SET007 Axioms: SET007+522.ax


%------------------------------------------------------------------------------
% File     : SET007+522 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Real Maps
% 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    : jordan5a [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   25 (   0 unit)
%            Number of atoms       :  340 (  66 equality)
%            Maximal formula depth :   35 (  17 average)
%            Number of connectives :  347 (  32 ~  ;  18  |; 149  &)
%                                         (   2 <=>; 146 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   30 (   0 propositional; 1-4 arity)
%            Number of functors    :   34 (   8 constant; 0-4 arity)
%            Number of variables   :  134 (   0 singleton; 129 !;   5 ?)
%            Maximal term depth    :    4 (   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_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & v3_compts_1(k15_euclid(A))
        & v1_borsuk_2(k15_euclid(A)) ) ) )).

fof(rc1_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] :
          ( m1_pre_topc(B,k15_euclid(A))
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v2_compts_1(B)
          & v3_compts_1(B) ) ) )).

fof(t1_jordan5a,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_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( r1_topreal1(k15_euclid(A),B,C,D)
                   => v6_compts_1(D,k15_euclid(A)) ) ) ) ) ) )).

fof(t2_jordan5a,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(np__0,A)
          & r1_xreal_0(A,np__1) )
      <=> r2_hidden(A,u1_struct_0(k5_topmetr)) ) ) )).

fof(t3_jordan5a,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] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ~ ( k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,D),A,B),k18_euclid(D,A,C)) = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,E),A,B),k18_euclid(E,A,C))
                          & D != E
                          & B != C ) ) ) ) ) ) )).

fof(t4_jordan5a,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)))
             => ~ ( B != C
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))))
                        & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C)))) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k1_rcomp_1(np__0,np__1))
                               => k1_funct_1(D,E) = k17_euclid(A,k18_euclid(k5_real_1(np__1,E),A,B),k18_euclid(E,A,C)) ) )
                          & v3_tops_2(D,k5_topmetr,k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C)))
                          & k1_funct_1(D,np__0) = B
                          & k1_funct_1(D,np__1) = C ) ) ) ) ) ) )).

fof(t5_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_borsuk_2(C,k15_euclid(np__2),A,B)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_compts_1(D)
                    & m1_pre_topc(D,k15_euclid(np__2)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(D))
                        & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(D)) )
                     => ( ( v2_funct_1(C)
                          & E = C
                          & k2_pre_topc(D) = k2_relat_1(C) )
                       => v3_tops_2(E,k5_topmetr,D) ) ) ) ) ) ) )).

fof(t6_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( r2_hidden(A,k4_pcomps_1(k8_metric_1))
      <=> v3_rcomp_1(A) ) ) )).

fof(t7_jordan5a,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr))
        & m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_topmetr))
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( r1_tmap_1(k3_topmetr,k3_topmetr,A,B)
                      & A = C
                      & B = D )
                   => r1_fcont_1(C,D) ) ) ) ) ) )).

fof(t8_jordan5a,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr))
        & v5_pre_topc(A,k3_topmetr,k3_topmetr)
        & m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( A = B
           => r2_fcont_1(B,k1_numbers) ) ) ) )).

fof(t9_jordan5a,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v2_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr))
        & v5_pre_topc(A,k3_topmetr,k3_topmetr)
        & m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ~ ( B = D
                                    & C = E
                                    & ~ r1_xreal_0(E,D)
                                    & F = k1_funct_1(A,B)
                                    & G = k1_funct_1(A,C)
                                    & r1_xreal_0(G,F) ) ) ) ) ) ) )
        | ! [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ~ ( B = D
                                    & C = E
                                    & ~ r1_xreal_0(E,D)
                                    & F = k1_funct_1(A,B)
                                    & G = k1_funct_1(A,C)
                                    & r1_xreal_0(F,G) ) ) ) ) ) ) ) ) ) )).

fof(t10_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_topmetr(C,D)))
                     => ( ( r1_xreal_0(C,D)
                          & E = A
                          & r1_tarski(k2_rcomp_1(k5_real_1(A,B),k3_real_1(A,B)),k1_rcomp_1(C,D)) )
                       => ( r1_xreal_0(B,np__0)
                          | k2_rcomp_1(k5_real_1(A,B),k3_real_1(A,B)) = k9_metric_1(k2_topmetr(C,D),E,B) ) ) ) ) ) ) ) )).

fof(t11_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
             => ( r2_hidden(C,k4_pcomps_1(k2_topmetr(A,B)))
               => ( r1_xreal_0(B,A)
                  | r2_hidden(A,C)
                  | r2_hidden(B,C)
                  | v3_rcomp_1(C) ) ) ) ) ) )).

fof(t12_jordan5a,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( r1_tarski(A,k1_rcomp_1(B,C))
               => ( ~ r2_hidden(B,A)
                  & ~ r2_hidden(C,A) ) ) ) ) ) )).

fof(t13_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_topmetr(A,B))))
                 => ( ( r1_xreal_0(A,B)
                      & D = C
                      & v3_rcomp_1(C) )
                   => r2_hidden(D,k4_pcomps_1(k2_topmetr(A,B))) ) ) ) ) ) )).

fof(t14_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                            & m2_relset_1(F,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k4_topmetr(A,B)))
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & m2_relset_1(H,k1_numbers,k1_numbers) )
                                 => ( ( r1_tmap_1(k4_topmetr(A,B),k4_topmetr(C,D),F,G)
                                      & k1_funct_1(F,A) = C
                                      & k1_funct_1(F,B) = D
                                      & v2_funct_1(F)
                                      & F = H
                                      & G = E )
                                   => ( r1_xreal_0(B,A)
                                      | r1_xreal_0(D,C)
                                      | r1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,H,k1_rcomp_1(A,B)),E) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                        & m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k1_numbers,k1_numbers) )
                         => ( ( v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
                              & v2_funct_1(E)
                              & E = F
                              & k1_funct_1(E,A) = C
                              & k1_funct_1(E,B) = D )
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | r2_fcont_1(F,k1_rcomp_1(A,B)) ) ) ) ) ) ) ) ) )).

fof(t16_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                        & m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                     => ( ( v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
                          & v2_funct_1(E)
                          & k1_funct_1(E,A) = C
                          & k1_funct_1(E,B) = D )
                       => ( r1_xreal_0(B,A)
                          | r1_xreal_0(D,C)
                          | ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k4_topmetr(A,B)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k4_topmetr(A,B)))
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ! [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                 => ~ ( F = H
                                                      & G = I
                                                      & ~ r1_xreal_0(I,H)
                                                      & J = k8_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)),E,F)
                                                      & K = k8_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)),E,G)
                                                      & r1_xreal_0(K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t17_jordan5a,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v2_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
        & v5_pre_topc(A,k5_topmetr,k5_topmetr)
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
     => ( ( k1_funct_1(A,np__0) = np__0
          & k1_funct_1(A,np__1) = np__1 )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ~ ( B = D
                                    & C = E
                                    & ~ r1_xreal_0(E,D)
                                    & F = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B)
                                    & G = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,C)
                                    & r1_xreal_0(G,F) ) ) ) ) ) ) ) ) ) )).

fof(t18_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                        & m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
                                 => ( ( G = F
                                      & v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
                                      & v2_funct_1(E)
                                      & v6_compts_1(G,k3_topmetr)
                                      & k1_funct_1(E,A) = C
                                      & k1_funct_1(E,B) = D
                                      & k4_pre_topc(k4_topmetr(A,B),k4_topmetr(C,D),E,F) = H )
                                   => ( r1_xreal_0(B,A)
                                      | r1_xreal_0(D,C)
                                      | k1_funct_1(E,k5_seq_4(k3_weierstr(G))) = k5_seq_4(k3_weierstr(H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                        & m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
                                     => ( ( H = F
                                          & I = G
                                          & v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
                                          & v2_funct_1(E)
                                          & v6_compts_1(H,k3_topmetr)
                                          & k1_funct_1(E,A) = C
                                          & k1_funct_1(E,B) = D
                                          & k4_pre_topc(k4_topmetr(A,B),k4_topmetr(C,D),E,F) = G )
                                       => ( r1_xreal_0(B,A)
                                          | r1_xreal_0(D,C)
                                          | k1_funct_1(E,k4_seq_4(k3_weierstr(H))) = k4_seq_4(k3_weierstr(I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_jordan5a,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( k5_seq_4(k1_rcomp_1(A,B)) = A
              & k4_seq_4(k1_rcomp_1(A,B)) = B ) ) ) ) )).

fof(t21_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & v1_funct_2(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                                        & m2_relset_1(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                                     => ( ( r1_xreal_0(A,E)
                                          & r1_xreal_0(F,B)
                                          & v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D))
                                          & k1_funct_1(I,A) = C
                                          & k1_funct_1(I,B) = D
                                          & G = k1_funct_1(I,E)
                                          & H = k1_funct_1(I,F) )
                                       => ( r1_xreal_0(B,A)
                                          | r1_xreal_0(D,C)
                                          | r1_xreal_0(F,E)
                                          | k4_pre_topc(k4_topmetr(A,B),k4_topmetr(C,D),I,k1_rcomp_1(E,F)) = k1_rcomp_1(G,H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( ~ r1_xboole_0(A,B)
                      & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
                      & r1_topreal1(k15_euclid(np__2),C,D,A)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B))
                              & ? [F] :
                                  ( v1_funct_1(F)
                                  & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                                  & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                                  & ? [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                      & v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
                                      & k1_funct_1(F,np__0) = C
                                      & k1_funct_1(F,np__1) = D
                                      & k1_funct_1(F,G) = E
                                      & r1_xreal_0(np__0,G)
                                      & r1_xreal_0(G,np__1)
                                      & ! [H] :
                                          ( m1_subset_1(H,k1_numbers)
                                         => ~ ( r1_xreal_0(np__0,H)
                                              & ~ r1_xreal_0(G,H)
                                              & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_jordan5a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( ~ r1_xboole_0(A,B)
                      & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
                      & r1_topreal1(k15_euclid(np__2),C,D,A)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B))
                              & ? [F] :
                                  ( v1_funct_1(F)
                                  & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                                  & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                                  & ? [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                      & v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
                                      & k1_funct_1(F,np__0) = C
                                      & k1_funct_1(F,np__1) = D
                                      & k1_funct_1(F,G) = E
                                      & r1_xreal_0(np__0,G)
                                      & r1_xreal_0(G,np__1)
                                      & ! [H] :
                                          ( m1_subset_1(H,k1_numbers)
                                         => ~ ( r1_xreal_0(H,np__1)
                                              & ~ r1_xreal_0(H,G)
                                              & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------