SET007 Axioms: SET007+876.ax
%------------------------------------------------------------------------------
% File : SET007+876 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 572 ( 71 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 482 ( 31 ~; 0 |; 282 &)
% ( 7 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 57 ( 55 usr; 1 prp; 0-3 aty)
% Number of functors : 80 ( 80 usr; 20 con; 0-6 aty)
% Number of variables : 157 ( 149 !; 8 ?)
% 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)) ) ) ) ).
%------------------------------------------------------------------------------