SET007 Axioms: SET007+695.ax
%------------------------------------------------------------------------------
% File : SET007+695 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Characterizations of Compactness
% 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 : yellow19 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 60 ( 2 unt; 0 def)
% Number of atoms : 560 ( 13 equ)
% Maximal formula atoms : 19 ( 9 avg)
% Number of connectives : 628 ( 128 ~; 1 |; 310 &)
% ( 32 <=>; 157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 1 con; 0-3 aty)
% Number of variables : 188 ( 172 !; 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_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k1_yellow19(A,B))
& v2_waybel_0(k1_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(k1_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(k1_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) ) ).
fof(cc1_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_yellow19(C,A,B)
=> ~ v1_xboole_0(C) ) ) ).
fof(fc2_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v1_xboole_0(k2_yellow19(A,B))
& v13_waybel_0(k2_yellow19(A,B),k3_yellow_1(k2_pre_topc(A))) ) ) ).
fof(fc3_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v1_xboole_0(k2_yellow19(A,B))
& v2_waybel_0(k2_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(k2_yellow19(A,B),k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(k2_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) ) ).
fof(fc4_yellow19,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> ( ~ v3_struct_0(k3_yellow19(A,B,C))
& v2_orders_2(k3_yellow19(A,B,C))
& v3_orders_2(k3_yellow19(A,B,C))
& v6_waybel_0(k3_yellow19(A,B,C),A) ) ) ).
fof(fc5_yellow19,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B))))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> ( ~ v3_struct_0(k3_yellow19(A,B,C))
& v2_orders_2(k3_yellow19(A,B,C))
& v3_orders_2(k3_yellow19(A,B,C))
& v6_waybel_0(k3_yellow19(A,B,C),A)
& v7_waybel_0(k3_yellow19(A,B,C)) ) ) ).
fof(cc2_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v3_orders_2(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_yellow_6(C,A,B)
=> ( v2_yellow_6(C,A,B)
=> ( v3_orders_2(C)
& v2_yellow_6(C,A,B) ) ) ) ) ).
fof(rc1_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ? [C] :
( m1_yellow_6(C,A,B)
& ~ v3_struct_0(C)
& v6_waybel_0(C,A)
& v7_waybel_0(C)
& v2_yellow_6(C,A,B) ) ) ).
fof(fc6_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ( ~ v3_struct_0(k3_yellow19(A,k2_pre_topc(A),B))
& v2_orders_2(k3_yellow19(A,k2_pre_topc(A),B))
& v3_orders_2(k3_yellow19(A,k2_pre_topc(A),B))
& v6_waybel_0(k3_yellow19(A,k2_pre_topc(A),B),A)
& v7_waybel_0(k3_yellow19(A,k2_pre_topc(A),B))
& v1_yellow19(k3_yellow19(A,k2_pre_topc(A),B),A) ) ) ).
fof(t1_yellow19,axiom,
$true ).
fof(t2_yellow19,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(A))
& v13_waybel_0(B,k3_yellow_1(A))
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> ! [C] :
~ ( r2_hidden(C,B)
& v1_xboole_0(C) ) ) ) ).
fof(t3_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r2_hidden(C,k1_yellow19(A,B))
<=> m1_connsp_2(C,A,B) ) ) ) ).
fof(t4_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ( r2_waybel_7(A,C,B)
<=> r1_tarski(k1_yellow19(A,B),C) ) ) ) ) ).
fof(t5_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_waybel_7(A,k1_yellow19(A,B),B) ) ) ).
fof(t6_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ( r2_waybel_7(A,D,C)
=> r2_hidden(B,D) ) ) ) ) ) ) ) ).
fof(d2_yellow19,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_yellow19(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& C = k5_relset_1(u1_struct_0(k5_waybel_9(A,B,D)),u1_struct_0(A),u1_waybel_0(A,k5_waybel_9(A,B,D))) ) ) ) ) ) ).
fof(t7_yellow19,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))
=> m1_yellow19(k5_relset_1(u1_struct_0(k5_waybel_9(A,B,C)),u1_struct_0(A),u1_waybel_0(A,k5_waybel_9(A,B,C))),A,B) ) ) ) ).
fof(t8_yellow19,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] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( r2_hidden(D,k5_relset_1(u1_struct_0(k6_waybel_9(A,B,C)),u1_struct_0(A),u1_waybel_0(A,k6_waybel_9(A,B,C))))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r1_orders_2(B,C,E)
& D = k3_waybel_0(A,B,E) ) ) ) ) ) ).
fof(t9_yellow19,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] :
( m1_yellow19(C,A,B)
=> r1_waybel_0(A,B,C) ) ) ) ).
fof(t10_yellow19,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] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ~ ( ! [D] :
( m1_subset_1(D,C)
=> m1_yellow19(D,A,B) )
& ! [D] :
( m1_yellow19(D,A,B)
=> ~ r1_tarski(D,k1_setfam_1(C)) ) ) ) ) ) ).
fof(t11_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r2_hidden(C,k2_yellow19(A,B))
<=> ( r1_waybel_0(A,B,C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t12_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(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))
=> ( r3_waybel_9(A,B,C)
<=> r1_waybel_7(A,k2_yellow19(A,B),C) ) ) ) ) ).
fof(t13_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(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))
=> ( r2_hidden(C,k11_yellow_6(A,B))
<=> r2_waybel_7(A,k2_yellow19(A,B),C) ) ) ) ) ).
fof(t14_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> k4_xboole_0(B,k1_tarski(k1_xboole_0)) = k2_yellow19(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) ).
fof(t15_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> B = k2_yellow19(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) ).
fof(t16_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(C,B)
<=> r1_waybel_0(A,k3_yellow19(A,k2_pre_topc(A),B),C) ) ) ) ) ).
fof(t17_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_waybel_9(A,k3_yellow19(A,k2_pre_topc(A),B),C)
<=> r1_waybel_7(A,B,C) ) ) ) ) ).
fof(t18_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k11_yellow_6(A,k3_yellow19(A,k2_pre_topc(A),B)))
<=> r2_waybel_7(A,B,C) ) ) ) ) ).
fof(t19_yellow19,axiom,
$true ).
fof(t20_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k6_pre_topc(A,C))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ( D = k1_yellow19(A,B)
=> r2_waybel_0(A,k3_yellow19(A,k2_pre_topc(A),D),C) ) ) ) ) ) ) ).
fof(t21_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B,C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r1_waybel_0(A,C,B)
=> ! [D] :
( m2_yellow_6(D,A,C)
=> r1_waybel_0(A,D,B) ) ) ) ) ).
fof(t22_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B,C,D] :
( ( r1_tarski(B,C)
& r2_waybel_7(A,B,D) )
=> r2_waybel_7(A,C,D) ) ) ).
fof(t23_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k6_pre_topc(A,B))
<=> ? [D] :
( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A)
& r1_waybel_0(A,D,B)
& r3_waybel_9(A,D,C) ) ) ) ) ) ).
fof(t24_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k6_pre_topc(A,B))
<=> ? [D] :
( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& v3_yellow_6(D,A)
& l1_waybel_0(D,A)
& r1_waybel_0(A,D,B)
& r2_hidden(C,k11_yellow_6(A,D)) ) ) ) ) ) ).
fof(t25_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r1_waybel_0(A,C,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_waybel_9(A,C,D)
=> r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t26_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v3_yellow_6(C,A)
& l1_waybel_0(C,A) )
=> ( r1_waybel_0(A,C,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k11_yellow_6(A,C))
=> r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t27_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k6_pre_topc(A,B))
<=> ? [D] :
( ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& r2_hidden(B,D)
& r1_waybel_7(A,D,C) ) ) ) ) ) ).
fof(t28_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k6_pre_topc(A,B))
<=> ? [D] :
( ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(D,k3_yellow_1(k2_pre_topc(A)))
& v3_waybel_7(D,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& r2_hidden(B,D)
& r2_waybel_7(A,D,C) ) ) ) ) ) ).
fof(t29_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ( r2_hidden(B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_waybel_7(A,C,D)
=> r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t30_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A)))
& v3_waybel_7(C,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ( r2_hidden(B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_waybel_7(A,C,D)
=> r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t31_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(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))
=> ( r3_waybel_9(A,B,C)
<=> ! [D] :
( m1_yellow19(D,A,B)
=> r2_hidden(C,k6_pre_topc(A,D)) ) ) ) ) ) ).
fof(t32_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tops_2(B,A)
=> v2_tops_2(k2_cantor_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t33_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_waybel_7(A,B,C) ) ) ) ) ).
fof(t34_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A)))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_waybel_7(A,B,C) ) ) ) ) ).
fof(t35_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(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))
& r3_waybel_9(A,B,C) ) ) ) ) ).
fof(t36_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ~ ( r2_hidden(B,k7_yellow_6(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r3_waybel_9(A,B,C) ) ) ) ) ) ).
fof(t37_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ? [C] :
( m2_yellow_6(C,A,B)
& v3_yellow_6(C,A) ) ) ) ) ).
fof(d5_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v1_yellow19(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_waybel_0(A,B,C)
| r1_waybel_0(A,B,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ) ).
fof(t38_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( v1_yellow19(B,A)
=> v3_yellow_6(B,A) ) ) ) ) ).
fof(dt_m1_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_yellow19(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ? [C] : m1_yellow19(C,A,B) ) ).
fof(dt_k1_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) ).
fof(dt_k2_yellow19,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> m1_subset_1(k2_yellow19(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) ).
fof(dt_k3_yellow19,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> ( ~ v3_struct_0(k3_yellow19(A,B,C))
& v6_waybel_0(k3_yellow19(A,B,C),A)
& l1_waybel_0(k3_yellow19(A,B,C),A) ) ) ).
fof(d1_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_yellow19(A,B) = a_2_0_yellow19(A,B) ) ) ).
fof(d3_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> k2_yellow19(A,B) = a_2_1_yellow19(A,B) ) ) ).
fof(d4_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k3_yellow19(A,B,C)
<=> ( u1_struct_0(D) = a_3_0_yellow19(A,B,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_tarski(k2_mcart_1(F),k2_mcart_1(E)) ) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> k3_waybel_0(A,D,E) = k1_mcart_1(E) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_yellow19,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_yellow19(B,C))
<=> ? [D] :
( m1_connsp_2(D,B,C)
& A = D ) ) ) ).
fof(fraenkel_a_2_1_yellow19,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_yellow19(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& r1_waybel_0(B,C,D) ) ) ) ).
fof(fraenkel_a_3_0_yellow19,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(C))
& v13_waybel_0(D,k3_yellow_1(C))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) )
=> ( r2_hidden(A,a_3_0_yellow19(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_struct_0(F,k3_yellow_1(C),D)
& A = k4_tarski(E,F)
& r2_hidden(E,F) ) ) ) ).
%------------------------------------------------------------------------------