SET007 Axioms: SET007+676.ax


%------------------------------------------------------------------------------
% File     : SET007+676 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Gauges and Cages. Part II
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : jordan1d [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   0 unit)
%            Number of atoms       :  383 (  21 equality)
%            Maximal formula depth :   17 (  10 average)
%            Number of connectives :  430 (  88 ~  ;   7  |; 239  &)
%                                         (   1 <=>;  95 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   0 propositional; 1-3 arity)
%            Number of functors    :   48 (   5 constant; 0-5 arity)
%            Number of variables   :  124 (   0 singleton;  96 !;  28 ?)
%            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(fc1_jordan1d,axiom,(
    ! [A] :
      ( ( v1_int_1(A)
        & v1_abian(A) )
     => ( v1_xreal_0(k2_xcmplx_0(A,np__2))
        & v1_int_1(k2_xcmplx_0(A,np__2))
        & v1_xcmplx_0(k2_xcmplx_0(A,np__2))
        & v1_abian(k2_xcmplx_0(A,np__2)) ) ) )).

fof(fc2_jordan1d,axiom,(
    ! [A] :
      ( ( v1_int_1(A)
        & ~ v1_abian(A) )
     => ( v1_xreal_0(k2_xcmplx_0(A,np__2))
        & v1_int_1(k2_xcmplx_0(A,np__2))
        & v1_xcmplx_0(k2_xcmplx_0(A,np__2))
        & ~ v1_abian(k2_xcmplx_0(A,np__2)) ) ) )).

fof(fc3_jordan1d,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers) )
     => ( v4_ordinal2(k2_newton(np__2,A))
        & v1_xreal_0(k2_newton(np__2,A))
        & ~ v3_xreal_0(k2_newton(np__2,A))
        & v1_int_1(k2_newton(np__2,A))
        & v1_xcmplx_0(k2_newton(np__2,A))
        & v1_abian(k2_newton(np__2,A)) ) ) )).

fof(fc4_jordan1d,axiom,(
    ! [A,B] :
      ( ( v1_abian(A)
        & m1_subset_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k5_numbers) )
     => ( v4_ordinal2(k2_newton(A,B))
        & v1_xreal_0(k2_newton(A,B))
        & ~ v3_xreal_0(k2_newton(A,B))
        & v1_int_1(k2_newton(A,B))
        & v1_xcmplx_0(k2_newton(A,B))
        & v1_abian(k2_newton(A,B)) ) ) )).

fof(t1_jordan1d,axiom,(
    ! [A,B] :
      ( ! [C] :
          ~ ( r2_hidden(C,A)
            & ! [D] :
                ~ ( r1_tarski(D,B)
                  & r1_tarski(C,k3_tarski(D)) ) )
     => r1_tarski(k3_tarski(A),k3_tarski(B)) ) )).

fof(t2_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( B != np__0
           => k3_xcmplx_0(k7_xcmplx_0(np__1,B),k2_newton(B,k1_nat_1(A,np__1))) = k2_newton(B,A) ) ) ) )).

fof(t3_jordan1d,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ v1_int_1(k7_xcmplx_0(A,B))
           => k4_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B))) = k2_xcmplx_0(k1_int_1(k7_xcmplx_0(k4_xcmplx_0(A),B)),np__1) ) ) ) )).

fof(t4_jordan1d,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v1_int_1(k7_xcmplx_0(A,B))
           => k4_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B))) = k1_int_1(k7_xcmplx_0(k4_xcmplx_0(A),B)) ) ) ) )).

fof(t5_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(A,np__0)
              & k4_nat_1(B,A) != np__0
              & k1_real_1(k3_nat_1(B,A)) != k2_xcmplx_0(k5_int_1(k1_real_1(B),A),np__1) ) ) ) )).

fof(t6_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k4_nat_1(B,A) = np__0
           => ( r1_xreal_0(A,np__0)
              | k1_real_1(k3_nat_1(B,A)) = k5_int_1(k1_real_1(B),A) ) ) ) ) )).

fof(t7_jordan1d,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__2,A)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,B)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(k1_jordan8(E,k1_nat_1(B,np__1)))) )
                       => ( r1_xreal_0(k3_finseq_1(k1_jordan8(E,B)),A)
                          | k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),A,C)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__2),D)) ) ) ) ) ) ) ) )).

fof(t8_jordan1d,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__2,A)
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,B)))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(k1_jordan8(E,k1_nat_1(B,np__1)))) )
                       => ( r1_xreal_0(k3_finseq_1(k1_jordan8(E,B)),A)
                          | k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,A)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,k1_nat_1(B,np__1)),D,k5_binarith(k2_nat_1(np__2,A),np__2))) ) ) ) ) ) ) ) )).

fof(t9_jordan1d,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)))) )
                 => ( ( r1_xreal_0(np__2,A)
                      & r1_xreal_0(np__2,C) )
                   => ( r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(A,np__1))
                      | r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(C,np__1))
                      | k3_goboard5(k1_jordan8(D,B),A,C) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__2),k5_binarith(k2_nat_1(np__2,C),np__2)),k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__1),k5_binarith(k2_nat_1(np__2,C),np__2))),k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__2),k5_binarith(k2_nat_1(np__2,C),np__1))),k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__1),k5_binarith(k2_nat_1(np__2,C),np__1))) ) ) ) ) ) ) )).

fof(t11_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k33_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t12_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k33_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t13_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k35_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t14_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k35_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t15_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k34_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t16_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k34_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t17_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k37_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t18_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k37_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t19_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k36_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t20_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k36_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t21_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k30_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t22_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k30_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t23_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k31_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).

fof(t24_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
              & r2_hidden(k31_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) )).

fof(t25_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
              & k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))) ) ) ) )).

fof(t26_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
              & k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))) ) ) ) )).

fof(t27_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k2_relat_1(k1_jordan9(B,A))) ) ) ) )).

fof(t28_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
              & k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) )).

fof(t29_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
              & k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) )).

fof(t30_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C),k2_relat_1(k1_jordan9(B,A))) ) ) ) )).

fof(t31_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
              & k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1) ) ) ) )).

fof(t32_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
              & k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1) ) ) ) )).

fof(t33_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k2_relat_1(k1_jordan9(B,A))) ) ) ) )).

fof(t34_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
              & k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,C) ) ) ) )).

fof(t35_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
              & k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,C) ) ) ) )).

fof(t36_jordan1d,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & 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)))) )
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
              & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,C),k2_relat_1(k1_jordan9(B,A))) ) ) ) )).

fof(t10_jordan1d,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)))) )
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__2,A)
                          & r1_xreal_0(np__2,C) )
                       => ( r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(A,np__1))
                          | r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(C,np__1))
                          | k3_goboard5(k1_jordan8(D,B),A,C) = k3_tarski(a_5_0_jordan1d(A,B,C,D,E)) ) ) ) ) ) ) ) )).

fof(fraenkel_a_5_0_jordan1d,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & m2_subset_1(D,k1_numbers,k5_numbers)
        & v6_compts_1(E,k15_euclid(np__2))
        & ~ v1_sppol_1(E)
        & ~ v2_sppol_1(E)
        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_subset_1(F,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_5_0_jordan1d(B,C,D,E,F))
      <=> ? [G,H] :
            ( m2_subset_1(G,k1_numbers,k5_numbers)
            & m2_subset_1(H,k1_numbers,k5_numbers)
            & A = k3_goboard5(k1_jordan8(E,k1_nat_1(C,F)),G,H)
            & r1_xreal_0(k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),B),k3_newton(np__2,k1_nat_1(F,np__1))),np__2),G)
            & r1_xreal_0(G,k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),B),k3_newton(np__2,F)),np__1))
            & r1_xreal_0(k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),D),k3_newton(np__2,k1_nat_1(F,np__1))),np__2),H)
            & r1_xreal_0(H,k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),D),k3_newton(np__2,F)),np__1)) ) ) ) )).
%------------------------------------------------------------------------------