SET007 Axioms: SET007+612.ax
%------------------------------------------------------------------------------
% File : SET007+612 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Isomorphism between Relational Structures
% Version : [Urb08] axioms.
% English : Some Properties of Isomorphism between Relational Structures On
% the Product of Topological Spaces
% 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 : yellow14 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 1 unt; 0 def)
% Number of atoms : 488 ( 34 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 506 ( 80 ~; 0 |; 235 &)
% ( 6 <=>; 185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 63 ( 62 usr; 0 prp; 1-4 aty)
% Number of functors : 38 ( 38 usr; 2 con; 0-5 aty)
% Number of variables : 180 ( 174 !; 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(rc1_yellow14,axiom,
? [A] :
( l1_orders_2(A)
& v3_struct_0(A)
& v1_orders_2(A) ) ).
fof(rc2_yellow14,axiom,
? [A] :
( l1_struct_0(A)
& v1_struct_0(A)
& ~ v3_struct_0(A)
& v1_monoid_0(A) ) ).
fof(rc3_yellow14,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v1_monoid_0(A) ) ).
fof(cc1_yellow14,axiom,
! [A] :
( ( v1_monoid_0(A)
& l1_struct_0(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> v1_yellow14(B,A) ) ) ).
fof(rc4_yellow14,axiom,
! [A] :
( ( v1_monoid_0(A)
& l1_struct_0(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& v6_waybel_0(B,A)
& v1_yellow14(B,A) ) ) ).
fof(rc5_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_monoid_0(A)
& l1_struct_0(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v6_waybel_0(B,A)
& v1_yellow14(B,A) ) ) ).
fof(fc1_yellow14,axiom,
! [A,B] :
( ( v1_monoid_0(A)
& l1_struct_0(A)
& v1_yellow14(B,A)
& l1_waybel_0(B,A) )
=> ( v1_relat_1(u1_waybel_0(A,B))
& v1_funct_1(u1_waybel_0(A,B))
& v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A))
& v1_funcop_1(u1_waybel_0(A,B)) ) ) ).
fof(rc6_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_monoid_0(A)
& l1_struct_0(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B)
& v1_yellow14(B,A) ) ) ).
fof(fc2_yellow14,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ~ v1_xboole_0(k2_relat_1(u1_waybel_0(A,B))) ) ).
fof(fc3_yellow14,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ~ v1_xboole_0(k2_relat_1(k2_waybel_0(A,B))) ) ).
fof(cc2_yellow14,axiom,
! [A,B] :
( ( l1_orders_2(A)
& 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)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(cc3_yellow14,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_struct_0(A)
=> ( v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc4_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> ( v13_waybel_0(B,A)
& v1_waybel11(B,A) ) ) ) ) ).
fof(cc5_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v13_waybel_0(B,A)
& v1_waybel11(B,A) )
=> v3_pre_topc(B,A) ) ) ) ).
fof(fc4_yellow14,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v1_relat_1(k4_tmap_1(A,B))
& v1_funct_1(k4_tmap_1(A,B))
& ~ v1_xboole_0(k4_tmap_1(A,B))
& v1_funct_2(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A))
& v5_pre_topc(k4_tmap_1(A,B),B,A)
& v1_partfun1(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(fc5_yellow14,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ( ~ v3_struct_0(k3_waybel18(A,k2_pre_circ(A,B)))
& v1_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
& v2_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
& v2_t_0topsp(k3_waybel18(A,k2_pre_circ(A,B)))
& v1_monoid_0(k3_waybel18(A,k2_pre_circ(A,B))) ) ) ).
fof(fc6_yellow14,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_urysohn1(B)
& l1_pre_topc(B) )
=> ( ~ v3_struct_0(k3_waybel18(A,k2_pre_circ(A,B)))
& v1_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
& v2_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
& v1_urysohn1(k3_waybel18(A,k2_pre_circ(A,B)))
& v1_monoid_0(k3_waybel18(A,k2_pre_circ(A,B))) ) ) ).
fof(t1_yellow14,axiom,
k1_zfmisc_1(np__1) = k2_tarski(np__0,np__1) ).
fof(t2_yellow14,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> k2_relat_1(k2_partfun1(A,A,k6_partfun1(A),B)) = B ) ).
fof(t3_yellow14,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] : k1_funct_1(k1_funct_4(A,k3_cqc_lang(B,C)),B) = C ) ).
fof(t4_yellow14,axiom,
! [A] :
( ( v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( l1_struct_0(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)) )
=> ( k1_yellow_2(A,B,C) = k2_pre_topc(B)
=> v3_struct_0(B) ) ) ) ) ).
fof(t5_yellow14,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( v3_struct_0(B)
& l1_struct_0(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)) )
=> ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = k2_pre_topc(A)
=> v3_struct_0(A) ) ) ) ) ).
fof(t6_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( l1_struct_0(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)) )
=> ~ ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = k2_pre_topc(A)
& v3_struct_0(B) ) ) ) ) ).
fof(t7_yellow14,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(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)) )
=> ~ ( k8_yellow_2(u1_struct_0(A),B,C) = k2_pre_topc(B)
& v3_struct_0(A) ) ) ) ) ).
fof(d1_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(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] :
( ( ~ 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) ) ) ) ) ) ).
fof(d2_yellow14,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ( v1_yellow14(B,A)
<=> v1_funcop_1(u1_waybel_0(A,B)) ) ) ) ).
fof(t8_yellow14,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [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(A),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_yellow_2(u1_struct_0(A),B,E,F)
& v5_orders_3(D,B,C) )
=> r1_yellow_2(u1_struct_0(A),C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),E,D),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,D)) ) ) ) ) ) ) ) ).
fof(t9_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_waybel_9(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_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_waybel24(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k3_waybel24(A,B)))
=> ( ( E = C
& F = D )
=> ( r1_orders_2(k3_waybel24(A,B),E,F)
<=> r1_yellow_2(u1_struct_0(A),B,C,D) ) ) ) ) ) ) ) ) ).
fof(t10_yellow14,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)) )
=> ( v23_waybel_0(C,A,B)
=> v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(t11_yellow14,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)
=> v23_waybel_0(k2_tops_2(A,B,C),B,A) ) ) ) ) ).
fof(t12_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v2_lattice3(A) )
=> v2_lattice3(B) ) ) ) ).
fof(t13_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v1_lattice3(A) )
=> v1_lattice3(B) ) ) ) ).
fof(t14_yellow14,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_struct_0(A)
=> v3_yellow_0(A) ) ) ).
fof(t15_yellow14,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( r5_waybel_1(A,B)
& v1_yellow_0(A) )
=> v1_yellow_0(B) ) ) ) ).
fof(t16_yellow14,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( r5_waybel_1(A,B)
& v2_yellow_0(A) )
=> v2_yellow_0(B) ) ) ) ).
fof(t17_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v23_waybel_0(D,A,B)
& r1_yellow_0(A,C) )
=> r1_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) ) ).
fof(t18_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v23_waybel_0(D,A,B)
& r2_yellow_0(A,C) )
=> r2_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) ) ).
fof(t19_yellow14,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ~ ( ~ r1_t_0topsp(A,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)) )
=> ~ ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = k2_pre_topc(A)
& k1_yellow_2(A,B,C) = k2_pre_topc(B) ) ) )
=> ( v3_struct_0(A)
<=> v3_struct_0(B) ) ) ) ) ).
fof(t20_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> r1_t_0topsp(A,g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ).
fof(t21_yellow14,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( D = k1_tarski(B)
& r1_tarski(k6_pre_topc(A,D),k6_pre_topc(A,E)) )
=> r2_hidden(B,k6_pre_topc(A,E)) ) ) ) ) ) ) ).
fof(t22_yellow14,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( D = k1_tarski(C)
& r2_hidden(B,k6_pre_topc(A,D))
& v3_pre_topc(E,A)
& r2_hidden(B,E) )
=> r2_hidden(C,E) ) ) ) ) ) ) ).
fof(t23_yellow14,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( D = k1_tarski(B)
& E = k1_tarski(C)
& ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(F,A)
& r2_hidden(B,F) )
=> r2_hidden(C,F) ) ) )
=> r1_tarski(k6_pre_topc(A,D),k6_pre_topc(A,E)) ) ) ) ) ) ) ).
fof(t24_yellow14,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] :
( ( v2_yellow_8(C,A)
& 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
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
=> v2_yellow_8(D,B) ) ) ) ) ) ).
fof(t25_yellow14,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] :
( 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(u1_struct_0(A)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( C = D
& E = F
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& r1_yellow_8(A,E,C) )
=> r1_yellow_8(B,F,D) ) ) ) ) ) ) ) ).
fof(t26_yellow14,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(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
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v6_compts_1(C,A) )
=> v6_compts_1(D,B) ) ) ) ) ) ).
fof(t27_yellow14,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) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v3_yellow_8(A) )
=> v3_yellow_8(B) ) ) ) ).
fof(t28_yellow14,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) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v6_waybel_3(A) )
=> v6_waybel_3(B) ) ) ) ).
fof(t29_yellow14,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v2_compts_1(A) )
=> v2_compts_1(B) ) ) ) ).
fof(t30_yellow14,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel18(A,B)))
=> ( r2_hidden(C,k6_pre_topc(k3_waybel18(A,B),k1_struct_0(k3_waybel18(A,B),D)))
<=> ! [E] :
( m1_subset_1(E,A)
=> r2_hidden(k5_waybel18(A,B,C,E),k6_pre_topc(k4_waybel18(A,B,E),k1_struct_0(k4_waybel18(A,B,E),k5_waybel18(A,B,D,E)))) ) ) ) ) ) ) ).
fof(t31_yellow14,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
=> ( r2_hidden(C,k6_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)),k1_struct_0(k3_waybel18(A,k2_pre_circ(A,B)),D)))
<=> ! [E] :
( m1_subset_1(E,A)
=> r2_hidden(k2_yellow14(A,B,C,E),k6_pre_topc(B,k1_struct_0(B,k2_yellow14(A,B,D,E)))) ) ) ) ) ) ) ).
fof(t32_yellow14,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v4_waybel_3(C)
& v1_waybel18(C)
& m1_pboole(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel18(A,C)))
=> k5_card_3(B,k6_pre_topc(k3_waybel18(A,C),k1_struct_0(k3_waybel18(A,C),D))) = k6_pre_topc(k4_waybel18(A,C,B),k1_struct_0(k4_waybel18(A,C,B),k5_waybel18(A,C,D,B))) ) ) ) ) ).
fof(t33_yellow14,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,C))))
=> k5_card_3(B,k6_pre_topc(k3_waybel18(A,k2_pre_circ(A,C)),k1_struct_0(k3_waybel18(A,k2_pre_circ(A,C)),D))) = k6_pre_topc(C,k1_struct_0(C,k2_yellow14(A,C,D,B))) ) ) ) ) ).
fof(t34_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(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_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)) )
=> ( ( C = k7_grcat_1(A)
& D = k7_grcat_1(A)
& v5_pre_topc(C,A,B)
& v5_pre_topc(D,B,A) )
=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ) ) ).
fof(t35_yellow14,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] :
( ( 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_pre_topc(k8_waybel18(A,B,C),A,k7_waybel18(A,B,C))
=> v5_pre_topc(C,A,B) ) ) ) ) ).
fof(t36_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,B) = B
=> k7_funct_2(u1_struct_0(k7_waybel18(A,A,B)),u1_struct_0(A),u1_struct_0(k7_waybel18(A,A,B)),k4_tmap_1(A,k7_waybel18(A,A,B)),k8_waybel18(A,A,B)) = k7_grcat_1(k7_waybel18(A,A,B)) ) ) ) ).
fof(t37_yellow14,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> v3_tops_2(k8_waybel18(B,A,k4_tmap_1(A,B)),B,k7_waybel18(B,A,k4_tmap_1(A,B))) ) ) ).
fof(t38_yellow14,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v2_pre_topc(k4_waybel18(A,B,C))
& v2_t_0topsp(k4_waybel18(A,B,C))
& l1_pre_topc(k4_waybel18(A,B,C)) ) )
=> v2_t_0topsp(k3_waybel18(A,B)) ) ) ) ).
fof(t39_yellow14,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v1_urysohn1(k4_waybel18(A,B,C))
& v2_pre_topc(k4_waybel18(A,B,C)) ) )
=> v1_urysohn1(k3_waybel18(A,B)) ) ) ) ).
fof(dt_k1_yellow14,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
& m1_subset_1(D,A) )
=> m1_subset_1(k1_yellow14(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k1_yellow14,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
& m1_subset_1(D,A) )
=> k1_yellow14(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k2_yellow14,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
& m1_subset_1(D,A) )
=> m1_subset_1(k2_yellow14(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k2_yellow14,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
& m1_subset_1(D,A) )
=> k2_yellow14(A,B,C,D) = k1_funct_1(C,D) ) ).
%------------------------------------------------------------------------------