SET007 Axioms: SET007+857.ax


%------------------------------------------------------------------------------
% File     : SET007+857 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Fundamental Groups of Products of Topological Spaces
% 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (   0 unit)
%            Number of atoms       :  899 (  50 equality)
%            Maximal formula depth :   35 (  18 average)
%            Number of connectives :  982 ( 143 ~  ;   0  |; 545  &)
%                                         (   2 <=>; 292 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   0 propositional; 1-6 arity)
%            Number of functors    :   37 (   3 constant; 0-8 arity)
%            Number of variables   :  387 (   0 singleton; 382 !;   5 ?)
%            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_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(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))
        & v1_borsuk_2(k6_borsuk_1(A,B)) ) ) )).

fof(fc2_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( v1_relat_1(k12_topalg_4(A,B,C,D))
        & v1_funct_1(k12_topalg_4(A,B,C,D))
        & v2_funct_1(k12_topalg_4(A,B,C,D))
        & v1_funct_2(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
        & v2_funct_2(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) ) ) )).

fof(t1_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & ? [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                      & C = k17_group_7(A,B,D,E) ) ) ) ) ) )).

fof(d1_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_group_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))))
                                & m2_relset_1(G,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D)))) )
                             => ( G = k1_topalg_4(A,B,C,D,E,F)
                              <=> ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))))
                                   => ? [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                        & ? [J] :
                                            ( m1_subset_1(J,u1_struct_0(B))
                                            & H = k17_group_7(A,B,I,J)
                                            & k8_funct_2(u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))),G,H) = k17_group_7(C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(C),E,I),k8_funct_2(u1_struct_0(B),u1_struct_0(D),F,J)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t2_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_group_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(B))
                                 => k8_funct_2(u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))),k1_topalg_4(A,B,C,D,E,F),k17_group_7(A,B,G,H)) = k17_group_7(C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(C),E,G),k8_funct_2(u1_struct_0(B),u1_struct_0(D),F,H)) ) ) ) ) ) ) ) ) )).

fof(t3_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_group_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v2_funct_1(E)
                              & v2_funct_1(F) )
                           => v2_funct_1(k1_topalg_4(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).

fof(t4_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_group_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v2_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                              & v2_funct_2(F,u1_struct_0(B),u1_struct_0(D)) )
                           => v2_funct_2(k1_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D)))) ) ) ) ) ) ) ) )).

fof(t5_topalg_4,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] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_group_1(D)
                    & v4_group_1(D)
                    & l1_group_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & v1_group_6(E,A,C)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & v1_group_6(F,B,D)
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v4_group_6(E,A,C)
                              & v4_group_6(F,B,D) )
                           => v4_group_6(k2_topalg_4(A,B,C,D,E,F),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D))) ) ) ) ) ) ) ) )).

fof(t6_topalg_4,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] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_group_1(D)
                    & v4_group_1(D)
                    & l1_group_1(D) )
                 => ( ( r1_group_6(A,C)
                      & r1_group_6(B,D) )
                   => r2_group_6(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D))) ) ) ) ) ) )).

fof(t7_topalg_4,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k1_relat_1(A) = k1_relat_1(B)
           => k15_mcart_1(k13_funct_3(A,B)) = A ) ) ) )).

fof(t8_topalg_4,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k1_relat_1(A) = k1_relat_1(B)
           => k16_mcart_1(k13_funct_3(A,B)) = B ) ) ) )).

fof(t9_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] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C)))
                    & v5_pre_topc(D,A,k6_borsuk_1(B,C))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) )
                 => v5_pre_topc(k4_topalg_4(B,C,A,D),A,B) ) ) ) ) )).

fof(t10_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] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C)))
                    & v5_pre_topc(D,A,k6_borsuk_1(B,C))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) )
                 => v5_pre_topc(k5_topalg_4(B,C,A,D),A,C) ) ) ) ) )).

fof(t11_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))
                         => ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                           => r1_borsuk_6(A,C,D) ) ) ) ) ) ) ) )).

fof(t12_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))
                         => ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                           => r1_borsuk_6(B,E,F) ) ) ) ) ) ) ) )).

fof(t13_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))
                         => ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                           => ! [G] :
                                ( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                               => m1_borsuk_2(k4_topalg_4(A,B,k5_topmetr,G),A,C,D) ) ) ) ) ) ) ) ) )).

fof(t14_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))
                         => ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                           => ! [G] :
                                ( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
                               => m1_borsuk_2(k5_topalg_4(A,B,k5_topmetr,G),B,E,F) ) ) ) ) ) ) ) ) )).

fof(t15_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))
                         => ( ( r1_borsuk_6(A,C,D)
                              & r1_borsuk_6(B,E,F) )
                           => r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) ) ) ) ) ) ) ) )).

fof(t16_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))
                         => ( ( r1_borsuk_6(A,C,D)
                              & r1_borsuk_6(B,E,F) )
                           => ! [G] :
                                ( m1_borsuk_2(G,A,C,D)
                               => ! [H] :
                                    ( m1_borsuk_2(H,B,E,F)
                                   => m1_borsuk_2(k3_topalg_4(A,B,k5_topmetr,G,H),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) ) ) ) ) ) ) ) ) ) )).

fof(t17_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_6(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,A,C,D)
                                         => ! [K] :
                                              ( m1_borsuk_2(K,A,C,D)
                                             => ( ( J = k4_topalg_4(A,B,k5_topmetr,G)
                                                  & K = k4_topalg_4(A,B,k5_topmetr,H)
                                                  & r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
                                               => m1_borsuk_6(k4_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),I),A,C,D,J,K) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_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_6(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,B,E,F)
                                         => ! [K] :
                                              ( m1_borsuk_2(K,B,E,F)
                                             => ( ( J = k5_topalg_4(A,B,k5_topmetr,G)
                                                  & K = k5_topalg_4(A,B,k5_topmetr,H)
                                                  & r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
                                               => m1_borsuk_6(k5_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),I),B,E,F,J,K) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_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)
                                         => ( ( I = k4_topalg_4(A,B,k5_topmetr,G)
                                              & J = k4_topalg_4(A,B,k5_topmetr,H)
                                              & r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
                                           => r3_borsuk_2(A,C,D,I,J) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_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,B,E,F)
                                     => ! [J] :
                                          ( m1_borsuk_2(J,B,E,F)
                                         => ( ( I = k5_topalg_4(A,B,k5_topmetr,G)
                                              & J = k5_topalg_4(A,B,k5_topmetr,H)
                                              & r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
                                           => r3_borsuk_2(B,E,F,I,J) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_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) )
                                                           => 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_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)
                                                 => ( ( 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) )
                                                   => r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_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(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(B))
                                 => ! [I] :
                                      ( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
                                     => ! [J] :
                                          ( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
                                         => ! [K] :
                                              ( m1_borsuk_2(K,A,C,D)
                                             => ! [L] :
                                                  ( m1_borsuk_2(L,A,D,E)
                                                 => ( ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
                                                      & r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
                                                      & K = k4_topalg_4(A,B,k5_topmetr,I)
                                                      & L = k4_topalg_4(A,B,k5_topmetr,J) )
                                                   => k4_topalg_4(A,B,k5_topmetr,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(A,C,D,E,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v1_borsuk_2(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(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(B))
                                 => ! [I] :
                                      ( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
                                     => ! [J] :
                                          ( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
                                         => k8_topalg_4(A,B,C,E,F,H,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(A,C,D,E,k8_topalg_4(A,B,C,D,F,G,I),k8_topalg_4(A,B,D,E,G,H,J)) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_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(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(B))
                                 => ! [I] :
                                      ( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
                                     => ! [J] :
                                          ( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
                                         => ! [K] :
                                              ( m1_borsuk_2(K,B,F,G)
                                             => ! [L] :
                                                  ( m1_borsuk_2(L,B,G,H)
                                                 => ( ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
                                                      & r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
                                                      & K = k5_topalg_4(A,B,k5_topmetr,I)
                                                      & L = k5_topalg_4(A,B,k5_topmetr,J) )
                                                   => k5_topalg_4(A,B,k5_topmetr,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(B,F,G,H,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v1_borsuk_2(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(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(B))
                                 => ! [I] :
                                      ( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
                                     => ! [J] :
                                          ( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
                                         => k9_topalg_4(A,B,C,E,F,H,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(B,F,G,H,k9_topalg_4(A,B,C,D,F,G,I),k9_topalg_4(A,B,D,E,G,H,J)) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_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(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
                        & m2_relset_1(E,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) )
                     => ( E = k12_topalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))))
                           => ? [G] :
                                ( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D))
                                & F = k6_eqrel_1(k1_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),G)
                                & k8_funct_2(u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))),E,F) = k10_finseq_1(k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),k10_topalg_4(A,B,C,D,G)),k6_eqrel_1(k1_topalg_1(B,D),k2_topalg_1(B,D),k11_topalg_4(A,B,C,D,G))) ) ) ) ) ) ) ) ) )).

fof(t27_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(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))))
                     => ! [F] :
                          ( m1_borsuk_2(F,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D))
                         => ( E = k6_eqrel_1(k1_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),F)
                           => k8_funct_2(u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))),k12_topalg_4(A,B,C,D),E) = k10_finseq_1(k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),k10_topalg_4(A,B,C,D,F)),k6_eqrel_1(k1_topalg_1(B,D),k2_topalg_1(B,D),k11_topalg_4(A,B,C,D,F))) ) ) ) ) ) ) ) )).

fof(t28_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(B))
                 => ! [E] :
                      ( m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D))
                     => k1_funct_1(k12_topalg_4(A,B,C,D),k6_eqrel_1(k1_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),E)) = k10_finseq_1(k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),k10_topalg_4(A,B,C,D,E)),k6_eqrel_1(k1_topalg_1(B,D),k2_topalg_1(B,D),k11_topalg_4(A,B,C,D,E))) ) ) ) ) ) )).

fof(t29_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(B))
                 => v4_group_6(k13_topalg_4(A,B,C,D),k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))) ) ) ) ) )).

fof(t30_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(B))
                 => r2_group_6(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))) ) ) ) ) )).

fof(t31_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] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,D)))
                                & v1_group_6(G,k3_topalg_1(A,C),k3_topalg_1(A,D))
                                & m2_relset_1(G,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,D))) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,u1_struct_0(k3_topalg_1(B,E)),u1_struct_0(k3_topalg_1(B,F)))
                                    & v1_group_6(H,k3_topalg_1(B,E),k3_topalg_1(B,F))
                                    & m2_relset_1(H,u1_struct_0(k3_topalg_1(B,E)),u1_struct_0(k3_topalg_1(B,F))) )
                                 => ( ( v4_group_6(G,k3_topalg_1(A,C),k3_topalg_1(A,D))
                                      & v4_group_6(H,k3_topalg_1(B,E),k3_topalg_1(B,F)) )
                                   => v4_group_6(k8_group_6(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,E))),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,D),k3_topalg_1(B,F))),k13_topalg_4(A,B,C,E),k2_topalg_4(k3_topalg_1(A,C),k3_topalg_1(B,E),k3_topalg_1(A,D),k3_topalg_1(B,F),G,H)),k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,D),k3_topalg_1(B,F)))) ) ) ) ) ) ) ) ) ) )).

fof(t32_topalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v1_borsuk_2(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))
                         => r2_group_6(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,D),k3_topalg_1(B,F)))) ) ) ) ) ) ) )).

fof(dt_k1_topalg_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C)
        & ~ v3_struct_0(D)
        & l1_group_1(D)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
        & m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
        & v1_funct_1(F)
        & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
        & m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
     => ( v1_funct_1(k1_topalg_4(A,B,C,D,E,F))
        & v1_funct_2(k1_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))))
        & m2_relset_1(k1_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D)))) ) ) )).

fof(dt_k2_topalg_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C)
        & ~ v3_struct_0(D)
        & v3_group_1(D)
        & v4_group_1(D)
        & l1_group_1(D)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
        & v1_group_6(E,A,C)
        & m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
        & v1_funct_1(F)
        & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
        & v1_group_6(F,B,D)
        & m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
     => ( v1_funct_1(k2_topalg_4(A,B,C,D,E,F))
        & v1_funct_2(k2_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D))))
        & v1_group_6(k2_topalg_4(A,B,C,D,E,F),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D)))
        & m2_relset_1(k2_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D)))) ) ) )).

fof(redefinition_k2_topalg_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C)
        & ~ v3_struct_0(D)
        & v3_group_1(D)
        & v4_group_1(D)
        & l1_group_1(D)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
        & v1_group_6(E,A,C)
        & m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
        & v1_funct_1(F)
        & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
        & v1_group_6(F,B,D)
        & m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
     => k2_topalg_4(A,B,C,D,E,F) = k1_topalg_4(A,B,C,D,E,F) ) )).

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))) ) ) )).

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) ) )).

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)) ) ) )).

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) ) )).

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)) ) ) )).

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) ) )).

fof(dt_k6_topalg_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B))
        & m1_borsuk_2(G,A,C,D)
        & m1_borsuk_2(H,B,E,F) )
     => m1_borsuk_2(k6_topalg_4(A,B,C,D,E,F,G,H),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) ) )).

fof(redefinition_k6_topalg_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B))
        & m1_borsuk_2(G,A,C,D)
        & m1_borsuk_2(H,B,E,F) )
     => k6_topalg_4(A,B,C,D,E,F,G,H) = k13_funct_3(G,H) ) )).

fof(dt_k7_topalg_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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_borsuk_2(E,A,C,C)
        & m1_borsuk_2(F,B,D,D) )
     => m1_borsuk_2(k7_topalg_4(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) ) )).

fof(redefinition_k7_topalg_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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_borsuk_2(E,A,C,C)
        & m1_borsuk_2(F,B,D,D) )
     => k7_topalg_4(A,B,C,D,E,F) = k13_funct_3(E,F) ) )).

fof(dt_k8_topalg_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B))
        & m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
     => m1_borsuk_2(k8_topalg_4(A,B,C,D,E,F,G),A,C,D) ) )).

fof(redefinition_k8_topalg_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B))
        & m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
     => k8_topalg_4(A,B,C,D,E,F,G) = k15_mcart_1(G) ) )).

fof(dt_k9_topalg_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B))
        & m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
     => m1_borsuk_2(k9_topalg_4(A,B,C,D,E,F,G),B,E,F) ) )).

fof(redefinition_k9_topalg_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_2(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B))
        & m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
     => k9_topalg_4(A,B,C,D,E,F,G) = k16_mcart_1(G) ) )).

fof(dt_k10_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
     => m1_borsuk_2(k10_topalg_4(A,B,C,D,E),A,C,C) ) )).

fof(redefinition_k10_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
     => k10_topalg_4(A,B,C,D,E) = k15_mcart_1(E) ) )).

fof(dt_k11_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
     => m1_borsuk_2(k11_topalg_4(A,B,C,D,E),B,D,D) ) )).

fof(redefinition_k11_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
     => k11_topalg_4(A,B,C,D,E) = k16_mcart_1(E) ) )).

fof(dt_k12_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( v1_funct_1(k12_topalg_4(A,B,C,D))
        & v1_funct_2(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
        & m2_relset_1(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) ) ) )).

fof(dt_k13_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( v1_funct_1(k13_topalg_4(A,B,C,D))
        & v1_funct_2(k13_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
        & v1_group_6(k13_topalg_4(A,B,C,D),k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))
        & m2_relset_1(k13_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) ) ) )).

fof(redefinition_k13_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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k13_topalg_4(A,B,C,D) = k12_topalg_4(A,B,C,D) ) )).
%------------------------------------------------------------------------------