SET007 Axioms: SET007+497.ax
%------------------------------------------------------------------------------
% File : SET007+497 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Prime Ideals and Filters
% 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_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 5 unt; 0 def)
% Number of atoms : 826 ( 11 equ)
% Maximal formula atoms : 23 ( 12 avg)
% Number of connectives : 877 ( 119 ~; 4 |; 535 &)
% ( 32 <=>; 187 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 60 ( 58 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 1 con; 0-4 aty)
% Number of variables : 195 ( 186 !; 9 ?)
% 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_7,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& ~ v1_yellow_3(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A))
& v9_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A))
& v11_waybel_1(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ).
fof(fc2_waybel_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k3_yellow_1(A))
& ~ v3_realset2(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& ~ v1_yellow_3(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A))
& v9_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A))
& v11_waybel_1(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ) ).
fof(rc1_waybel_7,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ).
fof(rc2_waybel_7,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ).
fof(rc3_waybel_7,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc4_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc5_waybel_7,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)
& v12_waybel_0(B,A)
& v1_waybel_7(B,A) ) ) ).
fof(rc6_waybel_7,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)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& v2_waybel_7(B,A) ) ) ).
fof(cc1_waybel_7,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& v3_waybel_7(B,A) )
=> ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ) ) ).
fof(rc7_waybel_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
& ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
& v2_waybel_0(B,k3_yellow_1(A))
& v13_waybel_0(B,k3_yellow_1(A))
& v3_waybel_7(B,k3_yellow_1(A)) ) ) ).
fof(fc3_waybel_7,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v5_waybel_4(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> v13_waybel_0(k6_waybel_4(A,C,B),A) ) ).
fof(t1_waybel_7,axiom,
$true ).
fof(t2_waybel_7,axiom,
$true ).
fof(t3_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B,C] :
( r1_tarski(B,C)
=> ( r3_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C))
& r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)) ) ) ) ).
fof(t4_waybel_7,axiom,
! [A] : u1_struct_0(k3_yellow_1(A)) = k1_zfmisc_1(A) ).
fof(t5_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ( v3_realset2(A)
<=> k4_yellow_0(A) = k3_yellow_0(A) ) ) ).
fof(t6_waybel_7,axiom,
$true ).
fof(t7_waybel_7,axiom,
$true ).
fof(t8_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))) )
=> ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
<=> ~ r2_hidden(k3_yellow_0(A),B) ) ) ) ).
fof(t9_waybel_7,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> k7_waybel_1(k3_yellow_1(A),B) = k4_xboole_0(A,B) ) ).
fof(t10_waybel_7,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
=> ( v12_waybel_0(B,k3_yellow_1(A))
<=> ! [C,D] :
( ( r1_tarski(C,D)
& r2_hidden(D,B) )
=> r2_hidden(C,B) ) ) ) ).
fof(t11_waybel_7,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
=> ( v13_waybel_0(B,k3_yellow_1(A))
<=> ! [C,D] :
( ( r1_tarski(C,D)
& r1_tarski(D,A)
& r2_hidden(C,B) )
=> r2_hidden(D,B) ) ) ) ).
fof(t12_waybel_7,axiom,
! [A,B] :
( ( v12_waybel_0(B,k3_yellow_1(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> ( v1_waybel_0(B,k3_yellow_1(A))
<=> ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k2_xboole_0(C,D),B) ) ) ) ).
fof(t13_waybel_7,axiom,
! [A,B] :
( ( v13_waybel_0(B,k3_yellow_1(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> ( v2_waybel_0(B,k3_yellow_1(A))
<=> ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k3_xboole_0(C,D),B) ) ) ) ).
fof(t14_waybel_7,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v12_waybel_0(B,k3_yellow_1(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> ( v1_waybel_0(B,k3_yellow_1(A))
<=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r1_tarski(C,B)
=> r2_hidden(k5_setfam_1(A,C),B) ) ) ) ) ).
fof(t15_waybel_7,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v13_waybel_0(B,k3_yellow_1(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> ( v2_waybel_0(B,k3_yellow_1(A))
<=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r1_tarski(C,B)
=> r2_hidden(k8_setfam_1(A,C),B) ) ) ) ) ).
fof(d1_waybel_7,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)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(k12_lattice3(A,C,D),B)
& ~ r2_hidden(C,B)
& ~ r2_hidden(D,B) ) ) ) ) ) ) ).
fof(t16_waybel_7,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)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_7(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(k2_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t17_waybel_7,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& v1_waybel_7(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,B)
& v12_waybel_0(C,B)
& v1_waybel_7(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ).
fof(d2_waybel_7,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)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(k13_lattice3(A,C,D),B)
& ~ r2_hidden(C,B)
& ~ r2_hidden(D,B) ) ) ) ) ) ) ).
fof(t18_waybel_7,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)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_waybel_7(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(k1_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t19_waybel_7,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& v13_waybel_0(C,A)
& v2_waybel_7(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(C)
& v2_waybel_0(C,B)
& v13_waybel_0(C,B)
& v2_waybel_7(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ).
fof(t20_waybel_7,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] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& v1_waybel_7(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k7_lattice3(A))
& v13_waybel_0(B,k7_lattice3(A))
& v2_waybel_7(B,k7_lattice3(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) ) ) ) ).
fof(t21_waybel_7,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] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& v2_waybel_7(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k7_lattice3(A))
& v12_waybel_0(B,k7_lattice3(A))
& v1_waybel_7(B,k7_lattice3(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) ) ) ) ).
fof(t22_waybel_7,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)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_7(B,A)
<=> ( ( ~ v1_xboole_0(k3_subset_1(u1_struct_0(A),B))
& v2_waybel_0(k3_subset_1(u1_struct_0(A),B),A)
& v13_waybel_0(k3_subset_1(u1_struct_0(A),B),A)
& m1_subset_1(k3_subset_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) )
| k3_subset_1(u1_struct_0(A),B) = k1_xboole_0 ) ) ) ) ).
fof(t23_waybel_7,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] :
( ( ~ 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))) )
=> ( v1_waybel_7(B,A)
<=> r2_hidden(B,k4_waybel_6(k2_yellow_1(k8_waybel_0(A)))) ) ) ) ).
fof(t24_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v11_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(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))) )
=> ( v2_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
| r2_hidden(k7_waybel_1(A,C),B) ) ) ) ) ) ).
fof(t25_waybel_7,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(A))
& v13_waybel_0(B,k3_yellow_1(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> ( v2_waybel_7(B,k3_yellow_1(A))
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( r2_hidden(C,B)
| r2_hidden(k4_xboole_0(A,C),B) ) ) ) ) ).
fof(d3_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_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))) )
=> ( v3_waybel_7(B,A)
<=> ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& ! [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)
& B != C
& C != u1_struct_0(A) ) ) ) ) ) ) ).
fof(t26_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v11_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(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))) )
=> ( ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_7(B,A) )
<=> v3_waybel_7(B,A) ) ) ) ).
fof(t27_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(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))) )
=> ! [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_subset_1(B,C)
& ! [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))) )
=> ~ ( v1_waybel_7(D,A)
& r1_tarski(B,D)
& r1_subset_1(D,C) ) ) ) ) ) ) ).
fof(t28_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(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))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ~ r2_hidden(C,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))) )
=> ~ ( v1_waybel_7(D,A)
& r1_tarski(B,D)
& ~ r2_hidden(C,D) ) ) ) ) ) ) ).
fof(t29_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(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))) )
=> ! [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_subset_1(B,C)
& ! [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))) )
=> ~ ( v2_waybel_7(D,A)
& r1_tarski(C,D)
& r1_subset_1(B,D) ) ) ) ) ) ) ).
fof(t30_waybel_7,axiom,
! [A] :
( ( ~ v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v11_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [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)
& v3_waybel_7(C,A) ) ) ) ).
fof(d4_waybel_7,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B,C] :
( r1_waybel_7(A,B,C)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(D,A)
& r2_hidden(C,D) )
=> ! [E] :
~ ( r2_hidden(E,B)
& r1_xboole_0(D,E) ) ) ) ) ) ).
fof(d5_waybel_7,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B,C] :
( r2_waybel_7(A,B,C)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(D,A)
& r2_hidden(C,D) )
=> r2_hidden(D,B) ) ) ) ) ).
fof(t31_waybel_7,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(u1_struct_0(A)))
& v13_waybel_0(B,k3_yellow_1(u1_struct_0(A)))
& v3_waybel_7(B,k3_yellow_1(u1_struct_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(u1_struct_0(A))))) )
=> ! [C] :
( r1_waybel_7(A,B,C)
<=> r2_waybel_7(A,B,C) ) ) ) ).
fof(t32_waybel_7,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))))
=> ( r1_waybel_3(k2_yellow_1(u1_pre_topc(A)),B,C)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_tex_2(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(u1_struct_0(A)))))
& v2_waybel_0(D,k3_yellow_1(u1_struct_0(A)))
& v13_waybel_0(D,k3_yellow_1(u1_struct_0(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(u1_struct_0(A))))) )
=> ~ ( r2_hidden(B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,C)
& r1_waybel_7(A,D,E) ) ) ) ) ) ) ) ) ).
fof(t33_waybel_7,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))))
=> ( r1_waybel_3(k2_yellow_1(u1_pre_topc(A)),B,C)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(u1_struct_0(A)))
& v13_waybel_0(D,k3_yellow_1(u1_struct_0(A)))
& v3_waybel_7(D,k3_yellow_1(u1_struct_0(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(u1_struct_0(A))))) )
=> ~ ( r2_hidden(B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,C)
& r2_waybel_7(A,D,E) ) ) ) ) ) ) ) ) ).
fof(t34_waybel_7,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))))
=> ( ( r1_tarski(B,C)
& ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(u1_struct_0(A)))
& v13_waybel_0(D,k3_yellow_1(u1_struct_0(A)))
& v3_waybel_7(D,k3_yellow_1(u1_struct_0(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(u1_struct_0(A))))) )
=> ~ ( r2_hidden(B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,C)
& r2_waybel_7(A,D,E) ) ) ) ) )
=> r1_waybel_3(k2_yellow_1(u1_pre_topc(A)),B,C) ) ) ) ) ).
fof(t35_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_1(u1_pre_topc(A))))
=> ( r1_tarski(C,D)
=> ( r1_waybel_3(k2_yellow_1(u1_pre_topc(A)),C,D)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(B))
=> ~ ( r1_tarski(D,k3_tarski(E))
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(E)) )
=> ~ r1_tarski(C,k3_tarski(F)) ) ) ) ) ) ) ) ) ) ).
fof(t36_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_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_waybel_3(A,B,C)
<=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& v12_waybel_0(D,A)
& v1_waybel_7(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,C,k1_yellow_0(A,D))
=> r2_hidden(B,D) ) ) ) ) ) ) ).
fof(t37_waybel_7,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,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
=> v1_waybel_7(k6_waybel_0(A,B),A) ) ) ) ).
fof(d6_waybel_7,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,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
<=> ? [C] :
( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& v1_waybel_7(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& B = k1_yellow_0(A,C) ) ) ) ) ).
fof(t38_waybel_7,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,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
=> v4_waybel_7(B,A) ) ) ) ).
fof(t39_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_waybel_3(A,k2_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r3_orders_2(A,D,B) ) ) ) ) ) ) ) ).
fof(t40_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_waybel_3(A,k2_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r3_orders_2(A,D,B) ) ) ) )
=> ( ( B = k4_yellow_0(A)
& v1_waybel_3(k4_yellow_0(A),A) )
| r1_subset_1(k5_waybel_0(A,k13_waybel_0(A,k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)))),k1_waybel_3(A,B)) ) ) ) ) ).
fof(t41_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v1_waybel_3(k4_yellow_0(A),A)
=> ( ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_waybel_3(A,k2_yellow_0(A,B),k4_yellow_0(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& r3_orders_2(A,C,k4_yellow_0(A)) ) ) ) )
& ~ r2_subset_1(k5_waybel_0(A,k13_waybel_0(A,k3_subset_1(u1_struct_0(A),k6_waybel_0(A,k4_yellow_0(A))))),k1_waybel_3(A,k4_yellow_0(A))) ) ) ) ).
fof(t42_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r1_subset_1(k5_waybel_0(A,k13_waybel_0(A,k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)))),k1_waybel_3(A,B))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_waybel_3(A,k2_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r3_orders_2(A,D,B) ) ) ) ) ) ) ) ).
fof(t43_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r1_subset_1(k5_waybel_0(A,k13_waybel_0(A,k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)))),k1_waybel_3(A,B))
=> v4_waybel_7(B,A) ) ) ) ).
fof(d7_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v5_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(k7_yellow_3(A,A,C,D),B)
& r2_hidden(k7_yellow_3(A,A,C,E),B) )
=> r2_hidden(k7_yellow_3(A,A,C,k11_lattice3(A,D,E)),B) ) ) ) ) ) ) ) ).
fof(t44_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> v2_waybel_0(k6_waybel_4(A,C,B),A) ) ) ) ) ).
fof(t45_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(k7_yellow_3(A,A,C,E),B)
& r2_hidden(k7_yellow_3(A,A,D,F),B) )
=> r2_hidden(k7_yellow_3(A,A,k12_lattice3(A,C,D),k12_lattice3(A,E,F)),B) ) ) ) ) ) ) ) ) ).
fof(t46_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_waybel_7(B,A)
<=> ! [C] :
( ( v4_yellow_0(C,k3_yellow_3(A,A))
& m1_yellow_0(C,k3_yellow_3(A,A)) )
=> ( u1_struct_0(C) = B
=> v5_yellow_0(C,k3_yellow_3(A,A)) ) ) ) ) ) ).
fof(t47_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_waybel_7(B,A)
<=> v19_waybel_0(k7_waybel_4(A,B),A,k2_yellow_1(k8_waybel_0(A))) ) ) ) ).
fof(t48_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v5_waybel_7(k1_waybel_4(A),A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,k12_lattice3(A,C,D),B)
& ~ r3_orders_2(A,C,B)
& ~ r3_orders_2(A,D,B) ) ) ) ) ) ) ) ).
fof(t49_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v5_waybel_7(k1_waybel_4(A),A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
=> v5_waybel_6(B,A) ) ) ) ) ).
fof(t50_waybel_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
=> v5_waybel_6(B,A) ) )
=> v5_waybel_7(k1_waybel_4(A),A) ) ) ).
%------------------------------------------------------------------------------