SET007 Axioms: SET007+581.ax


%------------------------------------------------------------------------------
% File     : SET007+581 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Bounded Domains and Unbounded Domains
% 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    : jordan2c [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  155 (   7 unit)
%            Number of atoms       : 1146 ( 205 equality)
%            Maximal formula depth :   38 (  10 average)
%            Number of connectives : 1166 ( 175 ~  ;   8  |; 489  &)
%                                         (  20 <=>; 474 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   50 (   1 propositional; 0-3 arity)
%            Number of functors    :   94 (  11 constant; 0-4 arity)
%            Number of variables   :  474 (   0 singleton; 452 !;  22 ?)
%            Maximal term depth    :    7 (   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(rc1_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_metric_1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v6_tbsp_1(B,A) ) ) )).

fof(fc1_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v1_xboole_0(k2_pre_topc(k15_euclid(A)))
        & v4_pre_topc(k2_pre_topc(k15_euclid(A)),k15_euclid(A))
        & v2_connsp_1(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) ) ) )).

fof(cc1_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( v6_compts_1(B,k15_euclid(A))
           => v1_jordan2c(B,A) ) ) ) )).

fof(fc2_jordan2c,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k1_topreal1(np__2,A,B))
        & v2_tops_1(k1_topreal1(np__2,A,B),k15_euclid(np__2)) ) ) )).

fof(fc3_jordan2c,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v1_jordan2c(k5_topreal1(np__2,A),np__2) ) ) )).

fof(t1_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( r1_xreal_0(A,np__0)
       => k18_complex1(A) = k7_binop_2(A) ) ) )).

fof(t2_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(B,k23_binop_2(A,np__2))
              & B != A
              & B != k23_binop_2(A,np__1)
              & B != k23_binop_2(A,np__2) ) ) ) )).

fof(t3_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(B,k23_binop_2(A,np__3))
              & B != A
              & B != k23_binop_2(A,np__1)
              & B != k23_binop_2(A,np__2)
              & B != k23_binop_2(A,np__3) ) ) ) )).

fof(t4_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(B,k23_binop_2(A,np__4))
              & B != A
              & B != k23_binop_2(A,np__1)
              & B != k23_binop_2(A,np__2)
              & B != k23_binop_2(A,np__3)
              & B != k23_binop_2(A,np__4) ) ) ) )).

fof(t5_jordan2c,axiom,(
    $true )).

fof(t6_jordan2c,axiom,(
    $true )).

fof(t7_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ~ ( k2_relat_1(C) = k2_tarski(A,B)
          & k3_finseq_1(C) = np__2
          & ~ ( k1_funct_1(C,np__1) = A
              & k1_funct_1(C,np__2) = B )
          & ~ ( k1_funct_1(C,np__1) = B
              & k1_funct_1(C,np__2) = A ) ) ) )).

fof(t8_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( v1_goboard1(C)
                & m2_finseq_1(C,k1_numbers) )
             => ( ( k2_relat_1(C) = k2_tarski(A,B)
                  & k3_finseq_1(C) = np__2
                  & r1_xreal_0(A,B) )
               => ( k1_goboard1(C,np__1) = A
                  & k1_goboard1(C,np__2) = B ) ) ) ) ) )).

fof(t9_jordan2c,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,k17_euclid(A,B,C),D) = k17_euclid(A,k20_euclid(A,B,D),C) ) ) ) ) )).

fof(t10_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => k18_complex1(k5_toprns_1(A,B)) = k5_toprns_1(A,B) ) ) )).

fof(t11_jordan2c,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_xreal_0(k18_complex1(k10_binop_2(k5_toprns_1(A,B),k5_toprns_1(A,C))),k5_toprns_1(A,k20_euclid(A,B,C))) ) ) ) )).

fof(t12_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k5_toprns_1(np__1,k2_jordan2b(A)) = k18_complex1(A) ) )).

fof(t13_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ( k20_euclid(A,B,k16_euclid(A)) = B
            & k20_euclid(A,k16_euclid(A),B) = k19_euclid(A,B) ) ) ) )).

fof(t14_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( v1_jordan1(B,A)
           => v2_connsp_1(B,k15_euclid(A)) ) ) ) )).

fof(t15_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C))))
                 => ( ( B = D
                      & v2_connsp_1(B,A) )
                   => v2_connsp_1(D,k3_pre_topc(A,C)) ) ) ) ) ) )).

fof(d1_jordan2c,axiom,(
    $true )).

fof(d2_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( v1_jordan2c(B,A)
          <=> ( v6_tbsp_1(B,k14_euclid(A))
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) )).

fof(t16_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( v1_jordan2c(C,A)
                  & r1_tarski(B,C) )
               => v1_jordan2c(B,A) ) ) ) ) )).

fof(d3_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r1_jordan2c(A,B,C)
              <=> ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C)
                  & v1_jordan2c(C,A) ) ) ) ) ) )).

fof(t17_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r1_jordan2c(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)))))
                    & D = C
                    & r3_connsp_1(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)),D)
                    & v6_tbsp_1(D,k14_euclid(A))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) ) )).

fof(d4_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r2_jordan2c(A,B,C)
              <=> ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C)
                  & ~ v1_jordan2c(C,A) ) ) ) ) ) )).

fof(t18_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r2_jordan2c(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)))))
                    & D = C
                    & r3_connsp_1(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)),D)
                    & ~ ( v6_tbsp_1(D,k14_euclid(A))
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) ) ) )).

fof(t19_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r1_jordan2c(A,B,C)
               => r1_tarski(C,k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) ) ) )).

fof(t20_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r2_jordan2c(A,B,C)
               => r1_tarski(C,k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) ) ) )).

fof(t21_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_jordan1(k2_pre_topc(k15_euclid(A)),A) ) )).

fof(t22_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v2_connsp_1(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) ) )).

fof(t23_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r3_connsp_1(k15_euclid(A),k2_pre_topc(k15_euclid(A))) ) )).

fof(t24_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => m1_connsp_3(k1_jordan2c(A,B),k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B))) ) ) )).

fof(t25_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => m1_connsp_3(k2_jordan2c(A,B),k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B))) ) ) )).

fof(t26_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r1_jordan2c(A,B,C)
               => r1_tarski(C,k1_jordan2c(A,B)) ) ) ) ) )).

fof(t27_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( r2_jordan2c(A,B,C)
               => r1_tarski(C,k2_jordan2c(A,B)) ) ) ) ) )).

fof(t28_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => r1_xboole_0(k1_jordan2c(A,B),k2_jordan2c(A,B)) ) ) )).

fof(t29_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => r1_tarski(k1_jordan2c(A,B),k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) )).

fof(t30_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => r1_tarski(k2_jordan2c(A,B),k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) )).

fof(t31_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => k4_subset_1(u1_struct_0(k15_euclid(A)),k1_jordan2c(A,B),k2_jordan2c(A,B)) = k3_subset_1(u1_struct_0(k15_euclid(A)),B) ) ) )).

fof(t32_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(A))
                            & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
                         => ~ ( v5_pre_topc(E,k5_topmetr,A)
                              & B = k1_funct_1(E,np__0)
                              & C = k1_funct_1(E,np__1)
                              & v5_pre_topc(F,k5_topmetr,A)
                              & C = k1_funct_1(F,np__0)
                              & D = k1_funct_1(F,np__1)
                              & ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(A))
                                    & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
                                 => ~ ( v5_pre_topc(G,k5_topmetr,A)
                                      & B = k1_funct_1(G,np__0)
                                      & D = k1_funct_1(G,np__1)
                                      & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),F))) ) ) ) ) ) ) ) ) ) )).

fof(t33_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( B = k1_euclid(A)
           => v2_connsp_1(B,k15_euclid(A)) ) ) ) )).

fof(d7_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k3_jordan2c(A) = k2_finseq_2(A,np__1) ) )).

fof(d8_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k5_jordan2c(A) = k4_jordan2c(A) ) )).

fof(t34_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k10_euclid(A,k4_jordan2c(A)) = k2_finseq_2(A,np__1) ) )).

fof(t35_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k12_euclid(k4_jordan2c(A)) = k9_square_1(A) ) )).

fof(t36_jordan2c,axiom,(
    k5_jordan2c(np__1) = k13_binarith(k1_numbers,np__1) )).

fof(t37_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k5_toprns_1(A,k5_jordan2c(A)) = k9_square_1(A) ) )).

fof(t38_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => r1_xreal_0(np__1,k5_toprns_1(A,k5_jordan2c(A))) ) ) )).

fof(t39_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
         => ~ ( r1_xreal_0(np__1,A)
              & B = k1_euclid(A)
              & v6_tbsp_1(B,k14_euclid(A)) ) ) ) )).

fof(t40_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( v1_jordan2c(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                   => ~ ( r2_hidden(D,B)
                        & r1_xreal_0(C,k5_toprns_1(A,D)) ) ) ) ) ) ) )).

fof(t41_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__1,A)
          & v1_jordan2c(k2_pre_topc(k15_euclid(A)),A) ) ) )).

fof(t42_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => k2_jordan2c(A,k1_pre_topc(k15_euclid(A))) = k1_euclid(A) ) ) )).

fof(t43_jordan2c,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)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
                            & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
                                & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
                             => ~ ( v5_pre_topc(F,k5_topmetr,k3_pre_topc(k15_euclid(A),E))
                                  & B = k1_funct_1(F,np__0)
                                  & C = k1_funct_1(F,np__1)
                                  & v5_pre_topc(G,k5_topmetr,k3_pre_topc(k15_euclid(A),E))
                                  & C = k1_funct_1(G,np__0)
                                  & D = k1_funct_1(G,np__1)
                                  & ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
                                        & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
                                     => ~ ( v5_pre_topc(H,k5_topmetr,k3_pre_topc(k15_euclid(A),E))
                                          & B = k1_funct_1(H,np__0)
                                          & D = k1_funct_1(H,np__1) ) ) ) ) ) ) ) ) ) ) )).

fof(t44_jordan2c,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ~ ( r2_hidden(C,B)
                          & r2_hidden(D,B)
                          & r2_hidden(E,B)
                          & r1_tarski(k3_topreal1(A,C,D),B)
                          & r1_tarski(k3_topreal1(A,D,E),B)
                          & ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
                                & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
                             => ~ ( v5_pre_topc(F,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
                                  & C = k1_funct_1(F,np__0)
                                  & E = k1_funct_1(F,np__1) ) ) ) ) ) ) ) ) )).

fof(t45_jordan2c,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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                         => ~ ( r2_hidden(C,B)
                              & r2_hidden(D,B)
                              & r2_hidden(E,B)
                              & r2_hidden(F,B)
                              & r1_tarski(k3_topreal1(A,C,D),B)
                              & r1_tarski(k3_topreal1(A,D,E),B)
                              & r1_tarski(k3_topreal1(A,E,F),B)
                              & ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
                                    & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
                                 => ~ ( v5_pre_topc(G,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
                                      & C = k1_funct_1(G,np__0)
                                      & F = k1_funct_1(G,np__1) ) ) ) ) ) ) ) ) ) )).

fof(t46_jordan2c,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)))
                 => ! [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)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k15_euclid(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k15_euclid(A)))
                                     => ~ ( r2_hidden(C,B)
                                          & r2_hidden(D,B)
                                          & r2_hidden(E,B)
                                          & r2_hidden(F,B)
                                          & r2_hidden(G,B)
                                          & r2_hidden(H,B)
                                          & r2_hidden(I,B)
                                          & r1_tarski(k3_topreal1(A,C,D),B)
                                          & r1_tarski(k3_topreal1(A,D,E),B)
                                          & r1_tarski(k3_topreal1(A,E,F),B)
                                          & r1_tarski(k3_topreal1(A,F,G),B)
                                          & r1_tarski(k3_topreal1(A,G,H),B)
                                          & r1_tarski(k3_topreal1(A,H,I),B)
                                          & ! [J] :
                                              ( ( v1_funct_1(J)
                                                & v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
                                                & m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
                                             => ~ ( v5_pre_topc(J,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
                                                  & C = k1_funct_1(J,np__0)
                                                  & I = k1_funct_1(J,np__1) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t47_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ~ ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( B != k18_euclid(D,A,C)
                        & C != k18_euclid(D,A,B) ) )
                  & r2_hidden(k16_euclid(A),k3_topreal1(A,B,C)) ) ) ) ) )).

fof(t48_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k14_euclid(A)))))
                 => ~ ( D = k3_topreal1(A,B,C)
                      & ~ r2_hidden(k16_euclid(A),k3_topreal1(A,B,C))
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                         => ~ ( r2_hidden(E,k3_topreal1(A,B,C))
                              & ~ r1_xreal_0(k5_toprns_1(A,E),np__0)
                              & k5_toprns_1(A,E) = k1_funct_1(k8_weierstr(k14_euclid(A),D),k16_euclid(A)) ) ) ) ) ) ) ) )).

fof(t51_jordan2c,axiom,(
    $true )).

fof(t52_jordan2c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ( m2_finseq_2(A,k1_numbers,k1_euclid(k3_finseq_1(A)))
        & m1_subset_1(A,u1_struct_0(k15_euclid(k3_finseq_1(A)))) ) ) )).

fof(t53_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ! [D] :
                  ( m2_finseq_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( ( C = B
                          & D = k9_euclid(A,E,B) )
                       => ( k3_finseq_1(C) = k3_finseq_1(D)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( ( r1_xreal_0(np__1,F)
                                  & r1_xreal_0(F,k3_finseq_1(C)) )
                               => k4_finseq_4(k5_numbers,k1_numbers,D,F) = k11_binop_2(E,k4_finseq_4(k5_numbers,k1_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).

fof(t54_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ~ ( B != k5_euclid(A)
                  & B = C
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,A)
                          & k1_funct_1(C,D) != np__0 ) ) ) ) ) ) )).

fof(t55_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k1_euclid(A))
         => ~ ( r1_xreal_0(np__2,A)
              & B != k5_euclid(A)
              & ! [C] :
                  ( m2_finseq_2(C,k1_numbers,k1_euclid(A))
                 => ~ ! [D] :
                        ( m1_subset_1(D,k1_numbers)
                       => ( C != k9_euclid(A,D,B)
                          & B != k9_euclid(A,D,C) ) ) ) ) ) ) )).

fof(t71_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
                     => ( ( B = E
                          & v2_connsp_1(B,k15_euclid(A))
                          & C = k1_connsp_3(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),D)),k4_connsp_3(k15_euclid(A),B,k3_subset_1(u1_struct_0(k15_euclid(A)),D)))
                          & r1_xboole_0(E,D) )
                       => ( v6_tbsp_1(E,k14_euclid(A))
                          | r2_jordan2c(A,D,C) ) ) ) ) ) ) ) )).

fof(t72_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_topmetr(k14_euclid(A),C))))
                 => ( ( r1_tarski(B,C)
                      & B = D
                      & v6_tbsp_1(D,k1_topmetr(k14_euclid(A),C)) )
                   => v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) ) )).

fof(t73_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( v6_compts_1(B,k15_euclid(A))
           => v1_jordan2c(B,A) ) ) ) )).

fof(t74_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ~ ( r1_xreal_0(np__1,A)
              & v1_jordan2c(B,A)
              & k3_subset_1(u1_struct_0(k15_euclid(A)),B) = k1_xboole_0 ) ) ) )).

fof(t76_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ~ ( r1_xreal_0(np__2,A)
              & v1_jordan2c(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ~ ( r2_jordan2c(A,B,C)
                      & C = k2_jordan2c(A,B) ) ) ) ) ) )).

fof(t78_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( D = k9_metric_1(k14_euclid(A),B,C)
                   => v1_jordan1(D,A) ) ) ) ) ) )).

fof(t80_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [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(k14_euclid(A)))
                     => ~ ( C != D
                          & r2_hidden(C,k9_metric_1(k14_euclid(A),E,B))
                          & r2_hidden(D,k9_metric_1(k14_euclid(A),E,B))
                          & ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                                & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                             => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(A))
                                  & k1_funct_1(F,np__0) = C
                                  & k1_funct_1(F,np__1) = D
                                  & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),F),k9_metric_1(k14_euclid(A),E,B)) ) ) ) ) ) ) ) ) )).

fof(t81_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [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)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                                & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                             => ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(A))
                                  & k1_funct_1(G,np__0) = C
                                  & k1_funct_1(G,np__1) = D
                                  & r2_hidden(E,k9_metric_1(k14_euclid(A),F,B))
                                  & r2_hidden(D,k9_metric_1(k14_euclid(A),F,B))
                                  & ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                                        & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                                     => ~ ( v5_pre_topc(H,k5_topmetr,k15_euclid(A))
                                          & k1_funct_1(H,np__0) = C
                                          & k1_funct_1(H,np__1) = E
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),H),k2_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),G),k9_metric_1(k14_euclid(A),F,B))) ) ) ) ) ) ) ) ) ) ) )).

fof(t82_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [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)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                                    & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                                 => ~ ( v5_pre_topc(H,k5_topmetr,k15_euclid(A))
                                      & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),H),G)
                                      & k1_funct_1(H,np__0) = C
                                      & k1_funct_1(H,np__1) = D
                                      & r2_hidden(E,k9_metric_1(k14_euclid(A),F,B))
                                      & r2_hidden(D,k9_metric_1(k14_euclid(A),F,B))
                                      & r1_tarski(k9_metric_1(k14_euclid(A),F,B),G)
                                      & ! [I] :
                                          ( ( v1_funct_1(I)
                                            & v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                                            & m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                                         => ~ ( v5_pre_topc(I,k5_topmetr,k15_euclid(A))
                                              & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),I),G)
                                              & k1_funct_1(I,np__0) = C
                                              & k1_funct_1(I,np__1) = E ) ) ) ) ) ) ) ) ) ) ) )).

fof(t87_jordan2c,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)))
                 => ~ ( v2_connsp_1(B,k15_euclid(A))
                      & v3_pre_topc(B,k15_euclid(A))
                      & r2_hidden(C,B)
                      & r2_hidden(D,B)
                      & C != D
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
                            & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
                         => ~ ( v5_pre_topc(E,k5_topmetr,k15_euclid(A))
                              & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),E),B)
                              & k1_funct_1(E,np__0) = C
                              & k1_funct_1(E,np__1) = D ) ) ) ) ) ) ) )).

fof(t89_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ( v3_pre_topc(B,k15_euclid(A))
           => v1_connsp_2(k3_pre_topc(k15_euclid(A),B)) ) ) ) )).

fof(t91_jordan2c,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(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
               => k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr),B,C) = k5_toprns_1(A,C) )
           => v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) ) )).

fof(t92_jordan2c,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(k3_topmetr))
          & m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
          & ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr),B,C) = k5_toprns_1(A,C) )
          & v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) )).

fof(d9_jordan2c,axiom,(
    $true )).

fof(d10_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_jordan2c(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) )).

fof(t93_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
         => ~ ( v5_pre_topc(B,k5_topmetr,k15_euclid(A))
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))
                    & m2_relset_1(C,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr)) )
                 => ~ ( ! [D] :
                          ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                         => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr),C,D) = k5_toprns_1(A,k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),B,D)) )
                      & v5_pre_topc(C,k5_topmetr,k3_topmetr) ) ) ) ) ) )).

fof(t94_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ~ ( v5_pre_topc(B,k5_topmetr,k15_euclid(A))
                  & r1_xreal_0(k5_toprns_1(A,k6_jordan2c(k5_topmetr,k15_euclid(A),B,np__0)),C)
                  & r1_xreal_0(C,k5_toprns_1(A,k6_jordan2c(k5_topmetr,k15_euclid(A),B,np__1)))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                     => k5_toprns_1(A,k6_jordan2c(k5_topmetr,k15_euclid(A),B,D)) != C ) ) ) ) ) )).

fof(t95_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( C = k13_binarith(k1_numbers,B)
               => k5_toprns_1(A,C) = k18_complex1(B) ) ) ) ) )).

fof(t97_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k3_finseq_1(k3_goboard2(k1_sprect_1(A))) = np__2
        & k1_matrix_1(k3_goboard2(k1_sprect_1(A))) = np__2
        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__1,np__2)
        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__2,np__2)
        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__3) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__2,np__1)
        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__4) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__1,np__1)
        & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__5) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__1,np__2) ) ) )).

fof(t98_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ v1_jordan2c(k2_goboard9(k1_sprect_1(A)),np__2) ) )).

fof(t99_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k2_goboard9(k1_sprect_1(A)),k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)))) ) )).

fof(t100_jordan2c,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r3_connsp_1(A,B)
                      & r3_connsp_1(A,C)
                      & v2_connsp_1(D,A) )
                   => ( r1_xboole_0(B,D)
                      | r1_xboole_0(C,D)
                      | B = C ) ) ) ) ) ) )).

fof(t101_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(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))))
         => ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_sprect_1(A))),B)
           => ( v1_jordan2c(B,np__2)
              | B = k2_goboard9(k1_sprect_1(A)) ) ) ) ) )).

fof(t102_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r1_tarski(k3_goboard9(k1_sprect_1(A)),k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
        & v1_jordan2c(k3_goboard9(k1_sprect_1(A)),np__2) ) ) )).

fof(t103_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k2_goboard9(k1_sprect_1(A)) = k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)))
        & k3_goboard9(k1_sprect_1(A)) = k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))) ) ) )).

fof(t104_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))) != k1_xboole_0
        & r2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)),k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
        & k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))) != k1_xboole_0
        & r1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)),k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)))) ) ) )).

fof(t105_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( k3_subset_1(u1_struct_0(A),B) != k1_xboole_0
           => ( v2_tops_1(B,A)
            <=> ! [C,D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r2_hidden(C,B)
                      & r2_hidden(C,D)
                      & v3_pre_topc(D,A)
                      & ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( r4_connsp_1(A,k3_subset_1(u1_struct_0(A),B),E)
                              & ~ r1_xboole_0(D,E) ) ) ) ) ) ) ) ) )).

fof(t106_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0
       => ( ( v2_tops_1(A,k15_euclid(np__2))
            & v2_jordan1(A) )
        <=> ? [B] :
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
              & ? [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                  & k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
                  & r1_xboole_0(B,C)
                  & k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),B),B) = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),C),C)
                  & A = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),B),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
                     => ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
                         => ( ( D = B
                              & E = C )
                           => ( r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),D)
                              & r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),E) ) ) ) ) ) ) ) ) ) )).

fof(t107_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( r1_xreal_0(np__1,A)
                  & C = k1_struct_0(k15_euclid(A),B) )
               => v2_tops_1(C,k15_euclid(A)) ) ) ) ) )).

fof(t108_jordan2c,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,k1_numbers)
             => ( ( k21_euclid(A) = k22_euclid(B)
                  & k7_binop_2(k22_euclid(A)) = k21_euclid(B)
                  & A = k18_euclid(C,np__2,B) )
               => ( k21_euclid(A) = np__0
                  & k22_euclid(A) = np__0
                  & A = k16_euclid(np__2) ) ) ) ) ) )).

fof(t109_jordan2c,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)))
         => v2_tops_1(k3_topreal1(np__2,A,B),k15_euclid(np__2)) ) ) )).

fof(t110_jordan2c,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) )).

fof(t111_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k14_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( D = C
                          & r2_hidden(E,k9_metric_1(k14_euclid(A),C,B)) )
                       => ( ~ r1_xreal_0(B,k5_toprns_1(A,k20_euclid(A,D,E)))
                          & ~ r1_xreal_0(B,k5_toprns_1(A,k20_euclid(A,E,D))) ) ) ) ) ) ) ) )).

fof(t112_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( ~ r1_xreal_0(B,np__0)
                  & r2_hidden(C,k5_topreal1(np__2,k1_sprect_1(A)))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r2_hidden(D,k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
                          & ~ r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,C,D))) ) ) ) ) ) ) )).

fof(t113_jordan2c,axiom,(
    k1_euclid(np__0) = k1_struct_0(k15_euclid(np__0),k16_euclid(np__0)) )).

fof(t114_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( v1_jordan2c(B,A)
           => v1_jordan2c(k1_jordan2c(A,B),A) ) ) ) )).

fof(t115_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r3_connsp_1(A,B)
                          & r3_connsp_1(A,C)
                          & r3_connsp_1(A,D)
                          & k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A)
                          & r1_xboole_0(D,B) )
                       => D = C ) ) ) ) ) ) )).

fof(t116_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ( v1_jordan2c(A,np__2)
          & v2_jordan1(A) )
       => r1_jordan2c(np__2,A,k1_jordan2c(np__2,A)) ) ) )).

fof(t117_jordan2c,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( ~ r1_xreal_0(B,np__0)
                  & r2_hidden(C,k5_topreal1(np__2,k1_sprect_1(A)))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r2_hidden(D,k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
                          & ~ r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,C,D))) ) ) ) ) ) ) )).

fof(t118_jordan2c,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
           => ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(B))
              | r2_hidden(B,k2_goboard9(A)) ) ) ) ) )).

fof(t119_jordan2c,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
           => ( r1_xreal_0(k21_euclid(B),k20_pscomp_1(k5_topreal1(np__2,A)))
              | r2_hidden(B,k2_goboard9(A)) ) ) ) ) )).

fof(t120_jordan2c,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
           => ( r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(B))
              | r2_hidden(B,k2_goboard9(A)) ) ) ) ) )).

fof(t121_jordan2c,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
           => ( r1_xreal_0(k22_euclid(B),k19_pscomp_1(k5_topreal1(np__2,A)))
              | r2_hidden(B,k2_goboard9(A)) ) ) ) ) )).

fof(dt_k1_jordan2c,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
     => m1_subset_1(k1_jordan2c(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) )).

fof(dt_k2_jordan2c,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
     => m1_subset_1(k2_jordan2c(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) )).

fof(dt_k3_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_finseq_1(k3_jordan2c(A),k1_numbers) ) )).

fof(dt_k4_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_finseq_2(k4_jordan2c(A),k1_numbers,k1_euclid(A)) ) )).

fof(redefinition_k4_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => k4_jordan2c(A) = k3_jordan2c(A) ) )).

fof(dt_k5_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k5_jordan2c(A),u1_struct_0(k15_euclid(A))) ) )).

fof(dt_k6_jordan2c,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k6_jordan2c(A,B,C,D),u1_struct_0(B)) ) )).

fof(d5_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => k1_jordan2c(A,B) = k3_tarski(a_2_0_jordan2c(A,B)) ) ) )).

fof(d6_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => k2_jordan2c(A,B) = k3_tarski(a_2_1_jordan2c(A,B)) ) ) )).

fof(t49_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(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)))
                     => ~ ( C = a_2_2_jordan2c(A,B)
                          & r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( D != k18_euclid(F,A,E)
                                & E != k18_euclid(F,A,D) ) )
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
                                 => ~ ( r2_hidden(F,C)
                                      & r2_hidden(G,C)
                                      & r1_tarski(k3_topreal1(A,D,F),C)
                                      & r1_tarski(k3_topreal1(A,F,G),C)
                                      & r1_tarski(k3_topreal1(A,G,E),C) ) ) ) ) ) ) ) ) ) )).

fof(t50_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(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)))
                     => ~ ( C = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B))
                          & r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( D != k18_euclid(F,A,E)
                                & E != k18_euclid(F,A,D) ) )
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
                                 => ~ ( r2_hidden(F,C)
                                      & r2_hidden(G,C)
                                      & r1_tarski(k3_topreal1(A,D,F),C)
                                      & r1_tarski(k3_topreal1(A,F,G),C)
                                      & r1_tarski(k3_topreal1(A,G,E),C) ) ) ) ) ) ) ) ) ) )).

fof(t56_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(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)))
                     => ~ ( r1_xreal_0(np__2,A)
                          & C = a_2_2_jordan2c(A,B)
                          & r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & ~ ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( D != k18_euclid(F,A,E)
                                  & E != k18_euclid(F,A,D) ) )
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(k15_euclid(A)))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(k15_euclid(A)))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(k15_euclid(A)))
                                             => ~ ( r2_hidden(F,C)
                                                  & r2_hidden(G,C)
                                                  & r2_hidden(H,C)
                                                  & r2_hidden(I,C)
                                                  & r2_hidden(J,C)
                                                  & r1_tarski(k3_topreal1(A,D,F),C)
                                                  & r1_tarski(k3_topreal1(A,F,G),C)
                                                  & r1_tarski(k3_topreal1(A,G,H),C)
                                                  & r1_tarski(k3_topreal1(A,H,I),C)
                                                  & r1_tarski(k3_topreal1(A,I,J),C)
                                                  & r1_tarski(k3_topreal1(A,J,E),C) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t57_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(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)))
                     => ~ ( r1_xreal_0(np__2,A)
                          & C = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B))
                          & r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & ~ ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( D != k18_euclid(F,A,E)
                                  & E != k18_euclid(F,A,D) ) )
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(k15_euclid(A)))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(k15_euclid(A)))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(k15_euclid(A)))
                                             => ~ ( r2_hidden(F,C)
                                                  & r2_hidden(G,C)
                                                  & r2_hidden(H,C)
                                                  & r2_hidden(I,C)
                                                  & r2_hidden(J,C)
                                                  & r1_tarski(k3_topreal1(A,D,F),C)
                                                  & r1_tarski(k3_topreal1(A,F,G),C)
                                                  & r1_tarski(k3_topreal1(A,G,H),C)
                                                  & r1_tarski(k3_topreal1(A,H,I),C)
                                                  & r1_tarski(k3_topreal1(A,I,J),C)
                                                  & r1_tarski(k3_topreal1(A,J,E),C) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t58_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( r1_xreal_0(np__1,A)
              & a_2_2_jordan2c(A,B) = k1_xboole_0 ) ) ) )).

fof(t59_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( r1_xreal_0(np__2,A)
                  & C = a_2_2_jordan2c(A,B) )
               => v2_connsp_1(C,k15_euclid(A)) ) ) ) ) )).

fof(t60_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( r1_xreal_0(np__1,A)
              & k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B)) = k1_xboole_0 ) ) ) )).

fof(t61_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( r1_xreal_0(np__2,A)
                  & C = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B)) )
               => v2_connsp_1(C,k15_euclid(A)) ) ) ) ) )).

fof(t62_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
             => ~ ( r1_xreal_0(np__1,B)
                  & C = k4_xboole_0(k1_euclid(B),a_2_4_jordan2c(A,B))
                  & v1_jordan2c(C,B) ) ) ) ) )).

fof(t63_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
         => ( B = a_1_0_jordan2c(A)
           => v1_jordan1(B,np__1) ) ) ) )).

fof(t64_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
         => ( B = a_1_1_jordan2c(A)
           => v1_jordan1(B,np__1) ) ) ) )).

fof(t65_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
         => ( B = a_1_0_jordan2c(A)
           => v2_connsp_1(B,k15_euclid(np__1)) ) ) ) )).

fof(t66_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
         => ( B = a_1_1_jordan2c(A)
           => v2_connsp_1(B,k15_euclid(np__1)) ) ) ) )).

fof(t67_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k14_euclid(np__1))))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
             => ( ( A = a_1_0_jordan2c(B)
                  & C = A )
               => ( v2_connsp_1(C,k15_euclid(np__1))
                  & ~ v6_tbsp_1(A,k14_euclid(np__1)) ) ) ) ) ) )).

fof(t68_jordan2c,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k14_euclid(np__1))))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
             => ( ( A = a_1_1_jordan2c(B)
                  & C = A )
               => ( v2_connsp_1(C,k15_euclid(np__1))
                  & ~ v6_tbsp_1(A,k14_euclid(np__1)) ) ) ) ) ) )).

fof(t69_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( ( r1_xreal_0(np__2,A)
                      & B = a_2_2_jordan2c(A,C)
                      & D = B )
                   => ( v2_connsp_1(D,k15_euclid(A))
                      & ~ v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) ) ) )).

fof(t70_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( ( r1_xreal_0(np__2,A)
                      & B = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,C))
                      & D = B )
                   => ( v2_connsp_1(D,k15_euclid(A))
                      & ~ v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) ) ) )).

fof(t75_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
                & C = a_2_3_jordan2c(A,B) )
            & ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
               => ( C = a_2_3_jordan2c(A,B)
                 => v6_tbsp_1(C,k14_euclid(A)) ) ) ) ) ) )).

fof(t77_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( C = a_2_3_jordan2c(A,B)
               => v1_jordan1(C,A) ) ) ) ) )).

fof(t79_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( C = a_2_3_jordan2c(A,B)
               => v2_connsp_1(C,k15_euclid(A)) ) ) ) ) )).

fof(t83_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( ( v2_connsp_1(B,k15_euclid(A))
                      & v3_pre_topc(B,k15_euclid(A))
                      & D = a_3_0_jordan2c(A,B,C) )
                   => v3_pre_topc(D,k15_euclid(A)) ) ) ) ) ) )).

fof(t84_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( ( v2_connsp_1(C,k15_euclid(A))
                      & v3_pre_topc(C,k15_euclid(A))
                      & r2_hidden(B,C)
                      & D = a_3_1_jordan2c(A,B,C) )
                   => v3_pre_topc(D,k15_euclid(A)) ) ) ) ) ) )).

fof(t85_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                 => ( ( r2_hidden(B,D)
                      & C = a_3_1_jordan2c(A,B,D) )
                   => r1_tarski(C,D) ) ) ) ) ) )).

fof(t86_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( ( v2_connsp_1(C,k15_euclid(A))
                      & v3_pre_topc(C,k15_euclid(A))
                      & r2_hidden(D,C)
                      & B = a_3_2_jordan2c(A,C,D) )
                   => r1_tarski(C,B) ) ) ) ) ) )).

fof(t88_jordan2c,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] :
              ( v1_xreal_0(C)
             => ( B = a_2_5_jordan2c(A,C)
               => ( v3_pre_topc(k3_subset_1(u1_struct_0(k15_euclid(A)),B),k15_euclid(A))
                  & v4_pre_topc(B,k15_euclid(A)) ) ) ) ) ) )).

fof(t90_jordan2c,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = a_2_5_jordan2c(A,D)
                      & k3_subset_1(u1_struct_0(k15_euclid(A)),C) = B )
                   => v1_connsp_2(k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) )).

fof(t96_jordan2c,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,k1_numbers)
             => ~ ( r1_xreal_0(np__1,A)
                  & ~ r1_xreal_0(C,np__0)
                  & B = a_2_6_jordan2c(A,C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                     => ~ ( r1_jordan2c(A,B,D)
                          & D = k1_jordan2c(A,B) ) ) ) ) ) ) )).

fof(fraenkel_a_2_0_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) )
     => ( r2_hidden(A,a_2_0_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
            & A = D
            & r1_jordan2c(B,C,D) ) ) ) )).

fof(fraenkel_a_2_1_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) )
     => ( r2_hidden(A,a_2_1_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
            & A = D
            & r2_jordan2c(B,C,D) ) ) ) )).

fof(fraenkel_a_2_2_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_2_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
            & A = D
            & ~ r1_xreal_0(k5_toprns_1(B,D),C) ) ) ) )).

fof(fraenkel_a_2_3_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_3_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
            & A = D
            & ~ r1_xreal_0(C,k5_toprns_1(B,D)) ) ) ) )).

fof(fraenkel_a_2_4_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_4_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(C)))
            & A = D
            & ~ r1_xreal_0(B,k5_toprns_1(C,D)) ) ) ) )).

fof(fraenkel_a_1_0_jordan2c,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_numbers)
     => ( r2_hidden(A,a_1_0_jordan2c(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__1)))
            & A = C
            & ? [D] :
                ( m1_subset_1(D,k1_numbers)
                & C = k13_binarith(k1_numbers,D)
                & ~ r1_xreal_0(D,B) ) ) ) ) )).

fof(fraenkel_a_1_1_jordan2c,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_numbers)
     => ( r2_hidden(A,a_1_1_jordan2c(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__1)))
            & A = C
            & ? [D] :
                ( m1_subset_1(D,k1_numbers)
                & C = k13_binarith(k1_numbers,D)
                & ~ r1_xreal_0(k7_binop_2(B),D) ) ) ) ) )).

fof(fraenkel_a_3_0_jordan2c,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
        & m1_subset_1(D,u1_struct_0(k15_euclid(B))) )
     => ( r2_hidden(A,a_3_0_jordan2c(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & E != D
            & r2_hidden(E,C)
            & ! [F] :
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)))
                  & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) )
               => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B))
                    & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)),F),C)
                    & k1_funct_1(F,np__0) = D
                    & k1_funct_1(F,np__1) = E ) ) ) ) ) )).

fof(fraenkel_a_3_1_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) )
     => ( r2_hidden(A,a_3_1_jordan2c(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & ~ ( E != C
                & ! [F] :
                    ( ( v1_funct_1(F)
                      & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)))
                      & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) )
                   => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B))
                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)),F),D)
                        & k1_funct_1(F,np__0) = C
                        & k1_funct_1(F,np__1) = E ) ) ) ) ) ) )).

fof(fraenkel_a_3_2_jordan2c,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
        & m1_subset_1(D,u1_struct_0(k15_euclid(B))) )
     => ( r2_hidden(A,a_3_2_jordan2c(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & ~ ( E != D
                & ! [F] :
                    ( ( v1_funct_1(F)
                      & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)))
                      & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) )
                   => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B))
                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)),F),C)
                        & k1_funct_1(F,np__0) = D
                        & k1_funct_1(F,np__1) = E ) ) ) ) ) ) )).

fof(fraenkel_a_2_5_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_5_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
            & A = D
            & k5_toprns_1(B,D) = C ) ) ) )).

fof(fraenkel_a_2_6_jordan2c,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_6_jordan2c(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
            & A = D
            & k5_toprns_1(B,D) = C ) ) ) )).
%------------------------------------------------------------------------------