SET007 Axioms: SET007+637.ax
%------------------------------------------------------------------------------
% File : SET007+637 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Characterization of the Continuity of Topologies
% 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 : waybel29 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 64 ( 4 unt; 0 def)
% Number of atoms : 906 ( 40 equ)
% Maximal formula atoms : 56 ( 14 avg)
% Number of connectives : 967 ( 125 ~; 0 |; 646 &)
% ( 15 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 64 ( 62 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 2 con; 0-6 aty)
% Number of variables : 182 ( 172 !; 10 ?)
% 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(cc1_waybel29,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v2_waybel18(A)
& v1_waybel25(A)
& v2_t_0topsp(A) ) ) ) ).
fof(rc1_waybel29,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& ~ v1_yellow_3(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v2_waybel18(A)
& v1_waybel25(A)
& v2_t_0topsp(A) ) ).
fof(fc1_waybel29,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v2_orders_2(k3_waybel24(A,B))
& v3_orders_2(k3_waybel24(A,B))
& v4_orders_2(k3_waybel24(A,B))
& v24_waybel_0(k3_waybel24(A,B))
& ~ v1_yellow_3(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(fc2_waybel29,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v2_orders_2(k6_yellow_1(A,B))
& v4_orders_2(k6_yellow_1(A,B))
& v1_yellow_0(k6_yellow_1(A,B))
& ~ v1_yellow_3(k6_yellow_1(A,B))
& v1_monoid_0(k6_yellow_1(A,B)) ) ) ).
fof(fc3_waybel29,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v2_orders_2(k3_waybel24(A,B))
& v3_orders_2(k3_waybel24(A,B))
& v4_orders_2(k3_waybel24(A,B))
& v1_yellow_0(k3_waybel24(A,B))
& ~ v1_yellow_3(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(cc2_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& ~ v1_yellow_3(B) ) ) ) ).
fof(cc3_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( v4_waybel11(B)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B) ) ) ) ) ).
fof(rc2_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B)
& v1_waybel_9(B)
& v4_waybel11(B) ) ) ).
fof(fc4_waybel29,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k2_waybel29(A,B,C))
& v1_funct_1(k2_waybel29(A,B,C))
& ~ v1_xboole_0(k2_waybel29(A,B,C))
& v1_funct_2(k2_waybel29(A,B,C),u1_struct_0(k1_waybel29(A)),u1_struct_0(k1_waybel29(B)))
& v1_partfun1(k2_waybel29(A,B,C),u1_struct_0(k1_waybel29(A)),u1_struct_0(k1_waybel29(B)))
& v5_pre_topc(k2_waybel29(A,B,C),k1_waybel29(A),k1_waybel29(B)) ) ) ).
fof(fc5_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_relat_1(k4_waybel29(A))
& v1_funct_1(k4_waybel29(A))
& v2_funct_1(k4_waybel29(A))
& ~ v1_xboole_0(k4_waybel29(A))
& v1_funct_2(k4_waybel29(A),u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
& v2_funct_2(k4_waybel29(A),u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
& v3_funct_2(k4_waybel29(A),u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
& v5_orders_3(k4_waybel29(A),k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)))
& v1_partfun1(k4_waybel29(A),u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
& v23_waybel_0(k4_waybel29(A),k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A))) ) ) ).
fof(fc6_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_relat_1(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)))
& v1_funct_1(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)))
& v2_funct_1(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)))
& ~ v1_xboole_0(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)))
& v1_funct_2(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))),u1_struct_0(k1_waybel26(A,k9_waybel18)))
& v2_funct_2(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))),u1_struct_0(k1_waybel26(A,k9_waybel18)))
& v3_funct_2(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))),u1_struct_0(k1_waybel26(A,k9_waybel18)))
& v1_funcop_1(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)))
& v5_orders_3(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),k2_yellow_1(u1_pre_topc(A)),k1_waybel26(A,k9_waybel18))
& v1_partfun1(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))),u1_struct_0(k1_waybel26(A,k9_waybel18)))
& v23_waybel_0(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),k2_yellow_1(u1_pre_topc(A)),k1_waybel26(A,k9_waybel18)) ) ) ).
fof(fc7_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_waybel18(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k1_waybel25(A))
& v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v4_orders_2(k1_waybel25(A))
& v1_yellow_0(k1_waybel25(A))
& v2_yellow_0(k1_waybel25(A))
& v3_yellow_0(k1_waybel25(A))
& v24_waybel_0(k1_waybel25(A))
& v25_waybel_0(k1_waybel25(A))
& v2_pre_topc(k1_waybel25(A))
& ~ v1_yellow_3(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A))
& v4_waybel11(k1_waybel25(A))
& v1_lattice3(k1_waybel25(A))
& v2_lattice3(k1_waybel25(A))
& v3_lattice3(k1_waybel25(A))
& v2_waybel_3(k1_waybel25(A))
& v3_waybel_3(k1_waybel25(A))
& v2_waybel18(k1_waybel25(A))
& v1_waybel25(k1_waybel25(A))
& v2_t_0topsp(k1_waybel25(A)) ) ) ).
fof(fc8_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k1_waybel26(A,k9_waybel18))
& v1_orders_2(k1_waybel26(A,k9_waybel18))
& v2_orders_2(k1_waybel26(A,k9_waybel18))
& v3_orders_2(k1_waybel26(A,k9_waybel18))
& v4_orders_2(k1_waybel26(A,k9_waybel18))
& v1_yellow_0(k1_waybel26(A,k9_waybel18))
& v2_yellow_0(k1_waybel26(A,k9_waybel18))
& v3_yellow_0(k1_waybel26(A,k9_waybel18))
& v24_waybel_0(k1_waybel26(A,k9_waybel18))
& v25_waybel_0(k1_waybel26(A,k9_waybel18))
& ~ v1_yellow_3(k1_waybel26(A,k9_waybel18))
& v1_lattice3(k1_waybel26(A,k9_waybel18))
& v2_lattice3(k1_waybel26(A,k9_waybel18))
& v3_lattice3(k1_waybel26(A,k9_waybel18))
& v1_monoid_0(k1_waybel26(A,k9_waybel18)) ) ) ).
fof(fc9_waybel29,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_waybel18(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ( ~ v3_struct_0(k3_waybel18(A,k7_waybel_5(A,B)))
& v1_pre_topc(k3_waybel18(A,k7_waybel_5(A,B)))
& v2_pre_topc(k3_waybel18(A,k7_waybel_5(A,B)))
& v2_waybel18(k3_waybel18(A,k7_waybel_5(A,B)))
& v1_waybel25(k3_waybel18(A,k7_waybel_5(A,B)))
& v2_t_0topsp(k3_waybel18(A,k7_waybel_5(A,B)))
& v1_monoid_0(k3_waybel18(A,k7_waybel_5(A,B))) ) ) ).
fof(fc10_waybel29,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( v1_relat_1(k5_waybel29(A,B,C))
& v1_funct_1(k5_waybel29(A,B,C))
& v2_funct_1(k5_waybel29(A,B,C))
& ~ v1_xboole_0(k5_waybel29(A,B,C))
& v1_funct_2(k5_waybel29(A,B,C),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C))))
& v2_funct_2(k5_waybel29(A,B,C),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C))))
& v3_funct_2(k5_waybel29(A,B,C),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C))))
& v1_funcop_1(k5_waybel29(A,B,C))
& v1_partfun1(k5_waybel29(A,B,C),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C)))) ) ) ).
fof(fc11_waybel29,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( v1_relat_1(k5_waybel29(A,B,k9_waybel18))
& v1_funct_1(k5_waybel29(A,B,k9_waybel18))
& v2_funct_1(k5_waybel29(A,B,k9_waybel18))
& ~ v1_xboole_0(k5_waybel29(A,B,k9_waybel18))
& v1_funct_2(k5_waybel29(A,B,k9_waybel18),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,k9_waybel18)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,k9_waybel18))))
& v2_funct_2(k5_waybel29(A,B,k9_waybel18),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,k9_waybel18)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,k9_waybel18))))
& v3_funct_2(k5_waybel29(A,B,k9_waybel18),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,k9_waybel18)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,k9_waybel18))))
& v1_funcop_1(k5_waybel29(A,B,k9_waybel18))
& v5_orders_3(k5_waybel29(A,B,k9_waybel18),k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,k9_waybel18))),k6_yellow_1(A,k1_waybel26(B,k9_waybel18)))
& v1_partfun1(k5_waybel29(A,B,k9_waybel18),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,k9_waybel18)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,k9_waybel18))))
& v23_waybel_0(k5_waybel29(A,B,k9_waybel18),k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,k9_waybel18))),k6_yellow_1(A,k1_waybel26(B,k9_waybel18))) ) ) ).
fof(t1_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v2_funct_1(C)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),k2_tops_2(A,B,C),C) = k7_grcat_1(B)
& k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,k2_tops_2(A,B,C)) = k7_grcat_1(A)
& v2_funct_1(k2_tops_2(A,B,C))
& v2_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ).
fof(t2_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_yellow_0(D,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
=> ( ( v2_waybel27(F)
& v2_funct_1(F)
& v2_funct_2(F,u1_struct_0(D),u1_struct_0(E)) )
=> v1_waybel27(k2_tops_2(D,E,F)) ) ) ) ) ) ) ) ).
fof(t3_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_yellow_0(D,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(E),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(E),u1_struct_0(D)) )
=> ( ( v1_waybel27(F)
& v2_funct_1(F)
& v2_funct_2(F,u1_struct_0(E),u1_struct_0(D)) )
=> v2_waybel27(k2_tops_2(E,D,F)) ) ) ) ) ) ) ) ).
fof(t4_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,k6_yellow_1(k2_zfmisc_1(A,B),C))
& m1_yellow_0(D,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C)))
& m1_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
=> ( ( v2_waybel27(F)
& v2_funct_1(F)
& v2_funct_2(F,u1_struct_0(D),u1_struct_0(E)) )
=> v23_waybel_0(F,D,E) ) ) ) ) ) ) ) ).
fof(t5_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,k6_yellow_1(k2_zfmisc_1(A,B),C))
& m1_yellow_0(D,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C)))
& m1_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(E),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(E),u1_struct_0(D)) )
=> ( ( v1_waybel27(F)
& v2_funct_1(F)
& v2_funct_2(F,u1_struct_0(E),u1_struct_0(D)) )
=> v23_waybel_0(F,E,D) ) ) ) ) ) ) ) ).
fof(t6_waybel29,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( l1_orders_2(C)
=> ! [D] :
( l1_orders_2(D)
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( v23_waybel_0(E,A,C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( F = E
=> v23_waybel_0(F,B,D) ) ) ) ) ) ) ) ) ) ).
fof(t7_waybel29,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( l1_orders_2(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(D,A,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v23_waybel_0(E,B,C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(C)) )
=> ( F = k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E)
=> v23_waybel_0(F,A,C) ) ) ) ) ) ) ) ) ) ).
fof(t8_waybel29,axiom,
$true ).
fof(t9_waybel29,axiom,
$true ).
fof(t10_waybel29,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v2_pre_topc(D)
& l1_pre_topc(D) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))
& g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) )
=> k6_borsuk_1(A,B) = k6_borsuk_1(C,D) ) ) ) ) ) ).
fof(t11_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_waybel24(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> ( v1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C))
& v1_funct_2(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),A,B)
& m2_relset_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(t12_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& l1_waybel_9(B) )
=> ( v4_waybel_0(k3_waybel24(A,B),k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(k3_waybel24(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ) ).
fof(t13_waybel29,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_waybel_9(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_waybel_9(D) )
=> ( g1_waybel_9(u1_struct_0(C),u1_orders_2(C),u1_pre_topc(C)) = g1_waybel_9(u1_struct_0(D),u1_orders_2(D),u1_pre_topc(D))
=> k3_waybel24(A,C) = k3_waybel24(B,D) ) ) ) ) ) ) ).
fof(t14_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> v24_waybel_0(k2_yellow16(A,B,C)) )
=> v24_waybel_0(k5_yellow_1(A,B)) ) ) ) ).
fof(t15_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v5_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v24_waybel_0(k2_yellow16(A,B,C))
& v1_yellow_0(k2_yellow16(A,B,C)) ) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_yellow_1(A,B)))
=> ( r1_waybel_3(k5_yellow_1(A,B),C,D)
<=> ( ! [E] :
( m1_subset_1(E,A)
=> r1_waybel_3(k6_waybel_3(A,B,E),k7_waybel_3(A,B,C,E),k7_waybel_3(A,B,D,E)) )
& ? [E] :
( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(A))
& ! [F] :
( m1_subset_1(F,A)
=> ( ~ r2_hidden(F,E)
=> k7_waybel_3(A,B,C,F) = k3_yellow_0(k2_yellow16(A,B,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_waybel29,axiom,
$true ).
fof(t17_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v4_waybel11(C)
& m1_yellow_9(C,A) )
=> u1_pre_topc(B) = u1_pre_topc(C) ) ) ) ).
fof(t18_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_waybel_9(B) )
=> ( ( g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) = g1_waybel_9(u1_struct_0(B),u1_orders_2(B),u1_pre_topc(B))
& v4_waybel11(A) )
=> v4_waybel11(B) ) ) ) ).
fof(d1_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_9(B)
& v4_waybel11(B)
& m1_yellow_9(B,A) )
=> B = k1_waybel29(A) ) ) ).
fof(t19_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> k1_waybel29(A) = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ).
fof(t20_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> k1_waybel29(A) = k1_waybel29(B) ) ) ) ).
fof(d2_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k2_waybel29(A,B,C) = C ) ) ) ).
fof(t21_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(C,A,B)
<=> v23_waybel_0(k2_waybel29(A,B,C),k1_waybel29(A),k1_waybel29(B)) ) ) ) ) ).
fof(t22_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> k1_waybel26(A,B) = k3_waybel24(A,B) ) ) ).
fof(d3_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k2_yellow_1(u1_pre_topc(k6_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k2_yellow_1(u1_pre_topc(B))))))
& m2_relset_1(C,u1_struct_0(k2_yellow_1(u1_pre_topc(k6_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k2_yellow_1(u1_pre_topc(B)))))) )
=> ( C = k3_waybel29(A,B)
<=> ! [D] :
( ( v3_pre_topc(D,k6_borsuk_1(A,B))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) )
=> k1_funct_1(C,D) = k6_waybel26(D,u1_struct_0(A)) ) ) ) ) ) ).
fof(d4_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
& m2_relset_1(B,u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A)))) )
=> ( B = k4_waybel29(A)
<=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k9_waybel18))
& v5_pre_topc(C,A,k9_waybel18)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k9_waybel18)) )
=> k1_funct_1(B,C) = k5_pre_topc(A,k9_waybel18,C,k1_tarski(np__1)) ) ) ) ) ).
fof(t23_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_funct_1(k2_tops_2(k1_waybel26(A,k9_waybel18),k2_yellow_1(u1_pre_topc(A)),k4_waybel29(A)),B) = k5_funct_3(B,u1_struct_0(A)) ) ) ).
fof(t24_waybel29,axiom,
k1_waybel25(k9_waybel18) = k1_waybel29(k3_yellow_1(np__1)) ).
fof(t25_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> k1_waybel25(k3_waybel18(A,k7_waybel_5(A,k1_waybel29(B)))) = k1_waybel29(k5_yellow_1(A,k7_waybel_5(A,B))) ) ) ).
fof(t26_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_waybel18(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> k1_waybel25(k3_waybel18(A,k7_waybel_5(A,B))) = k1_waybel29(k5_yellow_1(A,k7_waybel_5(A,k1_waybel25(B)))) ) ) ).
fof(d5_waybel29,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C))))
& m2_relset_1(D,u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C)))) )
=> ( D = k5_waybel29(A,B,C)
<=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(k3_waybel18(A,k7_waybel_5(A,C))))
& v5_pre_topc(E,B,k3_waybel18(A,k7_waybel_5(A,C)))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(k3_waybel18(A,k7_waybel_5(A,C)))) )
=> k1_funct_1(D,E) = k10_funct_6(E) ) ) ) ) ) ) ).
fof(t27_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v4_waybel11(C)
& m1_yellow_9(C,k2_yellow_1(u1_pre_topc(B))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel24(A,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_waybel24(A,C)))
=> ( r3_orders_2(k3_waybel24(A,C),D,E)
=> r1_tarski(k5_waybel26(D),k5_waybel26(E)) ) ) ) ) ) ) ).
fof(t28_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_waybel_9(C) )
=> ! [D] :
( ( v4_waybel11(D)
& m1_yellow_9(D,k3_waybel24(A,C)) )
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_waybel24(B,D)),u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)))
& m2_relset_1(E,u1_struct_0(k3_waybel24(B,D)),u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)))
& ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)),u1_struct_0(k3_waybel24(B,D)))
& m2_relset_1(F,u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)),u1_struct_0(k3_waybel24(B,D)))
& v1_waybel27(E)
& v2_funct_1(E)
& v2_funct_2(E,u1_struct_0(k3_waybel24(B,D)),u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)))
& v2_waybel27(F)
& v2_funct_1(F)
& v2_funct_2(F,u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)),u1_struct_0(k3_waybel24(B,D))) ) ) ) ) )
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_waybel_9(C) )
=> ! [D] :
( ( v4_waybel11(D)
& m1_yellow_9(D,k3_waybel24(A,C)) )
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_waybel24(B,D)),u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)))
& m2_relset_1(E,u1_struct_0(k3_waybel24(B,D)),u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)))
& ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)),u1_struct_0(k3_waybel24(B,D)))
& m2_relset_1(F,u1_struct_0(k3_waybel24(k6_borsuk_1(B,A),C)),u1_struct_0(k3_waybel24(B,D)))
& v1_waybel27(E)
& v23_waybel_0(E,k3_waybel24(B,D),k3_waybel24(k6_borsuk_1(B,A),C))
& v2_waybel27(F)
& v23_waybel_0(F,k3_waybel24(k6_borsuk_1(B,A),C),k3_waybel24(B,D)) ) ) ) ) ) ) ) ).
fof(t29_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( v3_waybel_3(k2_yellow_1(u1_pre_topc(A)))
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> v23_waybel_0(k3_waybel29(B,A),k2_yellow_1(u1_pre_topc(k6_borsuk_1(B,A))),k3_waybel24(B,k1_waybel29(k2_yellow_1(u1_pre_topc(A))))) ) ) ) ).
fof(t30_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( v3_waybel_3(k2_yellow_1(u1_pre_topc(A)))
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(k1_waybel29(k2_yellow_1(u1_pre_topc(A)))))
& v5_pre_topc(C,B,k1_waybel29(k2_yellow_1(u1_pre_topc(A))))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(k1_waybel29(k2_yellow_1(u1_pre_topc(A))))) )
=> ( v3_pre_topc(k5_waybel26(C),k6_borsuk_1(B,A))
& m1_subset_1(k5_waybel26(C),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,A)))) ) ) ) ) ) ).
fof(t32_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( v3_waybel_3(k2_yellow_1(u1_pre_topc(A)))
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v3_pre_topc(C,A)
& m1_connsp_2(C,A,B) )
=> ? [D] :
( v3_pre_topc(D,k1_waybel29(k2_yellow_1(u1_pre_topc(A))))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_waybel29(k2_yellow_1(u1_pre_topc(A))))))
& r2_hidden(C,D)
& m1_connsp_2(k1_setfam_1(D),A,B) ) ) ) ) ) ).
fof(t33_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ( v23_waybel_0(D,A,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( E = D
& v23_waybel_0(E,B,C) )
=> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) ) ) ) ) ) ) ) ).
fof(t34_waybel29,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
<=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> k5_waybel11(k3_yellow_3(B,A)) = u1_pre_topc(k6_borsuk_1(k1_waybel29(B),k1_waybel29(A))) ) ) ) ).
fof(t35_waybel29,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> k5_waybel11(k3_yellow_3(B,A)) = u1_pre_topc(k6_borsuk_1(k1_waybel29(B),k1_waybel29(A))) )
<=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> g1_pre_topc(u1_struct_0(k1_waybel29(k3_yellow_3(B,A))),u1_pre_topc(k1_waybel29(k3_yellow_3(B,A)))) = k6_borsuk_1(k1_waybel29(B),k1_waybel29(A)) ) ) ) ).
fof(t36_waybel29,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> k5_waybel11(k3_yellow_3(B,A)) = u1_pre_topc(k6_borsuk_1(k1_waybel29(B),k1_waybel29(A))) )
<=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> k1_waybel29(k3_yellow_3(B,A)) = k1_waybel25(k6_borsuk_1(k1_waybel29(B),k1_waybel29(A))) ) ) ) ).
fof(t37_waybel29,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
<=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> k1_waybel29(k3_yellow_3(B,A)) = k1_waybel25(k6_borsuk_1(k1_waybel29(B),k1_waybel29(A))) ) ) ) ).
fof(dt_k1_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_waybel_9(k1_waybel29(A))
& v4_waybel11(k1_waybel29(A))
& m1_yellow_9(k1_waybel29(A),A) ) ) ).
fof(dt_k2_waybel29,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k2_waybel29(A,B,C))
& v1_funct_2(k2_waybel29(A,B,C),u1_struct_0(k1_waybel29(A)),u1_struct_0(k1_waybel29(B)))
& m2_relset_1(k2_waybel29(A,B,C),u1_struct_0(k1_waybel29(A)),u1_struct_0(k1_waybel29(B))) ) ) ).
fof(dt_k3_waybel29,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( v1_funct_1(k3_waybel29(A,B))
& v1_funct_2(k3_waybel29(A,B),u1_struct_0(k2_yellow_1(u1_pre_topc(k6_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k2_yellow_1(u1_pre_topc(B))))))
& m2_relset_1(k3_waybel29(A,B),u1_struct_0(k2_yellow_1(u1_pre_topc(k6_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k2_yellow_1(u1_pre_topc(B)))))) ) ) ).
fof(dt_k4_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_funct_1(k4_waybel29(A))
& v1_funct_2(k4_waybel29(A),u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
& m2_relset_1(k4_waybel29(A),u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k2_yellow_1(u1_pre_topc(A)))) ) ) ).
fof(dt_k5_waybel29,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( v1_funct_1(k5_waybel29(A,B,C))
& v1_funct_2(k5_waybel29(A,B,C),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C))))
& m2_relset_1(k5_waybel29(A,B,C),u1_struct_0(k1_waybel26(B,k3_waybel18(A,k7_waybel_5(A,C)))),u1_struct_0(k6_yellow_1(A,k1_waybel26(B,C)))) ) ) ).
fof(t31_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( v3_waybel_3(k2_yellow_1(u1_pre_topc(A)))
<=> ( v3_pre_topc(a_1_0_waybel29(A),k6_borsuk_1(k1_waybel29(k2_yellow_1(u1_pre_topc(A))),A))
& m1_subset_1(a_1_0_waybel29(A),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k1_waybel29(k2_yellow_1(u1_pre_topc(A))),A)))) ) ) ) ).
fof(fraenkel_a_1_0_waybel29,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_0_waybel29(B))
<=> ? [C,D] :
( v3_pre_topc(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B))
& A = k4_tarski(C,D)
& r2_hidden(D,C) ) ) ) ).
%------------------------------------------------------------------------------