SET007 Axioms: SET007+523.ax


%------------------------------------------------------------------------------
% File     : SET007+523 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Ordering of Points on a Curve. Part I
% 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    : jordan5b [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   37 (   3 unit)
%            Number of atoms       :  278 (  47 equality)
%            Maximal formula depth :   29 (   9 average)
%            Number of connectives :  265 (  24 ~  ;  14  |; 106  &)
%                                         (   1 <=>; 120 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-4 arity)
%            Number of functors    :   36 (   7 constant; 0-4 arity)
%            Number of variables   :   94 (   0 singleton;  93 !;   1 ?)
%            Maximal term depth    :    6 (   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_jordan5b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__1,A)
          & r1_xreal_0(A,k5_binarith(A,np__1)) ) ) )).

fof(t2_jordan5b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(k1_nat_1(A,np__1),B)
           => r1_xreal_0(np__1,k5_binarith(B,A)) ) ) ) )).

fof(t3_jordan5b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,A)
              & r1_xreal_0(np__1,B) )
           => r1_xreal_0(k1_nat_1(k5_binarith(B,A),np__1),B) ) ) ) )).

fof(t4_jordan5b,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r2_hidden(A,u1_struct_0(k22_borsuk_1))
       => r2_hidden(k6_xcmplx_0(np__1,A),u1_struct_0(k22_borsuk_1)) ) ) )).

fof(t5_jordan5b,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)))
             => ( ( r2_hidden(C,k3_topreal1(np__2,A,B))
                  & k22_euclid(C) = k22_euclid(A) )
               => ( k22_euclid(A) = k22_euclid(B)
                  | C = A ) ) ) ) ) )).

fof(t6_jordan5b,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)))
             => ( ( r2_hidden(C,k3_topreal1(np__2,A,B))
                  & k21_euclid(C) = k21_euclid(A) )
               => ( k21_euclid(A) = k21_euclid(B)
                  | C = A ) ) ) ) ) )).

fof(t7_jordan5b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                & m2_relset_1(C,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                      & v4_topreal1(A)
                      & B = k5_topreal1(np__2,A)
                      & v3_tops_2(C,k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B))
                      & k1_funct_1(C,np__0) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
                      & k1_funct_1(C,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ~ ( ~ r1_xreal_0(F,E)
                                  & r1_xreal_0(np__0,E)
                                  & r1_xreal_0(E,np__1)
                                  & r1_xreal_0(np__0,F)
                                  & r1_xreal_0(F,np__1)
                                  & k4_topreal1(np__2,A,D) = k4_pre_topc(k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B),C,k1_rcomp_1(E,F))
                                  & k1_funct_1(C,E) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)
                                  & k1_funct_1(C,F) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)) ) ) ) ) ) ) ) ) )).

fof(t8_jordan5b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                    & m2_relset_1(D,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k22_borsuk_1))) )
                         => ~ ( v4_topreal1(A)
                              & v3_tops_2(D,k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B))
                              & k1_funct_1(D,np__0) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
                              & k1_funct_1(D,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
                              & r1_xreal_0(np__1,E)
                              & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                              & k4_pre_topc(k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B),D,F) = k4_topreal1(np__2,A,E)
                              & B = k5_topreal1(np__2,A)
                              & C = k4_topreal1(np__2,A,E)
                              & ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(k3_pre_topc(k22_borsuk_1,F)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
                                    & m2_relset_1(G,u1_struct_0(k3_pre_topc(k22_borsuk_1,F)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
                                 => ~ ( G = k7_relat_1(D,F)
                                      & v3_tops_2(G,k3_pre_topc(k22_borsuk_1,F),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ) ) ) )).

fof(t9_jordan5b,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)))
             => ( r2_hidden(C,k3_topreal1(np__2,A,B))
               => ( A = B
                  | r2_jordan3(A,B,C,C) ) ) ) ) ) )).

fof(t10_jordan5b,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)))
             => ( r2_hidden(A,k3_topreal1(np__2,B,C))
               => ( B = C
                  | r2_jordan3(B,C,B,A) ) ) ) ) ) )).

fof(t11_jordan5b,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)))
             => ( r2_hidden(A,k3_topreal1(np__2,B,C))
               => ( B = C
                  | r2_jordan3(B,C,A,C) ) ) ) ) ) )).

fof(t12_jordan5b,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r2_jordan3(A,B,C,D)
                          & r2_jordan3(A,B,D,E) )
                       => ( A = B
                          | r2_jordan3(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t14_jordan5b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r1_topreal1(k15_euclid(A),C,D,B)
                   => r1_topreal1(k15_euclid(A),D,C,B) ) ) ) ) ) )).

fof(t15_jordan5b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( ( v4_topreal1(B)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B))
                  & C = k4_topreal1(np__2,B,A) )
               => r1_topreal1(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(A,np__1)),C) ) ) ) ) )).

fof(t16_jordan5b,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(B,k3_finseq_1(A))
              & v4_topreal1(A)
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,k3_finseq_1(A)))) )
           => B = np__1 ) ) ) )).

fof(t17_jordan5b,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)))
         => ( ( v4_topreal1(A)
              & B = k1_funct_1(A,k3_finseq_1(A)) )
           => k3_jordan3(A,B) = k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B) ) ) ) )).

fof(t18_jordan5b,axiom,(
    $true )).

fof(t19_jordan5b,axiom,(
    $true )).

fof(t20_jordan5b,axiom,(
    $true )).

fof(t21_jordan5b,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)))
         => ( ( r2_hidden(B,k5_topreal1(np__2,A))
              & v4_topreal1(A) )
           => ( B = k1_funct_1(A,k3_finseq_1(A))
              | k2_jordan3(k3_jordan3(A,B),B) = np__1 ) ) ) ) )).

fof(t22_jordan5b,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)))
         => ( ( r2_hidden(B,k5_topreal1(np__2,A))
              & v4_topreal1(A) )
           => ( B = k1_funct_1(A,k3_finseq_1(A))
              | r2_hidden(B,k5_topreal1(np__2,k3_jordan3(A,B))) ) ) ) ) )).

fof(t23_jordan5b,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)))
         => ( ( r2_hidden(B,k5_topreal1(np__2,A))
              & v4_topreal1(A) )
           => ( B = k1_funct_1(A,np__1)
              | r2_hidden(B,k5_topreal1(np__2,k4_jordan3(A,B))) ) ) ) ) )).

fof(t24_jordan5b,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)))
         => ( ( r2_hidden(B,k5_topreal1(np__2,A))
              & v2_funct_1(A) )
           => k5_jordan3(A,B,B) = k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B) ) ) ) )).

fof(t25_jordan5b,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))
                  & B = k1_funct_1(A,k3_finseq_1(A))
                  & v4_topreal1(A) )
               => ( C = k1_funct_1(A,k3_finseq_1(A))
                  | r2_hidden(B,k5_topreal1(np__2,k3_jordan3(A,C))) ) ) ) ) ) )).

fof(t26_jordan5b,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)))
             => ~ ( ~ ( B = k1_funct_1(A,k3_finseq_1(A))
                      & C = k1_funct_1(A,k3_finseq_1(A)) )
                  & r2_hidden(B,k5_topreal1(np__2,A))
                  & r2_hidden(C,k5_topreal1(np__2,A))
                  & v4_topreal1(A)
                  & ~ r2_hidden(B,k5_topreal1(np__2,k3_jordan3(A,C)))
                  & ~ r2_hidden(C,k5_topreal1(np__2,k3_jordan3(A,B))) ) ) ) ) )).

fof(t27_jordan5b,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) )
               => r1_tarski(k5_topreal1(np__2,k5_jordan3(A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t28_jordan5b,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(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)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(C,k3_finseq_1(k3_goboard2(A))) )
               => ( r1_xreal_0(C,B)
                  | k3_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A)))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))))) = k1_xboole_0 ) ) ) ) ) )).

fof(t29_jordan5b,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(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)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(C,k1_matrix_1(k3_goboard2(A))) )
               => ( r1_xreal_0(C,B)
                  | k3_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))))) = k1_xboole_0 ) ) ) ) ) )).

fof(t30_jordan5b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_topreal1(A)
       => k3_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) = A ) ) )).

fof(t31_jordan5b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_topreal1(A)
       => k4_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = A ) ) )).

fof(t32_jordan5b,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)))
         => ( r2_hidden(B,k5_topreal1(np__2,A))
           => r2_hidden(B,k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)))) ) ) ) )).

fof(t33_jordan5b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( v2_topreal1(A)
              & v3_topreal1(A)
              & v2_funct_1(A)
              & r1_xreal_0(np__2,k3_finseq_1(A))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_topreal1(np__2,A,B)) )
           => B = np__1 ) ) ) )).

fof(t34_jordan5b,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,k1_matrix_1(k3_goboard2(A)))
                  & C = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B)) )
               => r1_topreal4(C,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B)) ) ) ) ) )).

fof(t35_jordan5b,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,k3_finseq_1(k3_goboard2(A)))
                  & C = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A)))) )
               => r1_topreal4(C,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A)))) ) ) ) ) )).

fof(t36_jordan5b,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)) )
               => ( ( r1_xreal_0(k2_jordan3(A,C),k2_jordan3(A,B))
                    & ~ ( k2_jordan3(A,B) = k2_jordan3(A,C)
                        & r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)),B,C) ) )
                  | B = C
                  | r1_tarski(k5_topreal1(np__2,k5_jordan3(A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) ) )).

fof(t13_jordan5b,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)))
         => ( A != B
           => k3_topreal1(np__2,A,B) = a_2_0_jordan5b(A,B) ) ) ) )).

fof(fraenkel_a_2_0_jordan5b,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_2_0_jordan5b(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
            & A = D
            & r2_jordan3(B,C,B,D)
            & r2_jordan3(B,C,D,C) ) ) ) )).
%------------------------------------------------------------------------------