SET007 Axioms: SET007+876.ax


%------------------------------------------------------------------------------
% File     : SET007+876 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Circles on the Plane
% 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    : toprealb [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  121 (  15 unit)
%            Number of atoms       :  572 (  71 equality)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :  482 (  31 ~  ;   0  |; 282  &)
%                                         (   7 <=>; 162 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   57 (   1 propositional; 0-3 arity)
%            Number of functors    :   80 (  20 constant; 0-6 arity)
%            Number of variables   :  157 (   0 singleton; 149 !;   8 ?)
%            Maximal term depth    :    9 (   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_toprealb,axiom,
    ( ~ v1_xboole_0(k2_rcomp_1(np__0,np__1))
    & v1_membered(k2_rcomp_1(np__0,np__1))
    & v2_membered(k2_rcomp_1(np__0,np__1))
    & v3_rcomp_1(k2_rcomp_1(np__0,np__1)) )).

fof(fc2_toprealb,axiom,
    ( ~ v1_xboole_0(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v1_membered(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v2_membered(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v1_rcomp_1(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v2_rcomp_1(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v1_seq_4(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v2_seq_4(k1_rcomp_1(k1_real_1(np__1),np__1))
    & v3_seq_4(k1_rcomp_1(k1_real_1(np__1),np__1)) )).

fof(fc3_toprealb,axiom,
    ( ~ v1_xboole_0(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))
    & v1_membered(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))
    & v2_membered(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))
    & v3_rcomp_1(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))) )).

fof(fc4_toprealb,axiom,
    ( v1_relat_1(k18_sin_cos)
    & v1_funct_1(k18_sin_cos)
    & v1_jordan16(k18_sin_cos)
    & v1_seq_1(k18_sin_cos) )).

fof(fc5_toprealb,axiom,
    ( v1_relat_1(k21_sin_cos)
    & v1_funct_1(k21_sin_cos)
    & v1_jordan16(k21_sin_cos)
    & v1_seq_1(k21_sin_cos) )).

fof(fc6_toprealb,axiom,
    ( v1_relat_1(k1_sin_cos6)
    & v1_funct_1(k1_sin_cos6)
    & v2_funct_1(k1_sin_cos6)
    & v1_jordan16(k1_sin_cos6)
    & v1_seq_1(k1_sin_cos6) )).

fof(fc7_toprealb,axiom,
    ( v1_relat_1(k4_sin_cos6)
    & v1_funct_1(k4_sin_cos6)
    & v2_funct_1(k4_sin_cos6)
    & v1_jordan16(k4_sin_cos6)
    & v1_seq_1(k4_sin_cos6) )).

fof(fc8_toprealb,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_jordan16(A,B))
        & v1_relat_1(k1_jordan16(A,B))
        & v1_funct_1(k1_jordan16(A,B))
        & v2_funct_1(k1_jordan16(A,B))
        & v1_funct_2(k1_jordan16(A,B),k1_numbers,k1_numbers)
        & v2_funct_2(k1_jordan16(A,B),k1_numbers,k1_numbers)
        & v1_jordan16(k1_jordan16(A,B))
        & v1_partfun1(k1_jordan16(A,B),k1_numbers,k1_numbers)
        & v1_seq_1(k1_jordan16(A,B)) ) ) )).

fof(fc9_toprealb,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ~ v1_xboole_0(k1_toprealb(A,B)) ) )).

fof(fc10_toprealb,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ v1_xboole_0(k5_toprealb(A)) ) )).

fof(fc11_toprealb,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => v3_pre_topc(k5_toprealb(A),k3_topalg_2) ) )).

fof(fc12_toprealb,axiom,(
    ! [A] :
      ( ( v2_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => v4_pre_topc(k5_toprealb(A),k3_topalg_2) ) )).

fof(fc13_toprealb,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v2_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v1_tsep_1(k3_pre_topc(k3_topalg_2,k5_toprealb(A)),k3_topalg_2)
        & v1_borsuk_6(k3_pre_topc(k3_topalg_2,k5_toprealb(A))) ) ) )).

fof(fc14_toprealb,axiom,(
    ! [A] :
      ( ( v2_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v2_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v1_borsuk_1(k3_pre_topc(k3_topalg_2,k5_toprealb(A)),k3_topalg_2)
        & v1_borsuk_6(k3_pre_topc(k3_topalg_2,k5_toprealb(A))) ) ) )).

fof(fc15_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_relat_1(k6_toprealb(A))
        & v1_funct_1(k6_toprealb(A))
        & v1_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A)))))
        & v2_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A))))) ) ) )).

fof(fc16_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v2_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_relat_1(k6_toprealb(A))
        & v1_funct_1(k6_toprealb(A))
        & v2_funct_1(k6_toprealb(A))
        & v1_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A)))))
        & v2_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A))))) ) ) )).

fof(fc17_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_jordan16(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_relat_1(k6_toprealb(A))
        & v1_funct_1(k6_toprealb(A))
        & v1_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A)))))
        & v2_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A)))))
        & v5_pre_topc(k6_toprealb(A),k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A))),k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A)))) ) ) )).

fof(fc18_toprealb,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_relat_1(k6_toprealb(k1_jordan16(A,B)))
        & v1_funct_1(k6_toprealb(k1_jordan16(A,B)))
        & v2_funct_1(k6_toprealb(k1_jordan16(A,B)))
        & v1_funct_2(k6_toprealb(k1_jordan16(A,B)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B))))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B))))))
        & v2_funct_2(k6_toprealb(k1_jordan16(A,B)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B))))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B))))))
        & v5_pre_topc(k6_toprealb(k1_jordan16(A,B)),k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B)))),k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B)))))
        & v1_t_0topsp(k6_toprealb(k1_jordan16(A,B)),k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B)))),k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,k1_jordan16(A,B))))) ) ) )).

fof(cc1_toprealb,axiom,(
    ! [A] :
      ( m1_pre_topc(A,k15_euclid(np__2))
     => ( v1_toprealb(A)
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_compts_1(A)
          & v10_pscomp_1(A)
          & v1_borsuk_2(A)
          & v1_monoid_0(A)
          & v2_monoid_0(A) ) ) ) )).

fof(fc19_toprealb,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k3_topreal9(np__2,B,A))
        & v4_pre_topc(k3_topreal9(np__2,B,A),k15_euclid(np__2))
        & v1_jordan2c(k3_topreal9(np__2,B,A),np__2)
        & v2_connsp_1(k3_topreal9(np__2,B,A),k15_euclid(np__2))
        & v6_compts_1(k3_topreal9(np__2,B,A),k15_euclid(np__2))
        & v1_topreal2(k3_topreal9(np__2,B,A)) ) ) )).

fof(fc20_toprealb,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ( ~ v3_struct_0(k7_toprealb(A,B,C))
        & v1_pre_topc(k7_toprealb(A,B,C))
        & v2_pre_topc(k7_toprealb(A,B,C))
        & v1_monoid_0(k7_toprealb(A,B,C))
        & v2_monoid_0(k7_toprealb(A,B,C)) ) ) )).

fof(fc21_toprealb,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xboole_0(C)
        & v1_xreal_0(C) )
     => ( v2_pre_topc(k7_toprealb(A,B,C))
        & v3_realset2(k7_toprealb(A,B,C))
        & v1_monoid_0(k7_toprealb(A,B,C))
        & v2_monoid_0(k7_toprealb(A,B,C)) ) ) )).

fof(fc22_toprealb,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( ~ v3_struct_0(k7_toprealb(np__2,A,B))
        & v1_pre_topc(k7_toprealb(np__2,A,B))
        & v2_pre_topc(k7_toprealb(np__2,A,B))
        & v2_compts_1(k7_toprealb(np__2,A,B))
        & v10_pscomp_1(k7_toprealb(np__2,A,B))
        & v1_borsuk_2(k7_toprealb(np__2,A,B))
        & v1_monoid_0(k7_toprealb(np__2,A,B))
        & v2_monoid_0(k7_toprealb(np__2,A,B))
        & v1_toprealb(k7_toprealb(np__2,A,B)) ) ) )).

fof(rc1_toprealb,axiom,(
    ? [A] :
      ( m1_pre_topc(A,k15_euclid(np__2))
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_compts_1(A)
      & v10_pscomp_1(A)
      & v1_borsuk_2(A)
      & v1_monoid_0(A)
      & v2_monoid_0(A)
      & v1_toprealb(A) ) )).

fof(fc23_toprealb,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers) )
     => ( ~ v3_struct_0(k8_toprealb(A))
        & v2_pre_topc(k8_toprealb(A))
        & v1_monoid_0(k8_toprealb(A))
        & v2_monoid_0(k8_toprealb(A)) ) ) )).

fof(fc24_toprealb,axiom,
    ( ~ v3_struct_0(k8_toprealb(np__2))
    & v2_pre_topc(k8_toprealb(np__2))
    & v2_compts_1(k8_toprealb(np__2))
    & v10_pscomp_1(k8_toprealb(np__2))
    & v1_borsuk_2(k8_toprealb(np__2))
    & v1_monoid_0(k8_toprealb(np__2))
    & v2_monoid_0(k8_toprealb(np__2))
    & v1_toprealb(k8_toprealb(np__2)) )).

fof(fc25_toprealb,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v3_struct_0(k7_toprealb(np__2,A,B))
        & v1_pre_topc(k7_toprealb(np__2,A,B))
        & v2_pre_topc(k7_toprealb(np__2,A,B))
        & v1_borsuk_2(k7_toprealb(np__2,A,B))
        & v1_monoid_0(k7_toprealb(np__2,A,B))
        & v2_monoid_0(k7_toprealb(np__2,A,B)) ) ) )).

fof(fc26_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ( ~ v3_struct_0(k11_toprealb(A))
        & v1_pre_topc(k11_toprealb(A))
        & v2_pre_topc(k11_toprealb(A))
        & v1_monoid_0(k11_toprealb(A))
        & v2_monoid_0(k11_toprealb(A)) ) ) )).

fof(fc27_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ( ~ v3_struct_0(k11_toprealb(A))
        & v1_pre_topc(k11_toprealb(A))
        & v2_pre_topc(k11_toprealb(A))
        & v1_tsep_1(k11_toprealb(A),k8_toprealb(np__2))
        & v1_monoid_0(k11_toprealb(A))
        & v2_monoid_0(k11_toprealb(A)) ) ) )).

fof(fc28_toprealb,axiom,
    ( v1_relat_1(k12_toprealb)
    & v1_funct_1(k12_toprealb)
    & v1_funct_2(k12_toprealb,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)))
    & v5_pre_topc(k12_toprealb,k3_topalg_2,k8_toprealb(np__2)) )).

fof(fc29_toprealb,axiom,
    ( v1_relat_1(k12_toprealb)
    & v1_funct_1(k12_toprealb)
    & v1_funct_2(k12_toprealb,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)))
    & v2_funct_2(k12_toprealb,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)))
    & v5_pre_topc(k12_toprealb,k3_topalg_2,k8_toprealb(np__2)) )).

fof(fc30_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v1_relat_1(k7_relat_1(k12_toprealb,k1_rcomp_2(A,k2_xcmplx_0(A,np__1))))
        & v1_funct_1(k7_relat_1(k12_toprealb,k1_rcomp_2(A,k2_xcmplx_0(A,np__1))))
        & v2_funct_1(k7_relat_1(k12_toprealb,k1_rcomp_2(A,k2_xcmplx_0(A,np__1)))) ) ) )).

fof(fc31_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v1_relat_1(k7_relat_1(k12_toprealb,k2_rcomp_1(A,k2_xcmplx_0(A,np__1))))
        & v1_funct_1(k7_relat_1(k12_toprealb,k2_rcomp_1(A,k2_xcmplx_0(A,np__1))))
        & v2_funct_1(k7_relat_1(k12_toprealb,k2_rcomp_1(A,k2_xcmplx_0(A,np__1)))) ) ) )).

fof(fc32_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topalg_2))
     => ( v1_relat_1(k13_toprealb(A))
        & v1_funct_1(k13_toprealb(A))
        & v2_funct_1(k13_toprealb(A))
        & v1_funct_2(k13_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(A,k2_xcmplx_0(A,np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,A))))
        & v2_funct_2(k13_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(A,k2_xcmplx_0(A,np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,A))))
        & v5_pre_topc(k13_toprealb(A),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(A,k2_xcmplx_0(A,np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,A))) ) ) )).

fof(fc33_toprealb,axiom,
    ( v1_relat_1(k14_toprealb)
    & v1_funct_1(k14_toprealb)
    & v2_funct_1(k14_toprealb)
    & v1_funct_2(k14_toprealb,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))))
    & v2_funct_2(k14_toprealb,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))))
    & v5_pre_topc(k14_toprealb,k11_toprealb(k9_toprealb),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))) )).

fof(fc34_toprealb,axiom,
    ( v1_relat_1(k15_toprealb)
    & v1_funct_1(k15_toprealb)
    & v2_funct_1(k15_toprealb)
    & v1_funct_2(k15_toprealb,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))))
    & v2_funct_2(k15_toprealb,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))))
    & v5_pre_topc(k15_toprealb,k11_toprealb(k10_toprealb),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))) )).

fof(fc35_toprealb,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( v1_relat_1(k13_toprealb(k4_toprealb(A)))
        & v1_funct_1(k13_toprealb(k4_toprealb(A)))
        & v2_funct_1(k13_toprealb(k4_toprealb(A)))
        & v1_funct_2(k13_toprealb(k4_toprealb(A)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(A),k2_xcmplx_0(k4_toprealb(A),np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(A)))))
        & v2_funct_2(k13_toprealb(k4_toprealb(A)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(A),k2_xcmplx_0(k4_toprealb(A),np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(A)))))
        & v5_pre_topc(k13_toprealb(k4_toprealb(A)),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(A),k2_xcmplx_0(k4_toprealb(A),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(A))))
        & v1_t_0topsp(k13_toprealb(k4_toprealb(A)),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(A),k2_xcmplx_0(k4_toprealb(A),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(A)))) ) ) )).

fof(fc36_toprealb,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( v1_relat_1(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))))
        & v1_funct_1(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))))
        & v2_funct_1(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))))
        & v1_funct_2(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),k2_xcmplx_0(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))))))
        & v2_funct_2(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),k2_xcmplx_0(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))))))
        & v5_pre_topc(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),k2_xcmplx_0(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)))))
        & v1_t_0topsp(k13_toprealb(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),k2_xcmplx_0(k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A)),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(k2_xcmplx_0(k6_real_1(np__1,np__2),A))))) ) ) )).

fof(fc37_toprealb,axiom,
    ( v1_relat_1(k14_toprealb)
    & v1_funct_1(k14_toprealb)
    & v2_funct_1(k14_toprealb)
    & v1_funct_2(k14_toprealb,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))))
    & v2_funct_2(k14_toprealb,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))))
    & v5_pre_topc(k14_toprealb,k11_toprealb(k9_toprealb),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1))))
    & v1_t_0topsp(k14_toprealb,k11_toprealb(k9_toprealb),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))) )).

fof(fc38_toprealb,axiom,
    ( v1_relat_1(k15_toprealb)
    & v1_funct_1(k15_toprealb)
    & v2_funct_1(k15_toprealb)
    & v1_funct_2(k15_toprealb,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))))
    & v2_funct_2(k15_toprealb,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))))
    & v5_pre_topc(k15_toprealb,k11_toprealb(k10_toprealb),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))))
    & v1_t_0topsp(k15_toprealb,k11_toprealb(k10_toprealb),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))) )).

fof(t1_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(A,B),C)) = k2_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_jordan16(A,C),k18_sin_cos),B) ) ) ) )).

fof(t2_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k22_sin_cos(k2_xcmplx_0(k3_xcmplx_0(A,B),C)) = k2_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_jordan16(A,C),k21_sin_cos),B) ) ) ) )).

fof(t3_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( r2_hidden(C,k1_toprealb(A,B))
            <=> ? [D] :
                  ( m1_subset_1(D,k4_numbers)
                  & C = k2_rcomp_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,D)) ) ) ) ) )).

fof(t4_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(k6_xcmplx_0(A,B),np__1)
           => v4_taxonom2(k1_toprealb(B,A)) ) ) ) )).

fof(d2_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k4_toprealb(A) = A ) )).

fof(d3_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k5_toprealb(A) = A ) )).

fof(d4_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => k6_toprealb(A) = A ) )).

fof(t5_toprealb,axiom,(
    k3_pre_topc(k3_topalg_2,k5_toprealb(k2_subset_1(k1_numbers))) = k3_topalg_2 )).

fof(t6_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( k4_relset_1(k1_numbers,k1_numbers,A) = k1_numbers
       => k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A))) = k3_topalg_2 ) ) )).

fof(t7_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_numbers,k1_numbers)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k1_pscomp_1(k1_numbers,k1_numbers,A)))))
        & m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k1_pscomp_1(k1_numbers,k1_numbers,A))))) ) ) )).

fof(t8_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_numbers,k1_numbers)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2))
        & m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2)) ) ) )).

fof(d5_toprealb,axiom,(
    ! [A] :
      ( m1_pre_topc(A,k15_euclid(np__2))
     => ( v1_toprealb(A)
      <=> ( v1_topreal2(u1_struct_0(A))
          & m1_subset_1(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ) )).

fof(d6_toprealb,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( v1_xreal_0(C)
             => k7_toprealb(A,B,C) = k3_pre_topc(k15_euclid(A),k3_topreal9(A,B,C)) ) ) ) )).

fof(t9_toprealb,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => u1_struct_0(k7_toprealb(A,C,B)) = k3_topreal9(A,C,B) ) ) ) )).

fof(t10_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_pre_topc(k7_toprealb(np__2,k16_euclid(np__2),A),k1_topreala(k4_xcmplx_0(A),A,k4_xcmplx_0(A),A)) ) )).

fof(t11_toprealb,axiom,(
    ! [A] :
      ( ( v1_toprealb(A)
        & m1_pre_topc(A,k15_euclid(np__2)) )
     => ! [B] :
          ( ( v1_toprealb(B)
            & m1_pre_topc(B,k15_euclid(np__2)) )
         => r1_borsuk_3(A,B) ) ) )).

fof(d7_toprealb,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k8_toprealb(A) = k7_toprealb(A,k16_euclid(A),np__1) ) )).

fof(t12_toprealb,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ( m1_subset_1(B,u1_struct_0(k8_toprealb(A)))
           => k5_toprns_1(A,B) = np__1 ) ) ) )).

fof(t13_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
       => ( r1_xreal_0(k1_real_1(np__1),k21_euclid(A))
          & r1_xreal_0(k21_euclid(A),np__1)
          & r1_xreal_0(k1_real_1(np__1),k22_euclid(A))
          & r1_xreal_0(k22_euclid(A),np__1) ) ) ) )).

fof(t14_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
          & k21_euclid(A) = np__1 )
       => k22_euclid(A) = np__0 ) ) )).

fof(t15_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
          & k21_euclid(A) = k1_real_1(np__1) )
       => k22_euclid(A) = np__0 ) ) )).

fof(t16_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
          & k22_euclid(A) = np__1 )
       => k21_euclid(A) = np__0 ) ) )).

fof(t17_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
          & k22_euclid(A) = k1_real_1(np__1) )
       => k21_euclid(A) = np__0 ) ) )).

fof(t18_toprealb,axiom,(
    m1_pre_topc(k8_toprealb(np__2),k1_topreala(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)) )).

fof(t19_toprealb,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k8_toprealb(A)),u1_struct_0(k7_toprealb(A,C,B)))
                    & m2_relset_1(D,u1_struct_0(k8_toprealb(A)),u1_struct_0(k7_toprealb(A,C,B))) )
                 => ( ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k8_toprealb(A)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
                           => ( E = F
                             => k8_funct_2(u1_struct_0(k8_toprealb(A)),u1_struct_0(k7_toprealb(A,C,B)),D,E) = k17_euclid(A,k18_euclid(B,A,F),C) ) ) )
                   => v3_tops_2(D,k8_toprealb(A),k7_toprealb(A,C,B)) ) ) ) ) ) )).

fof(t20_toprealb,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => r1_borsuk_3(k7_toprealb(A,D,B),k7_toprealb(A,E,C)) ) ) ) ) ) )).

fof(d8_toprealb,axiom,(
    k9_toprealb = k23_euclid(np__1,np__0) )).

fof(d9_toprealb,axiom,(
    k10_toprealb = k23_euclid(k1_real_1(np__1),np__0) )).

fof(t21_toprealb,axiom,(
    k9_toprealb != k10_toprealb )).

fof(d10_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ! [B] :
          ( ( v1_pre_topc(B)
            & m1_pre_topc(B,k8_toprealb(np__2)) )
         => ( B = k11_toprealb(A)
          <=> u1_struct_0(B) = k4_xboole_0(u1_struct_0(k8_toprealb(np__2)),k1_struct_0(k8_toprealb(np__2),A)) ) ) ) )).

fof(t22_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ~ m1_subset_1(A,u1_struct_0(k11_toprealb(A))) ) )).

fof(t23_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => k11_toprealb(A) = k3_pre_topc(k8_toprealb(np__2),k6_subset_1(u1_struct_0(k8_toprealb(np__2)),k2_pre_topc(k8_toprealb(np__2)),k1_struct_0(k8_toprealb(np__2),A))) ) )).

fof(t24_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k8_toprealb(np__2)))
         => ( A != B
           => m1_subset_1(B,u1_struct_0(k11_toprealb(A))) ) ) ) )).

fof(t25_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( m1_subset_1(A,u1_struct_0(k11_toprealb(k9_toprealb)))
          & k22_euclid(A) = np__0 )
       => A = k10_toprealb ) ) )).

fof(t26_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( m1_subset_1(A,u1_struct_0(k11_toprealb(k10_toprealb)))
          & k22_euclid(A) = np__0 )
       => A = k9_toprealb ) ) )).

fof(t27_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( m1_subset_1(B,u1_struct_0(k11_toprealb(A)))
           => ( r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
              & r1_xreal_0(k21_euclid(B),np__1)
              & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
              & r1_xreal_0(k22_euclid(B),np__1) ) ) ) ) )).

fof(t28_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( m1_subset_1(A,u1_struct_0(k11_toprealb(k9_toprealb)))
       => ( r1_xreal_0(k1_real_1(np__1),k21_euclid(A))
          & ~ r1_xreal_0(np__1,k21_euclid(A)) ) ) ) )).

fof(t29_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( m1_subset_1(A,u1_struct_0(k11_toprealb(k10_toprealb)))
       => ( ~ r1_xreal_0(k21_euclid(A),k1_real_1(np__1))
          & r1_xreal_0(k21_euclid(A),np__1) ) ) ) )).

fof(t30_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => r1_borsuk_3(k11_toprealb(A),k1_borsuk_4) ) )).

fof(t31_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k8_toprealb(np__2)))
         => r1_borsuk_3(k11_toprealb(A),k11_toprealb(B)) ) ) )).

fof(d11_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)))
        & m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2))) )
     => ( A = k12_toprealb
      <=> ! [B] :
            ( v1_xreal_0(B)
           => k1_funct_1(A,B) = k23_euclid(k22_sin_cos(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),k19_sin_cos(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) ) ) ) )).

fof(t32_toprealb,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k1_funct_1(k12_toprealb,B) = k1_funct_1(k12_toprealb,k2_xcmplx_0(B,A)) ) ) )).

fof(t33_toprealb,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => k1_funct_1(k12_toprealb,A) = k9_toprealb ) )).

fof(t34_toprealb,axiom,(
    k5_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,k1_struct_0(k8_toprealb(np__2),k9_toprealb)) = k4_numbers )).

fof(t35_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( k4_int_1(A) = k6_real_1(np__1,np__2)
       => k1_funct_1(k12_toprealb,A) = k23_euclid(k1_real_1(np__1),np__0) ) ) )).

fof(t36_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( k4_int_1(A) = k6_real_1(np__1,np__4)
       => k1_funct_1(k12_toprealb,A) = k23_euclid(np__0,np__1) ) ) )).

fof(t37_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( k4_int_1(A) = k6_real_1(np__3,np__4)
       => k1_funct_1(k12_toprealb,A) = k23_euclid(np__0,k1_real_1(np__1)) ) ) )).

fof(t38_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k1_funct_1(k12_toprealb,A) = k23_euclid(k2_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_jordan16(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),k21_sin_cos),A),k2_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_jordan16(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),C)),k18_sin_cos),A)) ) ) ) )).

fof(t39_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topalg_2)))
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k3_topalg_2,A)),u1_struct_0(k8_toprealb(np__2)))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k3_topalg_2,A)),u1_struct_0(k8_toprealb(np__2))) )
         => ( ( r1_tarski(k1_rcomp_2(np__0,np__1),A)
              & B = k2_partfun1(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,A) )
           => v2_funct_2(B,u1_struct_0(k3_pre_topc(k3_topalg_2,A)),u1_struct_0(k8_toprealb(np__2))) ) ) ) )).

fof(t40_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(k6_xcmplx_0(A,B),np__1)
           => ! [C] :
                ( r2_hidden(C,k3_toprealb(B,A))
               => v2_funct_1(k2_partfun1(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,C)) ) ) ) ) )).

fof(t41_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( r2_hidden(C,k3_toprealb(A,B))
             => k4_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,C) = k4_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,k5_setfam_1(u1_struct_0(k3_topalg_2),k3_toprealb(A,B))) ) ) ) )).

fof(d12_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topalg_2))
     => k13_toprealb(A) = k2_partfun1(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k2_rcomp_1(A,k2_xcmplx_0(A,np__1))) ) )).

fof(t42_toprealb,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k13_toprealb(k4_toprealb(k2_xcmplx_0(B,A))) = k1_partfun1(k1_numbers,k1_numbers,u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(B),k2_xcmplx_0(k4_toprealb(B),np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(B)))),k2_partfun1(k1_numbers,k1_numbers,k1_jordan16(np__1,k4_xcmplx_0(A)),k2_rcomp_1(k2_xcmplx_0(B,A),k2_xcmplx_0(k2_xcmplx_0(B,A),np__1))),k13_toprealb(k4_toprealb(B))) ) ) )).

fof(d13_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))))
        & m2_relset_1(A,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1))))) )
     => ( A = k14_toprealb
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k11_toprealb(k9_toprealb)))
           => ? [C] :
                ( v1_xreal_0(C)
                & ? [D] :
                    ( v1_xreal_0(D)
                    & B = k23_euclid(C,D)
                    & ( r1_xreal_0(np__0,D)
                     => k8_funct_2(u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))),A,B) = k6_real_1(k6_sin_cos6(C),k4_real_1(np__2,k32_sin_cos)) )
                    & ( r1_xreal_0(D,np__0)
                     => k8_funct_2(u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))),A,B) = k5_real_1(np__1,k6_real_1(k6_sin_cos6(C),k4_real_1(np__2,k32_sin_cos))) ) ) ) ) ) ) )).

fof(d14_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))))
        & m2_relset_1(A,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))))) )
     => ( A = k15_toprealb
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k11_toprealb(k10_toprealb)))
           => ? [C] :
                ( v1_xreal_0(C)
                & ? [D] :
                    ( v1_xreal_0(D)
                    & B = k23_euclid(C,D)
                    & ( r1_xreal_0(np__0,D)
                     => k8_funct_2(u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))),A,B) = k3_real_1(np__1,k6_real_1(k6_sin_cos6(C),k4_real_1(np__2,k32_sin_cos))) )
                    & ( r1_xreal_0(D,np__0)
                     => k8_funct_2(u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))),A,B) = k5_real_1(np__1,k6_real_1(k6_sin_cos6(C),k4_real_1(np__2,k32_sin_cos))) ) ) ) ) ) ) )).

fof(t43_toprealb,axiom,(
    k2_tops_2(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(np__0),k2_xcmplx_0(k4_toprealb(np__0),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(np__0))),k13_toprealb(k4_toprealb(np__0))) = k14_toprealb )).

fof(t44_toprealb,axiom,(
    k2_tops_2(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k6_real_1(np__1,np__2)),k2_xcmplx_0(k4_toprealb(k6_real_1(np__1,np__2)),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(k6_real_1(np__1,np__2)))),k13_toprealb(k4_toprealb(k6_real_1(np__1,np__2)))) = k15_toprealb )).

fof(t45_toprealb,axiom,(
    $true )).

fof(t46_toprealb,axiom,(
    v3_tops_2(k13_toprealb(k4_toprealb(k6_real_1(np__1,np__2))),k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k6_real_1(np__1,np__2)),k2_xcmplx_0(k4_toprealb(k6_real_1(np__1,np__2)),np__1)))),k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,k4_toprealb(k6_real_1(np__1,np__2))))) )).

fof(t47_toprealb,axiom,(
    $true )).

fof(t48_toprealb,axiom,(
    $true )).

fof(t49_toprealb,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k8_toprealb(np__2)))))
      & A = k2_tarski(k4_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,k2_rcomp_1(np__0,np__1)),k4_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))
      & r1_pre_topc(k8_toprealb(np__2),A)
      & v1_tops_2(A,k8_toprealb(np__2))
      & ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k8_toprealb(np__2))))
         => ( ( B = k4_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,k2_rcomp_1(np__0,np__1))
             => ( k5_setfam_1(u1_struct_0(k3_topalg_2),k3_toprealb(np__0,np__1)) = k5_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,B)
                & ! [C] :
                    ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topalg_2)))
                   => ( r2_hidden(C,k3_toprealb(np__0,np__1))
                     => ! [D] :
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_topalg_2,C)),u1_struct_0(k3_pre_topc(k8_toprealb(np__2),B)))
                            & m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_topalg_2,C)),u1_struct_0(k3_pre_topc(k8_toprealb(np__2),B))) )
                         => ( D = k2_partfun1(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,C)
                           => v3_tops_2(D,k3_pre_topc(k3_topalg_2,C),k3_pre_topc(k8_toprealb(np__2),B)) ) ) ) ) ) )
            & ( B = k4_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))
             => ( k5_setfam_1(u1_struct_0(k3_topalg_2),k3_toprealb(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))) = k5_pre_topc(k3_topalg_2,k8_toprealb(np__2),k12_toprealb,B)
                & ! [C] :
                    ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topalg_2)))
                   => ( r2_hidden(C,k3_toprealb(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))
                     => ! [D] :
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_topalg_2,C)),u1_struct_0(k3_pre_topc(k8_toprealb(np__2),B)))
                            & m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_topalg_2,C)),u1_struct_0(k3_pre_topc(k8_toprealb(np__2),B))) )
                         => ( D = k2_partfun1(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,C)
                           => v3_tops_2(D,k3_pre_topc(k3_topalg_2,C),k3_pre_topc(k8_toprealb(np__2),B)) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_toprealb,axiom,(
    $true )).

fof(dt_k2_toprealb,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_toprealb(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topalg_2)))) ) )).

fof(redefinition_k2_toprealb,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k2_toprealb(A,B) = k1_toprealb(A,B) ) )).

fof(dt_k3_toprealb,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_tops_2(k3_toprealb(A,B),k3_topalg_2)
        & m1_subset_1(k3_toprealb(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topalg_2)))) ) ) )).

fof(redefinition_k3_toprealb,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k3_toprealb(A,B) = k1_toprealb(A,B) ) )).

fof(dt_k4_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k4_toprealb(A),u1_struct_0(k3_topalg_2)) ) )).

fof(dt_k5_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k5_toprealb(A),k1_zfmisc_1(u1_struct_0(k3_topalg_2))) ) )).

fof(dt_k6_toprealb,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_funct_1(k6_toprealb(A))
        & v1_funct_2(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A)))))
        & m2_relset_1(k6_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k4_relset_1(k1_numbers,k1_numbers,A)))),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k5_relset_1(k1_numbers,k1_numbers,A))))) ) ) )).

fof(dt_k7_toprealb,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_pre_topc(k7_toprealb(A,B,C),k15_euclid(A)) ) )).

fof(dt_k8_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_pre_topc(k8_toprealb(A),k15_euclid(A)) ) )).

fof(dt_k9_toprealb,axiom,(
    m1_subset_1(k9_toprealb,u1_struct_0(k8_toprealb(np__2))) )).

fof(dt_k10_toprealb,axiom,(
    m1_subset_1(k10_toprealb,u1_struct_0(k8_toprealb(np__2))) )).

fof(dt_k11_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_toprealb(np__2)))
     => ( v1_pre_topc(k11_toprealb(A))
        & m1_pre_topc(k11_toprealb(A),k8_toprealb(np__2)) ) ) )).

fof(dt_k12_toprealb,axiom,
    ( v1_funct_1(k12_toprealb)
    & v1_funct_2(k12_toprealb,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)))
    & m2_relset_1(k12_toprealb,u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2))) )).

fof(dt_k13_toprealb,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topalg_2))
     => ( v1_funct_1(k13_toprealb(A))
        & v1_funct_2(k13_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(A,k2_xcmplx_0(A,np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,A))))
        & m2_relset_1(k13_toprealb(A),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(A,k2_xcmplx_0(A,np__1))))),u1_struct_0(k11_toprealb(k8_funct_2(u1_struct_0(k3_topalg_2),u1_struct_0(k8_toprealb(np__2)),k12_toprealb,A)))) ) ) )).

fof(dt_k14_toprealb,axiom,
    ( v1_funct_1(k14_toprealb)
    & v1_funct_2(k14_toprealb,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1)))))
    & m2_relset_1(k14_toprealb,u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(np__0,np__1))))) )).

fof(dt_k15_toprealb,axiom,
    ( v1_funct_1(k15_toprealb)
    & v1_funct_2(k15_toprealb,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2))))))
    & m2_relset_1(k15_toprealb,u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k3_pre_topc(k3_topalg_2,k5_toprealb(k2_rcomp_1(k6_real_1(np__1,np__2),k6_real_1(np__3,np__2)))))) )).

fof(d1_toprealb,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k1_toprealb(A,B) = a_2_0_toprealb(A,B) ) ) )).

fof(fraenkel_a_2_0_toprealb,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_0_toprealb(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k4_numbers)
            & A = k2_rcomp_1(k2_xcmplx_0(B,D),k2_xcmplx_0(C,D)) ) ) ) )).
%------------------------------------------------------------------------------