SET007 Axioms: SET007+520.ax
%------------------------------------------------------------------------------
% File : SET007+520 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Scott Topology. Part II
% 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 : waybel14 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 55 ( 0 unt; 0 def)
% Number of atoms : 647 ( 44 equ)
% Maximal formula atoms : 21 ( 11 avg)
% Number of connectives : 644 ( 52 ~; 1 |; 417 &)
% ( 18 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 52 ( 51 usr; 0 prp; 1-3 aty)
% Number of functors : 41 ( 41 usr; 0 con; 1-3 aty)
% Number of variables : 158 ( 142 !; 16 ?)
% 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_waybel14,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,u1_struct_0(A)) )
=> v1_waybel_0(k2_waybel_8(A,B),A) ) ).
fof(fc2_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A)))
& v1_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v2_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v3_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v4_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v1_lattice3(k2_yellow_1(u1_pre_topc(A)))
& v2_lattice3(k2_yellow_1(u1_pre_topc(A)))
& v3_lattice3(k2_yellow_1(u1_pre_topc(A)))
& v1_yellow_0(k2_yellow_1(u1_pre_topc(A)))
& v2_yellow_0(k2_yellow_1(u1_pre_topc(A)))
& v3_yellow_0(k2_yellow_1(u1_pre_topc(A)))
& v24_waybel_0(k2_yellow_1(u1_pre_topc(A)))
& v25_waybel_0(k2_yellow_1(u1_pre_topc(A)))
& v2_waybel_1(k2_yellow_1(u1_pre_topc(A)))
& ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) ).
fof(fc3_waybel14,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_xboole_0(k5_waybel11(A)) ) ).
fof(t1_waybel14,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] :
( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
& r1_tarski(C,B)
& k5_setfam_1(A,C) = k5_setfam_1(A,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ~ ( r2_hidden(D,C)
& r1_tarski(D,k5_setfam_1(A,k6_subset_1(k1_zfmisc_1(A),C,k6_domain_1(k1_zfmisc_1(A),D)))) ) ) ) ) ).
fof(t2_waybel14,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A)
<=> v1_xboole_0(B) ) ) ) ).
fof(t3_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(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,k12_lattice3(A,B,C)) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,B),k6_waybel_0(A,C)) ) ) ) ).
fof(t4_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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,k13_lattice3(A,B,C)) = k5_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k7_waybel_0(A,C)) ) ) ) ).
fof(t5_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(k1_yellow_0(A,B),B)
=> B = k6_waybel_0(A,k1_yellow_0(A,B)) ) ) ) ).
fof(t6_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(k2_yellow_0(A,B),B)
=> B = k7_waybel_0(A,k2_yellow_0(A,B)) ) ) ) ).
fof(t7_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(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_waybel_3(A,B,C)
<=> r1_tarski(k7_waybel_0(A,C),k2_waybel_3(A,B)) ) ) ) ) ).
fof(t8_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(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_waybel_3(A,B,C)
<=> r1_tarski(k6_waybel_0(A,B),k1_waybel_3(A,C)) ) ) ) ) ).
fof(t9_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r3_orders_2(A,k1_yellow_0(A,k1_waybel_3(A,B)),B)
& r3_orders_2(A,B,k2_yellow_0(A,k2_waybel_3(A,B))) ) ) ) ).
fof(t10_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> k7_waybel_0(A,k3_yellow_0(A)) = u1_struct_0(A) ) ).
fof(t11_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> k6_waybel_0(A,k4_yellow_0(A)) = u1_struct_0(A) ) ).
fof(t12_waybel14,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,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k2_yellow_4(A,k2_waybel_3(A,B),k2_waybel_3(A,C)),k7_waybel_0(A,k13_lattice3(A,B,C))) ) ) ) ).
fof(t13_waybel14,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,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k4_yellow_4(A,k1_waybel_3(A,B),k1_waybel_3(A,C)),k6_waybel_0(A,k12_lattice3(A,B,C))) ) ) ) ).
fof(t14_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(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,u1_struct_0(A))
=> ( v6_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r3_orders_2(A,B,k13_lattice3(A,C,D))
& ~ r3_orders_2(A,B,C)
& ~ r3_orders_2(A,B,D) ) ) ) ) ) ) ).
fof(t17_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_yellow_8(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ( C = k3_subset_1(u1_struct_0(A),B)
=> v5_waybel_6(C,k2_yellow_1(u1_pre_topc(A))) ) ) ) ) ).
fof(t18_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ( k13_lattice3(k2_yellow_1(u1_pre_topc(A)),B,C) = k2_xboole_0(B,C)
& k12_lattice3(k2_yellow_1(u1_pre_topc(A)),B,C) = k3_xboole_0(B,C) ) ) ) ) ).
fof(t19_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ( v5_waybel_6(B,k2_yellow_1(u1_pre_topc(A)))
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ~ ( r1_tarski(k3_xboole_0(C,D),B)
& ~ r1_tarski(C,B)
& ~ r1_tarski(D,B) ) ) ) ) ) ) ).
fof(t20_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ( v6_waybel_6(B,k2_yellow_1(u1_pre_topc(A)))
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ~ ( r1_tarski(B,k2_xboole_0(C,D))
& ~ r1_tarski(B,C)
& ~ r1_tarski(B,D) ) ) ) ) ) ) ).
fof(t21_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& C = D
& m1_yellow_8(E,B,D) )
=> m1_yellow_8(E,A,C) ) ) ) ) ) ) ).
fof(t22_waybel14,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(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)
=> v13_waybel_0(C,A) ) )
=> v6_compts_1(k7_waybel_0(A,B),A) ) ) ) ).
fof(t23_waybel14,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) )
=> k5_waybel11(A) = u1_pre_topc(A) ) ).
fof(t24_waybel14,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k5_waybel11(A))
<=> v3_pre_topc(B,A) ) ) ) ).
fof(t26_waybel14,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))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(C,A)
& r2_hidden(B,C) )
=> r1_waybel_3(A,k2_yellow_0(A,C),B) ) ) ) ) ).
fof(d1_waybel14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) )
=> ( v1_waybel14(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ~ ( g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k14_yellow_6(A,k2_waybel11(A))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k6_borsuk_1(C,C)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k6_borsuk_1(C,C)),u1_struct_0(C)) )
=> ~ ( D = B
& v5_pre_topc(D,k6_borsuk_1(C,C),C) ) ) ) ) ) ) ) ).
fof(t27_waybel14,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ( C = B
=> ( v6_waybel_6(C,k2_yellow_1(k5_waybel11(A)))
<=> ( v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ) ) ) ) ).
fof(t28_waybel14,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ( C = B
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> B != k3_subset_1(u1_struct_0(A),k6_waybel_0(A,D)) )
| ( v5_waybel_6(C,k2_yellow_1(k5_waybel11(A)))
& C != u1_struct_0(A) ) ) ) ) ) ) ).
fof(t29_waybel14,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ~ ( C = B
& v1_waybel14(k5_waybel_2(A),A)
& v5_waybel_6(C,k2_yellow_1(k5_waybel11(A)))
& C != u1_struct_0(A)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> B != k3_subset_1(u1_struct_0(A),k6_waybel_0(A,D)) ) ) ) ) ) ).
fof(t30_waybel14,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)
=> v1_waybel14(k5_waybel_2(A),A) ) ) ).
fof(t31_waybel14,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) )
=> ( v1_waybel14(k5_waybel_2(A),A)
=> v3_yellow_8(A) ) ) ).
fof(t32_waybel14,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)
=> ( v2_compts_1(A)
& v6_waybel_3(A)
& v3_yellow_8(A)
& v1_yellow_8(A) ) ) ) ).
fof(t35_waybel14,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))
=> ~ ( v3_waybel_3(A)
& ! [C] :
( m1_yellow_8(C,A,B)
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& r2_hidden(D,C)
& ~ ( v3_pre_topc(D,A)
& v2_waybel_0(D,A) ) ) ) ) ) ) ).
fof(t36_waybel14,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)
=> v3_waybel_3(k2_yellow_1(k5_waybel11(A))) ) ) ).
fof(t39_waybel14,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))
=> ? [C] :
( m1_yellow_8(C,A,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,C)
=> ( v3_pre_topc(D,A)
& v2_waybel_0(D,A) ) ) ) ) )
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A)))))
& B = k1_yellow_0(k2_yellow_1(k5_waybel11(A)),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ( r2_hidden(D,C)
=> v6_waybel_6(D,k2_yellow_1(k5_waybel11(A))) ) ) ) ) ) ) ).
fof(t40_waybel14,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(k2_yellow_1(k5_waybel11(A))))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A)))))
& B = k1_yellow_0(k2_yellow_1(k5_waybel11(A)),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ( r2_hidden(D,C)
=> v6_waybel_6(D,k2_yellow_1(k5_waybel11(A))) ) ) ) )
& v3_waybel_3(k2_yellow_1(k5_waybel11(A))) )
<=> v1_waybel_5(k2_yellow_1(k5_waybel11(A))) ) ) ).
fof(t41_waybel14,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) )
=> ( v1_waybel_5(k2_yellow_1(k5_waybel11(A)))
<=> ( v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
& v3_waybel_3(k7_lattice3(k2_yellow_1(k5_waybel11(A)))) ) ) ) ).
fof(t15_waybel14,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) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_waybel_0(A,k2_yellow_0(A,B)) = k1_setfam_1(a_2_0_waybel14(A,B)) ) ) ).
fof(t16_waybel14,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) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k7_waybel_0(A,k1_yellow_0(A,B)) = k1_setfam_1(a_2_1_waybel14(A,B)) ) ) ).
fof(t25_waybel14,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,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A)))))
=> ! [C] :
( ( v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = a_2_2_waybel14(A,C)
=> v1_waybel_0(B,k2_yellow_1(k5_waybel11(A))) ) ) ) ) ).
fof(t33_waybel14,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_waybel_3(A)
& r2_hidden(B,k5_waybel11(A)) )
=> B = k3_tarski(a_2_3_waybel14(A,B)) ) ) ) ).
fof(t34_waybel14,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k5_waybel11(A))
=> B = k3_tarski(a_2_3_waybel14(A,B)) ) )
=> v3_waybel_3(A) ) ) ).
fof(t37_waybel14,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))
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_yellow_8(D,A,C)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(E,D)
=> ( v3_pre_topc(E,A)
& v2_waybel_0(E,A) ) ) ) ) )
& v3_waybel_3(k2_yellow_1(k5_waybel11(A))) )
=> B = k1_yellow_0(A,a_2_4_waybel14(A,B)) ) ) ) ).
fof(t38_waybel14,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))
=> B = k1_yellow_0(A,a_2_4_waybel14(A,B)) )
=> v3_waybel_3(A) ) ) ).
fof(t42_waybel14,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) )
=> ~ ( v2_waybel_8(A)
& ! [B] :
( m1_cantor_1(B,A)
=> B != a_1_0_waybel14(A) ) ) ) ).
fof(t43_waybel14,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_cantor_1(B,A)
& B = a_1_0_waybel14(A) )
=> ( v2_waybel_8(k2_yellow_1(k5_waybel11(A)))
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A)))))
& B = k1_yellow_0(k2_yellow_1(k5_waybel11(A)),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ( r2_hidden(D,C)
=> v6_waybel_6(D,k2_yellow_1(k5_waybel11(A))) ) ) ) ) ) ) ) ).
fof(t44_waybel14,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) )
=> ~ ( v2_waybel_8(k2_yellow_1(k5_waybel11(A)))
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A)))))
& B = k1_yellow_0(k2_yellow_1(k5_waybel11(A)),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(k5_waybel11(A))))
=> ( r2_hidden(D,C)
=> v6_waybel_6(D,k2_yellow_1(k5_waybel11(A))) ) ) ) )
& ! [B] :
( m1_cantor_1(B,A)
=> B != a_1_0_waybel14(A) ) ) ) ).
fof(t45_waybel14,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_cantor_1(B,A)
& B = a_1_0_waybel14(A) )
=> v2_waybel_8(A) ) ) ).
fof(fraenkel_a_2_0_waybel14,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_waybel14(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_1_waybel14,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_1_waybel14(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_waybel14,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v4_waybel11(B)
& l1_waybel_9(B)
& v2_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_2_waybel14(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,D))
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_3_waybel14,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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_3_waybel14(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k2_waybel_3(B,D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_4_waybel14,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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_4_waybel14(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = k2_yellow_0(B,D)
& r2_hidden(C,D)
& r2_hidden(D,k5_waybel11(B)) ) ) ) ).
fof(fraenkel_a_1_0_waybel14,axiom,
! [A,B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v4_waybel11(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_0_waybel14(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = k7_waybel_0(B,C)
& r2_hidden(C,u1_struct_0(k1_waybel_8(B))) ) ) ) ).
%------------------------------------------------------------------------------