),k15_euclid(A),B,C,D,E) ) )).

fof(redefinition_k7_topalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A)))
        & m1_borsuk_2(D,k15_euclid(A),B,C)
        & m1_borsuk_2(E,k15_euclid(A),B,C) )
     => k7_topalg_1(A,B,C,D,E) = k6_topalg_1(A,B,C,D,E) ) )).
%------------------------------------------------------------------------------