SET007 Axioms: SET007+524.ax


%------------------------------------------------------------------------------
% File     : SET007+524 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Ordering of Points on a Curve. Part II
% 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    : jordan5c [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   35 (   0 unit)
%            Number of atoms       :  430 (  51 equality)
%            Maximal formula depth :   30 (  15 average)
%            Number of connectives :  413 (  18 ~  ;  11  |; 181  &)
%                                         (   4 <=>; 199 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   0 propositional; 1-5 arity)
%            Number of functors    :   21 (   6 constant; 0-4 arity)
%            Number of variables   :  165 (   0 singleton; 165 !;   0 ?)
%            Maximal term depth    :    5 (   2 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(t1_jordan5c,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [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)
                             => ( ( r2_hidden(E,A)
                                  & r2_hidden(E,B)
                                  & k1_funct_1(F,G) = E
                                  & 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
                                  & 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) ) ) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                                      & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
                                   => ! [I] :
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( ( v3_tops_2(H,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
                                            & k1_funct_1(H,np__0) = C
                                            & k1_funct_1(H,np__1) = D
                                            & k1_funct_1(H,I) = E
                                            & r1_xreal_0(np__0,I)
                                            & r1_xreal_0(I,np__1) )
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ~ ( r1_xreal_0(np__0,J)
                                                  & ~ r1_xreal_0(I,J)
                                                  & r2_hidden(k1_funct_1(H,J),B) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_jordan5c,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)))
                 => ( ( 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) )
                   => ( r1_xboole_0(A,B)
                      | ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ( E = k1_jordan5c(A,B,C,D)
                          <=> ( 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(t2_jordan5c,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r2_hidden(C,A)
                          & r1_topreal1(k15_euclid(np__2),D,E,A)
                          & B = k1_struct_0(k15_euclid(np__2),C) )
                       => k1_jordan5c(A,B,D,E) = C ) ) ) ) ) ) )).

fof(t3_jordan5c,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)))
                 => ( ( r2_hidden(C,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) )
                   => k1_jordan5c(A,B,C,D) = C ) ) ) ) ) )).

fof(t4_jordan5c,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [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)
                             => ( ( r2_hidden(E,A)
                                  & r2_hidden(E,B)
                                  & k1_funct_1(F,G) = E
                                  & 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
                                  & 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) ) ) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                                      & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
                                   => ! [I] :
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( ( v3_tops_2(H,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
                                            & k1_funct_1(H,np__0) = C
                                            & k1_funct_1(H,np__1) = D
                                            & k1_funct_1(H,I) = E
                                            & r1_xreal_0(np__0,I)
                                            & r1_xreal_0(I,np__1) )
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ~ ( r1_xreal_0(J,np__1)
                                                  & ~ r1_xreal_0(J,I)
                                                  & r2_hidden(k1_funct_1(H,J),B) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_jordan5c,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)))
                 => ( ( 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) )
                   => ( r1_xboole_0(A,B)
                      | ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ( E = k2_jordan5c(A,B,C,D)
                          <=> ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t5_jordan5c,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r2_hidden(C,A)
                          & r1_topreal1(k15_euclid(np__2),D,E,A)
                          & B = k1_struct_0(k15_euclid(np__2),C) )
                       => k2_jordan5c(A,B,D,E) = C ) ) ) ) ) ) )).

fof(t6_jordan5c,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)))
                 => ( ( r2_hidden(D,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) )
                   => k2_jordan5c(A,B,C,D) = D ) ) ) ) ) )).

fof(t7_jordan5c,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_tarski(A,B)
                      & v4_pre_topc(A,k15_euclid(np__2))
                      & r1_topreal1(k15_euclid(np__2),C,D,A) )
                   => ( k1_jordan5c(A,B,C,D) = C
                      & k2_jordan5c(A,B,C,D) = D ) ) ) ) ) ) )).

fof(d3_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( r1_jordan5c(A,B,C,D,E)
                      <=> ( r2_hidden(D,A)
                          & r2_hidden(E,A)
                          & ! [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)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ( ( v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
                                          & k1_funct_1(F,np__0) = B
                                          & k1_funct_1(F,np__1) = C
                                          & k1_funct_1(F,G) = D
                                          & r1_xreal_0(np__0,G)
                                          & r1_xreal_0(G,np__1)
                                          & k1_funct_1(F,H) = E
                                          & r1_xreal_0(np__0,H)
                                          & r1_xreal_0(H,np__1) )
                                       => r1_xreal_0(G,H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [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)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                                      & v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
                                      & k1_funct_1(F,np__0) = B
                                      & k1_funct_1(F,np__1) = C
                                      & k1_funct_1(F,G) = D
                                      & r1_xreal_0(np__0,G)
                                      & r1_xreal_0(G,np__1)
                                      & k1_funct_1(F,H) = E
                                      & r1_xreal_0(np__0,H)
                                      & r1_xreal_0(H,np__1)
                                      & r1_xreal_0(G,H) )
                                   => r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).

fof(t9_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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)))
                 => ( r2_hidden(D,A)
                   => r1_jordan5c(A,B,C,D,D) ) ) ) ) ) )).

fof(t10_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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_topreal1(k15_euclid(np__2),B,C,A)
                      & r2_hidden(D,A) )
                   => ( r1_jordan5c(A,B,C,B,D)
                      & r1_jordan5c(A,B,C,D,C) ) ) ) ) ) ) )).

fof(t11_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal1(k15_euclid(np__2),B,C,A)
               => r1_jordan5c(A,B,C,B,C) ) ) ) ) )).

fof(t12_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
                          & r1_jordan5c(A,B,C,D,E)
                          & r1_jordan5c(A,B,C,E,D) )
                       => D = E ) ) ) ) ) ) )).

fof(t13_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( ( r1_jordan5c(A,B,C,D,E)
                              & r1_jordan5c(A,B,C,E,F) )
                           => r1_jordan5c(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t14_jordan5c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
                          & r2_hidden(D,A)
                          & r2_hidden(E,A)
                          & D != E
                          & ~ ( r1_jordan5c(A,B,C,D,E)
                              & ~ r1_jordan5c(A,B,C,E,D) )
                          & ~ ( r1_jordan5c(A,B,C,E,D)
                              & ~ r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t15_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,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)))
             => ( ( v4_topreal1(A)
                  & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),B),k15_euclid(np__2))
                  & r2_hidden(C,k5_topreal1(np__2,A))
                  & r2_hidden(C,B) )
               => r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),C) ) ) ) ) )).

fof(t16_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,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)))
             => ( ( v4_topreal1(A)
                  & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),B),k15_euclid(np__2))
                  & r2_hidden(C,k5_topreal1(np__2,A))
                  & r2_hidden(C,B) )
               => r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),C,k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))) ) ) ) ) )).

fof(t17_jordan5c,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_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( r1_jordan5c(k3_topreal1(np__2,C,D),C,D,A,B)
                   => ( C = D
                      | r2_jordan3(C,D,A,B) ) ) ) ) ) ) )).

fof(t18_jordan5c,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_topreal1(k15_euclid(np__2),C,D,A)
                      & v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2)) )
                   => ( r1_xboole_0(A,B)
                      | ( k1_jordan5c(A,B,C,D) = k2_jordan5c(A,B,D,C)
                        & k2_jordan5c(A,B,C,D) = k1_jordan5c(A,B,D,C) ) ) ) ) ) ) ) )).

fof(t19_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v4_pre_topc(B,k15_euclid(np__2))
                  & v4_topreal1(A)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,C)) )
               => ( r1_xboole_0(k5_topreal1(np__2,A),B)
                  | k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k1_jordan5c(k4_topreal1(np__2,A,C),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1))) ) ) ) ) ) )).

fof(t20_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v4_pre_topc(B,k15_euclid(np__2))
                  & v4_topreal1(A)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r2_hidden(k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,C)) )
               => ( r1_xboole_0(k5_topreal1(np__2,A),B)
                  | k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k2_jordan5c(k4_topreal1(np__2,A,C),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1))) ) ) ) ) ) )).

fof(t21_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,B)
              & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
              & v4_topreal1(A)
              & r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,B)) )
           => k1_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) ) ) ) )).

fof(t22_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,B)
              & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
              & v4_topreal1(A)
              & r2_hidden(k2_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,B)) )
           => k2_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) ) ) ) )).

fof(t23_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( v4_topreal1(A)
              & r1_xreal_0(np__1,B)
              & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
           => r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))) ) ) ) )).

fof(t24_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v4_topreal1(A)
                  & r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,C)
                  & r1_xreal_0(C,k3_finseq_1(A)) )
               => r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) )).

fof(t25_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v4_topreal1(A)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r2_hidden(B,k4_topreal1(np__2,A,C)) )
               => r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),B) ) ) ) ) )).

fof(t26_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v4_topreal1(A)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r2_hidden(B,k4_topreal1(np__2,A,C)) )
               => r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1))) ) ) ) ) )).

fof(t27_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( v4_topreal1(A)
                          & v4_pre_topc(B,k15_euclid(np__2))
                          & r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,D))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                          & r2_hidden(C,k4_topreal1(np__2,A,E))
                          & r1_xreal_0(np__1,E)
                          & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                          & r2_hidden(C,B) )
                       => ( r1_xboole_0(k5_topreal1(np__2,A),B)
                          | k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = C
                          | ( r1_xreal_0(D,E)
                            & ( D = E
                             => r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),C) ) ) ) ) ) ) ) ) ) )).

fof(t28_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( v4_topreal1(A)
                          & v4_pre_topc(B,k15_euclid(np__2))
                          & r2_hidden(k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,D))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                          & r2_hidden(C,k4_topreal1(np__2,A,E))
                          & r1_xreal_0(np__1,E)
                          & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                          & r2_hidden(C,B) )
                       => ( r1_xboole_0(k5_topreal1(np__2,A),B)
                          | k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = C
                          | ( r1_xreal_0(E,D)
                            & ( D = E
                             => r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),C,k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))) ) ) ) ) ) ) ) ) ) )).

fof(t29_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(B,k4_topreal1(np__2,A,D))
                      & r2_hidden(C,k4_topreal1(np__2,A,D))
                      & v4_topreal1(A)
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                      & r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B,C) )
                   => r1_jordan5c(k4_topreal1(np__2,A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),B,C) ) ) ) ) ) )).

fof(t30_jordan5c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r2_hidden(B,k5_topreal1(np__2,A))
                  & r2_hidden(C,k5_topreal1(np__2,A))
                  & v4_topreal1(A) )
               => ( B = C
                  | ( r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B,C)
                  <=> ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( ( r2_hidden(B,k4_topreal1(np__2,A,D))
                                & r2_hidden(C,k4_topreal1(np__2,A,E))
                                & r1_xreal_0(np__1,D)
                                & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                                & r1_xreal_0(np__1,E)
                                & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A)) )
                             => ( r1_xreal_0(D,E)
                                & ( D = E
                                 => r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),B,C) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_jordan5c,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k1_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k2_jordan5c,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
     => m1_subset_1(k2_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(np__2))) ) )).
%------------------------------------------------------------------------------