SET007 Axioms: SET007+505.ax
%------------------------------------------------------------------------------
% File : SET007+505 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Scott Topology
% 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 : waybel11 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 102 ( 0 unt; 0 def)
% Number of atoms : 1028 ( 41 equ)
% Maximal formula atoms : 22 ( 10 avg)
% Number of connectives : 1031 ( 105 ~; 0 |; 677 &)
% ( 33 <=>; 216 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 81 ( 80 usr; 0 prp; 1-3 aty)
% Number of functors : 52 ( 52 usr; 4 con; 0-3 aty)
% Number of variables : 247 ( 227 !; 20 ?)
% 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_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_waybel_0(B,A) ) ) ).
fof(rc2_waybel11,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(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)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v1_waybel_5(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v9_waybel_1(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(rc3_waybel11,axiom,
? [A] :
( l1_struct_0(A)
& v1_struct_0(A)
& ~ v3_struct_0(A)
& v6_group_1(A) ) ).
fof(cc1_waybel11,axiom,
! [A] :
( ( v6_group_1(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v1_finset_1(B) ) ) ).
fof(fc1_waybel11,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_xboole_0(k1_pre_topc(A))
& v1_finset_1(k1_pre_topc(A))
& v5_orders_2(k1_pre_topc(A),A)
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A))
& v1_waybel_0(k1_pre_topc(A),A)
& v2_waybel_0(k1_pre_topc(A),A)
& v12_waybel_0(k1_pre_topc(A),A)
& v13_waybel_0(k1_pre_topc(A),A) ) ) ).
fof(cc2_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v13_waybel_0(B,A) ) ) ).
fof(fc2_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_xboole_0(k1_pre_topc(A))
& v1_finset_1(k1_pre_topc(A))
& v5_orders_2(k1_pre_topc(A),A)
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A))
& v1_waybel_0(k1_pre_topc(A),A)
& v2_waybel_0(k1_pre_topc(A),A)
& v12_waybel_0(k1_pre_topc(A),A)
& v13_waybel_0(k1_pre_topc(A),A)
& v2_waybel11(k1_pre_topc(A),A)
& v3_waybel11(k1_pre_topc(A),A) ) ) ).
fof(rc4_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel11(B,A)
& v3_waybel11(B,A) ) ) ).
fof(fc3_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& v3_waybel11(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(cc3_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v6_group_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_finset_1(B)
& v1_waybel11(B,A) ) ) ) ).
fof(rc5_waybel11,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)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v1_waybel_5(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_waybel_9(A)
& v9_waybel_1(A)
& v3_realset2(A)
& v4_waybel11(A) ) ).
fof(fc4_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v12_waybel_0(k2_pre_topc(A),A)
& v13_waybel_0(k2_pre_topc(A),A)
& v1_waybel11(k2_pre_topc(A),A)
& v2_waybel11(k2_pre_topc(A),A) ) ) ).
fof(rc6_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(B,A)
& v13_waybel_0(B,A)
& v1_waybel11(B,A)
& v2_waybel11(B,A) ) ) ).
fof(fc5_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& v1_waybel11(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(fc6_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& v2_waybel11(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(cc4_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
=> v3_waybel11(B,A) ) ) ) ).
fof(fc7_waybel11,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_waybel11(A,B,C))
& v6_waybel_0(k3_waybel11(A,B,C),A)
& v8_waybel_0(k3_waybel11(A,B,C),A) ) ) ).
fof(fc8_waybel11,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_waybel11(A,B,C))
& v3_orders_2(k3_waybel11(A,B,C))
& v6_waybel_0(k3_waybel11(A,B,C),A)
& v8_waybel_0(k3_waybel11(A,B,C),A) ) ) ).
fof(fc9_waybel11,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_waybel11(A,B,C))
& v2_orders_2(k3_waybel11(A,B,C))
& v6_waybel_0(k3_waybel11(A,B,C),A)
& v8_waybel_0(k3_waybel11(A,B,C),A) ) ) ).
fof(rc7_waybel11,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B)
& v8_waybel_0(B,A)
& v10_waybel_0(B,A) ) ) ).
fof(fc10_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k4_waybel11(A,B))
& v6_waybel_0(k4_waybel11(A,B),A) ) ) ).
fof(fc11_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k4_waybel11(A,B))
& v2_orders_2(k4_waybel11(A,B))
& v3_orders_2(k4_waybel11(A,B))
& v4_orders_2(k4_waybel11(A,B))
& v6_waybel_0(k4_waybel11(A,B),A)
& v7_waybel_0(k4_waybel11(A,B)) ) ) ).
fof(fc12_waybel11,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) )
=> ( v1_relat_1(k2_waybel11(A))
& v4_yellow_6(k2_waybel11(A),A) ) ) ).
fof(fc13_waybel11,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) )
=> ( v1_relat_1(k2_waybel11(A))
& v4_yellow_6(k2_waybel11(A),A)
& v5_yellow_6(k2_waybel11(A),A) ) ) ).
fof(fc14_waybel11,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k2_waybel11(A))
& v4_yellow_6(k2_waybel11(A),A)
& v5_yellow_6(k2_waybel11(A),A)
& v6_yellow_6(k2_waybel11(A),A)
& v7_yellow_6(k2_waybel11(A),A)
& v8_yellow_6(k2_waybel11(A),A) ) ) ).
fof(t1_waybel11,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_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r4_yellow_4(A,B,C)
=> r3_orders_2(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ) ) ).
fof(t2_waybel11,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_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r3_yellow_4(A,B,C)
=> r3_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) ) ).
fof(t3_waybel11,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ).
fof(t4_waybel11,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_hidden(k1_yellow_0(A,B),B) ) ) ).
fof(t5_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ r2_hidden(B,C)
=> r1_xboole_0(C,k6_waybel_0(A,B)) ) ) ) ) ).
fof(t6_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(B,C)
=> r1_tarski(k6_waybel_0(A,B),C) ) ) ) ) ).
fof(d1_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel11(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(k1_yellow_0(A,C),B)
& r1_xboole_0(C,B) ) ) ) ) ) ).
fof(d2_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel11(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_tarski(C,B)
=> r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) ).
fof(d3_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_waybel11(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(k1_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(E,C)
& r1_orders_2(A,D,E) )
=> r2_hidden(E,B) ) ) ) ) ) ) ) ) ) ).
fof(d4_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_waybel_9(A) )
=> ( v4_waybel11(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ( v1_waybel11(B,A)
& v13_waybel_0(B,A) ) ) ) ) ) ).
fof(d5_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v6_group_1(A)
& l1_waybel_9(A) )
=> ( v4_waybel11(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> v13_waybel_0(B,A) ) ) ) ) ).
fof(t7_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> ( v2_waybel11(B,A)
& v12_waybel_0(B,A) ) ) ) ) ).
fof(t8_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v2_waybel11(k6_waybel_0(A,B),A) ) ) ).
fof(t9_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_pre_topc(A,k1_struct_0(A,B)) = k6_waybel_0(A,B) ) ) ).
fof(t10_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) ) ) ).
fof(t11_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v4_pre_topc(k6_waybel_0(A,B),A) ) ) ).
fof(t12_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v3_pre_topc(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A) ) ) ).
fof(t13_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ r2_hidden(B,C)
=> m2_connsp_2(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A,C) ) ) ) ) ).
fof(t14_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& B = k6_setfam_1(u1_struct_0(A),C)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,C)
=> m2_connsp_2(D,A,B) ) ) ) ) ) ).
fof(t15_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ( v13_waybel_0(B,A)
& v3_waybel11(B,A) ) ) ) ) ).
fof(d7_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_waybel11(A,B,C)
<=> r3_orders_2(A,C,k1_waybel11(A,B)) ) ) ) ) ).
fof(d8_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( B = k2_waybel11(A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v6_waybel_0(C,A)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r2_hidden(C,k7_yellow_6(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> r1_waybel11(A,C,D) ) ) ) ) ) ) ) ).
fof(t17_waybel11,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] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_waybel11(A,B,C)
& r1_waybel_0(A,B,k6_waybel_0(A,D)) )
=> r3_orders_2(A,C,D) ) ) ) ) ) ).
fof(t18_waybel11,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] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_waybel_0(A,B,k7_waybel_0(A,D))
=> r1_orders_2(A,D,k1_waybel11(A,B)) ) ) ) ) ) ).
fof(d9_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v8_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_orders_2(B,C,D)
=> r3_orders_2(A,k3_waybel_0(A,B,C),k3_waybel_0(A,B,D)) ) ) ) ) ) ) ).
fof(d10_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k3_waybel11(A,B,C)
<=> ( u1_struct_0(D) = B
& u1_waybel_0(A,D) = C
& ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( r1_orders_2(D,E,F)
<=> r1_orders_2(A,k3_waybel_0(A,D,E),k3_waybel_0(A,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(t20_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ( v1_waybel_0(k8_yellow_2(B,A,C),A)
=> v7_waybel_0(k3_waybel11(A,B,C)) ) ) ) ) ).
fof(t21_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ( ( r1_tarski(B,u1_struct_0(A))
& v7_waybel_0(k3_waybel11(A,B,C)) )
=> r2_hidden(k3_waybel11(A,B,C),k7_yellow_6(A)) ) ) ) ) ).
fof(t22_waybel11,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] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v8_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> k1_waybel11(A,B) = k1_waybel_2(A,B) ) ) ).
fof(t23_waybel11,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] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> k5_yellow_6(A,B) = k1_waybel11(A,B) ) ) ).
fof(t24_waybel11,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] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> r1_waybel11(A,B,k5_yellow_6(A,B)) ) ) ).
fof(d11_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v6_waybel_0(C,A)
& l1_waybel_0(C,A) )
=> ( C = k4_waybel11(A,B)
<=> ( u1_struct_0(C) = k1_struct_0(A,B)
& u1_orders_2(C) = k1_tarski(k4_tarski(B,B))
& u1_waybel_0(A,C) = k6_partfun1(k1_struct_0(A,B)) ) ) ) ) ) ).
fof(t25_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_waybel11(A,B)))
=> C = B ) ) ) ).
fof(t26_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_waybel11(A,B)))
=> k3_waybel_0(A,k4_waybel11(A,B),C) = B ) ) ) ).
fof(t27_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r1_waybel_0(A,k4_waybel11(A,B),C)
<=> r2_hidden(B,C) ) ) ) ).
fof(t28_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> B = k1_waybel11(A,k4_waybel11(A,B)) ) ) ).
fof(t29_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_hidden(k4_waybel11(A,B),k7_yellow_6(A)) ) ) ).
fof(t31_waybel11,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_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))))
<=> ( v1_waybel11(B,A)
& v13_waybel_0(B,A) ) ) ) ) ).
fof(t32_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k14_yellow_6(A,k2_waybel11(A)) ) ).
fof(t33_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k14_yellow_6(A,k2_waybel11(A))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ( v1_waybel11(B,A)
& v13_waybel_0(B,A) ) ) ) ) ) ).
fof(t34_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k14_yellow_6(A,k2_waybel11(A))
=> v4_waybel11(A) ) ) ).
fof(t35_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C,D] :
( m2_yellow_6(D,A,B)
=> ( D = k6_yellow_6(A,B,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> r2_hidden(k3_waybel_0(A,D,E),C) ) ) ) ) ) ).
fof(d12_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> k5_waybel11(A) = u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))) ) ).
fof(t36_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v3_pre_topc(k2_waybel_3(A,B),A) ) ) ).
fof(t37_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ( u1_pre_topc(A) = k5_waybel11(A)
=> v4_waybel11(A) ) ) ).
fof(t38_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r2_hidden(C,k7_yellow_6(A))
=> ( r1_waybel11(A,C,B)
<=> r2_hidden(B,k11_yellow_6(A,C)) ) ) ) ) ) ).
fof(t39_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v7_yellow_6(k2_waybel11(A),A)
=> v3_waybel_3(A) ) ) ).
fof(t40_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ( v3_waybel_3(A)
<=> k13_yellow_6(A) = k2_waybel11(A) ) ) ).
fof(t41_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_6(B,A)
=> v3_pre_topc(B,A) ) ) ) ).
fof(t42_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> r1_tarski(k7_waybel_0(A,C),B) ) ) ) ) ).
fof(t43_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(C,A)
& r2_hidden(B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,D,B)
& r2_hidden(D,C) ) ) ) ) ) ) ).
fof(t46_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_pre_topc(B,A)
<=> v1_waybel_6(B,A) ) ) ) ).
fof(t47_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_tops_1(A,k7_waybel_0(A,B)) = k2_waybel_3(A,B) ) ) ).
fof(dt_k1_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> m1_subset_1(k1_waybel11(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> m4_yellow_6(k2_waybel11(A),A) ) ).
fof(dt_k3_waybel11,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_waybel11(A,B,C))
& v6_waybel_0(k3_waybel11(A,B,C),A)
& l1_waybel_0(k3_waybel11(A,B,C),A) ) ) ).
fof(dt_k4_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v6_waybel_0(k4_waybel11(A,B),A)
& l1_waybel_0(k4_waybel11(A,B),A) ) ) ).
fof(dt_k5_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> m1_subset_1(k5_waybel11(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(t16_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_waybel_9(A) )
=> ( u1_pre_topc(A) = a_1_0_waybel11(A)
=> v2_pre_topc(A) ) ) ).
fof(d6_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> k1_waybel11(A,B) = k1_yellow_0(A,a_2_0_waybel11(A,B)) ) ) ).
fof(t19_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)) = a_2_1_waybel11(A,B) ) ) ).
fof(t30_waybel11,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] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = a_2_2_waybel11(A,B)
=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A) ) ) ) ) ) ).
fof(t44_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m1_yellow_8(a_2_3_waybel11(A,B),A,B) ) ) ).
fof(t45_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> m1_cantor_1(a_1_1_waybel11(A),A) ) ).
fof(t48_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_tops_1(A,B) = k3_tarski(a_2_4_waybel11(A,B)) ) ) ).
fof(s1_waybel11,axiom,
( ! [A] :
( m1_subset_1(A,f2_s1_waybel11)
=> ! [B] :
( m1_subset_1(B,f1_s1_waybel11)
=> f3_s1_waybel11(B) = f4_s1_waybel11(A,B) ) )
=> a_0_0_waybel11 = a_0_1_waybel11 ) ).
fof(fraenkel_a_1_0_waybel11,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_0_waybel11(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& v3_waybel11(C,B) ) ) ) ).
fof(fraenkel_a_2_0_waybel11,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_0_waybel11(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_yellow_0(B,a_3_0_waybel11(B,C,D)) ) ) ) ).
fof(fraenkel_a_3_0_waybel11,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_waybel11(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
fof(fraenkel_a_2_1_waybel11,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v3_struct_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_1_waybel11(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k3_waybel_0(B,C,D) ) ) ) ).
fof(fraenkel_a_2_2_waybel11,axiom,
! [A,B,C] :
( ( 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)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_2_waybel11(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_yellow_0(B,a_3_1_waybel11(B,C,D)) ) ) ) ).
fof(fraenkel_a_3_1_waybel11,axiom,
! [A,B,C,D] :
( ( 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)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_1_waybel11(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
fof(fraenkel_a_2_3_waybel11,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_waybel_3(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v4_waybel11(B)
& l1_waybel_9(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_3_waybel11(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k2_waybel_3(B,D)
& r1_waybel_3(B,D,C) ) ) ) ).
fof(fraenkel_a_1_1_waybel11,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_waybel_3(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v4_waybel11(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_1_waybel11(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = k2_waybel_3(B,C) ) ) ) ).
fof(fraenkel_a_2_4_waybel11,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_waybel_3(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v4_waybel11(B)
& l1_waybel_9(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_4_waybel11(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k2_waybel_3(B,D)
& r1_tarski(k2_waybel_3(B,D),C) ) ) ) ).
fof(fraenkel_a_0_0_waybel11,axiom,
! [A] :
( r2_hidden(A,a_0_0_waybel11)
<=> ? [B] :
( m1_subset_1(B,f1_s1_waybel11)
& A = f3_s1_waybel11(B)
& p1_s1_waybel11(B) ) ) ).
fof(fraenkel_a_0_1_waybel11,axiom,
! [A] :
( r2_hidden(A,a_0_1_waybel11)
<=> ? [B,C] :
( m1_subset_1(B,f2_s1_waybel11)
& m1_subset_1(C,f1_s1_waybel11)
& A = f4_s1_waybel11(B,C)
& p1_s1_waybel11(C) ) ) ).
%------------------------------------------------------------------------------