SET007 Axioms: SET007+500.ax
%------------------------------------------------------------------------------
% File : SET007+500 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Topological Properties of Meet-Continuous Lattices
% 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_9 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 104 ( 1 unt; 0 def)
% Number of atoms : 950 ( 51 equ)
% Maximal formula atoms : 35 ( 9 avg)
% Number of connectives : 987 ( 141 ~; 0 |; 586 &)
% ( 10 <=>; 250 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 81 ( 80 usr; 0 prp; 1-3 aty)
% Number of functors : 52 ( 52 usr; 0 con; 1-5 aty)
% Number of variables : 294 ( 286 !; 8 ?)
% 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_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k7_grcat_1(A))
& v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(fc2_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
& v6_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C),A)
& v7_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C)) ) ) ).
fof(fc3_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
& v3_orders_2(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
& v6_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C),A)
& v7_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C)) ) ) ).
fof(fc4_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k3_waybel_2(A,B,C))
& v2_orders_2(k3_waybel_2(A,B,C))
& v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) ).
fof(fc5_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& v4_orders_2(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k3_waybel_2(A,B,C))
& v4_orders_2(k3_waybel_2(A,B,C))
& v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) ).
fof(fc6_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& v3_orders_2(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k3_waybel_2(A,B,C))
& v3_orders_2(k3_waybel_2(A,B,C))
& v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) ).
fof(fc7_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m1_relset_1(C,B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_waybel_2(A,B,C))
& v3_orders_2(k2_waybel_2(A,B,C))
& v7_waybel_0(k2_waybel_2(A,B,C)) ) ) ).
fof(fc8_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k3_waybel_9(A))
& v6_waybel_0(k3_waybel_9(A),A) ) ) ).
fof(fc9_waybel_9,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ( v2_orders_2(k3_waybel_9(A))
& v6_waybel_0(k3_waybel_9(A),A) ) ) ).
fof(fc10_waybel_9,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v4_orders_2(k3_waybel_9(A))
& v6_waybel_0(k3_waybel_9(A),A) ) ) ).
fof(fc11_waybel_9,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ( v3_orders_2(k3_waybel_9(A))
& v6_waybel_0(k3_waybel_9(A),A) ) ) ).
fof(fc12_waybel_9,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k3_waybel_9(A))
& v6_waybel_0(k3_waybel_9(A),A)
& v7_waybel_0(k3_waybel_9(A)) ) ) ).
fof(fc13_waybel_9,axiom,
! [A] :
( ( v7_waybel_0(A)
& l1_orders_2(A) )
=> ( v6_waybel_0(k3_waybel_9(A),A)
& v7_waybel_0(k3_waybel_9(A)) ) ) ).
fof(fc14_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k3_waybel_9(A))
& v6_waybel_0(k3_waybel_9(A),A)
& v8_waybel_0(k3_waybel_9(A),A)
& v10_waybel_0(k3_waybel_9(A),A) ) ) ).
fof(fc15_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k4_waybel_9(A))
& v6_waybel_0(k4_waybel_9(A),A) ) ) ).
fof(fc16_waybel_9,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ( v2_orders_2(k4_waybel_9(A))
& v6_waybel_0(k4_waybel_9(A),A) ) ) ).
fof(fc17_waybel_9,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v4_orders_2(k4_waybel_9(A))
& v6_waybel_0(k4_waybel_9(A),A) ) ) ).
fof(fc18_waybel_9,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ( v3_orders_2(k4_waybel_9(A))
& v6_waybel_0(k4_waybel_9(A),A) ) ) ).
fof(fc19_waybel_9,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k4_waybel_9(A))
& v6_waybel_0(k4_waybel_9(A),A)
& v7_waybel_0(k4_waybel_9(A)) ) ) ).
fof(fc20_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k4_waybel_9(A))
& v6_waybel_0(k4_waybel_9(A),A)
& v9_waybel_0(k4_waybel_9(A),A)
& v11_waybel_0(k4_waybel_9(A),A) ) ) ).
fof(fc21_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k5_waybel_9(A,B,C))
& v2_orders_2(k5_waybel_9(A,B,C))
& v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) ).
fof(fc22_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k5_waybel_9(A,B,C))
& v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) ).
fof(fc23_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k5_waybel_9(A,B,C))
& v2_orders_2(k5_waybel_9(A,B,C))
& v4_orders_2(k5_waybel_9(A,B,C))
& v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) ).
fof(fc24_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k5_waybel_9(A,B,C))
& v4_orders_2(k5_waybel_9(A,B,C))
& v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) ).
fof(fc25_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k5_waybel_9(A,B,C))
& v2_orders_2(k5_waybel_9(A,B,C))
& v3_orders_2(k5_waybel_9(A,B,C))
& v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) ).
fof(fc26_waybel_9,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k5_waybel_9(A,B,C))
& v3_orders_2(k5_waybel_9(A,B,C))
& v6_waybel_0(k5_waybel_9(A,B,C),A)
& v7_waybel_0(k5_waybel_9(A,B,C)) ) ) ).
fof(rc1_waybel_9,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) )
=> ? [C] :
( m2_yellow_6(C,A,B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v6_waybel_0(C,A)
& v7_waybel_0(C) ) ) ).
fof(fc27_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ~ v3_struct_0(D)
& l1_waybel_0(D,A) )
=> ( ~ v3_struct_0(k7_waybel_9(A,B,C,D))
& v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(fc28_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v2_orders_2(D)
& l1_waybel_0(D,A) )
=> ( v2_orders_2(k7_waybel_9(A,B,C,D))
& v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(fc29_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v4_orders_2(D)
& l1_waybel_0(D,A) )
=> ( v4_orders_2(k7_waybel_9(A,B,C,D))
& v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(fc30_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v3_orders_2(D)
& l1_waybel_0(D,A) )
=> ( v3_orders_2(k7_waybel_9(A,B,C,D))
& v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(fc31_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( v6_waybel_0(k7_waybel_9(A,B,C,D),B)
& v7_waybel_0(k7_waybel_9(A,B,C,D)) ) ) ).
fof(rc2_waybel_9,axiom,
? [A] :
( l1_waybel_9(A)
& v1_waybel_9(A) ) ).
fof(fc32_waybel_9,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(B,A,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ~ v3_struct_0(g1_waybel_9(A,B,C))
& v1_waybel_9(g1_waybel_9(A,B,C)) ) ) ).
fof(fc33_waybel_9,axiom,
! [A,B,C] :
( ( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k1_tarski(A)))) )
=> ( ~ v3_struct_0(g1_waybel_9(k1_tarski(A),B,C))
& v3_realset2(g1_waybel_9(k1_tarski(A),B,C))
& v1_waybel_9(g1_waybel_9(k1_tarski(A),B,C)) ) ) ).
fof(fc34_waybel_9,axiom,
! [A,B,C] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( v2_orders_2(g1_waybel_9(A,B,C))
& v3_orders_2(g1_waybel_9(A,B,C))
& v4_orders_2(g1_waybel_9(A,B,C))
& v1_waybel_9(g1_waybel_9(A,B,C)) ) ) ).
fof(rc3_waybel_9,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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A)
& v2_waybel_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v1_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v6_group_1(A)
& v3_realset2(A)
& v1_waybel_9(A) ) ).
fof(rc4_waybel_9,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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A)
& v2_waybel_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v2_compts_1(A)
& v3_compts_1(A)
& v4_compts_1(A)
& v5_compts_1(A)
& v1_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v6_waybel_3(A)
& v6_group_1(A)
& v3_realset2(A)
& v1_waybel_9(A) ) ).
fof(cc1_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_struct_0(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_compts_1(B) ) ) ) ) ).
fof(d1_waybel_9,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)) )
=> ( v5_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_orders_2(A,D,E)
=> r1_orders_2(B,k3_yellow_6(u1_struct_0(A),B,C,E),k3_yellow_6(u1_struct_0(A),B,C,D)) ) ) ) ) ) ) ) ).
fof(t1_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ! [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(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& E = F
& v5_orders_3(E,A,B) )
=> v5_orders_3(F,C,D) ) ) ) ) ) ) ) ).
fof(t2_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ! [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(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& E = F
& v5_waybel_0(E,A,B) )
=> v5_waybel_0(F,C,D) ) ) ) ) ) ) ) ).
fof(t3_waybel_9,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& C = D
& r1_pre_topc(A,C) )
=> r1_pre_topc(B,D) ) ) ) ) ) ).
fof(t4_waybel_9,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_0(A,B) = k2_yellow_4(A,k1_struct_0(A,B),k2_pre_topc(A)) ) ) ).
fof(t5_waybel_9,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_waybel_0(A,B) = k4_yellow_4(A,k1_struct_0(A,B),k2_pre_topc(A)) ) ) ).
fof(t6_waybel_9,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_pre_topc(A,A,k4_waybel_1(A,B),k7_waybel_0(A,B)) = k1_struct_0(A,B) ) ) ).
fof(t7_waybel_9,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_pre_topc(A,A,k4_waybel_1(A,B),k1_struct_0(A,B)) = k7_waybel_0(A,B) ) ) ).
fof(t8_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> r1_waybel_0(A,B,k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B))) ) ) ).
fof(t9_waybel_9,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] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( v10_waybel_0(C,A)
=> k11_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) )
=> v1_waybel_2(A) ) ) ).
fof(t10_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k3_waybel_2(A,B,C))
& v3_orders_2(k3_waybel_2(A,B,C))
& v7_waybel_0(k3_waybel_2(A,B,C))
& l1_waybel_0(k3_waybel_2(A,B,C),A) ) ) ) ) ).
fof(d2_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> k2_waybel_9(A,B) = k6_yellow_2(A,u1_waybel_0(A,B)) ) ) ).
fof(d3_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ( r1_waybel_9(A,B)
<=> r1_yellow_0(A,k1_yellow_2(B,A,u1_waybel_0(A,B))) ) ) ) ).
fof(d4_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ( r2_waybel_9(A,B)
<=> r2_yellow_0(A,k1_yellow_2(B,A,u1_waybel_0(A,B))) ) ) ) ).
fof(d5_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v6_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> ( B = k3_waybel_9(A)
<=> ( g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A))
& u1_waybel_0(A,B) = k7_grcat_1(A) ) ) ) ) ).
fof(d6_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v6_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> ( B = k4_waybel_9(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& u1_orders_2(B) = k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))
& u1_waybel_0(A,B) = k7_grcat_1(A) ) ) ) ) ).
fof(t11_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> g1_orders_2(u1_struct_0(k7_lattice3(A)),u1_orders_2(k7_lattice3(A))) = g1_orders_2(u1_struct_0(k4_waybel_9(A)),u1_orders_2(k4_waybel_9(A))) ) ).
fof(d7_waybel_9,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))
=> ! [D] :
( ( v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k5_waybel_9(A,B,C)
<=> ( ! [E] :
( r2_hidden(E,u1_struct_0(D))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& F = E
& r1_orders_2(B,C,F) ) )
& u1_orders_2(D) = k1_toler_1(u1_orders_2(B),u1_struct_0(D))
& u1_waybel_0(A,D) = k2_partfun1(u1_struct_0(B),u1_struct_0(A),u1_waybel_0(A,B),u1_struct_0(D)) ) ) ) ) ) ) ).
fof(t13_waybel_9,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))
=> r1_tarski(u1_struct_0(k5_waybel_9(A,B,C)),u1_struct_0(B)) ) ) ) ).
fof(t14_waybel_9,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))
=> ( v2_yellow_6(k5_waybel_9(A,B,C),A,B)
& m1_yellow_6(k5_waybel_9(A,B,C),A,B) ) ) ) ) ).
fof(t15_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_waybel_9(A,B,C)))
=> ( D = E
=> k3_waybel_0(A,B,D) = k3_waybel_0(A,k5_waybel_9(A,B,C),E) ) ) ) ) ) ) ).
fof(t16_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_waybel_9(A,B,C)))
=> ( D = E
=> k3_waybel_0(A,B,D) = k3_waybel_0(A,k5_waybel_9(A,B,C),E) ) ) ) ) ) ) ).
fof(t17_waybel_9,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))
=> m2_yellow_6(k5_waybel_9(A,B,C),A,B) ) ) ) ).
fof(d8_waybel_9,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)) )
=> ! [D] :
( l1_waybel_0(D,A)
=> ! [E] :
( ( v6_waybel_0(E,B)
& l1_waybel_0(E,B) )
=> ( E = k7_waybel_9(A,B,C,D)
<=> ( g1_orders_2(u1_struct_0(E),u1_orders_2(E)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(B,E) = k7_funct_2(u1_struct_0(D),u1_struct_0(A),u1_struct_0(B),u1_waybel_0(A,D),C) ) ) ) ) ) ) ) ).
fof(t18_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k7_waybel_9(A,A,k4_waybel_1(A,C),B) = k3_waybel_2(A,C,B) ) ) ) ).
fof(t19_waybel_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [D] :
( m1_subset_1(D,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
& v1_tops_2(C,A) )
=> v1_tops_2(D,B) ) ) ) ) ) ).
fof(t20_waybel_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [D] :
( m1_subset_1(D,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
& v2_tops_2(C,A) )
=> v2_tops_2(D,B) ) ) ) ) ) ).
fof(t21_waybel_9,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,u1_struct_0(k10_yellow_6(A,B)))
=> m1_connsp_2(C,A,B) ) ) ) ).
fof(t22_waybel_9,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,u1_struct_0(k10_yellow_6(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k10_yellow_6(A,B)))
=> m1_subset_1(k3_xboole_0(C,D),u1_struct_0(k10_yellow_6(A,B))) ) ) ) ) ).
fof(t23_waybel_9,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,u1_struct_0(k10_yellow_6(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k10_yellow_6(A,B)))
=> m1_subset_1(k2_xboole_0(C,D),u1_struct_0(k10_yellow_6(A,B))) ) ) ) ) ).
fof(t24_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r2_hidden(B,k11_yellow_6(A,C))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C))
=> r2_hidden(B,k6_pre_topc(A,D)) ) ) ) ) ) ) ).
fof(t25_waybel_9,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_compts_1(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v3_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_pre_topc(C,A,A)
=> r2_hidden(k3_yellow_6(u1_struct_0(A),A,C,k12_yellow_6(A,B)),k11_yellow_6(A,k7_waybel_9(A,A,C,B))) ) ) ) ) ).
fof(t26_waybel_9,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_compts_1(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v3_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v5_pre_topc(k4_waybel_1(A,C),A,A)
=> r2_hidden(k12_lattice3(A,C,k12_yellow_6(A,B)),k11_yellow_6(A,k1_waybel_9(A,C,B))) ) ) ) ) ).
fof(t27_waybel_9,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_compts_1(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,C),A,A) )
=> v4_pre_topc(k7_waybel_0(A,B),A) ) ) ) ).
fof(t28_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,C),A,A) )
=> v4_pre_topc(k6_waybel_0(A,B),A) ) ) ) ).
fof(d9_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_waybel_9(A,B,C)
<=> ! [D] :
( m1_connsp_2(D,A,C)
=> r2_waybel_0(A,B,D) ) ) ) ) ) ).
fof(t29_waybel_9,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))
=> r3_waybel_9(A,B,C) ) ) ) ) ).
fof(t30_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_compts_1(A)
& v3_compts_1(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) ) ) ) ).
fof(t31_waybel_9,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] :
( m2_yellow_6(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_waybel_9(A,C,D)
=> r3_waybel_9(A,B,D) ) ) ) ) ) ).
fof(t32_waybel_9,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] :
( m2_yellow_6(D,A,B)
=> ~ r2_hidden(C,k11_yellow_6(A,D)) ) ) ) ) ) ).
fof(t33_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_compts_1(A)
& v3_compts_1(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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_waybel_9(A,B,C)
& r3_waybel_9(A,B,D) )
=> C = D ) ) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_waybel_9(A,B,C)
=> r2_hidden(C,k11_yellow_6(A,B)) ) ) ) ) ) ).
fof(t34_waybel_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r3_waybel_9(A,C,B)
& v4_pre_topc(D,A)
& r1_tarski(k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)),D) )
=> r2_hidden(B,D) ) ) ) ) ) ).
fof(t35_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,D),A,A) )
& v10_waybel_0(C,A)
& r3_waybel_9(A,C,B) )
=> B = k1_waybel_2(A,C) ) ) ) ) ).
fof(t36_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,D),A,A) )
& v11_waybel_0(C,A)
& r3_waybel_9(A,C,B) )
=> B = k2_waybel_9(A,C) ) ) ) ) ).
fof(t37_waybel_9,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_compts_1(A)
& l1_waybel_9(A) )
=> ( ( ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( v10_waybel_0(B,A)
=> ( r1_waybel_9(A,B)
& r2_hidden(k1_waybel_2(A,B),k11_yellow_6(A,B)) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,B),A,A) ) )
=> v2_waybel_2(A) ) ) ).
fof(t38_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,B),A,A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( v10_waybel_0(B,A)
=> ( r1_waybel_9(A,B)
& r2_hidden(k1_waybel_2(A,B),k11_yellow_6(A,B)) ) ) ) ) ) ).
fof(t39_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,B),A,A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( v11_waybel_0(B,A)
=> ( r2_waybel_9(A,B)
& r2_hidden(k2_waybel_9(A,B),k11_yellow_6(A,B)) ) ) ) ) ) ).
fof(t40_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,B),A,A) )
=> v3_yellow_0(A) ) ) ).
fof(t41_waybel_9,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& l1_waybel_9(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,B),A,A) )
=> v2_waybel_2(A) ) ) ).
fof(dt_l1_waybel_9,axiom,
! [A] :
( l1_waybel_9(A)
=> ( l1_pre_topc(A)
& l1_orders_2(A) ) ) ).
fof(existence_l1_waybel_9,axiom,
? [A] : l1_waybel_9(A) ).
fof(abstractness_v1_waybel_9,axiom,
! [A] :
( l1_waybel_9(A)
=> ( v1_waybel_9(A)
=> A = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) ).
fof(dt_k1_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k1_waybel_9(A,B,C))
& v3_orders_2(k1_waybel_9(A,B,C))
& v6_waybel_0(k1_waybel_9(A,B,C),A)
& v7_waybel_0(k1_waybel_9(A,B,C))
& l1_waybel_0(k1_waybel_9(A,B,C),A) ) ) ).
fof(redefinition_k1_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> k1_waybel_9(A,B,C) = k3_waybel_2(A,B,C) ) ).
fof(dt_k2_waybel_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& l1_waybel_0(B,A) )
=> m1_subset_1(k2_waybel_9(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ( v6_waybel_0(k3_waybel_9(A),A)
& l1_waybel_0(k3_waybel_9(A),A) ) ) ).
fof(dt_k4_waybel_9,axiom,
! [A] :
( l1_orders_2(A)
=> ( v6_waybel_0(k4_waybel_9(A),A)
& l1_waybel_0(k4_waybel_9(A),A) ) ) ).
fof(dt_k5_waybel_9,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( v6_waybel_0(k5_waybel_9(A,B,C),A)
& l1_waybel_0(k5_waybel_9(A,B,C),A) ) ) ).
fof(dt_k6_waybel_9,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( v6_waybel_0(k6_waybel_9(A,B,C),A)
& m2_yellow_6(k6_waybel_9(A,B,C),A,B) ) ) ).
fof(redefinition_k6_waybel_9,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(C,u1_struct_0(B)) )
=> k6_waybel_9(A,B,C) = k5_waybel_9(A,B,C) ) ).
fof(dt_k7_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& l1_waybel_0(D,A) )
=> ( v6_waybel_0(k7_waybel_9(A,B,C,D),B)
& l1_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(dt_g1_waybel_9,axiom,
! [A,B,C] :
( ( m1_relset_1(B,A,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( v1_waybel_9(g1_waybel_9(A,B,C))
& l1_waybel_9(g1_waybel_9(A,B,C)) ) ) ).
fof(free_g1_waybel_9,axiom,
! [A,B,C] :
( ( m1_relset_1(B,A,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [D,E,F] :
( g1_waybel_9(A,B,C) = g1_waybel_9(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(t12_waybel_9,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))
=> u1_struct_0(k5_waybel_9(A,B,C)) = a_3_0_waybel_9(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_waybel_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v3_struct_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_waybel_9(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = E
& r1_orders_2(C,D,E) ) ) ) ).
%------------------------------------------------------------------------------