SET007 Axioms: SET007+839.ax


%------------------------------------------------------------------------------
% File     : SET007+839 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Intersections of Intervals and Balls in E^n_ T
% 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    : topreal9 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   97 (   0 unit)
%            Number of atoms       :  619 (  99 equality)
%            Maximal formula depth :   34 (  10 average)
%            Number of connectives :  572 (  50 ~  ;   6  |; 169  &)
%                                         (  13 <=>; 334 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   30 (   0 propositional; 1-3 arity)
%            Number of functors    :   63 (   5 constant; 0-4 arity)
%            Number of variables   :  366 (   0 singleton; 360 !;   6 ?)
%            Maximal term depth    :   11 (   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(fc1_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v2_xreal_0(C) )
     => v1_xboole_0(k1_topreal9(A,B,C)) ) )).

fof(fc2_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & v2_xreal_0(C) )
     => ~ v1_xboole_0(k1_topreal9(A,B,C)) ) )).

fof(fc3_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & v3_xreal_0(C) )
     => v1_xboole_0(k2_topreal9(A,B,C)) ) )).

fof(fc4_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ~ v1_xboole_0(k2_topreal9(A,B,C)) ) )).

fof(fc5_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v3_pre_topc(k1_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k1_topreal9(A,B,C),A) ) ) )).

fof(fc6_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k2_topreal9(A,B,C),A) ) ) )).

fof(fc7_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) )).

fof(fc8_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v3_pre_topc(k1_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k1_topreal9(A,B,C),A)
        & v1_jordan1(k1_topreal9(A,B,C),A) ) ) )).

fof(fc9_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k2_topreal9(A,B,C),A)
        & v1_jordan1(k2_topreal9(A,B,C),A) ) ) )).

fof(fc10_topreal9,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_funct_1(k3_borsuk_1(k15_euclid(A),k15_euclid(A),k16_euclid(A)))
        & v1_funct_2(k3_borsuk_1(k15_euclid(A),k15_euclid(A),k16_euclid(A)),u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)))
        & v1_topreal9(k3_borsuk_1(k15_euclid(A),k15_euclid(A),k16_euclid(A)),A)
        & v2_topreal9(k3_borsuk_1(k15_euclid(A),k15_euclid(A),k16_euclid(A)),A) ) ) )).

fof(rc1_topreal9,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)))
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)))
          & v5_pre_topc(B,k15_euclid(A),k15_euclid(A))
          & v1_topreal9(B,A)
          & v2_topreal9(B,A) ) ) )).

fof(fc11_topreal9,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_funct_1(k2_jgraph_2(A,np__0,B,np__0))
        & v1_funct_2(k2_jgraph_2(A,np__0,B,np__0),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
        & v1_topreal9(k2_jgraph_2(A,np__0,B,np__0),np__2)
        & v2_topreal9(k2_jgraph_2(A,np__0,B,np__0),np__2) ) ) )).

fof(fc12_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => ~ v1_xboole_0(k4_topreal9(A,B,C)) ) )).

fof(fc13_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => ( ~ v1_xboole_0(k4_topreal9(A,B,C))
        & v1_jordan1(k4_topreal9(A,B,C),A) ) ) )).

fof(fc14_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & v3_xreal_0(C) )
     => ( v1_xboole_0(k3_topreal9(A,B,C))
        & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) )).

fof(fc15_topreal9,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ( ~ v1_xboole_0(k3_topreal9(A,B,C))
        & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) )).

fof(fc16_topreal9,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v2_xreal_0(C) )
     => ~ v1_xboole_0(k6_jgraph_6(A,B,C)) ) )).

fof(fc17_topreal9,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ~ v1_xboole_0(k7_jgraph_6(A,B,C)) ) )).

fof(fc18_topreal9,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => v1_jordan1(k6_jgraph_6(A,B,C),np__2) ) )).

fof(fc19_topreal9,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => v1_jordan1(k7_jgraph_6(A,B,C),np__2) ) )).

fof(t1_topreal9,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,u1_struct_0(k15_euclid(A)))
                 => k20_euclid(A,k20_euclid(A,B,C),D) = k20_euclid(A,k20_euclid(A,B,D),C) ) ) ) ) )).

fof(t2_topreal9,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,u1_struct_0(k15_euclid(A)))
                 => ( k17_euclid(A,B,C) = k17_euclid(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t3_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ~ ( ~ v1_xboole_0(A)
              & B = k17_euclid(A,B,k5_jordan2c(A)) ) ) ) )).

fof(t4_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( E = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,B),A,C),k18_euclid(B,A,D))
                     => ( ~ ( E = C
                            & B != np__0
                            & C != D )
                        & ( ( B = np__0
                            | C = D )
                         => E = C )
                        & ~ ( E = D
                            & B != np__1
                            & C != D )
                        & ( ( B = np__1
                            | C = D )
                         => E = D ) ) ) ) ) ) ) )).

fof(t5_topreal9,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => k7_square_1(k12_euclid(A)) = k15_rvsum_1(k11_rvsum_1(A)) ) )).

fof(t6_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_metric_1(B)
            & v7_metric_1(B)
            & v8_metric_1(B)
            & v9_metric_1(B)
            & l1_metric_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ~ ( C != D
                          & r2_hidden(C,k10_metric_1(B,E,A))
                          & r2_hidden(D,k10_metric_1(B,E,A))
                          & r1_xreal_0(A,np__0) ) ) ) ) ) ) )).

fof(t7_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(C,k1_topreal9(A,D,B))
                  <=> ~ r1_xreal_0(B,k5_toprns_1(A,k20_euclid(A,C,D))) ) ) ) ) ) )).

fof(t8_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(C,k2_topreal9(A,D,B))
                  <=> r1_xreal_0(k5_toprns_1(A,k20_euclid(A,C,D)),B) ) ) ) ) ) )).

fof(t9_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(C,k3_topreal9(A,D,B))
                  <=> k5_toprns_1(A,k20_euclid(A,C,D)) = B ) ) ) ) ) )).

fof(t10_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ~ ( r2_hidden(C,k1_topreal9(A,k16_euclid(A),B))
                  & r1_xreal_0(B,k5_toprns_1(A,C)) ) ) ) ) )).

fof(t11_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( r2_hidden(C,k2_topreal9(A,k16_euclid(A),B))
               => r1_xreal_0(k5_toprns_1(A,C),B) ) ) ) ) )).

fof(t12_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( r2_hidden(C,k3_topreal9(A,k16_euclid(A),B))
               => k5_toprns_1(A,C) = B ) ) ) ) )).

fof(t13_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => k9_metric_1(k14_euclid(A),D,B) = k1_topreal9(A,C,B) ) ) ) ) ) )).

fof(t14_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => k10_metric_1(k14_euclid(A),D,B) = k2_topreal9(A,C,B) ) ) ) ) ) )).

fof(t15_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => k11_metric_1(k14_euclid(A),D,B) = k3_topreal9(A,C,B) ) ) ) ) ) )).

fof(t16_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => r1_tarski(k1_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) )).

fof(t17_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => r1_tarski(k3_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) )).

fof(t18_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => k4_subset_1(u1_struct_0(k15_euclid(A)),k1_topreal9(A,C,B),k3_topreal9(A,C,B)) = k2_topreal9(A,C,B) ) ) ) )).

fof(t19_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => r1_xboole_0(k1_topreal9(A,C,B),k3_topreal9(A,C,B)) ) ) ) )).

fof(t20_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ~ ( ~ v1_xboole_0(k1_topreal9(A,C,B))
                  & r1_xreal_0(B,np__0) ) ) ) ) )).

fof(t21_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( v1_xboole_0(k1_topreal9(A,C,B))
               => r1_xreal_0(B,np__0) ) ) ) ) )).

fof(t22_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( ~ v1_xboole_0(k2_topreal9(A,C,B))
               => r1_xreal_0(np__0,B) ) ) ) ) )).

fof(t23_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ~ ( v1_xboole_0(k2_topreal9(A,C,B))
                  & r1_xreal_0(np__0,B) ) ) ) ) )).

fof(t24_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
                             => ( ( k2_xcmplx_0(B,C) = np__1
                                  & k3_real_1(k18_complex1(B),k18_complex1(C)) = np__1
                                  & r2_hidden(E,k2_topreal9(A,F,D))
                                  & r2_hidden(G,k1_topreal9(A,F,D)) )
                               => ( C = np__0
                                  | r2_hidden(k17_euclid(A,k18_euclid(B,A,E),k18_euclid(C,A,G)),k1_topreal9(A,F,D)) ) ) ) ) ) ) ) ) ) )).

fof(d4_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))) )
         => ( v1_topreal9(B,A)
          <=> ! [C] :
                ( v1_xreal_0(C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                   => k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),B,k18_euclid(C,A,D)) = k18_euclid(C,A,k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),B,D)) ) ) ) ) ) )).

fof(d5_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))) )
         => ( v2_topreal9(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                   => k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),B,k17_euclid(A,C,D)) = k17_euclid(A,k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),B,C),k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),B,D)) ) ) ) ) ) )).

fof(t25_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)))
            & v1_topreal9(B,A)
            & v2_topreal9(B,A)
            & m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))) )
         => ! [C] :
              ( ( v1_jordan1(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
             => v1_jordan1(k4_pre_topc(k15_euclid(A),k15_euclid(A),B,C),A) ) ) ) )).

fof(t26_topreal9,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] :
                  ( r2_hidden(D,k4_topreal9(A,B,C))
                <=> ? [E] :
                      ( v1_xreal_0(E)
                      & D = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,E),A,B),k18_euclid(E,A,C))
                      & r1_xreal_0(np__0,E) ) ) ) ) ) )).

fof(t27_topreal9,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)))
             => r2_hidden(B,k4_topreal9(A,B,C)) ) ) ) )).

fof(t28_topreal9,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)))
             => r2_hidden(B,k4_topreal9(A,C,B)) ) ) ) )).

fof(t29_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => k4_topreal9(A,B,B) = k1_struct_0(k15_euclid(A),B) ) ) )).

fof(t30_topreal9,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,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(B,k4_topreal9(A,C,D))
                   => r1_tarski(k4_topreal9(A,C,B),k4_topreal9(A,C,D)) ) ) ) ) ) )).

fof(t31_topreal9,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,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(B,k4_topreal9(A,C,D))
                   => ( B = C
                      | k4_topreal9(A,C,D) = k4_topreal9(A,C,B) ) ) ) ) ) ) )).

fof(t32_topreal9,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)))
             => r1_tarski(k3_topreal1(A,B,C),k4_topreal9(A,B,C)) ) ) ) )).

fof(t33_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r2_hidden(C,k3_topreal9(A,D,B))
                          & r2_hidden(E,k1_topreal9(A,D,B)) )
                       => k5_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,C,E),k3_topreal9(A,D,B)) = k1_struct_0(k15_euclid(A),C) ) ) ) ) ) ) )).

fof(t34_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r2_hidden(C,k3_topreal9(A,D,B))
                          & r2_hidden(E,k3_topreal9(A,D,B)) )
                       => r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,C,E),k2_struct_0(k15_euclid(A),C,E)),k1_topreal9(A,D,B)) ) ) ) ) ) ) )).

fof(t35_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r2_hidden(C,k3_topreal9(A,D,B))
                          & r2_hidden(E,k3_topreal9(A,D,B)) )
                       => k5_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,C,E),k3_topreal9(A,D,B)) = k2_struct_0(k15_euclid(A),C,E) ) ) ) ) ) ) )).

fof(t36_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r2_hidden(C,k3_topreal9(A,D,B))
                          & r2_hidden(E,k3_topreal9(A,D,B)) )
                       => k5_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal9(A,C,E),k3_topreal9(A,D,B)) = k2_struct_0(k15_euclid(A),C,E) ) ) ) ) ) ) )).

fof(t37_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ! [G] :
                              ( m2_finseq_2(G,k1_numbers,k1_euclid(A))
                             => ! [H] :
                                  ( m2_finseq_2(H,k1_numbers,k1_euclid(A))
                                 => ! [I] :
                                      ( m2_finseq_2(I,k1_numbers,k1_euclid(A))
                                     => ~ ( G = D
                                          & H = E
                                          & I = F
                                          & D != E
                                          & r2_hidden(D,k1_topreal9(A,F,B))
                                          & C = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(np__2,k2_euclid_2(A,k20_euclid(A,E,D),k20_euclid(A,D,F)))),k8_square_1(k1_quin_1(k15_rvsum_1(k11_euclid(A,k8_euclid(A,H,G))),k3_xcmplx_0(np__2,k2_euclid_2(A,k20_euclid(A,E,D),k20_euclid(A,D,F))),k6_xcmplx_0(k15_rvsum_1(k11_euclid(A,k8_euclid(A,G,I))),k5_square_1(B))))),k4_real_1(np__2,k15_rvsum_1(k11_euclid(A,k8_euclid(A,H,G)))))
                                          & ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(k15_euclid(A)))
                                             => ~ ( k1_struct_0(k15_euclid(A),J) = k5_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal9(A,D,E),k3_topreal9(A,F,B))
                                                  & J = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,C),A,D),k18_euclid(C,A,E)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ! [G] :
                              ( m2_finseq_2(G,k1_numbers,k1_euclid(A))
                             => ! [H] :
                                  ( m2_finseq_2(H,k1_numbers,k1_euclid(A))
                                 => ! [I] :
                                      ( m2_finseq_2(I,k1_numbers,k1_euclid(A))
                                     => ~ ( G = k17_euclid(A,k18_euclid(k6_real_1(np__1,np__2),A,D),k18_euclid(k6_real_1(np__1,np__2),A,E))
                                          & H = E
                                          & I = F
                                          & D != E
                                          & r2_hidden(D,k3_topreal9(A,F,B))
                                          & r2_hidden(E,k2_topreal9(A,F,B))
                                          & ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(k15_euclid(A)))
                                             => ~ ( J != D
                                                  & k2_struct_0(k15_euclid(A),D,J) = k5_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal9(A,D,E),k3_topreal9(A,F,B))
                                                  & ( r2_hidden(E,k3_topreal9(A,F,B))
                                                   => J = E )
                                                  & ( C = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(np__2,k2_euclid_2(A,k20_euclid(A,E,k17_euclid(A,k18_euclid(k6_real_1(np__1,np__2),A,D),k18_euclid(k6_real_1(np__1,np__2),A,E))),k20_euclid(A,k17_euclid(A,k18_euclid(k6_real_1(np__1,np__2),A,D),k18_euclid(k6_real_1(np__1,np__2),A,E)),F)))),k8_square_1(k1_quin_1(k15_rvsum_1(k11_euclid(A,k8_euclid(A,H,G))),k3_xcmplx_0(np__2,k2_euclid_2(A,k20_euclid(A,E,k17_euclid(A,k18_euclid(k6_real_1(np__1,np__2),A,D),k18_euclid(k6_real_1(np__1,np__2),A,E))),k20_euclid(A,k17_euclid(A,k18_euclid(k6_real_1(np__1,np__2),A,D),k18_euclid(k6_real_1(np__1,np__2),A,E)),F))),k6_xcmplx_0(k15_rvsum_1(k11_euclid(A,k8_euclid(A,G,I))),k5_square_1(B))))),k4_real_1(np__2,k15_rvsum_1(k11_euclid(A,k8_euclid(A,H,G)))))
                                                   => ( r2_hidden(E,k3_topreal9(A,F,B))
                                                      | J = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,C),A,k17_euclid(A,k18_euclid(k6_real_1(np__1,np__2),A,D),k18_euclid(k6_real_1(np__1,np__2),A,E))),k18_euclid(C,A,E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( ~ v1_xboole_0(k3_topreal9(A,C,B))
               => r1_xreal_0(np__0,B) ) ) ) ) )).

fof(t40_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ~ ( ~ v1_xboole_0(A)
                  & v1_xboole_0(k3_topreal9(A,C,B))
                  & r1_xreal_0(np__0,B) ) ) ) ) )).

fof(t41_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => k21_euclid(k17_euclid(np__2,k18_euclid(A,np__2,C),k18_euclid(B,np__2,D))) = k2_xcmplx_0(k3_xcmplx_0(A,k21_euclid(C)),k3_xcmplx_0(B,k21_euclid(D))) ) ) ) ) )).

fof(t42_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => k22_euclid(k17_euclid(np__2,k18_euclid(A,np__2,C),k18_euclid(B,np__2,D))) = k2_xcmplx_0(k3_xcmplx_0(A,k22_euclid(C)),k3_xcmplx_0(B,k22_euclid(D))) ) ) ) ) )).

fof(t43_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(D,k5_jgraph_6(A,B,C))
                  <=> k5_toprns_1(np__2,k20_euclid(np__2,D,k23_euclid(A,B))) = C ) ) ) ) ) )).

fof(t44_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(D,k7_jgraph_6(A,B,C))
                  <=> r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,D,k23_euclid(A,B))),C) ) ) ) ) ) )).

fof(t45_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(D,k6_jgraph_6(A,B,C))
                  <=> ~ r1_xreal_0(C,k5_toprns_1(np__2,k20_euclid(np__2,D,k23_euclid(A,B)))) ) ) ) ) ) )).

fof(t46_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => r1_tarski(k5_jgraph_6(A,B,C),k7_jgraph_6(A,B,C)) ) ) ) )).

fof(t47_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(np__2)))
                 => ( D = k23_euclid(A,B)
                   => k10_metric_1(k14_euclid(np__2),D,C) = k7_jgraph_6(A,B,C) ) ) ) ) ) )).

fof(t48_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(np__2)))
                 => ( D = k23_euclid(A,B)
                   => k9_metric_1(k14_euclid(np__2),D,C) = k6_jgraph_6(A,B,C) ) ) ) ) ) )).

fof(t49_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(np__2)))
                 => ( D = k23_euclid(A,B)
                   => k11_metric_1(k14_euclid(np__2),D,C) = k5_jgraph_6(A,B,C) ) ) ) ) ) )).

fof(t50_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k1_topreal9(np__2,k23_euclid(A,B),C) = k6_jgraph_6(A,B,C) ) ) ) )).

fof(t51_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k2_topreal9(np__2,k23_euclid(A,B),C) = k7_jgraph_6(A,B,C) ) ) ) )).

fof(t52_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k3_topreal9(np__2,k23_euclid(A,B),C) = k5_jgraph_6(A,B,C) ) ) ) )).

fof(t53_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => r1_tarski(k6_jgraph_6(A,B,C),k7_jgraph_6(A,B,C)) ) ) ) )).

fof(t54_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => r1_xboole_0(k6_jgraph_6(A,B,C),k5_jgraph_6(A,B,C)) ) ) ) )).

fof(t55_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k4_subset_1(u1_struct_0(k15_euclid(np__2)),k6_jgraph_6(A,B,C),k5_jgraph_6(A,B,C)) = k7_jgraph_6(A,B,C) ) ) ) )).

fof(t56_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k3_topreal9(np__2,k16_euclid(np__2),A))
           => k3_real_1(k7_square_1(k21_euclid(B)),k7_square_1(k22_euclid(B))) = k5_square_1(A) ) ) ) )).

fof(t57_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( D != E
                          & r2_hidden(D,k7_jgraph_6(A,B,C))
                          & r2_hidden(E,k7_jgraph_6(A,B,C))
                          & r1_xreal_0(C,np__0) ) ) ) ) ) ) )).

fof(t58_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ! [G] :
                              ( m2_finseq_2(G,k1_numbers,k1_euclid(np__2))
                             => ! [H] :
                                  ( m2_finseq_2(H,k1_numbers,k1_euclid(np__2))
                                 => ! [I] :
                                      ( m2_finseq_2(I,k1_numbers,k1_euclid(np__2))
                                     => ~ ( G = E
                                          & H = F
                                          & I = k23_euclid(A,B)
                                          & C = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(np__2,k2_euclid_2(np__2,k20_euclid(np__2,F,E),k20_euclid(np__2,E,k23_euclid(A,B))))),k8_square_1(k1_quin_1(k15_rvsum_1(k11_euclid(np__2,k8_euclid(np__2,H,G))),k3_xcmplx_0(np__2,k2_euclid_2(np__2,k20_euclid(np__2,F,E),k20_euclid(np__2,E,k23_euclid(A,B)))),k6_xcmplx_0(k15_rvsum_1(k11_euclid(np__2,k8_euclid(np__2,G,I))),k5_square_1(D))))),k4_real_1(np__2,k15_rvsum_1(k11_euclid(np__2,k8_euclid(np__2,H,G)))))
                                          & E != F
                                          & r2_hidden(E,k6_jgraph_6(A,B,D))
                                          & ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
                                             => ~ ( k1_struct_0(k15_euclid(np__2),J) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal9(np__2,E,F),k5_jgraph_6(A,B,D))
                                                  & J = k17_euclid(np__2,k18_euclid(k6_xcmplx_0(np__1,C),np__2,E),k18_euclid(C,np__2,F)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t59_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [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(D,k5_jgraph_6(A,B,C))
                          & r2_hidden(E,k6_jgraph_6(A,B,C)) )
                       => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,D,E),k5_jgraph_6(A,B,C)) = k1_struct_0(k15_euclid(np__2),D) ) ) ) ) ) ) )).

fof(t60_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [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(D,k5_jgraph_6(A,B,C))
                          & r2_hidden(E,k5_jgraph_6(A,B,C)) )
                       => r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,D,E),k2_struct_0(k15_euclid(np__2),D,E)),k6_jgraph_6(A,B,C)) ) ) ) ) ) ) )).

fof(t61_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [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(D,k5_jgraph_6(A,B,C))
                          & r2_hidden(E,k5_jgraph_6(A,B,C)) )
                       => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,D,E),k5_jgraph_6(A,B,C)) = k2_struct_0(k15_euclid(np__2),D,E) ) ) ) ) ) ) )).

fof(t62_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [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(D,k5_jgraph_6(A,B,C))
                          & r2_hidden(E,k5_jgraph_6(A,B,C)) )
                       => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal9(np__2,D,E),k5_jgraph_6(A,B,C)) = k2_struct_0(k15_euclid(np__2),D,E) ) ) ) ) ) ) )).

fof(t63_topreal9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ! [G] :
                              ( m2_finseq_2(G,k1_numbers,k1_euclid(np__2))
                             => ! [H] :
                                  ( m2_finseq_2(H,k1_numbers,k1_euclid(np__2))
                                 => ! [I] :
                                      ( m2_finseq_2(I,k1_numbers,k1_euclid(np__2))
                                     => ~ ( G = k17_euclid(np__2,k18_euclid(k6_real_1(np__1,np__2),np__2,E),k18_euclid(k6_real_1(np__1,np__2),np__2,F))
                                          & H = F
                                          & I = k23_euclid(A,B)
                                          & E != F
                                          & r2_hidden(E,k5_jgraph_6(A,B,C))
                                          & r2_hidden(F,k7_jgraph_6(A,B,C))
                                          & ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
                                             => ~ ( J != E
                                                  & k2_struct_0(k15_euclid(np__2),E,J) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal9(np__2,E,F),k5_jgraph_6(A,B,C))
                                                  & ( r2_hidden(F,k3_topreal9(np__2,k23_euclid(A,B),C))
                                                   => J = F )
                                                  & ( D = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(np__2,k2_euclid_2(np__2,k20_euclid(np__2,F,k17_euclid(np__2,k18_euclid(k6_real_1(np__1,np__2),np__2,E),k18_euclid(k6_real_1(np__1,np__2),np__2,F))),k20_euclid(np__2,k17_euclid(np__2,k18_euclid(k6_real_1(np__1,np__2),np__2,E),k18_euclid(k6_real_1(np__1,np__2),np__2,F)),k23_euclid(A,B))))),k8_square_1(k1_quin_1(k15_rvsum_1(k11_euclid(np__2,k8_euclid(np__2,H,G))),k3_xcmplx_0(np__2,k2_euclid_2(np__2,k20_euclid(np__2,F,k17_euclid(np__2,k18_euclid(k6_real_1(np__1,np__2),np__2,E),k18_euclid(k6_real_1(np__1,np__2),np__2,F))),k20_euclid(np__2,k17_euclid(np__2,k18_euclid(k6_real_1(np__1,np__2),np__2,E),k18_euclid(k6_real_1(np__1,np__2),np__2,F)),k23_euclid(A,B)))),k6_xcmplx_0(k15_rvsum_1(k11_euclid(np__2,k8_euclid(np__2,G,I))),k5_square_1(C))))),k4_real_1(np__2,k15_rvsum_1(k11_euclid(np__2,k8_euclid(np__2,H,G)))))
                                                   => ( r2_hidden(F,k3_topreal9(np__2,k23_euclid(A,B),C))
                                                      | J = k17_euclid(np__2,k18_euclid(k6_xcmplx_0(np__1,D),np__2,k17_euclid(np__2,k18_euclid(k6_real_1(np__1,np__2),np__2,E),k18_euclid(k6_real_1(np__1,np__2),np__2,F))),k18_euclid(D,np__2,F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_subset_1(k1_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) )).

fof(dt_k2_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_subset_1(k2_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) )).

fof(dt_k3_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_subset_1(k3_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) )).

fof(dt_k4_topreal9,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k4_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) )).

fof(d1_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( v1_xreal_0(C)
             => k1_topreal9(A,B,C) = a_3_0_topreal9(A,B,C) ) ) ) )).

fof(d2_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( v1_xreal_0(C)
             => k2_topreal9(A,B,C) = a_3_1_topreal9(A,B,C) ) ) ) )).

fof(d3_topreal9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( v1_xreal_0(C)
             => k3_topreal9(A,B,C) = a_3_2_topreal9(A,B,C) ) ) ) )).

fof(d6_topreal9,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)))
             => k4_topreal9(A,B,C) = a_3_3_topreal9(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_topreal9,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,u1_struct_0(k15_euclid(B)))
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_0_topreal9(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & ~ r1_xreal_0(D,k5_toprns_1(B,k20_euclid(B,E,C))) ) ) ) )).

fof(fraenkel_a_3_1_topreal9,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,u1_struct_0(k15_euclid(B)))
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_1_topreal9(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & r1_xreal_0(k5_toprns_1(B,k20_euclid(B,E,C)),D) ) ) ) )).

fof(fraenkel_a_3_2_topreal9,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,u1_struct_0(k15_euclid(B)))
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_2_topreal9(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & k5_toprns_1(B,k20_euclid(B,E,C)) = D ) ) ) )).

fof(fraenkel_a_3_3_topreal9,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,u1_struct_0(k15_euclid(B)))
        & m1_subset_1(D,u1_struct_0(k15_euclid(B))) )
     => ( r2_hidden(A,a_3_3_topreal9(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_numbers)
            & A = k17_euclid(B,k18_euclid(k5_real_1(np__1,E),B,C),k18_euclid(E,B,D))
            & r1_xreal_0(np__0,E) ) ) ) )).
%------------------------------------------------------------------------------