SET007 Axioms: SET007+602.ax


%------------------------------------------------------------------------------
% File     : SET007+602 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of Left and Right Components
% 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    : gobrd14 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   61 (   0 unit)
%            Number of atoms       :  597 (  43 equality)
%            Maximal formula depth :   29 (  11 average)
%            Number of connectives :  655 ( 119 ~  ;   4  |; 375  &)
%                                         (   4 <=>; 153 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   42 (   0 propositional; 1-3 arity)
%            Number of functors    :   58 (   9 constant; 0-5 arity)
%            Number of variables   :  140 (   0 singleton; 138 !;   2 ?)
%            Maximal term depth    :    8 (   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_gobrd14,axiom,(
    ! [A] :
      ( ( v4_pre_topc(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => v3_pre_topc(k1_jordan2c(np__2,A),k15_euclid(np__2)) ) )).

fof(fc2_gobrd14,axiom,(
    ! [A] :
      ( ( v4_pre_topc(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => v3_pre_topc(k2_jordan2c(np__2,A),k15_euclid(np__2)) ) )).

fof(fc3_gobrd14,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => v2_connsp_1(k2_jordan2c(np__2,A),k15_euclid(np__2)) ) )).

fof(fc4_gobrd14,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)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k5_topreal1(np__2,A))
        & v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v2_connsp_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v2_jordan1(k5_topreal1(np__2,A))
        & v1_jordan2c(k5_topreal1(np__2,A),np__2)
        & ~ v1_sppol_1(k5_topreal1(np__2,A))
        & ~ v2_sppol_1(k5_topreal1(np__2,A))
        & v1_topreal2(k5_topreal1(np__2,A))
        & v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ) )).

fof(t1_gobrd14,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)))
             => ( r4_connsp_1(A,B,C)
               => v2_connsp_1(C,A) ) ) ) ) )).

fof(t2_gobrd14,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)
               => v2_connsp_1(C,k15_euclid(A)) ) ) ) ) )).

fof(t3_gobrd14,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)
               => v2_connsp_1(C,k15_euclid(A)) ) ) ) ) )).

fof(t4_gobrd14,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))))
             => ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C)
               => r1_xboole_0(B,C) ) ) ) ) )).

fof(t5_gobrd14,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( ( r2_jordan2c(np__2,B,A)
                  & r1_jordan2c(np__2,B,C) )
               => r1_xboole_0(A,C) ) ) ) ) )).

fof(t6_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__2,A)
       => ! [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))))
                   => ( ( v1_jordan2c(D,A)
                        & r2_jordan2c(A,D,B)
                        & r2_jordan2c(A,D,C) )
                     => B = C ) ) ) ) ) ) )).

fof(t7_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k14_euclid(np__2)))
             => ~ ( C = k16_euclid(np__2)
                  & r2_jordan2c(np__2,k5_topreal1(np__2,A),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & r1_tarski(k3_subset_1(u1_struct_0(k14_euclid(np__2)),k9_metric_1(k14_euclid(np__2),C,D)),B) ) ) ) ) ) ) )).

fof(t8_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(A)))
         => ( k5_topreal1(A,B) != k1_xboole_0
           => r1_xreal_0(np__2,k3_finseq_1(B)) ) ) ) )).

fof(d1_gobrd14,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)
                 => ( D = k1_gobrd14(A,B,C)
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
                        & ? [F] :
                            ( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
                            & E = B
                            & F = C
                            & D = k4_metric_1(k14_euclid(A),E,F) ) ) ) ) ) ) ) )).

fof(t9_gobrd14,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)))
         => k1_gobrd14(np__2,A,B) = k9_square_1(k3_real_1(k7_square_1(k5_real_1(k21_euclid(A),k21_euclid(B))),k7_square_1(k5_real_1(k22_euclid(A),k22_euclid(B))))) ) ) )).

fof(t10_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => k1_gobrd14(A,B,B) = np__0 ) ) )).

fof(t11_gobrd14,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)))
                 => r1_xreal_0(k1_gobrd14(A,B,D),k3_real_1(k1_gobrd14(A,B,C),k1_gobrd14(A,C,D))) ) ) ) ) )).

fof(t12_gobrd14,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)))
                         => ( ( r1_xreal_0(A,k21_euclid(E))
                              & r1_xreal_0(k21_euclid(E),B)
                              & r1_xreal_0(C,k22_euclid(E))
                              & r1_xreal_0(k22_euclid(E),D)
                              & r1_xreal_0(A,k21_euclid(F))
                              & r1_xreal_0(k21_euclid(F),B)
                              & r1_xreal_0(C,k22_euclid(F))
                              & r1_xreal_0(k22_euclid(F),D) )
                           => r1_xreal_0(k1_gobrd14(np__2,E,F),k2_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) )).

fof(t13_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(np__1,B) )
               => ( r1_xreal_0(k3_finseq_1(C),A)
                  | r1_xreal_0(k1_matrix_1(C),B)
                  | k3_goboard5(C,A,B) = k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,k1_rcomp_1(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,np__1)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),np__1))),k1_rcomp_1(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1,B)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1,k1_nat_1(B,np__1)))))) ) ) ) ) ) )).

fof(t14_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(np__1,B) )
               => ( r1_xreal_0(k3_finseq_1(C),A)
                  | r1_xreal_0(k1_matrix_1(C),B)
                  | v6_compts_1(k3_goboard5(C,A,B),k15_euclid(np__2)) ) ) ) ) ) )).

fof(t15_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                      & r2_hidden(k4_tarski(k1_nat_1(A,C),B),k2_matrix_1(D)) )
                   => k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,C),B)) = k5_real_1(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,C),B)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B))) ) ) ) ) ) )).

fof(t16_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                      & r2_hidden(k4_tarski(A,k1_nat_1(B,C)),k2_matrix_1(D)) )
                   => k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,k1_nat_1(B,C))) = k5_real_1(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,k1_nat_1(B,C))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B))) ) ) ) ) ) )).

fof(t17_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => r1_xreal_0(np__3,k5_binarith(k3_finseq_1(k1_jordan8(B,A)),np__1)) ) ) )).

fof(t18_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v6_compts_1(C,k15_euclid(np__2))
                & ~ v1_sppol_1(C)
                & ~ v2_sppol_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ( r1_xreal_0(A,B)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(np__2,D)
                            & r1_xreal_0(D,k5_real_1(k3_finseq_1(k1_jordan8(C,A)),np__1))
                            & r1_xreal_0(np__2,E)
                            & r1_xreal_0(E,k5_real_1(k3_finseq_1(k1_jordan8(C,A)),np__1))
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ~ ( r1_xreal_0(np__2,F)
                                        & r1_xreal_0(F,k5_real_1(k3_finseq_1(k1_jordan8(C,B)),np__1))
                                        & r1_xreal_0(np__2,G)
                                        & r1_xreal_0(G,k5_real_1(k3_finseq_1(k1_jordan8(C,B)),np__1))
                                        & r2_hidden(k4_tarski(F,G),k2_matrix_1(k1_jordan8(C,B)))
                                        & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),D,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),F,G)
                                        & F = k1_nat_1(np__2,k2_nat_1(k1_card_4(np__2,k5_binarith(B,A)),k5_binarith(D,np__2)))
                                        & G = k1_nat_1(np__2,k2_nat_1(k1_card_4(np__2,k5_binarith(B,A)),k5_binarith(E,np__2))) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v6_compts_1(D,k15_euclid(np__2))
                    & ~ v1_sppol_1(D)
                    & ~ v2_sppol_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(k1_jordan8(D,C)))
                      & r2_hidden(k4_tarski(A,k1_nat_1(B,np__1)),k2_matrix_1(k1_jordan8(D,C))) )
                   => k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,C),A,k1_nat_1(B,np__1))) = k6_real_1(k5_real_1(k19_pscomp_1(D),k21_pscomp_1(D)),k1_card_4(np__2,C)) ) ) ) ) ) )).

fof(t20_gobrd14,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v6_compts_1(D,k15_euclid(np__2))
                    & ~ v1_sppol_1(D)
                    & ~ v2_sppol_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(k1_jordan8(D,C)))
                      & r2_hidden(k4_tarski(k1_nat_1(A,np__1),B),k2_matrix_1(k1_jordan8(D,C))) )
                   => k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,C),k1_nat_1(A,np__1),B)) = k6_real_1(k5_real_1(k20_pscomp_1(D),k18_pscomp_1(D)),k1_card_4(np__2,C)) ) ) ) ) ) )).

fof(t21_gobrd14,axiom,(
    ! [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] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,np__0)
                  & ~ r1_xreal_0(C,np__0)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__1)
                          & ~ r1_xreal_0(B,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__1,np__2)))
                          & ~ r1_xreal_0(C,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__2,np__1))) ) ) ) ) ) ) )).

fof(t22_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A))))))
         => ~ ( r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A))),B)
              & B != k3_goboard9(A)
              & B != k2_goboard9(A) ) ) ) )).

fof(t23_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( 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)),k5_topreal1(np__2,A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
                  & r1_xboole_0(B,C)
                  & ! [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)),k5_topreal1(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)),k5_topreal1(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)),k5_topreal1(np__2,A))),D)
                              & r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A))),E) ) ) ) )
                  & ~ ( B = k3_goboard9(A)
                      & C = k2_goboard9(A) )
                  & ~ ( B = k2_goboard9(A)
                      & C = k3_goboard9(A) ) ) ) ) ) )).

fof(t24_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_subset_1(k2_goboard9(A),k3_goboard9(A)) ) )).

fof(t25_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k3_goboard9(A)),k2_goboard9(A)) = u1_struct_0(k15_euclid(np__2)) ) )).

fof(t26_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k5_topreal1(np__2,A))
          <=> ( ~ r2_hidden(B,k2_goboard9(A))
              & ~ r2_hidden(B,k3_goboard9(A)) ) ) ) ) )).

fof(t27_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k2_goboard9(A))
          <=> ( ~ r2_hidden(B,k5_topreal1(np__2,A))
              & ~ r2_hidden(B,k3_goboard9(A)) ) ) ) ) )).

fof(t28_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k3_goboard9(A))
          <=> ( ~ r2_hidden(B,k5_topreal1(np__2,A))
              & ~ r2_hidden(B,k2_goboard9(A)) ) ) ) ) )).

fof(t29_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k5_topreal1(np__2,A) = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),k3_goboard9(A)),k3_goboard9(A)) ) )).

fof(t30_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k5_topreal1(np__2,A) = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),k2_goboard9(A)),k2_goboard9(A)) ) )).

fof(t31_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k6_pre_topc(k15_euclid(np__2),k3_goboard9(A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard9(A),k5_topreal1(np__2,A)) ) )).

fof(t32_gobrd14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k6_pre_topc(k15_euclid(np__2),k2_goboard9(A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k2_goboard9(A),k5_topreal1(np__2,A)) ) )).

fof(t33_gobrd14,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & ~ v5_seqm_3(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & v1_sprect_2(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(A,k3_goboard9(B))
              & r1_xreal_0(k21_euclid(A),k18_pscomp_1(k5_topreal1(np__2,B))) ) ) ) )).

fof(t34_gobrd14,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & ~ v5_seqm_3(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & v1_sprect_2(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(A,k3_goboard9(B))
              & r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(A)) ) ) ) )).

fof(t35_gobrd14,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & ~ v5_seqm_3(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & v1_sprect_2(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(A,k3_goboard9(B))
              & r1_xreal_0(k19_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(A)) ) ) ) )).

fof(t36_gobrd14,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & ~ v5_seqm_3(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & v1_sprect_2(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(A,k3_goboard9(B))
              & r1_xreal_0(k22_euclid(A),k21_pscomp_1(k5_topreal1(np__2,B))) ) ) ) )).

fof(t37_gobrd14,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] :
              ( ( ~ v1_xboole_0(C)
                & ~ v5_seqm_3(C)
                & v1_topreal1(C)
                & v2_topreal1(C)
                & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                & v1_goboard5(C)
                & v2_goboard5(C)
                & v1_sprect_2(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ~ ( r2_hidden(A,k3_goboard9(C))
                  & r2_hidden(B,k2_goboard9(C))
                  & r2_subset_1(k3_topreal1(np__2,A,B),k5_topreal1(np__2,C)) ) ) ) ) )).

fof(t38_gobrd14,axiom,(
    ! [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)))) )
     => k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_sprect_1(A))) = k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,k1_rcomp_1(k18_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))),k20_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A)))),k1_rcomp_1(k21_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))),k19_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A)))))) ) )).

fof(t39_gobrd14,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))) )
     => k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k6_pre_topc(k15_euclid(np__2),k3_goboard9(A))) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k5_topreal1(np__2,A)) ) )).

fof(t40_gobrd14,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))) )
     => k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k6_pre_topc(k15_euclid(np__2),k3_goboard9(A))) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_topreal1(np__2,A)) ) )).

fof(t41_gobrd14,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))) )
     => r1_tarski(k3_goboard9(A),k3_goboard9(k1_sprect_1(k5_topreal1(np__2,A)))) ) )).

fof(t42_gobrd14,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))) )
     => v6_compts_1(k6_pre_topc(k15_euclid(np__2),k3_goboard9(A)),k15_euclid(np__2)) ) )).

fof(t43_gobrd14,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))) )
     => ~ v1_jordan2c(k2_goboard9(A),np__2) ) )).

fof(t44_gobrd14,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))) )
     => r2_jordan2c(np__2,k5_topreal1(np__2,A),k2_goboard9(A)) ) )).

fof(t45_gobrd14,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))) )
     => r1_jordan2c(np__2,k5_topreal1(np__2,A),k3_goboard9(A)) ) )).

fof(t46_gobrd14,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))) )
     => k2_jordan2c(np__2,k5_topreal1(np__2,A)) = k2_goboard9(A) ) )).

fof(t47_gobrd14,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))) )
     => k1_jordan2c(np__2,k5_topreal1(np__2,A)) = k3_goboard9(A) ) )).

fof(t48_gobrd14,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,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( r2_jordan2c(np__2,k5_topreal1(np__2,A),B)
           => B = k2_goboard9(A) ) ) ) )).

fof(t49_gobrd14,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,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ~ ( r1_jordan2c(np__2,k5_topreal1(np__2,A),B)
              & r1_xboole_0(B,k3_goboard9(A)) ) ) ) )).

fof(t50_gobrd14,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,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( r1_jordan2c(np__2,k5_topreal1(np__2,A),B)
           => B = k1_jordan2c(np__2,k5_topreal1(np__2,A)) ) ) ) )).

fof(t51_gobrd14,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))) )
     => k18_pscomp_1(k5_topreal1(np__2,A)) = k18_pscomp_1(k3_goboard9(A)) ) )).

fof(t52_gobrd14,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))) )
     => k20_pscomp_1(k5_topreal1(np__2,A)) = k20_pscomp_1(k3_goboard9(A)) ) )).

fof(t53_gobrd14,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))) )
     => k19_pscomp_1(k5_topreal1(np__2,A)) = k19_pscomp_1(k3_goboard9(A)) ) )).

fof(t54_gobrd14,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))) )
     => k21_pscomp_1(k5_topreal1(np__2,A)) = k21_pscomp_1(k3_goboard9(A)) ) )).

fof(dt_k1_gobrd14,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(k1_gobrd14(A,B,C),k1_numbers) ) )).

fof(commutativity_k1_gobrd14,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))) )
     => k1_gobrd14(A,B,C) = k1_gobrd14(A,C,B) ) )).
%------------------------------------------------------------------------------