SET007 Axioms: SET007+573.ax
%------------------------------------------------------------------------------
% File : SET007+573 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bases of 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 : waybel23 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 127 ( 1 unt; 0 def)
% Number of atoms : 1197 ( 39 equ)
% Maximal formula atoms : 20 ( 9 avg)
% Number of connectives : 1198 ( 128 ~; 0 |; 738 &)
% ( 29 <=>; 303 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 65 ( 63 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 1 con; 0-5 aty)
% Number of variables : 311 ( 300 !; 11 ?)
% 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_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_waybel23(B,A)
=> v1_waybel23(B,A) ) ) ) ).
fof(cc2_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel23(B,A)
=> v2_waybel23(B,A) ) ) ) ).
fof(rc1_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel23(B,A)
& v2_waybel23(B,A)
& v3_waybel23(B,A)
& v4_waybel23(B,A) ) ) ).
fof(fc1_waybel23,axiom,
! [A,B] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k5_yellow_0(A,B))
& v1_orders_2(k5_yellow_0(A,B))
& v3_orders_2(k5_yellow_0(A,B))
& v4_orders_2(k5_yellow_0(A,B))
& v2_lattice3(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(fc2_waybel23,axiom,
! [A,B] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k5_yellow_0(A,B))
& v1_orders_2(k5_yellow_0(A,B))
& v3_orders_2(k5_yellow_0(A,B))
& v4_orders_2(k5_yellow_0(A,B))
& v1_lattice3(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(cc3_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel23(B,A)
=> v2_waybel_0(B,A) ) ) ) ).
fof(cc4_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel23(B,A)
=> v1_waybel_0(B,A) ) ) ) ).
fof(fc3_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k6_waybel_0(A,B))
& v1_waybel_0(k6_waybel_0(A,B),A)
& v12_waybel_0(k6_waybel_0(A,B),A)
& v2_waybel23(k6_waybel_0(A,B),A) ) ) ).
fof(fc4_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k7_waybel_0(A,B))
& v1_waybel_0(k7_waybel_0(A,B),A)
& v2_waybel_0(k7_waybel_0(A,B),A)
& v13_waybel_0(k7_waybel_0(A,B),A)
& v2_waybel23(k7_waybel_0(A,B),A) ) ) ).
fof(fc5_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k6_waybel_0(A,B))
& v1_waybel_0(k6_waybel_0(A,B),A)
& v2_waybel_0(k6_waybel_0(A,B),A)
& v12_waybel_0(k6_waybel_0(A,B),A)
& v1_waybel23(k6_waybel_0(A,B),A) ) ) ).
fof(fc6_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k7_waybel_0(A,B))
& v2_waybel_0(k7_waybel_0(A,B),A)
& v13_waybel_0(k7_waybel_0(A,B),A)
& v1_waybel23(k7_waybel_0(A,B),A) ) ) ).
fof(fc7_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_waybel_0(k1_waybel_3(A,B),A)
& v12_waybel_0(k1_waybel_3(A,B),A)
& v2_waybel23(k1_waybel_3(A,B),A) ) ) ).
fof(fc8_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_waybel_0(k2_waybel_3(A,B),A)
& v13_waybel_0(k2_waybel_3(A,B),A)
& v2_waybel23(k2_waybel_3(A,B),A) ) ) ).
fof(fc9_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v2_waybel_0(k1_waybel_3(A,B),A)
& v12_waybel_0(k1_waybel_3(A,B),A)
& v1_waybel23(k1_waybel_3(A,B),A) ) ) ).
fof(cc5_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_waybel23(B,A)
=> ~ v1_xboole_0(B) ) ) ) ).
fof(cc6_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v7_waybel23(B,A)
=> ~ v1_xboole_0(B) ) ) ) ).
fof(rc2_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v6_waybel23(B,A) ) ) ).
fof(rc3_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v7_waybel23(B,A) ) ) ).
fof(rc4_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_waybel23(B,A)
& ~ v1_xboole_0(B)
& v6_waybel23(B,A) ) ) ).
fof(rc5_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_waybel23(B,A)
& ~ v1_xboole_0(B)
& v7_waybel23(B,A) ) ) ).
fof(fc10_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A)
& v6_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k5_yellow_0(A,B))
& v1_orders_2(k5_yellow_0(A,B))
& v4_orders_2(k5_yellow_0(A,B))
& v1_yellow_0(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(cc7_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_waybel23(B,A)
=> ( v1_waybel_0(B,A)
& v2_waybel23(B,A) ) ) ) ).
fof(rc6_waybel23,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& ~ v3_realset2(A) ) ).
fof(cc8_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& ~ v3_realset2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_waybel23(B,A)
=> ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v2_waybel23(B,A) ) ) ) ).
fof(fc11_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v2_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(fc12_waybel23,axiom,
! [A,B] :
( ( v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v3_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(fc13_waybel23,axiom,
! [A,B] :
( ( v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v4_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(fc14_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_relat_1(k3_waybel23(A,B))
& v1_funct_1(k3_waybel23(A,B))
& v1_funct_2(k3_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A))
& v5_orders_3(k3_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),A) ) ) ).
fof(fc15_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_relat_1(k4_waybel23(A,B))
& v1_funct_1(k4_waybel23(A,B))
& v1_funct_2(k4_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& v5_orders_3(k4_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(fc16_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A)
& v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( v1_relat_1(k5_waybel23(A,B))
& v1_funct_1(k5_waybel23(A,B))
& v1_funct_2(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
& v5_orders_3(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ).
fof(fc17_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A)
& v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( v1_relat_1(k3_waybel23(A,k5_yellow_0(A,B)))
& v1_funct_1(k3_waybel23(A,k5_yellow_0(A,B)))
& v1_funct_2(k3_waybel23(A,k5_yellow_0(A,B)),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))),u1_struct_0(A))
& v5_orders_3(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v17_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v18_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v19_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v20_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v21_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v22_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) ).
fof(fc18_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A)
& v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( v1_relat_1(k5_waybel23(A,B))
& v1_funct_1(k5_waybel23(A,B))
& v1_funct_2(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
& v5_orders_3(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v18_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v20_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v22_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ).
fof(t1_waybel23,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,u1_struct_0(A))
=> k2_waybel_8(A,B) = k3_xboole_0(k1_waybel_3(A,B),u1_struct_0(k1_waybel_8(A))) ) ) ).
fof(t2_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k12_waybel_0(A,B),k12_waybel_0(A,C)) ) ) ) ) ).
fof(t3_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v8_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [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
=> r1_tarski(k12_waybel_0(A,C),k12_waybel_0(B,D)) ) ) ) ) ) ).
fof(t4_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v8_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [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
=> k12_waybel_0(A,C) = k12_waybel_0(B,D) ) ) ) ) ) ).
fof(t5_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( r2_hidden(k3_yellow_0(A),u1_struct_0(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
=> r1_tarski(k12_waybel_0(B,D),k12_waybel_0(A,C)) ) ) ) ) ) ) ).
fof(t6_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))
=> k1_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k4_waybel_0(A,k12_waybel_0(A,k1_waybel23(A,B))) ) ) ).
fof(t7_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k4_waybel_0(A,k4_waybel_0(A,B)) = k4_waybel_0(A,B) ) ) ).
fof(t8_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k5_waybel_0(A,k5_waybel_0(A,B)) = k5_waybel_0(A,B) ) ) ).
fof(t9_waybel23,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))
=> k4_waybel_0(A,k6_waybel_0(A,B)) = k6_waybel_0(A,B) ) ) ).
fof(t10_waybel23,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))
=> k5_waybel_0(A,k7_waybel_0(A,B)) = k7_waybel_0(A,B) ) ) ).
fof(t11_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [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
=> r1_tarski(k4_waybel_0(B,D),k4_waybel_0(A,C)) ) ) ) ) ) ).
fof(t12_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [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
=> r1_tarski(k5_waybel_0(B,D),k5_waybel_0(A,C)) ) ) ) ) ) ).
fof(t13_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> r1_tarski(k6_waybel_0(B,D),k6_waybel_0(A,C)) ) ) ) ) ) ).
fof(t14_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> r1_tarski(k7_waybel_0(B,D),k7_waybel_0(A,C)) ) ) ) ) ) ).
fof(d1_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel23(B,A)
<=> v5_yellow_0(k5_yellow_0(A,B),A) ) ) ) ).
fof(d2_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel23(B,A)
<=> v6_yellow_0(k5_yellow_0(A,B),A) ) ) ) ).
fof(d3_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_waybel23(B,A)
<=> v7_yellow_0(k5_yellow_0(A,B),A) ) ) ) ).
fof(d4_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel23(B,A)
<=> v8_yellow_0(k5_yellow_0(A,B),A) ) ) ) ).
fof(t15_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B)
& r2_yellow_0(A,k2_struct_0(A,C,D)) )
=> r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) ).
fof(t16_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B)
& r1_yellow_0(A,k2_struct_0(A,C,D)) )
=> r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) ).
fof(t17_waybel23,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) ).
fof(t18_waybel23,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) ).
fof(t19_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ( r2_yellow_0(A,C)
=> r2_hidden(k2_yellow_0(A,C),B) ) ) ) ) ) ).
fof(t20_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ( r1_yellow_0(A,C)
=> r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) ).
fof(t21_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v3_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ( r2_yellow_0(A,C)
=> ( r2_yellow_0(k5_yellow_0(A,B),C)
& k2_yellow_0(k5_yellow_0(A,B),C) = k2_yellow_0(A,C) ) ) ) ) ) ).
fof(t22_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v4_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ( r1_yellow_0(A,C)
=> ( r1_yellow_0(k5_yellow_0(A,B),C)
& k1_yellow_0(k5_yellow_0(A,B),C) = k1_yellow_0(A,C) ) ) ) ) ) ).
fof(t23_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_struct_0(C,A,B)
=> ! [D] :
( m1_struct_0(D,A,B)
=> ( r2_yellow_0(A,k2_struct_0(A,C,D))
=> ( r2_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D))
& k2_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D)) = k2_yellow_0(A,k2_struct_0(A,C,D)) ) ) ) ) ) ) ).
fof(t24_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_struct_0(C,A,B)
=> ! [D] :
( m1_struct_0(D,A,B)
=> ( r1_yellow_0(A,k2_struct_0(A,C,D))
=> ( r1_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D))
& k1_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D)) = k1_yellow_0(A,k2_struct_0(A,C,D)) ) ) ) ) ) ) ).
fof(t25_waybel23,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_lattice3(k5_yellow_0(A,B)) ) ) ).
fof(t26_waybel23,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_lattice3(k5_yellow_0(A,B)) ) ) ).
fof(t27_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v3_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> k2_yellow_0(k5_yellow_0(A,B),C) = k2_yellow_0(A,C) ) ) ) ).
fof(t28_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v4_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> k1_yellow_0(k5_yellow_0(A,B),C) = k1_yellow_0(A,C) ) ) ) ).
fof(t29_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel_0(B,A) ) ) ).
fof(t30_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel_0(B,A) ) ) ).
fof(t31_waybel23,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)
& v13_waybel_0(B,A)
& 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)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> v1_waybel23(B,A) ) ) ) ).
fof(t32_waybel23,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)
& v12_waybel_0(B,A)
& 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)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> v2_waybel23(B,A) ) ) ) ).
fof(t33_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v2_waybel23(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel23(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ).
fof(t34_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_waybel23(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel23(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ).
fof(t35_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v2_waybel23(k6_waybel_0(A,B),A) ) ) ).
fof(t36_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_waybel23(k6_waybel_0(A,B),A) ) ) ).
fof(t37_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v2_waybel23(k7_waybel_0(A,B),A) ) ) ).
fof(t38_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_waybel23(k7_waybel_0(A,B),A) ) ) ).
fof(t39_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v2_waybel23(k1_waybel_3(A,B),A) ) ) ).
fof(t40_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_waybel23(k1_waybel_3(A,B),A) ) ) ).
fof(t41_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v2_waybel23(k2_waybel_3(A,B),A) ) ) ).
fof(d6_waybel23,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v5_waybel23(A)
<=> r1_tarski(k2_waybel23(A),k5_ordinal2) ) ) ).
fof(d7_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_waybel23(B,A)
<=> ( v2_waybel23(B,A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C = k1_yellow_0(A,k5_subset_1(u1_struct_0(A),k1_waybel_3(A,C),B)) ) ) ) ) ) ).
fof(d8_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_waybel23(B,A)
<=> r2_hidden(k3_yellow_0(A),B) ) ) ) ).
fof(d9_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v7_waybel23(B,A)
<=> r2_hidden(k4_yellow_0(A),B) ) ) ) ).
fof(t42_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_yellow_0(k5_yellow_0(A,B)) ) ) ).
fof(t43_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel23(u1_struct_0(k1_waybel_8(A)),A)
& m1_subset_1(u1_struct_0(k1_waybel_8(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(t44_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ( v6_waybel23(u1_struct_0(k1_waybel_8(A)),A)
& m1_waybel23(u1_struct_0(k1_waybel_8(A)),A) ) ) ).
fof(t45_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( m1_waybel23(u1_struct_0(k1_waybel_8(A)),A)
=> v2_waybel_8(A) ) ) ).
fof(t46_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m1_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( ~ r3_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& ~ r3_orders_2(A,E,C)
& r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) ).
fof(t47_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(k3_yellow_0(A),B)
=> ( m1_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& r3_orders_2(A,C,E)
& r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) ) ).
fof(t48_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(k3_yellow_0(A),B)
=> ( m1_waybel23(B,A)
<=> ( r1_tarski(u1_struct_0(k1_waybel_8(A)),B)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( ~ r3_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& ~ r3_orders_2(A,E,C)
& r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel23(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(k3_yellow_0(A),B)
=> ( m1_waybel23(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( ~ r3_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& ~ r3_orders_2(A,E,C)
& r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ).
fof(t50_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( ( r2_hidden(k3_yellow_0(A),u1_struct_0(B))
& v2_waybel23(u1_struct_0(B),A)
& m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ v1_xboole_0(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)))
& v1_waybel_0(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)),B)
& v12_waybel_0(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)),B)
& m1_subset_1(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ).
fof(d10_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A)) )
=> ( C = k3_waybel23(A,B)
<=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,B)
& v12_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> k1_funct_1(C,D) = k1_yellow_0(A,D) ) ) ) ) ) ).
fof(d11_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
=> ( C = k4_waybel23(A,B)
<=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,B)
& v12_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
& D = E
& k1_funct_1(C,D) = k4_waybel_0(A,E) ) ) ) ) ) ) ).
fof(d12_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))) )
=> ( C = k5_waybel23(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),C,D) = k5_subset_1(u1_struct_0(A),k1_waybel_3(A,D),B) ) ) ) ) ) ).
fof(t51_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( k1_relat_1(k3_waybel23(A,B)) = k8_waybel_0(B)
& m1_subset_1(k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),A,k3_waybel23(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t52_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( r2_hidden(C,k1_relat_1(k3_waybel23(A,B)))
<=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,B)
& v12_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ).
fof(t53_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( k1_relat_1(k4_waybel23(A,B)) = k8_waybel_0(B)
& m1_subset_1(k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),k2_yellow_1(k8_waybel_0(A)),k4_waybel23(A,B)),k1_zfmisc_1(k8_waybel_0(A))) ) ) ) ).
fof(t54_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( r2_hidden(C,k1_relat_1(k4_waybel23(A,B)))
<=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,B)
& v12_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ).
fof(t55_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( r2_hidden(C,k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),k2_yellow_1(k8_waybel_0(A)),k4_waybel23(A,B)))
=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t56_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( k1_relat_1(k5_waybel23(A,B)) = u1_struct_0(A)
& m1_subset_1(k8_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),k5_waybel23(A,B)),k1_zfmisc_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ) ).
fof(t57_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ! [C] :
( r2_hidden(C,k8_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),k5_waybel23(A,B)))
=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,k5_yellow_0(A,B))
& v12_waybel_0(C,k5_yellow_0(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_0(A,B)))) ) ) ) ) ).
fof(t58_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> v5_orders_3(k3_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),A) ) ) ).
fof(t59_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> v5_orders_3(k4_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(t60_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> v5_orders_3(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ).
fof(t61_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> v18_waybel_0(k4_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(t62_waybel23,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> k3_waybel23(A,B) = k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),k4_waybel23(A,B),k3_yellow_2(A)) ) ) ).
fof(t63_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> v3_waybel_1(k1_waybel_1(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A,k3_waybel23(A,k5_yellow_0(A,B)),k5_waybel23(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) ).
fof(t64_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( v4_waybel_1(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v5_waybel_1(k5_waybel23(A,B),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) ) ).
fof(t65_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))),A,k3_waybel23(A,k5_yellow_0(A,B))) = u1_struct_0(A) ) ) ).
fof(t66_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( v17_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
& v18_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) ) ).
fof(t67_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> v18_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ).
fof(t68_waybel23,axiom,
$true ).
fof(t70_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> r5_waybel_1(k1_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))),k5_yellow_0(A,B)) ) ) ).
fof(t71_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( ! [C] :
( ( v6_waybel23(C,A)
& m1_waybel23(C,A) )
=> r1_tarski(B,C) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
=> C = k5_subset_1(u1_struct_0(A),k1_waybel_3(A,k1_yellow_0(A,C)),B) ) ) ) ) ).
fof(t72_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v2_waybel_8(A)
<=> ( v6_waybel23(u1_struct_0(k1_waybel_8(A)),A)
& m1_waybel23(u1_struct_0(k1_waybel_8(A)),A)
& ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> r1_tarski(u1_struct_0(k1_waybel_8(A)),B) ) ) ) ) ).
fof(t73_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v2_waybel_8(A)
<=> ? [B] :
( v6_waybel23(B,A)
& m1_waybel23(B,A)
& ! [C] :
( ( v6_waybel23(C,A)
& m1_waybel23(C,A) )
=> r1_tarski(B,C) ) ) ) ) ).
fof(dt_m1_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_waybel23(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ? [B] : m1_waybel23(B,A) ) ).
fof(dt_k1_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
=> m1_subset_1(k1_waybel23(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(redefinition_k1_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
=> k1_waybel23(A,B) = k3_tarski(B) ) ).
fof(dt_k2_waybel23,axiom,
! [A] :
( l1_pre_topc(A)
=> v1_card_1(k2_waybel23(A)) ) ).
fof(dt_k3_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_funct_1(k3_waybel23(A,B))
& v1_funct_2(k3_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A))
& m2_relset_1(k3_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A)) ) ) ).
fof(dt_k4_waybel23,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_funct_1(k4_waybel23(A,B))
& v1_funct_2(k4_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(k4_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) ).
fof(dt_k5_waybel23,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A)
& v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( v1_funct_1(k5_waybel23(A,B))
& v1_funct_2(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
& m2_relset_1(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))) ) ) ).
fof(d5_waybel23,axiom,
! [A] :
( l1_pre_topc(A)
=> k2_waybel23(A) = k1_setfam_1(a_1_0_waybel23(A)) ) ).
fof(t69_waybel23,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> u1_struct_0(k1_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))) = a_2_0_waybel23(A,B) ) ) ).
fof(fraenkel_a_1_0_waybel23,axiom,
! [A,B] :
( l1_pre_topc(B)
=> ( r2_hidden(A,a_1_0_waybel23(B))
<=> ? [C] :
( m1_cantor_1(C,B)
& A = k1_card_1(C) ) ) ) ).
fof(fraenkel_a_2_0_waybel23,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v1_yellow_0(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v6_waybel23(C,B)
& m1_waybel23(C,B) )
=> ( r2_hidden(A,a_2_0_waybel23(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k5_yellow_0(B,C)))
& A = k6_waybel_0(k5_yellow_0(B,C),D) ) ) ) ).
%------------------------------------------------------------------------------