SET007 Axioms: SET007+488.ax
%------------------------------------------------------------------------------
% File : SET007+488 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 95 ( 0 unt; 0 def)
% Number of atoms : 1042 ( 64 equ)
% Maximal formula atoms : 23 ( 10 avg)
% Number of connectives : 1096 ( 149 ~; 0 |; 673 &)
% ( 21 <=>; 253 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 52 ( 51 usr; 0 prp; 1-4 aty)
% Number of functors : 58 ( 58 usr; 2 con; 0-4 aty)
% Number of variables : 265 ( 252 !; 13 ?)
% 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_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ~ v1_xboole_0(k9_relat_1(C,D)) ) ).
fof(cc1_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v16_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(fc2_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A)
& v2_waybel_0(k2_pre_topc(A),A)
& v12_waybel_0(k2_pre_topc(A),A)
& v13_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc3_waybel_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(cc2_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v10_waybel_1(A) ) ) ) ).
fof(rc1_waybel_2,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v3_realset2(A) ) ).
fof(fc4_waybel_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(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))
& v7_waybel_0(k2_waybel_2(A,B,C))
& v8_waybel_0(k2_waybel_2(A,B,C),A)
& v10_waybel_0(k2_waybel_2(A,B,C),A) ) ) ).
fof(fc5_waybel_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k3_waybel_2(A,B,C))
& v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) ).
fof(fc6_waybel_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( ~ v3_struct_0(k3_waybel_2(A,B,C))
& v6_waybel_0(k3_waybel_2(A,B,C),A)
& v7_waybel_0(k3_waybel_2(A,B,C)) ) ) ).
fof(fc7_waybel_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k4_waybel_2(A))
& v1_relat_1(k4_waybel_2(A))
& v1_funct_1(k4_waybel_2(A))
& v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v5_orders_3(k4_waybel_2(A),k3_yellow_3(A,A),A)
& v1_partfun1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) ).
fof(fc8_waybel_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k5_waybel_2(A))
& v1_relat_1(k5_waybel_2(A))
& v1_funct_1(k5_waybel_2(A))
& v1_funct_2(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v5_orders_3(k5_waybel_2(A),k3_yellow_3(A,A),A)
& v1_partfun1(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) ).
fof(cc3_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A) ) ) ) ).
fof(cc4_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_waybel_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A) ) ) ) ).
fof(cc5_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v1_waybel_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& ~ v1_yellow_3(A)
& v2_waybel_2(A) ) ) ) ).
fof(rc2_waybel_2,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v3_realset2(A)
& v1_waybel_2(A)
& v2_waybel_2(A) ) ).
fof(fc9_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k3_yellow_2(A))
& v1_relat_1(k3_yellow_2(A))
& v1_funct_1(k3_yellow_2(A))
& v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
& v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v20_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v1_partfun1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) ) ) ).
fof(fc10_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_2(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k3_yellow_2(A))
& v1_relat_1(k3_yellow_2(A))
& v1_funct_1(k3_yellow_2(A))
& v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
& v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v20_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v1_partfun1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) ) ) ).
fof(fc11_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_waybel_2(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k4_waybel_2(A))
& v1_relat_1(k4_waybel_2(A))
& v1_funct_1(k4_waybel_2(A))
& v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v5_orders_3(k4_waybel_2(A),k3_yellow_3(A,A),A)
& v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
& v1_partfun1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) ).
fof(fc12_waybel_2,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_waybel_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k4_waybel_1(A,B))
& v1_relat_1(k4_waybel_1(A,B))
& v1_funct_1(k4_waybel_1(A,B))
& v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k4_waybel_1(A,B),A,A)
& v22_waybel_0(k4_waybel_1(A,B),A,A)
& v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(cc6_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v1_waybel_2(A)
& v2_waybel_2(A) ) ) ) ).
fof(cc7_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v2_waybel_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A) ) ) ) ).
fof(t1_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) ).
fof(t2_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) ).
fof(t3_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_lattice3(A,B,k1_yellow_0(A,k2_yellow_4(A,B,C))) ) ) ) ).
fof(t4_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_yellow_0(A,k2_yellow_4(A,B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) ).
fof(t11_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( v24_waybel_0(k3_yellow_3(A,B))
=> ( v24_waybel_0(A)
& v24_waybel_0(B) ) ) ) ) ).
fof(t12_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> k1_yellow_0(k3_yellow_3(A,A),B) = k7_yellow_3(A,A,k1_yellow_0(A,k4_yellow_3(A,A,B)),k1_yellow_0(A,k5_yellow_3(A,A,B))) ) ) ).
fof(t13_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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)) )
=> ( v5_orders_3(D,A,B)
=> r1_tarski(k4_pre_topc(A,B,D,k4_waybel_0(A,C)),k4_waybel_0(B,k4_pre_topc(A,B,D,C))) ) ) ) ) ) ).
fof(t14_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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)) )
=> ( v5_orders_3(D,A,B)
=> r1_tarski(k4_pre_topc(A,B,D,k5_waybel_0(A,C)),k5_waybel_0(B,k4_pre_topc(A,B,D,C))) ) ) ) ) ) ).
fof(t15_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) = k12_lattice3(A,B,k1_yellow_0(A,C)) ) ) ) ).
fof(t16_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,B),C)) = k13_lattice3(A,B,k2_yellow_0(A,C)) ) ) ) ).
fof(t17_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_waybel_0(A,A,k4_waybel_1(A,B),C) ) ) ) ).
fof(t18_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( v10_waybel_0(B,A)
=> v1_waybel_0(k8_yellow_2(u1_struct_0(B),A,k2_waybel_0(A,B)),A) ) ) ) ).
fof(t19_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_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))
& v7_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
& l1_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C),A) ) ) ) ) ).
fof(t20_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( ( C = k6_partfun1(B)
& D = g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C) )
=> v10_waybel_0(D,A) ) ) ) ) ) ).
fof(d1_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> k1_waybel_2(A,B) = k5_yellow_2(A,u1_waybel_0(A,B)) ) ) ).
fof(d2_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( D = k2_waybel_2(A,B,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k5_finsub_1(B),u1_struct_0(A))
& m2_relset_1(E,k5_finsub_1(B),u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,k5_finsub_1(B))
=> ( k7_yellow_2(k5_finsub_1(B),A,E,F) = k1_yellow_0(A,k2_funct_2(B,u1_struct_0(A),C,F))
& D = g1_waybel_0(A,k5_finsub_1(B),k1_yellow_1(k5_finsub_1(B)),E) ) ) ) ) ) ) ) ).
fof(t21_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m2_relset_1(D,B,u1_struct_0(A)) )
=> ( m1_subset_1(C,u1_struct_0(k2_waybel_2(A,B,D)))
<=> m1_subset_1(C,k5_finsub_1(B)) ) ) ) ).
fof(d3_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( ( v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k3_waybel_2(A,B,C)
<=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& F = k1_funct_1(u1_waybel_0(A,C),E)
& k1_funct_1(u1_waybel_0(A,D),E) = k11_lattice3(A,B,F) ) ) ) ) ) ) ) ) ).
fof(t22_waybel_2,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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
<=> m1_subset_1(D,u1_struct_0(k3_waybel_2(A,C,B))) ) ) ) ) ).
fof(t23_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> k8_yellow_2(u1_struct_0(k3_waybel_2(A,B,C)),A,u1_waybel_0(A,k3_waybel_2(A,B,C))) = k3_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C))) ) ) ) ).
fof(t24_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ( ! [D] : r1_yellow_0(A,k2_funct_2(B,u1_struct_0(A),C,D))
=> r1_tarski(k8_yellow_2(u1_struct_0(k2_waybel_2(A,B,C)),A,k2_waybel_0(A,k2_waybel_2(A,B,C))),k12_waybel_0(A,k8_yellow_2(B,A,C))) ) ) ) ).
fof(t25_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> r1_tarski(k8_yellow_2(B,A,C),k8_yellow_2(u1_struct_0(k2_waybel_2(A,B,C)),A,k2_waybel_0(A,k2_waybel_2(A,B,C)))) ) ) ).
fof(t26_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_struct_0(A))
& m2_relset_1(C,B,u1_struct_0(A)) )
=> ( ( r1_yellow_0(A,k8_yellow_2(B,A,C))
& r1_yellow_0(A,k8_yellow_2(u1_struct_0(k2_waybel_2(A,B,C)),A,k2_waybel_0(A,k2_waybel_2(A,B,C))))
& ! [D] :
( m1_subset_1(D,k5_finsub_1(B))
=> r1_yellow_0(A,k2_funct_2(B,u1_struct_0(A),C,D)) ) )
=> k5_yellow_2(A,C) = k1_waybel_2(A,k2_waybel_2(A,B,C)) ) ) ) ).
fof(t27_waybel_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v10_waybel_0(B,A)
=> v10_waybel_0(k3_waybel_2(A,C,B),A) ) ) ) ) ).
fof(t28_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,B,k1_yellow_0(A,C))
=> r3_orders_2(A,B,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C))) ) ) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) ) ).
fof(t29_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ( v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k11_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,C),B)) ) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_yellow_0(A,B)
=> k11_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,C),k12_waybel_0(A,B))) ) ) ) ) ) ).
fof(t30_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),k12_waybel_0(A,B))) ) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) ) ).
fof(d4_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) )
=> ( B = k4_waybel_2(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,B,k7_yellow_3(A,A,C,D)) = k11_lattice3(A,C,D) ) ) ) ) ) ).
fof(t31_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_3(A,A)))
=> k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,k4_waybel_2(A),B) = k11_lattice3(A,k8_yellow_3(A,A,B),k9_yellow_3(A,A,B)) ) ) ).
fof(t32_waybel_2,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)))
=> k4_pre_topc(k3_yellow_3(A,A),A,k4_waybel_2(A),k6_yellow_3(A,A,B,C)) = k3_yellow_4(A,B,C) ) ) ) ).
fof(t33_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> k1_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k4_waybel_2(A),B)) = k1_yellow_0(A,k4_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B))) ) ) ).
fof(d5_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) )
=> ( B = k5_waybel_2(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,B,k7_yellow_3(A,A,C,D)) = k10_lattice3(A,C,D) ) ) ) ) ) ).
fof(t34_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_3(A,A)))
=> k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,k5_waybel_2(A),B) = k10_lattice3(A,k8_yellow_3(A,A,B),k9_yellow_3(A,A,B)) ) ) ).
fof(t35_waybel_2,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)))
=> k4_pre_topc(k3_yellow_3(A,A),A,k5_waybel_2(A),k6_yellow_3(A,A,B,C)) = k1_yellow_4(A,B,C) ) ) ) ).
fof(t36_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> k2_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k5_waybel_2(A),B)) = k2_yellow_0(A,k2_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B))) ) ) ).
fof(d6_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_waybel_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k11_lattice3(A,B,k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) ).
fof(d7_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ( v24_waybel_0(A)
& v1_waybel_2(A) ) ) ) ).
fof(t38_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) ).
fof(t39_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) )
=> v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ).
fof(t40_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) ).
fof(t41_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_waybel_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(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)))) ) ) ) ) ) ).
fof(t42_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(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(t43_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k11_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,B,C)) ) ) ) ) ).
fof(t44_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k11_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,B,C)) ) )
=> v1_waybel_2(A) ) ) ).
fof(t45_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v1_waybel_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,B,k1_yellow_0(A,C))
=> B = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) ).
fof(t46_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,B,k1_yellow_0(A,C))
=> r3_orders_2(A,B,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C))) ) ) )
=> v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A) ) ) ).
fof(t47_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( v10_waybel_0(C,A)
=> k12_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u1_struct_0(A))
& m2_relset_1(D,C,u1_struct_0(A)) )
=> k12_lattice3(A,B,k5_yellow_2(A,D)) = k1_waybel_2(A,k3_waybel_2(A,B,k2_waybel_2(A,C,D))) ) ) ) ) ).
fof(t48_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u1_struct_0(A))
& m2_relset_1(D,C,u1_struct_0(A)) )
=> k12_lattice3(A,B,k5_yellow_2(A,D)) = k1_waybel_2(A,k3_waybel_2(A,B,k2_waybel_2(A,C,D))) ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( v10_waybel_0(C,A)
=> k12_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) ) ) ) ).
fof(t49_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ( v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v20_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ) ).
fof(t50_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) ).
fof(t51_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) ).
fof(t52_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,B,k1_yellow_0(A,C))
=> B = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) ) ).
fof(t53_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A) ) ) ).
fof(t54_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( v10_waybel_0(C,A)
=> k12_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) ) ) ) ).
fof(t55_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u1_struct_0(A))
& m2_relset_1(D,C,u1_struct_0(A)) )
=> k12_lattice3(A,B,k5_yellow_2(A,D)) = k1_waybel_2(A,k3_waybel_2(A,B,k2_waybel_2(A,C,D))) ) ) ) ) ).
fof(t56_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
<=> ( v2_waybel_2(A)
& v2_waybel_1(A) ) ) ) ).
fof(s1_waybel_2,axiom,
? [A] :
( ~ v3_struct_0(A)
& v7_waybel_0(A)
& l1_waybel_0(A,f1_s1_waybel_2)
& g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(f2_s1_waybel_2),u1_orders_2(f2_s1_waybel_2))
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),f1_s1_waybel_2,u1_waybel_0(f1_s1_waybel_2,A),B) = f3_s1_waybel_2(k1_funct_1(u1_waybel_0(f1_s1_waybel_2,f2_s1_waybel_2),B)) ) ) ).
fof(dt_k1_waybel_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& l1_waybel_0(B,A) )
=> m1_subset_1(k1_waybel_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_waybel_2,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))
& v7_waybel_0(k2_waybel_2(A,B,C))
& l1_waybel_0(k2_waybel_2(A,B,C),A) ) ) ).
fof(dt_k3_waybel_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ( v6_waybel_0(k3_waybel_2(A,B,C),A)
& l1_waybel_0(k3_waybel_2(A,B,C),A) ) ) ).
fof(dt_k4_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k4_waybel_2(A))
& v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& m2_relset_1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) ).
fof(dt_k5_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k5_waybel_2(A))
& v1_funct_2(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& m2_relset_1(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) ).
fof(t5_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> a_2_0_waybel_2(A,B) = a_2_1_waybel_2(A,B) ) ) ).
fof(t6_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> k3_tarski(a_2_2_waybel_2(A,B)) = k4_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) ).
fof(t7_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> r1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B))) ) ) ).
fof(t8_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> r1_yellow_0(A,a_2_1_waybel_2(A,B)) ) ) ).
fof(t9_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> r3_orders_2(A,k1_yellow_0(A,a_2_1_waybel_2(A,B)),k1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B)))) ) ) ).
fof(t10_waybel_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k3_yellow_3(A,A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> k1_yellow_0(A,a_2_1_waybel_2(A,B)) = k1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B))) ) ) ).
fof(t37_waybel_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k11_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_0_waybel_2(A,B,C)) ) )
=> v1_waybel_2(A) ) ) ).
fof(fraenkel_a_2_0_waybel_2,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_yellow_3(B,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
=> ( r2_hidden(A,a_2_0_waybel_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k1_yellow_0(B,k4_yellow_4(B,k1_struct_0(B,D),k5_yellow_3(B,B,C)))
& r2_hidden(D,k4_yellow_3(B,B,C)) ) ) ) ).
fof(fraenkel_a_2_1_waybel_2,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_yellow_3(B,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
=> ( r2_hidden(A,a_2_1_waybel_2(B,C))
<=> ? [D] :
( ~ v1_xboole_0(D)
& v1_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = k1_yellow_0(B,D)
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k4_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
& r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) ).
fof(fraenkel_a_2_2_waybel_2,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_yellow_3(B,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
=> ( r2_hidden(A,a_2_2_waybel_2(B,C))
<=> ? [D] :
( ~ v1_xboole_0(D)
& v1_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k4_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
& r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) ).
fof(fraenkel_a_2_3_waybel_2,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_yellow_3(B,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
=> ( r2_hidden(A,a_2_3_waybel_2(B,C))
<=> ? [D] :
( ~ v1_xboole_0(D)
& v1_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k4_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
& r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) ).
fof(fraenkel_a_3_0_waybel_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_waybel_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k11_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
%------------------------------------------------------------------------------