SET007 Axioms: SET007+696.ax
%------------------------------------------------------------------------------
% File : SET007+696 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Compactness of Lim-inf Topology
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : waybel33 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 41 ( 0 unt; 0 def)
% Number of atoms : 559 ( 38 equ)
% Maximal formula atoms : 29 ( 13 avg)
% Number of connectives : 581 ( 63 ~; 0 |; 396 &)
% ( 5 <=>; 117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 54 ( 53 usr; 0 prp; 1-3 aty)
% Number of functors : 29 ( 29 usr; 0 con; 1-3 aty)
% Number of variables : 111 ( 105 !; 6 ?)
% 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(cc1_waybel33,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v1_waybel33(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A) ) ) ) ).
fof(cc2_waybel33,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel33(A) ) ) ) ).
fof(rc1_waybel33,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel33(A) ) ).
fof(cc3_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v1_yellow_0(B)
& v25_waybel_0(B) ) ) ) ).
fof(cc4_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B) ) ) ) ).
fof(rc2_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v2_lattice3(B)
& ~ v1_yellow_3(B)
& v1_waybel_9(B)
& v1_waybel33(B) ) ) ).
fof(fc1_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_waybel33(A))
& v2_pre_topc(k2_waybel33(A))
& v2_orders_2(k2_waybel33(A))
& v3_orders_2(k2_waybel33(A))
& v4_orders_2(k2_waybel33(A))
& v1_yellow_0(k2_waybel33(A))
& v24_waybel_0(k2_waybel33(A))
& v25_waybel_0(k2_waybel33(A))
& v2_lattice3(k2_waybel33(A))
& ~ v1_yellow_3(k2_waybel33(A))
& v1_waybel_9(k2_waybel33(A))
& v1_waybel33(k2_waybel33(A)) ) ) ).
fof(t1_waybel33,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ( 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)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v2_waybel_0(E,k3_yellow_1(C))
& v13_waybel_0(E,k3_yellow_1(C))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& v2_waybel_0(F,k3_yellow_1(D))
& v13_waybel_0(F,k3_yellow_1(D))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_yellow_1(D)))) )
=> ( E = F
=> k1_waybel33(A,C,E) = k1_waybel33(B,D,F) ) ) ) ) ) ) ) ) ).
fof(d2_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_waybel_9(A) )
=> ( v1_waybel33(A)
<=> u1_pre_topc(A) = k4_waybel28(A) ) ) ).
fof(t2_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( l1_waybel_0(C,A)
=> ? [D] :
( v6_waybel_0(D,B)
& l1_waybel_0(D,B)
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) ) ) ) ) ) ).
fof(t3_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( l1_waybel_0(C,A)
=> ~ ( r2_hidden(C,k7_yellow_6(A))
& ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v6_waybel_0(D,B)
& v7_waybel_0(D)
& l1_waybel_0(D,B) )
=> ~ ( r2_hidden(D,k7_yellow_6(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) ) ) ) ) ) ) ) ).
fof(t4_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(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] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> k1_waybel11(A,C) = k1_waybel11(B,D) ) ) ) ) ) ) ).
fof(t5_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> ! [E] :
( m2_yellow_6(E,A,C)
=> ? [F] :
( v6_waybel_0(F,B)
& m2_yellow_6(F,B,D)
& g1_orders_2(u1_struct_0(E),u1_orders_2(E)) = g1_orders_2(u1_struct_0(F),u1_orders_2(F))
& u1_waybel_0(A,E) = u1_waybel_0(B,F) ) ) ) ) ) ) ) ) ).
fof(t6_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(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] :
( l1_waybel_0(C,A)
=> ! [D] :
~ ( r2_hidden(k4_tarski(C,D),k3_waybel28(A))
& ! [E] :
( ( ~ v3_struct_0(E)
& v3_orders_2(E)
& v6_waybel_0(E,B)
& v7_waybel_0(E)
& l1_waybel_0(E,B) )
=> ~ ( r2_hidden(k4_tarski(E,D),k3_waybel28(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(E),u1_orders_2(E))
& u1_waybel_0(A,C) = u1_waybel_0(B,E) ) ) ) ) ) ) ) ).
fof(t7_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_waybel_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> ! [E] :
( r1_waybel_0(A,C,E)
=> r1_waybel_0(B,D,E) ) ) ) ) ) ) ).
fof(t8_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(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))
=> k14_yellow_6(A,k3_waybel28(A)) = k14_yellow_6(B,k3_waybel28(B)) ) ) ) ).
fof(t9_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(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))
=> k4_waybel28(A) = k4_waybel28(B) ) ) ) ).
fof(t10_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel33(B)
& m1_yellow_9(B,A) )
=> k4_waybel28(A) = u1_pre_topc(B) ) ) ).
fof(d3_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_9(B)
& m1_yellow_9(B,A) )
=> ( B = k2_waybel33(A)
<=> v1_waybel33(B) ) ) ) ).
fof(t12_waybel33,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] :
( ( ~ 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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)))
=> ( k2_mcart_1(D) = C
=> k2_yellow_0(A,C) = k2_waybel_9(A,k6_waybel_9(A,k3_yellow19(A,k2_pre_topc(A),B),D)) ) ) ) ) ) ) ).
fof(t13_waybel33,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] :
( ( ~ 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))))) )
=> k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) ).
fof(t14_waybel33,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] :
( ( ~ 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))))) )
=> r2_hidden(k3_yellow19(A,k2_pre_topc(A),B),k7_yellow_6(A)) ) ) ).
fof(t15_waybel33,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] :
( ( ~ 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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)),u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)))
& v1_waybel28(C,k3_yellow19(A,k2_pre_topc(A),B))
& m2_relset_1(C,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B)),u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B))) )
=> r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,k3_yellow19(A,k2_pre_topc(A),B),C)),k1_waybel33(A,k2_pre_topc(A),B)) ) ) ) ).
fof(t16_waybel33,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] :
( ( ~ 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] :
( m2_yellow_6(C,A,k3_yellow19(A,k2_pre_topc(A),B))
=> k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,C) ) ) ) ).
fof(t17_waybel33,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] :
~ ( r2_waybel_0(A,B,C)
& ! [D] :
( ( v6_waybel_0(D,A)
& m2_yellow_6(D,A,B) )
=> ~ ( r1_tarski(k8_yellow_2(u1_struct_0(D),A,u1_waybel_0(A,D)),C)
& m1_yellow_6(D,A,B) ) ) ) ) ) ).
fof(t18_waybel33,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)
& v1_waybel33(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v1_xboole_0(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)
=> r2_hidden(k1_waybel33(A,k2_pre_topc(A),C),B) ) ) ) ) ) ).
fof(t19_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> r1_tarski(k5_waybel11(A),k4_waybel28(A)) ) ).
fof(t20_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m2_cantor_1(C,A)
=> ( ( r1_tarski(C,u1_pre_topc(B))
& r2_hidden(u1_struct_0(A),u1_pre_topc(B)) )
=> r1_tarski(u1_pre_topc(A),u1_pre_topc(B)) ) ) ) ) ).
fof(t21_waybel33,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) )
=> r1_tarski(k1_waybel19(A),k4_waybel28(A)) ) ).
fof(t22_waybel33,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( ( m2_yellow_9(C,A)
& m2_yellow_9(C,B) )
=> ! [D] :
( m3_yellow_9(D,A,B)
=> m2_yellow_9(C,D) ) ) ) ) ) ).
fof(t23_waybel33,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_yellow_9(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(C,A)
=> ( v3_pre_topc(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) )
& ( v4_pre_topc(C,A)
=> ( v4_pre_topc(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ) ).
fof(t24_waybel33,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) )
=> r1_tarski(k2_waybel19(A),k4_waybel28(A)) ) ).
fof(t25_waybel33,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] :
( ( v1_waybel33(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v2_pre_topc(C)
& v2_waybel19(C)
& m1_yellow_9(C,A) )
=> m2_yellow_9(B,C) ) ) ) ).
fof(t26_waybel33,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)
& v1_waybel33(A)
& l1_waybel_9(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))))) )
=> r2_waybel_7(A,B,k1_waybel33(A,k2_pre_topc(A),B)) ) ) ).
fof(t27_waybel33,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)
& v1_waybel33(A)
& l1_waybel_9(A) )
=> ( v2_compts_1(A)
& v1_urysohn1(A) ) ) ).
fof(dt_k1_waybel33,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_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(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)))) )
=> m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v1_waybel_9(k2_waybel33(A))
& m1_yellow_9(k2_waybel33(A),A) ) ) ).
fof(d1_waybel33,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)
& 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)))) )
=> k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) ).
fof(t11_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> k1_waybel11(A,B) = k1_yellow_0(A,a_2_0_waybel33(A,B)) ) ) ).
fof(fraenkel_a_3_0_waybel33,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(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_waybel33(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = k2_yellow_0(B,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_2_0_waybel33,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_0_waybel33(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_waybel_9(B,k6_waybel_9(B,C,D)) ) ) ) ).
%------------------------------------------------------------------------------