SET007 Axioms: SET007+481.ax
%------------------------------------------------------------------------------
% File : SET007+481 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Directed Sets, Nets, Ideals, Filters, and Maps
% 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 : waybel_0 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 197 ( 4 unt; 0 def)
% Number of atoms : 1772 ( 100 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 1872 ( 297 ~; 11 |; 900 &)
% ( 75 <=>; 589 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 76 ( 74 usr; 1 prp; 0-4 aty)
% Number of functors : 51 ( 51 usr; 4 con; 0-4 aty)
% Number of variables : 586 ( 545 !; 41 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_xboole_0(k1_pre_topc(A))
& v5_orders_2(k1_pre_topc(A),A)
& v1_finset_1(k1_pre_topc(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) ) ) ).
fof(rc1_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ).
fof(rc2_waybel_0,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)
& v2_waybel_0(B,A) ) ) ).
fof(fc2_waybel_0,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc4_waybel_0,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v2_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc5_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v2_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(cc1_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v7_yellow_0(B,A)
=> v3_waybel_0(B,A) ) ) ) ).
fof(cc2_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
=> v4_waybel_0(B,A) ) ) ) ).
fof(rc3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& v6_yellow_0(B,A)
& v7_yellow_0(B,A)
& v8_yellow_0(B,A)
& v3_waybel_0(B,A)
& v4_waybel_0(B,A) ) ) ).
fof(rc4_waybel_0,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( l1_waybel_0(B,A)
& v6_waybel_0(B,A) ) ) ).
fof(fc6_waybel_0,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& ~ v1_xboole_0(B)
& m1_relset_1(C,B,B)
& v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m1_relset_1(D,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(g1_waybel_0(A,B,C,D))
& v6_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ).
fof(rc5_waybel_0,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B) ) ) ).
fof(cc3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& v8_waybel_0(B,A) )
=> ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& v10_waybel_0(B,A) ) ) ) ) ).
fof(cc4_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& v9_waybel_0(B,A) )
=> ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& v11_waybel_0(B,A) ) ) ) ) ).
fof(rc6_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B)
& v8_waybel_0(B,A)
& v9_waybel_0(B,A)
& v10_waybel_0(B,A)
& v11_waybel_0(B,A) ) ) ).
fof(fc7_waybel_0,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))) )
=> ~ v1_xboole_0(k4_waybel_0(A,B)) ) ).
fof(fc8_waybel_0,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))) )
=> ~ v1_xboole_0(k5_waybel_0(A,B)) ) ).
fof(fc9_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k6_waybel_0(A,B))
& v1_waybel_0(k6_waybel_0(A,B),A) ) ) ).
fof(fc10_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k7_waybel_0(A,B))
& v2_waybel_0(k7_waybel_0(A,B),A) ) ) ).
fof(rc7_waybel_0,axiom,
! [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) ) ) ).
fof(fc11_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v12_waybel_0(k4_waybel_0(A,B),A) ) ).
fof(fc12_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v13_waybel_0(k5_waybel_0(A,B),A) ) ).
fof(fc13_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> v12_waybel_0(k6_waybel_0(A,B),A) ) ).
fof(fc14_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> v13_waybel_0(k7_waybel_0(A,B),A) ) ).
fof(fc15_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(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) ) ) ).
fof(rc8_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc9_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A) ) ) ).
fof(rc10_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc11_waybel_0,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v2_waybel_0(B,A)
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(fc16_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_0(k4_waybel_0(A,B),A)
& v12_waybel_0(k4_waybel_0(A,B),A) ) ) ).
fof(fc17_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_waybel_0(k5_waybel_0(A,B),A)
& v13_waybel_0(k5_waybel_0(A,B),A) ) ) ).
fof(fc18_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k12_waybel_0(A,B)) ) ).
fof(fc19_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k13_waybel_0(A,B)) ) ).
fof(fc20_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k12_waybel_0(A,B)) ) ).
fof(fc21_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k13_waybel_0(A,B)) ) ).
fof(fc22_waybel_0,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel_0(k12_waybel_0(A,B),A) ) ).
fof(fc23_waybel_0,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel_0(k13_waybel_0(A,B),A) ) ).
fof(cc5_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v16_waybel_0(A) ) ) ) ).
fof(rc12_waybel_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A) ) ).
fof(fc24_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v2_orders_2(k7_lattice3(A))
& v3_orders_2(k7_lattice3(A))
& v4_orders_2(k7_lattice3(A))
& v16_waybel_0(k7_lattice3(A)) ) ) ).
fof(cc6_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& v21_waybel_0(C,A,B) ) ) ) ) ).
fof(cc7_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(cc8_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v23_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v2_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B) ) ) ) ) ).
fof(cc9_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v1_lattice3(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc10_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ) ) ).
fof(cc11_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_yellow_0(A) ) ) ) ).
fof(cc12_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc13_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A) ) ) ) ).
fof(cc14_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(rc13_waybel_0,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_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ).
fof(d1_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& r1_orders_2(A,C,E)
& r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ).
fof(d2_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& r1_orders_2(A,E,C)
& r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ).
fof(t1_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A) )
<=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(D,B)
& r2_lattice3(A,C,D) ) ) ) ) ) ).
fof(t2_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A) )
<=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(D,B)
& r1_lattice3(A,C,D) ) ) ) ) ) ).
fof(t3_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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_waybel_0(C,A) )
=> v1_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t4_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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
& v2_waybel_0(C,A) )
=> v2_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t5_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel_0(k1_struct_0(A,B),A)
& v2_waybel_0(k1_struct_0(A,B),A) ) ) ) ).
fof(d3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v3_waybel_0(B,A)
<=> ! [C] :
( ( v2_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_yellow_0(A,C)
=> ( C = k1_xboole_0
| r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ) ).
fof(d4_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_waybel_0(B,A)
<=> ! [C] :
( ( v1_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r1_yellow_0(A,C)
=> ( C = k1_xboole_0
| r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ) ).
fof(t6_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v3_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v2_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_yellow_0(A,C)
=> ( C = k1_xboole_0
| ( r2_yellow_0(B,C)
& k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) ) ).
fof(t7_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v1_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r1_yellow_0(A,C)
=> ( C = k1_xboole_0
| ( r1_yellow_0(B,C)
& k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) ) ).
fof(d5_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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)) )
=> ( v5_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_orders_2(A,D,E)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( F = k1_funct_1(C,D)
& G = k1_funct_1(C,E) )
=> r1_orders_2(B,G,F) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v7_waybel_0(A)
<=> v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(d7_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> k2_waybel_0(A,B) = u1_waybel_0(A,B) ) ) ).
fof(d8_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_waybel_0(A,B,C) = k1_waybel_0(B,A,u1_waybel_0(A,B),C) ) ) ) ).
fof(d9_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v8_waybel_0(B,A)
<=> v5_orders_3(k2_waybel_0(A,B),B,A) ) ) ) ).
fof(d10_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v9_waybel_0(B,A)
<=> v5_waybel_0(k2_waybel_0(A,B),B,A) ) ) ) ).
fof(d11_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r1_waybel_0(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_orders_2(B,D,E)
=> r2_hidden(k3_waybel_0(A,B,E),C) ) ) ) ) ) ) ).
fof(d12_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r2_waybel_0(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r1_orders_2(B,D,E)
& r2_hidden(k3_waybel_0(A,B,E),C) ) ) ) ) ) ).
fof(t8_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C,D] :
( r1_tarski(C,D)
=> ( ( r1_waybel_0(A,B,C)
=> r1_waybel_0(A,B,D) )
& ( r2_waybel_0(A,B,C)
=> r2_waybel_0(A,B,D) ) ) ) ) ) ).
fof(t9_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r1_waybel_0(A,B,C)
<=> ~ r2_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) ) ) ) ).
fof(t10_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r2_waybel_0(A,B,C)
<=> ~ r1_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) ) ) ) ).
fof(t11_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v10_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_orders_2(B,D,E)
=> r1_orders_2(A,k3_waybel_0(A,B,C),k3_waybel_0(A,B,E)) ) ) ) ) ) ) ) ).
fof(t12_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v11_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_orders_2(B,D,E)
=> r1_orders_2(A,k3_waybel_0(A,B,E),k3_waybel_0(A,B,C)) ) ) ) ) ) ) ) ).
fof(d15_waybel_0,axiom,
! [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)))
=> ( C = k4_waybel_0(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_orders_2(A,D,E)
& r2_hidden(E,B) ) ) ) ) ) ) ) ).
fof(d16_waybel_0,axiom,
! [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)))
=> ( C = k5_waybel_0(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_orders_2(A,E,D)
& r2_hidden(E,B) ) ) ) ) ) ) ) ).
fof(t13_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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
=> ( k4_waybel_0(A,C) = k4_waybel_0(B,D)
& k5_waybel_0(A,C) = k5_waybel_0(B,D) ) ) ) ) ) ) ) ).
fof(t16_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,k4_waybel_0(A,B))
& r1_tarski(B,k5_waybel_0(A,B)) ) ) ) ).
fof(d17_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_waybel_0(A,B) = k4_waybel_0(A,k1_struct_0(A,B)) ) ) ).
fof(d18_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_0(A,B) = k5_waybel_0(A,k1_struct_0(A,B)) ) ) ).
fof(t17_waybel_0,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,k6_waybel_0(A,B))
<=> r1_orders_2(A,C,B) ) ) ) ) ).
fof(t18_waybel_0,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,k7_waybel_0(A,B))
<=> r1_orders_2(A,B,C) ) ) ) ) ).
fof(t19_waybel_0,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k6_waybel_0(A,B) = k6_waybel_0(A,C)
=> B = C ) ) ) ) ).
fof(t20_waybel_0,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k7_waybel_0(A,B) = k7_waybel_0(A,C)
=> B = C ) ) ) ) ).
fof(t21_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
=> r1_tarski(k6_waybel_0(A,B),k6_waybel_0(A,C)) ) ) ) ) ).
fof(t22_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
=> r1_tarski(k7_waybel_0(A,C),k7_waybel_0(A,B)) ) ) ) ) ).
fof(d19_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r1_orders_2(A,D,C) )
=> r2_hidden(D,B) ) ) ) ) ) ) ).
fof(d20_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v13_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r1_orders_2(A,C,D) )
=> r2_hidden(D,B) ) ) ) ) ) ) ).
fof(t23_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
<=> r1_tarski(k4_waybel_0(A,B),B) ) ) ) ).
fof(t24_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v13_waybel_0(B,A)
<=> r1_tarski(k5_waybel_0(A,B),B) ) ) ) ).
fof(t25_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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
=> ( ( v12_waybel_0(C,A)
=> v12_waybel_0(D,B) )
& ( v13_waybel_0(C,A)
=> v13_waybel_0(D,B) ) ) ) ) ) ) ) ) ).
fof(t26_waybel_0,axiom,
! [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)))
=> ( r2_hidden(C,B)
=> v12_waybel_0(C,A) ) )
=> ( v12_waybel_0(k5_setfam_1(u1_struct_0(A),B),A)
& m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t27_waybel_0,axiom,
! [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)))
=> ( ( v12_waybel_0(B,A)
& v12_waybel_0(C,A) )
=> ( v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
& v12_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(t28_waybel_0,axiom,
! [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)))
=> ( r2_hidden(C,B)
=> v13_waybel_0(C,A) ) )
=> ( v13_waybel_0(k5_setfam_1(u1_struct_0(A),B),A)
& m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t29_waybel_0,axiom,
! [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)))
=> ( ( v13_waybel_0(B,A)
& v13_waybel_0(C,A) )
=> ( v13_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
& v13_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(t30_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel_0(B,A)
<=> v1_waybel_0(k4_waybel_0(A,B),A) ) ) ) ).
fof(t31_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_lattice3(A,B,C)
<=> r2_lattice3(A,k4_waybel_0(A,B),C) ) ) ) ) ).
fof(t32_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_yellow_0(A,B)
<=> r1_yellow_0(A,k4_waybel_0(A,B)) ) ) ) ).
fof(t33_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_yellow_0(A,B)
=> k1_yellow_0(A,B) = k1_yellow_0(A,k4_waybel_0(A,B)) ) ) ) ).
fof(t34_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r1_yellow_0(A,k6_waybel_0(A,B))
& k1_yellow_0(A,k6_waybel_0(A,B)) = B ) ) ) ).
fof(t35_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel_0(B,A)
<=> v2_waybel_0(k5_waybel_0(A,B),A) ) ) ) ).
fof(t36_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_lattice3(A,B,C)
<=> r1_lattice3(A,k5_waybel_0(A,B),C) ) ) ) ) ).
fof(t37_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_yellow_0(A,B)
<=> r2_yellow_0(A,k5_waybel_0(A,B)) ) ) ) ).
fof(t38_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_yellow_0(A,B)
=> k2_yellow_0(A,B) = k2_yellow_0(A,k5_waybel_0(A,B)) ) ) ) ).
fof(t39_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_yellow_0(A,k7_waybel_0(A,B))
& k2_yellow_0(A,k7_waybel_0(A,B)) = B ) ) ) ).
fof(t40_waybel_0,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k13_lattice3(A,C,D),B) ) ) ) ) ) ) ).
fof(t41_waybel_0,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k12_lattice3(A,C,D),B) ) ) ) ) ) ) ).
fof(t42_waybel_0,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)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_0(B,A)
<=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ( C != k1_xboole_0
=> r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) ).
fof(t43_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_waybel_0(B,A)
<=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ( C != k1_xboole_0
=> r2_hidden(k2_yellow_0(A,C),B) ) ) ) ) ) ).
fof(t44_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( ( v1_lattice3(A)
| v2_lattice3(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)))
=> ( ( v12_waybel_0(B,A)
& v1_waybel_0(B,A)
& v12_waybel_0(C,A)
& v1_waybel_0(C,A) )
=> v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(t45_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( ( v1_lattice3(A)
| v2_lattice3(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)))
=> ( ( v13_waybel_0(B,A)
& v2_waybel_0(B,A)
& v13_waybel_0(C,A)
& v2_waybel_0(C,A) )
=> v2_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(t46_waybel_0,axiom,
! [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)))
=> ( r2_hidden(C,B)
=> v1_waybel_0(C,A) ) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,B)
& r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E) ) ) ) ) ) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k5_setfam_1(u1_struct_0(A),B)
=> v1_waybel_0(C,A) ) ) ) ) ) ).
fof(t47_waybel_0,axiom,
! [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)))
=> ( r2_hidden(C,B)
=> v2_waybel_0(C,A) ) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,B)
& r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E) ) ) ) ) ) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k5_setfam_1(u1_struct_0(A),B)
=> v2_waybel_0(C,A) ) ) ) ) ) ).
fof(d21_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v14_waybel_0(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_hidden(C,B)
& r2_lattice3(A,B,C) ) ) ) ) ).
fof(d22_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v15_waybel_0(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_hidden(C,B)
& r1_lattice3(A,B,C) ) ) ) ) ).
fof(t48_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v14_waybel_0(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& B = k6_waybel_0(A,C) ) ) ) ) ).
fof(t49_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v15_waybel_0(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& B = k7_waybel_0(A,C) ) ) ) ) ).
fof(d25_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k10_waybel_0(A) = k2_xboole_0(k8_waybel_0(A),k1_tarski(k1_xboole_0)) ) ).
fof(d26_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k11_waybel_0(A) = k2_xboole_0(k9_waybel_0(A),k1_tarski(k1_xboole_0)) ) ).
fof(t50_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,k12_waybel_0(A,B))
& r1_tarski(B,k13_waybel_0(A,B)) ) ) ) ).
fof(t51_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r1_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r1_yellow_0(A,E)
& D = k1_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k1_yellow_0(A,D),C) ) ) )
=> v1_waybel_0(C,A) ) ) ) ) ).
fof(t52_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r1_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r1_yellow_0(A,E)
& D = k1_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k1_yellow_0(A,D),C) ) ) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
<=> r2_lattice3(A,C,D) ) ) ) ) ) ) ).
fof(t53_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r1_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r1_yellow_0(A,E)
& D = k1_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k1_yellow_0(A,D),C) ) ) )
=> ( r1_yellow_0(A,B)
<=> r1_yellow_0(A,C) ) ) ) ) ) ).
fof(t54_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r1_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r1_yellow_0(A,E)
& D = k1_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k1_yellow_0(A,D),C) ) )
& r1_yellow_0(A,B) )
=> k1_yellow_0(A,C) = k1_yellow_0(A,B) ) ) ) ) ).
fof(t55_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_yellow_0(A,B)
| v3_lattice3(A) )
=> k1_yellow_0(A,B) = k1_yellow_0(A,k12_waybel_0(A,B)) ) ) ) ).
fof(t56_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r2_yellow_0(A,E)
& D = k2_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k2_yellow_0(A,D),C) ) ) )
=> v2_waybel_0(C,A) ) ) ) ) ).
fof(t57_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r2_yellow_0(A,E)
& D = k2_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k2_yellow_0(A,D),C) ) ) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
<=> r1_lattice3(A,C,D) ) ) ) ) ) ) ).
fof(t58_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r2_yellow_0(A,E)
& D = k2_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k2_yellow_0(A,D),C) ) ) )
=> ( r2_yellow_0(A,B)
<=> r2_yellow_0(A,C) ) ) ) ) ) ).
fof(t59_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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)))
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_yellow_0(A,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ~ ( r2_yellow_0(A,E)
& D = k2_yellow_0(A,E) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( D != k1_xboole_0
=> r2_hidden(k2_yellow_0(A,D),C) ) )
& r2_yellow_0(A,B) )
=> k2_yellow_0(A,C) = k2_yellow_0(A,B) ) ) ) ) ).
fof(t60_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_yellow_0(A,B)
| v3_lattice3(A) )
=> k2_yellow_0(A,B) = k2_yellow_0(A,k13_waybel_0(A,B)) ) ) ) ).
fof(t61_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,k4_waybel_0(A,k12_waybel_0(A,B)))
& ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_tarski(B,C)
=> r1_tarski(k4_waybel_0(A,k12_waybel_0(A,B)),C) ) ) ) ) ) ).
fof(t62_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,k5_waybel_0(A,k13_waybel_0(A,B)))
& ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_tarski(B,C)
=> r1_tarski(k5_waybel_0(A,k13_waybel_0(A,B)),C) ) ) ) ) ) ).
fof(d29_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v16_waybel_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
| r1_orders_2(A,C,B) ) ) ) ) ) ).
fof(t63_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> v5_yellow_0(k5_yellow_0(A,B),A) ) ) ) ).
fof(t64_waybel_0,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)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> v6_yellow_0(k5_yellow_0(A,B),A) ) ) ) ).
fof(d30_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r3_waybel_0(A,B,C,D)
<=> ( r2_yellow_0(A,D)
=> ( r2_yellow_0(B,k4_pre_topc(A,B,C,D))
& k2_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k2_yellow_0(A,D)) ) ) ) ) ) ) ) ).
fof(d31_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r4_waybel_0(A,B,C,D)
<=> ( r1_yellow_0(A,D)
=> ( r1_yellow_0(B,k4_pre_topc(A,B,C,D))
& k1_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k1_yellow_0(A,D)) ) ) ) ) ) ) ) ).
fof(t65_waybel_0,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] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = 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(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( E = F
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(C)))
=> ( G = H
=> ( ( r4_waybel_0(A,B,E,G)
=> r4_waybel_0(C,D,F,H) )
& ( r3_waybel_0(A,B,E,G)
=> r3_waybel_0(C,D,F,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d32_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ( v17_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r3_waybel_0(A,B,C,D) ) ) ) ) ) ).
fof(d33_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ( v18_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r4_waybel_0(A,B,C,D) ) ) ) ) ) ).
fof(d34_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ( v19_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r3_waybel_0(A,B,C,k2_struct_0(A,D,E)) ) ) ) ) ) ) ).
fof(d35_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ( v20_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r4_waybel_0(A,B,C,k2_struct_0(A,D,E)) ) ) ) ) ) ) ).
fof(d36_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ( v21_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel_0(D,A)
=> ( v1_xboole_0(D)
| r3_waybel_0(A,B,C,D) ) ) ) ) ) ) ) ).
fof(d37_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)) )
=> ( v22_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel_0(D,A)
=> ( v1_xboole_0(D)
| r4_waybel_0(A,B,C,D) ) ) ) ) ) ) ) ).
fof(d38_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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)) )
=> ( ~ ( ~ v3_struct_0(A)
& ~ v3_struct_0(B)
& ~ ( v23_waybel_0(C,A,B)
<=> ( v2_funct_1(C)
& v5_orders_3(C,A,B)
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& D = k2_funct_1(C)
& v5_orders_3(D,B,A) ) ) ) )
& ( ~ ( ~ v3_struct_0(A)
& ~ v3_struct_0(B) )
=> ( v23_waybel_0(C,A,B)
<=> ( v3_struct_0(A)
& v3_struct_0(B) ) ) ) ) ) ) ) ).
fof(t66_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)
<=> ( v2_funct_1(C)
& k2_relat_1(C) = u1_struct_0(B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_orders_2(A,D,E)
<=> r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(t67_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)
=> ( v1_funct_1(k2_funct_1(C))
& v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
& k2_relat_1(k2_funct_1(C)) = u1_struct_0(A) ) ) ) ) ) ).
fof(t68_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( D = k2_funct_1(C)
=> v23_waybel_0(D,B,A) ) ) ) ) ) ) ).
fof(t69_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,A)
& v13_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) )
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t70_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,A)
& v13_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) )
=> v21_waybel_0(C,A,B) ) ) ) ) ).
fof(t71_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) )
& ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) )
=> v17_waybel_0(C,A,B) ) ) ) ) ).
fof(t72_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& v12_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_waybel_0(A,B,C,D) )
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t73_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& v12_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_waybel_0(A,B,C,D) )
=> v22_waybel_0(C,A,B) ) ) ) ) ).
fof(t74_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ( ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_waybel_0(A,B,C,D) )
& ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_waybel_0(A,B,C,D) ) )
=> v18_waybel_0(C,A,B) ) ) ) ) ).
fof(d39_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v24_waybel_0(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_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_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
=> r3_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(t75_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v24_waybel_0(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_yellow_0(A,B) ) ) ) ).
fof(d40_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v25_waybel_0(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
=> r1_orders_2(A,D,C) ) ) ) ) ) ) ).
fof(t76_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v25_waybel_0(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_yellow_0(A,B) ) ) ) ).
fof(dt_l1_waybel_0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> l1_orders_2(B) ) ) ).
fof(existence_l1_waybel_0,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] : l1_waybel_0(B,A) ) ).
fof(abstractness_v6_waybel_0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_waybel_0(B,A) )
=> ( v6_waybel_0(B,A)
=> B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) ) ) ).
fof(dt_k1_waybel_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(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))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k1_waybel_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(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))
& m1_subset_1(D,u1_struct_0(A)) )
=> k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k2_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v1_funct_1(k2_waybel_0(A,B))
& v1_funct_2(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k3_waybel_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k4_waybel_0,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k4_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_waybel_0,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k6_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k7_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k8_waybel_0,axiom,
$true ).
fof(dt_k9_waybel_0,axiom,
$true ).
fof(dt_k10_waybel_0,axiom,
$true ).
fof(dt_k11_waybel_0,axiom,
$true ).
fof(dt_k12_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k12_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k13_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k13_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_u1_waybel_0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_waybel_0(B,A) )
=> ( v1_funct_1(u1_waybel_0(A,B))
& v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_g1_waybel_0,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& m1_relset_1(C,B,B)
& v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m1_relset_1(D,B,u1_struct_0(A)) )
=> ( v6_waybel_0(g1_waybel_0(A,B,C,D),A)
& l1_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ).
fof(free_g1_waybel_0,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& m1_relset_1(C,B,B)
& v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m1_relset_1(D,B,u1_struct_0(A)) )
=> ! [E,F,G,H] :
( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(d13_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v10_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> r1_waybel_0(A,B,a_3_0_waybel_0(A,B,C)) ) ) ) ) ).
fof(d14_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v11_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> r1_waybel_0(A,B,a_3_1_waybel_0(A,B,C)) ) ) ) ) ).
fof(t14_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k4_waybel_0(A,B) = a_2_0_waybel_0(A,B) ) ) ).
fof(t15_waybel_0,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) = a_2_1_waybel_0(A,B) ) ) ).
fof(d23_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k8_waybel_0(A) = a_1_0_waybel_0(A) ) ).
fof(d24_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k9_waybel_0(A) = a_1_1_waybel_0(A) ) ).
fof(d27_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k12_waybel_0(A,B) = a_2_2_waybel_0(A,B) ) ) ).
fof(d28_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k13_waybel_0(A,B) = a_2_3_waybel_0(A,B) ) ) ).
fof(s1_waybel_0,axiom,
( r1_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,a_0_0_waybel_0)
<=> ? [A] :
( m1_subset_1(A,u1_struct_0(f2_s1_waybel_0))
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s1_waybel_0))
=> ( r1_orders_2(f2_s1_waybel_0,A,B)
=> p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B)) ) ) ) ) ).
fof(fraenkel_a_3_0_waybel_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_waybel_0(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(B,k3_waybel_0(B,C,D),k3_waybel_0(B,C,E)) ) ) ) ).
fof(fraenkel_a_3_1_waybel_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_1_waybel_0(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(B,k3_waybel_0(B,C,E),k3_waybel_0(B,C,D)) ) ) ) ).
fof(fraenkel_a_2_0_waybel_0,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_0_waybel_0(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r1_orders_2(B,D,E)
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_1_waybel_0,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_waybel_0(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r1_orders_2(B,E,D)
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_1_0_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( r2_hidden(A,a_1_0_waybel_0(B))
<=> ? [C] :
( ~ v1_xboole_0(C)
& v1_waybel_0(C,B)
& v12_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C ) ) ) ).
fof(fraenkel_a_1_1_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( r2_hidden(A,a_1_1_waybel_0(B))
<=> ? [C] :
( ~ v1_xboole_0(C)
& v2_waybel_0(C,B)
& v13_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C ) ) ) ).
fof(fraenkel_a_2_2_waybel_0,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_waybel_0(B,C))
<=> ? [D] :
( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(C))
& A = k1_yellow_0(B,D)
& r1_yellow_0(B,D) ) ) ) ).
fof(fraenkel_a_2_3_waybel_0,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_waybel_0(B,C))
<=> ? [D] :
( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(C))
& A = k2_yellow_0(B,D)
& r2_yellow_0(B,D) ) ) ) ).
fof(fraenkel_a_0_0_waybel_0,axiom,
! [A] :
( r2_hidden(A,a_0_0_waybel_0)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f2_s1_waybel_0))
& A = k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B)
& p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B)) ) ) ).
%------------------------------------------------------------------------------