SET007 Axioms: SET007+542.ax
%------------------------------------------------------------------------------
% File : SET007+542 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bases and Refinements 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 : yellow_9 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 121 ( 1 unt; 0 def)
% Number of atoms : 912 ( 89 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 905 ( 114 ~; 2 |; 480 &)
% ( 29 <=>; 280 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 71 ( 70 usr; 0 prp; 1-3 aty)
% Number of functors : 76 ( 76 usr; 20 con; 0-4 aty)
% Number of variables : 340 ( 308 !; 32 ?)
% 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(rc1_yellow_9,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_pre_topc(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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_waybel_9(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(rc2_yellow_9,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_pre_topc(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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_waybel_9(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_realset2(A) ) ).
fof(rc3_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& v19_waybel_0(C,A,B)
& v21_waybel_0(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(rc4_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(fc1_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ( v1_relat_1(k1_yellow_9(A,B))
& v1_funct_1(k1_yellow_9(A,B))
& ~ v1_xboole_0(k1_yellow_9(A,B))
& v1_funct_2(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A))
& v1_partfun1(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A))
& v5_orders_3(k1_yellow_9(A,B),B,A) ) ) ).
fof(fc2_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k2_yellow_9(A,B))
& v2_orders_2(k2_yellow_9(A,B))
& v6_waybel_0(k2_yellow_9(A,B),A) ) ) ).
fof(fc3_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_yellow_9(A,B))
& v2_orders_2(k3_yellow_9(A,B))
& v6_waybel_0(k3_yellow_9(A,B),A) ) ) ).
fof(fc4_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k2_yellow_9(A,B))
& v3_orders_2(k2_yellow_9(A,B))
& v6_waybel_0(k2_yellow_9(A,B),A) ) ) ).
fof(fc5_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_yellow_9(A,B))
& v3_orders_2(k3_yellow_9(A,B))
& v6_waybel_0(k3_yellow_9(A,B),A) ) ) ).
fof(fc6_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v2_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A)
& v7_waybel_0(k5_yellow_0(A,B)) ) ) ).
fof(fc7_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k2_yellow_9(A,B))
& v2_orders_2(k2_yellow_9(A,B))
& v6_waybel_0(k2_yellow_9(A,B),A)
& v7_waybel_0(k2_yellow_9(A,B)) ) ) ).
fof(fc8_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k4_waybel_9(k5_yellow_0(A,B)))
& v2_orders_2(k4_waybel_9(k5_yellow_0(A,B)))
& v6_waybel_0(k4_waybel_9(k5_yellow_0(A,B)),k5_yellow_0(A,B))
& v7_waybel_0(k4_waybel_9(k5_yellow_0(A,B)))
& v9_waybel_0(k4_waybel_9(k5_yellow_0(A,B)),k5_yellow_0(A,B))
& v11_waybel_0(k4_waybel_9(k5_yellow_0(A,B)),k5_yellow_0(A,B)) ) ) ).
fof(fc9_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_yellow_9(A,B))
& v2_orders_2(k3_yellow_9(A,B))
& v6_waybel_0(k3_yellow_9(A,B),A)
& v7_waybel_0(k3_yellow_9(A,B)) ) ) ).
fof(rc5_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_yellow_9(B,A)
& v2_pre_topc(B)
& v1_waybel_9(B)
& v1_tdlat_3(B)
& v3_tdlat_3(B) ) ) ).
fof(cc1_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ~ v3_struct_0(B) ) ) ).
fof(cc2_yellow_9,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v2_orders_2(B) ) ) ).
fof(cc3_yellow_9,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v3_orders_2(B) ) ) ).
fof(cc4_yellow_9,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v4_orders_2(B) ) ) ).
fof(cc5_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ) ).
fof(rc6_yellow_9,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] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v1_waybel_9(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ).
fof(cc6_yellow_9,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] :
( m1_yellow_9(B,A)
=> ( v4_waybel11(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ) ) ).
fof(rc7_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m2_yellow_9(B,A)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v3_tdlat_3(B) ) ) ).
fof(cc7_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& l1_pre_topc(B) )
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ~ v3_struct_0(C) ) ) ).
fof(cc8_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& l1_pre_topc(B) )
=> ! [C] :
( m3_yellow_9(C,B,A)
=> ~ v3_struct_0(C) ) ) ).
fof(t1_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k3_subset_1(u1_struct_0(A),k7_waybel_0(A,B)))
<=> ~ r1_orders_2(A,B,C) ) ) ) ) ).
fof(t2_yellow_9,axiom,
! [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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> k3_subset_1(u1_struct_0(A),k5_pre_topc(A,B,C,D)) = k5_pre_topc(A,B,C,k3_subset_1(u1_struct_0(B),D)) ) ) ) ) ).
fof(d1_yellow_9,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
=> k1_yellow_9(A,B) = k6_relat_1(u1_struct_0(B)) ) ) ) ).
fof(d2_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_yellow_9(A,B) = k7_waybel_9(k5_yellow_0(A,B),A,k1_yellow_9(A,k5_yellow_0(A,B)),k3_waybel_9(k5_yellow_0(A,B))) ) ) ).
fof(d3_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_yellow_9(A,B) = k7_waybel_9(k5_yellow_0(A,B),A,k1_yellow_9(A,k5_yellow_0(A,B)),k4_waybel_9(k5_yellow_0(A,B))) ) ) ).
fof(t6_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( u1_struct_0(k2_yellow_9(A,B)) = B
& v4_yellow_0(k2_yellow_9(A,B),A)
& m1_yellow_0(k2_yellow_9(A,B),A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_9(A,B)))
=> k3_waybel_0(A,k2_yellow_9(A,B),C) = C ) ) ) ) ).
fof(t7_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( u1_struct_0(k3_yellow_9(A,B)) = B
& v4_yellow_0(k3_yellow_9(A,B),k7_lattice3(A))
& m1_yellow_0(k3_yellow_9(A,B),k7_lattice3(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_9(A,B)))
=> k3_waybel_0(A,k3_yellow_9(A,B),C) = C ) ) ) ) ).
fof(t8_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_struct_0(A)
=> u1_pre_topc(A) = k1_tarski(k1_xboole_0) ) ) ).
fof(t9_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_realset2(A)
& l1_pre_topc(A) )
=> ( u1_pre_topc(A) = k1_zfmisc_1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( u1_struct_0(A) = k1_struct_0(A,B)
& u1_pre_topc(A) = k2_tarski(k1_xboole_0,k1_struct_0(A,B)) ) ) ) ) ).
fof(t10_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_realset2(A)
& l1_pre_topc(A) )
=> ( m1_cantor_1(k1_tarski(u1_struct_0(A)),A)
& m2_cantor_1(k1_xboole_0,A)
& m2_cantor_1(k1_tarski(k1_xboole_0),A) ) ) ).
fof(t11_yellow_9,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( C = k1_tarski(B)
=> ( k2_cantor_1(A,C) = k2_tarski(B,A)
& k1_cantor_1(A,C) = k2_tarski(B,k1_xboole_0) ) ) ) ).
fof(t12_yellow_9,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( B = k2_xboole_0(C,k1_tarski(A))
| C = k4_xboole_0(B,k1_tarski(A)) )
=> k8_setfam_1(A,B) = k8_setfam_1(A,C) ) ) ) ).
fof(t13_yellow_9,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( B = k2_xboole_0(C,k1_tarski(A))
| C = k4_xboole_0(B,k1_tarski(A)) )
=> k2_cantor_1(A,B) = k2_cantor_1(A,C) ) ) ) ).
fof(t14_yellow_9,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( r2_hidden(A,B)
=> ! [C] :
( r2_hidden(C,k2_cantor_1(A,B))
<=> ? [D] :
( ~ v1_xboole_0(D)
& v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
& r1_tarski(D,B)
& C = k8_setfam_1(A,D) ) ) ) ) ).
fof(t15_yellow_9,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> k1_cantor_1(A,k1_cantor_1(A,B)) = k1_cantor_1(A,B) ) ).
fof(t16_yellow_9,axiom,
! [A,B] :
( ( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k1_cantor_1(A,B) = k1_tarski(k1_xboole_0) ) ).
fof(t17_yellow_9,axiom,
! [A,B] :
( ( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k2_cantor_1(A,B) = k1_tarski(A) ) ).
fof(t18_yellow_9,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( B = k2_tarski(k1_xboole_0,A)
=> ( k1_cantor_1(A,B) = B
& k2_cantor_1(A,B) = B ) ) ) ).
fof(t19_yellow_9,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
=> ( ( r1_tarski(C,D)
=> r1_tarski(k1_cantor_1(A,C),k1_cantor_1(B,D)) )
& ( C = D
=> k1_cantor_1(A,C) = k1_cantor_1(B,D) ) ) ) ) ).
fof(t20_yellow_9,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
=> ( ( C = D
& r2_hidden(A,C)
& r1_tarski(A,B) )
=> k2_cantor_1(B,D) = k2_xboole_0(k1_tarski(B),k2_cantor_1(A,C)) ) ) ) ).
fof(t21_yellow_9,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> k1_cantor_1(A,k2_cantor_1(A,k1_cantor_1(A,B))) = k1_cantor_1(A,k2_cantor_1(A,B)) ) ).
fof(t22_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( u1_pre_topc(A) = k1_cantor_1(u1_struct_0(A),B)
<=> m1_cantor_1(B,A) ) ) ) ).
fof(t23_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( m2_cantor_1(B,A)
<=> m1_cantor_1(k2_cantor_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t24_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( m2_cantor_1(k1_cantor_1(u1_struct_0(A),B),A)
=> m2_cantor_1(B,A) ) ) ) ).
fof(t25_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_cantor_1(C,A)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& m1_cantor_1(C,B) )
=> u1_pre_topc(A) = u1_pre_topc(B) ) ) ) ) ).
fof(t26_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m2_cantor_1(C,A)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& m2_cantor_1(C,B) )
=> u1_pre_topc(A) = u1_pre_topc(B) ) ) ) ) ).
fof(t27_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> ( v1_tops_2(B,A)
& m2_cantor_1(B,A) ) ) ) ).
fof(t28_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> v1_tops_2(B,A) ) ) ).
fof(t29_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> m2_cantor_1(k2_xboole_0(B,k1_tarski(u1_struct_0(A))),A) ) ) ).
fof(t30_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> m1_cantor_1(k2_xboole_0(B,k1_tarski(u1_struct_0(A))),A) ) ) ).
fof(t31_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,B)
& r2_hidden(D,E)
& r1_tarski(E,C) ) ) ) ) ) ) ) ) ).
fof(t32_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ( r1_tarski(B,u1_pre_topc(A))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,B)
& r2_hidden(D,E)
& r1_tarski(E,C) ) ) ) ) ) ) )
=> m1_cantor_1(B,A) ) ) ) ).
fof(t33_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_cantor_1(C,B)
=> ! [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)) )
=> ( v5_pre_topc(D,A,B)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(E,C)
=> v4_pre_topc(k5_pre_topc(A,B,D,k3_subset_1(u1_struct_0(B),E)),A) ) ) ) ) ) ) ) ).
fof(t34_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_cantor_1(C,B)
=> ! [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)) )
=> ( v5_pre_topc(D,A,B)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(E,C)
=> v3_pre_topc(k5_pre_topc(A,B,D,E),A) ) ) ) ) ) ) ) ).
fof(t35_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m2_cantor_1(C,B)
=> ! [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)) )
=> ( v5_pre_topc(D,A,B)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(E,C)
=> v4_pre_topc(k5_pre_topc(A,B,D,k3_subset_1(u1_struct_0(B),E)),A) ) ) ) ) ) ) ) ).
fof(t36_yellow_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m2_cantor_1(C,B)
=> ! [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)) )
=> ( v5_pre_topc(D,A,B)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(E,C)
=> v3_pre_topc(k5_pre_topc(A,B,D,E),A) ) ) ) ) ) ) ) ).
fof(t37_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_cantor_1(D,A)
=> ( ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,D)
& r2_hidden(B,E)
& r1_xboole_0(E,C) ) )
=> r2_hidden(B,k6_pre_topc(A,C)) ) ) ) ) ) ).
fof(t38_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m2_cantor_1(D,A)
=> ( ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> ~ ( r1_tarski(E,D)
& r2_hidden(B,k8_setfam_1(u1_struct_0(A),E))
& r1_xboole_0(k8_setfam_1(u1_struct_0(A),E),C) ) )
=> r2_hidden(B,k6_pre_topc(A,C)) ) ) ) ) ) ).
fof(t39_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_hidden(E,B)
& r2_hidden(C,E) )
=> r1_waybel_0(A,D,E) ) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(k5_relset_1(u1_struct_0(D),u1_struct_0(A),k2_waybel_0(A,D)),E)
=> r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ) ).
fof(d4_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_waybel_9(B)
=> ( m1_yellow_9(B,A)
<=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ) ).
fof(t44_yellow_9,axiom,
! [A] :
( l1_waybel_9(A)
=> m1_yellow_9(A,A) ) ).
fof(t45_yellow_9,axiom,
! [A] :
( l1_waybel_9(A)
=> ! [B] :
( m1_yellow_9(B,A)
=> m1_yellow_9(A,B) ) ) ).
fof(t46_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_9(B,A)
=> ! [C] :
( m1_yellow_9(C,B)
=> m1_yellow_9(C,A) ) ) ) ).
fof(t47_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(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))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( C = D
& v1_waybel11(C,A) )
=> v1_waybel11(D,B) ) ) ) ) ) ) ).
fof(t48_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( u1_pre_topc(B) = k5_waybel11(A)
=> v2_pre_topc(B) ) ) ) ).
fof(t49_yellow_9,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] :
( m1_yellow_9(B,A)
=> ( u1_pre_topc(B) = k5_waybel11(A)
=> v4_waybel11(B) ) ) ) ).
fof(t50_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( C = D
& v3_pre_topc(C,A) )
=> v3_pre_topc(D,B) ) ) ) ) ) ) ).
fof(t51_yellow_9,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] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> u1_pre_topc(B) = k5_waybel11(A) ) ) ).
fof(t52_yellow_9,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) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> k5_waybel11(A) = k5_waybel11(B) ) ) ) ).
fof(d5_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( m2_yellow_9(B,A)
<=> ( u1_struct_0(A) = u1_struct_0(B)
& r1_tarski(u1_pre_topc(A),u1_pre_topc(B)) ) ) ) ) ).
fof(t53_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m2_yellow_9(B,A)
& v1_pre_topc(B)
& m2_cantor_1(u1_pre_topc(A),B) ) ) ).
fof(d6_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( ( v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( m3_yellow_9(C,A,B)
<=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
& m2_cantor_1(k2_xboole_0(u1_pre_topc(A),u1_pre_topc(B)),C) ) ) ) ) ) ).
fof(t54_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m3_yellow_9(D,A,B)
=> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) ) ) ) ) ).
fof(t55_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> m3_yellow_9(C,B,A) ) ) ) ).
fof(t56_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C))))
=> ( D = k2_xboole_0(u1_pre_topc(A),u1_pre_topc(B))
=> u1_pre_topc(C) = k1_cantor_1(u1_struct_0(C),k2_cantor_1(u1_struct_0(C),D)) ) ) ) ) ) ).
fof(t57_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ( m2_yellow_9(C,A)
& m2_yellow_9(C,B) ) ) ) ) ) ).
fof(t58_yellow_9,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] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m2_cantor_1(D,A)
=> ! [E] :
( m2_cantor_1(E,B)
=> m2_cantor_1(k2_xboole_0(k2_xboole_0(D,E),k2_tarski(u1_struct_0(A),u1_struct_0(B))),C) ) ) ) ) ) ).
fof(t59_yellow_9,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] :
( m1_cantor_1(C,A)
=> ! [D] :
( m1_cantor_1(D,B)
=> ! [E] :
( m3_yellow_9(E,A,B)
=> m1_cantor_1(k2_xboole_0(k2_xboole_0(C,D),k3_setfam_1(C,D)),E) ) ) ) ) ) ).
fof(t60_yellow_9,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) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> m1_cantor_1(k3_setfam_1(u1_pre_topc(A),u1_pre_topc(B)),C) ) ) ) ) ).
fof(t61_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v2_pre_topc(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( m3_yellow_9(D,B,C)
=> m1_cantor_1(k3_setfam_1(u1_pre_topc(B),u1_pre_topc(C)),D) ) ) ) ) ).
fof(dt_m1_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_9(B,A)
=> l1_waybel_9(B) ) ) ).
fof(existence_m1_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] : m1_yellow_9(B,A) ) ).
fof(dt_m2_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m2_yellow_9(B,A)
=> ( v2_pre_topc(B)
& l1_pre_topc(B) ) ) ) ).
fof(existence_m2_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] : m2_yellow_9(B,A) ) ).
fof(dt_m3_yellow_9,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& l1_pre_topc(B) )
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ( v2_pre_topc(C)
& l1_pre_topc(C) ) ) ) ).
fof(existence_m3_yellow_9,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& l1_pre_topc(B) )
=> ? [C] : m3_yellow_9(C,A,B) ) ).
fof(dt_k1_yellow_9,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ( v1_funct_1(k1_yellow_9(A,B))
& v1_funct_2(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k2_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k2_yellow_9(A,B))
& v6_waybel_0(k2_yellow_9(A,B),A)
& l1_waybel_0(k2_yellow_9(A,B),A) ) ) ).
fof(dt_k3_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_yellow_9(A,B))
& v6_waybel_0(k3_yellow_9(A,B),A)
& l1_waybel_0(k3_yellow_9(A,B),A) ) ) ).
fof(t3_yellow_9,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k7_setfam_1(u1_struct_0(A),B) = a_2_0_yellow_9(A,B) ) ) ).
fof(t4_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( k5_waybel_0(A,B) = k3_tarski(a_2_1_yellow_9(A,B))
& k4_waybel_0(A,B) = k3_tarski(a_2_2_yellow_9(A,B)) ) ) ) ).
fof(t5_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = a_2_3_yellow_9(A,C)
=> k8_setfam_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),k5_waybel_0(A,C)) ) ) ) ) ).
fof(t40_yellow_9,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] :
( m1_cantor_1(C,A)
=> ! [D] :
( m1_cantor_1(D,B)
=> m1_cantor_1(a_4_0_yellow_9(A,B,C,D),k6_borsuk_1(A,B)) ) ) ) ) ).
fof(t41_yellow_9,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] :
( m2_cantor_1(C,A)
=> ! [D] :
( m2_cantor_1(D,B)
=> m2_cantor_1(k2_xboole_0(a_3_0_yellow_9(A,B,D),a_3_1_yellow_9(A,B,C)),k6_borsuk_1(A,B)) ) ) ) ) ).
fof(t42_yellow_9,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B))))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(B))) )
=> ( C = a_4_1_yellow_9(A,B,D,E)
=> k8_setfam_1(k2_zfmisc_1(A,B),C) = k12_mcart_1(A,B,k8_setfam_1(A,D),k8_setfam_1(B,E)) ) ) ) ) ).
fof(t43_yellow_9,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] :
( m2_cantor_1(C,A)
=> ! [D] :
( m2_cantor_1(D,B)
=> ( ( k5_setfam_1(u1_struct_0(A),C) = u1_struct_0(A)
& k5_setfam_1(u1_struct_0(B),D) = u1_struct_0(B) )
=> m2_cantor_1(a_4_2_yellow_9(A,B,C,D),k6_borsuk_1(A,B)) ) ) ) ) ) ).
fof(s1_yellow_9,axiom,
( ( f3_s1_yellow_9 = a_0_0_yellow_9
& ! [A] :
( m1_subset_1(A,f1_s1_yellow_9)
=> f4_s1_yellow_9(f4_s1_yellow_9(A)) = A ) )
=> f2_s1_yellow_9 = a_0_1_yellow_9 ) ).
fof(s2_yellow_9,axiom,
( f2_s2_yellow_9 = a_0_2_yellow_9
=> k7_setfam_1(u1_struct_0(f1_s2_yellow_9),f2_s2_yellow_9) = a_0_3_yellow_9 ) ).
fof(s3_yellow_9,axiom,
( f2_s3_yellow_9 = a_0_4_yellow_9
=> k7_setfam_1(u1_struct_0(f1_s3_yellow_9),f2_s3_yellow_9) = a_0_5_yellow_9 ) ).
fof(s4_yellow_9,axiom,
k10_relat_1(f3_s4_yellow_9,k3_tarski(a_0_6_yellow_9)) = k3_tarski(a_0_7_yellow_9) ).
fof(fraenkel_a_2_0_yellow_9,axiom,
! [A,B,C] :
( ( l1_struct_0(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_0_yellow_9(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = k3_subset_1(u1_struct_0(B),D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_1_yellow_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_1_yellow_9(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k7_waybel_0(B,D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_2_yellow_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_2_yellow_9(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k6_waybel_0(B,D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_3_yellow_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_3_yellow_9(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k3_subset_1(u1_struct_0(B),k7_waybel_0(B,D))
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_4_0_yellow_9,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C)
& m1_cantor_1(D,B)
& m1_cantor_1(E,C) )
=> ( r2_hidden(A,a_4_0_yellow_9(B,C,D,E))
<=> ? [F,G] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C)))
& A = k7_borsuk_1(B,C,F,G)
& r2_hidden(F,D)
& r2_hidden(G,E) ) ) ) ).
fof(fraenkel_a_3_0_yellow_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C)
& m2_cantor_1(D,C) )
=> ( r2_hidden(A,a_3_0_yellow_9(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
& A = k2_zfmisc_1(u1_struct_0(B),E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_1_yellow_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C)
& m2_cantor_1(D,B) )
=> ( r2_hidden(A,a_3_1_yellow_9(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = k2_zfmisc_1(E,u1_struct_0(C))
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_4_1_yellow_9,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
& ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(C))) )
=> ( r2_hidden(A,a_4_1_yellow_9(B,C,D,E))
<=> ? [F,G] :
( m1_subset_1(F,k1_zfmisc_1(B))
& m1_subset_1(G,k1_zfmisc_1(C))
& A = k12_mcart_1(B,C,F,G)
& r2_hidden(F,D)
& r2_hidden(G,E) ) ) ) ).
fof(fraenkel_a_4_2_yellow_9,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C)
& m2_cantor_1(D,B)
& m2_cantor_1(E,C) )
=> ( r2_hidden(A,a_4_2_yellow_9(B,C,D,E))
<=> ? [F,G] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C)))
& A = k7_borsuk_1(B,C,F,G)
& r2_hidden(F,D)
& r2_hidden(G,E) ) ) ) ).
fof(fraenkel_a_0_0_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_0_yellow_9)
<=> ? [B] :
( m1_subset_1(B,f1_s1_yellow_9)
& A = f4_s1_yellow_9(B)
& r2_hidden(B,f2_s1_yellow_9) ) ) ).
fof(fraenkel_a_0_1_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_1_yellow_9)
<=> ? [B] :
( m1_subset_1(B,f1_s1_yellow_9)
& A = f4_s1_yellow_9(B)
& r2_hidden(B,f3_s1_yellow_9) ) ) ).
fof(fraenkel_a_0_2_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_2_yellow_9)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_yellow_9))
& A = f4_s2_yellow_9(B)
& r2_hidden(B,f3_s2_yellow_9) ) ) ).
fof(fraenkel_a_0_3_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_3_yellow_9)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_yellow_9))
& A = k3_subset_1(u1_struct_0(f1_s2_yellow_9),f4_s2_yellow_9(B))
& r2_hidden(B,f3_s2_yellow_9) ) ) ).
fof(fraenkel_a_0_4_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_4_yellow_9)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s3_yellow_9))
& A = k3_subset_1(u1_struct_0(f1_s3_yellow_9),f4_s3_yellow_9(B))
& r2_hidden(B,f3_s3_yellow_9) ) ) ).
fof(fraenkel_a_0_5_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_5_yellow_9)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s3_yellow_9))
& A = f4_s3_yellow_9(B)
& r2_hidden(B,f3_s3_yellow_9) ) ) ).
fof(fraenkel_a_0_6_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_6_yellow_9)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s4_yellow_9)))
& A = f2_s4_yellow_9(B)
& p1_s4_yellow_9(B) ) ) ).
fof(fraenkel_a_0_7_yellow_9,axiom,
! [A] :
( r2_hidden(A,a_0_7_yellow_9)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s4_yellow_9)))
& A = k10_relat_1(f3_s4_yellow_9,f2_s4_yellow_9(B))
& p1_s4_yellow_9(B) ) ) ).
%------------------------------------------------------------------------------