SET007 Axioms: SET007+490.ax
%------------------------------------------------------------------------------
% File : SET007+490 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Auxiliary and Approximating Relations
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 142 ( 4 unt; 0 def)
% Number of atoms : 1417 ( 59 equ)
% Maximal formula atoms : 36 ( 9 avg)
% Number of connectives : 1366 ( 91 ~; 0 |; 919 &)
% ( 41 <=>; 315 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-4 aty)
% Number of functors : 49 ( 49 usr; 1 con; 0-5 aty)
% Number of variables : 352 ( 334 !; 18 ?)
% 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_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v5_waybel_4(B,A)
=> ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A) ) ) ) ) ).
fof(cc2_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A) )
=> v5_waybel_4(B,A) ) ) ) ).
fof(rc1_waybel_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& v5_waybel_4(B,A) ) ) ).
fof(cc3_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A) )
=> v8_relat_2(B) ) ) ) ).
fof(fc1_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_relat_1(k2_waybel_4(A))
& v1_waybel_4(k2_waybel_4(A),A) ) ) ).
fof(fc2_waybel_4,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k2_waybel_4(A))
& v1_waybel_4(k2_waybel_4(A),A)
& v2_waybel_4(k2_waybel_4(A),A) ) ) ).
fof(fc3_waybel_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k2_waybel_4(A))
& v1_waybel_4(k2_waybel_4(A),A)
& v3_waybel_4(k2_waybel_4(A),A) ) ) ).
fof(fc4_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k2_waybel_4(A))
& v1_waybel_4(k2_waybel_4(A),A)
& v4_waybel_4(k2_waybel_4(A),A) ) ) ).
fof(fc5_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ~ v1_xboole_0(k3_waybel_4(A)) ) ).
fof(fc6_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
& v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v2_yellow_0(k2_yellow_1(k3_waybel_4(A))) ) ) ).
fof(fc7_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k4_waybel_4(A))
& v8_relat_2(k4_waybel_4(A))
& v1_waybel_4(k4_waybel_4(A),A)
& v2_waybel_4(k4_waybel_4(A),A)
& v3_waybel_4(k4_waybel_4(A),A)
& v4_waybel_4(k4_waybel_4(A),A)
& v5_waybel_4(k4_waybel_4(A),A) ) ) ).
fof(fc8_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
& v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v1_yellow_0(k2_yellow_1(k3_waybel_4(A)))
& v2_yellow_0(k2_yellow_1(k3_waybel_4(A))) ) ) ).
fof(fc9_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
& v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v1_yellow_0(k2_yellow_1(k3_waybel_4(A)))
& v2_yellow_0(k2_yellow_1(k3_waybel_4(A)))
& v2_lattice3(k2_yellow_1(k3_waybel_4(A))) ) ) ).
fof(fc10_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
& v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
& v1_yellow_0(k2_yellow_1(k3_waybel_4(A)))
& v2_yellow_0(k2_yellow_1(k3_waybel_4(A)))
& v3_yellow_0(k2_yellow_1(k3_waybel_4(A)))
& v24_waybel_0(k2_yellow_1(k3_waybel_4(A)))
& v25_waybel_0(k2_yellow_1(k3_waybel_4(A)))
& v1_lattice3(k2_yellow_1(k3_waybel_4(A)))
& v2_lattice3(k2_yellow_1(k3_waybel_4(A)))
& v3_lattice3(k2_yellow_1(k3_waybel_4(A))) ) ) ).
fof(fc11_waybel_4,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& v4_waybel_4(C,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ~ v1_xboole_0(k5_waybel_4(A,B,C)) ) ).
fof(fc12_waybel_4,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& v2_waybel_4(C,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> v12_waybel_0(k5_waybel_4(A,B,C),A) ) ).
fof(fc13_waybel_4,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& v3_waybel_4(C,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> v1_waybel_0(k5_waybel_4(A,B,C),A) ) ).
fof(fc14_waybel_4,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_relat_1(k7_waybel_4(A,B))
& v1_funct_1(k7_waybel_4(A,B))
& v1_funct_2(k7_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& v5_orders_3(k7_waybel_4(A,B),A,k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(fc15_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k8_waybel_4(A))
& v1_orders_2(k8_waybel_4(A)) ) ) ).
fof(fc16_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k8_waybel_4(A))
& v1_orders_2(k8_waybel_4(A))
& v2_yellow_0(k8_waybel_4(A)) ) ) ).
fof(fc17_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k9_waybel_4(A))
& v1_funct_1(k9_waybel_4(A))
& v1_funct_2(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
& v5_orders_3(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ) ).
fof(fc18_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k10_waybel_4(A))
& v1_funct_1(k10_waybel_4(A))
& v1_funct_2(k10_waybel_4(A),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
& v5_orders_3(k10_waybel_4(A),k8_waybel_4(A),k2_yellow_1(k3_waybel_4(A))) ) ) ).
fof(fc19_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k9_waybel_4(A))
& v1_funct_1(k9_waybel_4(A))
& v2_funct_1(k9_waybel_4(A))
& v1_funct_2(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
& v5_orders_3(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ) ).
fof(cc4_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A) )
=> ( ~ v3_struct_0(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)
& 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) ) ) ) ).
fof(fc20_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v1_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(fc21_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v2_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(fc22_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v1_waybel_4(k1_waybel_4(A),A)
& v2_waybel_4(k1_waybel_4(A),A)
& v3_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(fc23_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v1_waybel_4(k1_waybel_4(A),A)
& v2_waybel_4(k1_waybel_4(A),A)
& v3_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(fc24_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v1_waybel_4(k1_waybel_4(A),A)
& v4_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(fc25_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v8_relat_2(k1_waybel_4(A))
& v1_waybel_4(k1_waybel_4(A),A)
& v2_waybel_4(k1_waybel_4(A),A)
& v3_waybel_4(k1_waybel_4(A),A)
& v4_waybel_4(k1_waybel_4(A),A)
& v5_waybel_4(k1_waybel_4(A),A)
& v6_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(rc2_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v8_relat_2(B)
& v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& v5_waybel_4(B,A)
& v6_waybel_4(B,A) ) ) ).
fof(fc26_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ~ v1_xboole_0(k12_waybel_4(A)) ) ).
fof(cc5_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v8_waybel_4(B,A)
=> v9_waybel_4(B,A) ) ) ) ).
fof(fc27_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_waybel_4(A))
& v8_relat_2(k1_waybel_4(A))
& v1_waybel_4(k1_waybel_4(A),A)
& v2_waybel_4(k1_waybel_4(A),A)
& v3_waybel_4(k1_waybel_4(A),A)
& v4_waybel_4(k1_waybel_4(A),A)
& v5_waybel_4(k1_waybel_4(A),A)
& v6_waybel_4(k1_waybel_4(A),A)
& v8_waybel_4(k1_waybel_4(A),A)
& v9_waybel_4(k1_waybel_4(A),A) ) ) ).
fof(cc6_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v5_waybel_4(B,A)
& v6_waybel_4(B,A)
& v9_waybel_4(B,A) )
=> ( v8_relat_2(B)
& v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& v5_waybel_4(B,A)
& v6_waybel_4(B,A)
& v8_waybel_4(B,A)
& v9_waybel_4(B,A) ) ) ) ) ).
fof(d1_waybel_4,axiom,
$true ).
fof(d2_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k1_waybel_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> r1_waybel_3(A,C,D) ) ) ) ) ) ) ).
fof(d3_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> k2_waybel_4(A) = u1_orders_2(A) ) ).
fof(d4_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v1_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
=> r1_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(d5_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v2_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r1_orders_2(A,F,C)
& r2_hidden(k4_tarski(C,D),B)
& r1_orders_2(A,D,E) )
=> r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ) ) ).
fof(d6_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v3_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(k4_tarski(C,E),B)
& r2_hidden(k4_tarski(D,E),B) )
=> r2_hidden(k4_tarski(k10_lattice3(A,C,D),E),B) ) ) ) ) ) ) ) ).
fof(d7_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v4_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_hidden(k4_tarski(k3_yellow_0(A),C),B) ) ) ) ) ).
fof(d8_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v5_waybel_4(B,A)
<=> ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A) ) ) ) ) ).
fof(t1_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(k4_tarski(C,E),B)
& r2_hidden(k4_tarski(D,F),B) )
=> r2_hidden(k4_tarski(k13_lattice3(A,C,D),k13_lattice3(A,E,F)),B) ) ) ) ) ) ) ) ).
fof(d9_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( B = k3_waybel_4(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v5_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t2_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> r1_tarski(B,k2_waybel_4(A)) ) ) ).
fof(t3_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> k4_yellow_0(k2_yellow_1(k3_waybel_4(A))) = k2_waybel_4(A) ) ).
fof(d10_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k4_waybel_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> C = k3_yellow_0(A) ) ) ) ) ) ) ).
fof(t4_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> r1_tarski(k4_waybel_4(A),B) ) ) ).
fof(t5_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> k3_yellow_0(k2_yellow_1(k3_waybel_4(A))) = k4_waybel_4(A) ) ).
fof(t6_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
& m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t7_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v2_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v2_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
& m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t8_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v3_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v3_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v3_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
& m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t9_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v4_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
& m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t10_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v5_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
& m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t11_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k3_waybel_4(A))))) )
=> ( v5_waybel_4(k1_setfam_1(B),A)
& m2_relset_1(k1_setfam_1(B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ).
fof(t12_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> r1_tarski(k5_waybel_4(A,B,C),k6_waybel_0(A,B)) ) ) ) ).
fof(d13_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
=> ( C = k7_waybel_4(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k5_waybel_4(A,D,B) ) ) ) ) ) ).
fof(t13_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C,D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(C,k5_waybel_4(A,D,B))
<=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ).
fof(t14_waybel_4,axiom,
! [A,B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m2_relset_1(C,u1_struct_0(B),u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(A,k6_waybel_4(B,D,C))
<=> r2_hidden(k4_tarski(D,A),C) ) ) ) ) ).
fof(t15_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B = u1_orders_2(A)
=> k5_waybel_4(A,C,B) = k6_waybel_0(A,C) ) ) ) ) ).
fof(d14_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_orders_2(B)
& l1_orders_2(B) )
=> ( B = k8_waybel_4(A)
<=> ! [C] :
( ~ ( r2_hidden(C,u1_struct_0(B))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
=> ~ ( C = D
& v5_orders_3(D,A,k2_yellow_1(k8_waybel_0(A)))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_tarski(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),D,E),k6_waybel_0(A,E)) ) ) ) )
& ( ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& C = D
& v5_orders_3(D,A,k2_yellow_1(k8_waybel_0(A)))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_tarski(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),D,E),k6_waybel_0(A,E)) ) )
=> r2_hidden(C,u1_struct_0(B)) )
& ! [D,E] :
( r2_hidden(k4_tarski(D,E),u1_orders_2(B))
<=> ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& ? [G] :
( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& D = F
& E = G
& r2_hidden(D,u1_struct_0(B))
& r2_hidden(E,u1_struct_0(B))
& r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),F,G) ) ) ) ) ) ) ) ).
fof(t16_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v4_yellow_0(k8_waybel_4(A),k6_yellow_1(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A))))
& m1_yellow_0(k8_waybel_4(A),k6_yellow_1(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)))) ) ) ).
fof(t17_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_orders_2(A,C,D)
=> r1_tarski(k5_waybel_4(A,C,B),k5_waybel_4(A,D,B)) ) ) ) ) ) ).
fof(t18_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> r2_hidden(k7_waybel_4(A,B),u1_struct_0(k8_waybel_4(A))) ) ) ).
fof(t19_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> r2_hidden(k4_yellow_2(A),u1_struct_0(k8_waybel_4(A))) ) ).
fof(t20_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),k7_waybel_4(A,B),k4_yellow_2(A)) ) ) ).
fof(t21_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))) )
=> r2_hidden(k3_yellow_0(A),B) ) ) ).
fof(t22_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ 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))) )
=> r2_hidden(k4_yellow_0(A),B) ) ) ).
fof(t23_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> k6_waybel_0(A,k3_yellow_0(A)) = k1_struct_0(A,k3_yellow_0(A)) ) ).
fof(t24_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> k7_waybel_0(A,k4_yellow_0(A)) = k1_struct_0(A,k4_yellow_0(A)) ) ).
fof(t25_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))))
& v1_funct_2(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) ).
fof(t26_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> r2_hidden(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(k8_waybel_4(A))) ) ).
fof(t27_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> r2_hidden(k4_tarski(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),k7_waybel_4(A,B)),u1_orders_2(k8_waybel_4(A))) ) ) ).
fof(d15_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
& m2_relset_1(B,u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) )
=> ( B = k9_waybel_4(A)
<=> ! [C] :
( ( v5_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> k1_funct_1(B,C) = k7_waybel_4(A,C) ) ) ) ) ).
fof(t28_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v5_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( r1_tarski(B,C)
=> r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),k7_waybel_4(A,B),k7_waybel_4(A,C)) ) ) ) ) ).
fof(t29_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> ! [D] :
( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
=> ( r1_tarski(C,D)
=> r1_tarski(k5_waybel_4(A,B,C),k5_waybel_4(A,B,D)) ) ) ) ) ) ).
fof(d16_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
& m2_relset_1(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A)))) )
=> ( B = k10_waybel_4(A)
<=> ! [C] :
~ ( r2_hidden(C,u1_struct_0(k8_waybel_4(A)))
& ! [D] :
( ( v5_waybel_4(D,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( D = k1_funct_1(B,C)
& ! [E,F] :
( r2_hidden(k4_tarski(E,F),D)
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(I,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& G = E
& H = F
& I = C
& r2_hidden(G,k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),I,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> k7_funct_2(u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),k9_waybel_4(A),k10_waybel_4(A)) = k6_partfun1(k4_relset_1(u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),k9_waybel_4(A))) ) ).
fof(t31_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> k7_funct_2(u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),k10_waybel_4(A),k9_waybel_4(A)) = k6_partfun1(u1_struct_0(k8_waybel_4(A))) ) ).
fof(t32_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> k2_funct_1(k9_waybel_4(A)) = k10_waybel_4(A) ) ).
fof(t33_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> v23_waybel_0(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ).
fof(d17_waybel_4,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,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
=> ( C = k11_waybel_4(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_orders_2(A,D,k1_yellow_0(A,B))
=> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,D),B) )
& ( ~ r3_orders_2(A,D,k1_yellow_0(A,B))
=> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k6_waybel_0(A,D) ) ) ) ) ) ) ) ).
fof(t35_waybel_4,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,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_hidden(k11_waybel_4(A,B),u1_struct_0(k8_waybel_4(A))) ) ) ).
fof(t36_waybel_4,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))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_yellow_4(A,k1_struct_0(A,B),C) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,B),C) ) ) ) ).
fof(d18_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v6_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C = k1_yellow_0(A,k5_waybel_4(A,C,B)) ) ) ) ) ).
fof(d19_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
=> ( v7_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& D = k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C)
& C = k1_yellow_0(A,D) ) ) ) ) ) ).
fof(t37_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_waybel_2(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))) )
=> v7_waybel_4(k11_waybel_4(A,B),A) ) ) ).
fof(t38_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> v2_waybel_2(A) ) ).
fof(t39_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(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))) )
=> v7_waybel_4(k11_waybel_4(A,B),A) ) ) ).
fof(t40_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_waybel_4(A,B,k1_waybel_4(A)) = k1_waybel_3(A,B) ) ) ).
fof(t41_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> v6_waybel_4(k2_waybel_4(A),A) ) ).
fof(d20_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( B = k12_waybel_4(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v5_waybel_4(C,A)
& v6_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t42_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
=> ~ ( v7_waybel_4(B,A)
& r2_hidden(B,u1_struct_0(k8_waybel_4(A)))
& ! [C] :
( ( v5_waybel_4(C,A)
& v6_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> C != k1_funct_1(k10_waybel_4(A),B) ) ) ) ) ).
fof(t45_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ! [B] :
( ( v5_waybel_4(B,A)
& v6_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( r1_tarski(k1_waybel_4(A),B)
& v6_waybel_4(k1_waybel_4(A),A) ) ) ) ) ).
fof(t46_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ( v2_waybel_2(A)
& ? [B] :
( v5_waybel_4(B,A)
& v6_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& ! [C] :
( ( v5_waybel_4(C,A)
& v6_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> r1_tarski(B,C) ) ) ) ) ) ).
fof(d21_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v8_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(k4_tarski(C,D),B)
& C != D
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(k4_tarski(C,E),B)
& r2_hidden(k4_tarski(E,D),B)
& C != E ) ) ) ) ) ) ) ) ).
fof(d22_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v9_waybel_4(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(k4_tarski(C,D),B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(k4_tarski(C,E),B)
& r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) ) ) ) ).
fof(t47_waybel_4,axiom,
$true ).
fof(t48_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v8_waybel_4(B,A)
=> v9_waybel_4(B,A) ) ) ) ).
fof(t49_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v6_waybel_4(D,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( ~ r3_orders_2(A,B,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(k4_tarski(E,B),D)
& ~ r3_orders_2(A,E,C) ) ) ) ) ) ) ) ).
fof(t50_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_waybel_4(D,A)
& v3_waybel_4(D,A)
& v6_waybel_4(D,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( r2_hidden(k4_tarski(B,C),D)
& B != C
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r3_orders_2(A,B,E)
& r2_hidden(k4_tarski(E,C),D)
& B != E ) ) ) ) ) ) ) ).
fof(t51_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v5_waybel_4(D,A)
& v6_waybel_4(D,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( r1_waybel_3(A,B,C)
& B != C
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(k4_tarski(B,E),D)
& r2_hidden(k4_tarski(E,C),D)
& B != E ) ) ) ) ) ) ) ).
fof(t52_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> v8_waybel_4(k1_waybel_4(A),A) ) ).
fof(t53_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,B,D)
& r1_waybel_3(A,D,C) ) ) ) ) ) ) ).
fof(t54_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_waybel_3(A,B,C)
<=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r3_orders_2(A,C,k1_yellow_0(A,D))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,D)
& r1_waybel_3(A,B,E) ) ) ) ) ) ) ) ) ).
fof(d23_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> ( r1_waybel_4(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,B)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_hidden(F,B)
& r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(E,F),C) ) ) ) ) ) ) ) ) ) ).
fof(t55_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_waybel_4(A,B,u1_orders_2(A))
=> v1_waybel_0(B,A) ) ) ) ).
fof(d24_waybel_4,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_waybel_4(A,B,C)
<=> ( r2_hidden(B,A)
& ! [D] :
~ ( r2_hidden(D,A)
& D != B
& r2_hidden(k4_tarski(B,D),C) ) ) ) ) ).
fof(d25_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_waybel_4(A,B,C)
<=> r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ).
fof(t56_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_waybel_4(A,B,C)
<=> ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(d26_waybel_4,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r4_waybel_4(A,B,C)
<=> ( r2_hidden(B,A)
& ! [D] :
~ ( r2_hidden(D,A)
& D != B
& r2_hidden(k4_tarski(D,B),C) ) ) ) ) ).
fof(d27_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r5_waybel_4(A,B,C)
<=> r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ).
fof(t57_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r5_waybel_4(A,B,C)
<=> ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_orders_2(A,D,C) ) ) ) ) ) ) ).
fof(t58_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v8_waybel_4(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_waybel_4(k5_waybel_4(A,C,B),D,B) )
=> r2_hidden(k4_tarski(C,C),B) ) ) ) ) ) ).
fof(t59_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_waybel_4(k5_waybel_4(A,C,B),D,B) )
=> r2_hidden(k4_tarski(C,C),B) ) )
=> v8_waybel_4(B,A) ) ) ) ).
fof(t60_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v9_waybel_4(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_waybel_4(A,k5_waybel_4(A,C,B),B) ) ) ) ) ).
fof(t61_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_waybel_4(A,k5_waybel_4(A,C,B),B) )
=> v9_waybel_4(B,A) ) ) ) ).
fof(t62_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v6_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v9_waybel_4(B,A)
=> v8_waybel_4(B,A) ) ) ) ).
fof(s1_waybel_4,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& k1_relat_1(A) = f1_s1_waybel_4
& ! [B] :
( m1_subset_1(B,f1_s1_waybel_4)
=> ( ( p1_s1_waybel_4(B)
=> k1_funct_1(A,B) = f2_s1_waybel_4(B) )
& ( ~ p1_s1_waybel_4(B)
=> k1_funct_1(A,B) = f3_s1_waybel_4(B) ) ) ) ) ).
fof(dt_k1_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> m2_relset_1(k1_waybel_4(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k2_waybel_4,axiom,
! [A] :
( l1_orders_2(A)
=> m2_relset_1(k2_waybel_4(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k3_waybel_4,axiom,
$true ).
fof(dt_k4_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m2_relset_1(k4_waybel_4(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k5_waybel_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> m1_subset_1(k5_waybel_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_waybel_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> m1_subset_1(k6_waybel_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k7_waybel_4,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_funct_1(k7_waybel_4(A,B))
& v1_funct_2(k7_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(k7_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) ).
fof(dt_k8_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k8_waybel_4(A))
& l1_orders_2(k8_waybel_4(A)) ) ) ).
fof(dt_k9_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k9_waybel_4(A))
& v1_funct_2(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
& m2_relset_1(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) ) ) ).
fof(dt_k10_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k10_waybel_4(A))
& v1_funct_2(k10_waybel_4(A),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
& m2_relset_1(k10_waybel_4(A),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A)))) ) ) ).
fof(dt_k11_waybel_4,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(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))) )
=> ( v1_funct_1(k11_waybel_4(A,B))
& v1_funct_2(k11_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(k11_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) ).
fof(dt_k12_waybel_4,axiom,
$true ).
fof(d11_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> k5_waybel_4(A,B,C) = a_3_0_waybel_4(A,B,C) ) ) ) ).
fof(d12_waybel_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> k6_waybel_4(A,B,C) = a_3_1_waybel_4(A,B,C) ) ) ) ).
fof(t34_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_setfam_1(a_2_0_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) ).
fof(t43_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_setfam_1(a_2_1_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) ).
fof(t44_waybel_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_waybel_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_setfam_1(a_2_2_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) ).
fof(fraenkel_a_3_0_waybel_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_waybel_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r2_hidden(k4_tarski(E,C),D) ) ) ) ).
fof(fraenkel_a_3_1_waybel_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_waybel_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r2_hidden(k4_tarski(C,E),D) ) ) ) ).
fof(fraenkel_a_2_0_waybel_4,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_waybel_4(B,C))
<=> ? [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)))
& A = D
& r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) ).
fof(fraenkel_a_2_1_waybel_4,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_1_waybel_4(B,C))
<=> ? [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)))
& A = k1_waybel_0(B,k2_yellow_1(k8_waybel_0(B)),k11_waybel_4(B,D),C) ) ) ) ).
fof(fraenkel_a_2_2_waybel_4,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_waybel_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_2_waybel_4(B,C))
<=> ? [D] :
( v5_waybel_4(D,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(B))
& A = k5_waybel_4(B,C,D)
& r2_hidden(D,k12_waybel_4(B)) ) ) ) ).
%------------------------------------------------------------------------------