SET007 Axioms: SET007+485.ax
%------------------------------------------------------------------------------
% File : SET007+485 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Galois Connections
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 160 ( 2 unt; 0 def)
% Number of atoms : 1819 ( 89 equ)
% Maximal formula atoms : 26 ( 11 avg)
% Number of connectives : 1881 ( 222 ~; 2 |;1100 &)
% ( 47 <=>; 510 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 65 ( 63 usr; 1 prp; 0-4 aty)
% Number of functors : 47 ( 47 usr; 0 con; 1-5 aty)
% Number of variables : 484 ( 458 !; 26 ?)
% 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_1,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A)) ) ).
fof(fc2_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v23_waybel_0(k7_grcat_1(A),A,A) ) ) ).
fof(cc1_waybel_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v4_waybel_1(C,A,B) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& v19_waybel_0(C,A,B)
& v21_waybel_0(C,A,B) ) ) ) ) ).
fof(cc2_waybel_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_waybel_1(C,B,A) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(fc3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A) ) ) ).
fof(rc1_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) ) ) ).
fof(cc3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A) )
=> ( v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) ) ) ) ) ).
fof(rc2_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A)
& v7_waybel_1(B,A) ) ) ).
fof(fc4_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A)
& v7_waybel_1(k7_grcat_1(A),A) ) ) ).
fof(cc4_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(B,A) )
=> ( v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) ) ) ) ) ).
fof(rc3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A)
& v8_waybel_1(B,A) ) ) ).
fof(fc5_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A)
& v7_waybel_1(k7_grcat_1(A),A)
& v8_waybel_1(k7_grcat_1(A),A) ) ) ).
fof(fc6_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k2_waybel_1(A,B,C))
& v1_funct_1(k2_waybel_1(A,B,C))
& ~ v1_xboole_0(k2_waybel_1(A,B,C))
& v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
& v2_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
& v1_partfun1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) ) ) ).
fof(fc7_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k3_waybel_1(A,B,C))
& v1_funct_1(k3_waybel_1(A,B,C))
& v2_funct_1(k3_waybel_1(A,B,C))
& ~ v1_xboole_0(k3_waybel_1(A,B,C))
& v1_funct_2(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B))
& v1_partfun1(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B))
& v5_orders_3(k3_waybel_1(A,B,C),k2_yellow_2(A,B,C),B) ) ) ).
fof(fc8_waybel_1,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_relat_1(k4_waybel_1(A,B))
& v1_funct_1(k4_waybel_1(A,B))
& ~ v1_xboole_0(k4_waybel_1(A,B))
& v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k4_waybel_1(A,B),A,A) ) ) ).
fof(cc5_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc6_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_waybel_1(A) ) ) ) ).
fof(cc7_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(fc9_waybel_1,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A)) ) ).
fof(cc8_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v11_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A) ) ) ) ).
fof(cc9_waybel_1,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_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A) ) ) ) ).
fof(cc10_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v11_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v2_waybel_1(A)
& v9_waybel_1(A) ) ) ) ).
fof(rc4_waybel_1,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_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A) ) ).
fof(rc5_waybel_1,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_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v2_waybel_1(A)
& v9_waybel_1(A) ) ).
fof(d1_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_funct_1(C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k7_yellow_2(u1_struct_0(A),B,C,D) = k7_yellow_2(u1_struct_0(A),B,C,E)
=> D = E ) ) ) ) ) ) ) ).
fof(d2_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_orders_3(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_orders_2(A,D,E)
=> r1_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) ) ).
fof(t1_waybel_1,axiom,
$true ).
fof(t2_waybel_1,axiom,
! [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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t3_waybel_1,axiom,
! [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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t4_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( v2_lattice3(A)
=> k11_lattice3(A,k3_yellow_0(A),B) = k3_yellow_0(A) )
& ( ( v1_lattice3(A)
& v2_orders_2(A)
& v3_orders_2(A) )
=> k10_lattice3(A,k3_yellow_0(A),B) = B ) ) ) ) ).
fof(t5_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( ( v2_lattice3(A)
& v3_orders_2(A)
& v2_orders_2(A) )
=> k11_lattice3(A,k4_yellow_0(A),B) = B )
& ( v1_lattice3(A)
=> k10_lattice3(A,k4_yellow_0(A),B) = k4_yellow_0(A) ) ) ) ) ).
fof(d3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k11_lattice3(A,B,k10_lattice3(A,C,D)) = k10_lattice3(A,k11_lattice3(A,B,C),k11_lattice3(A,B,D)) ) ) ) ) ) ).
fof(t6_waybel_1,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k13_lattice3(A,B,k12_lattice3(A,C,D)) = k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D)) ) ) ) ) ) ).
fof(d4_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( r1_waybel_1(A,B)
<=> ( r2_yellow_0(A,B)
& r2_hidden(k2_yellow_0(A,B),B) ) ) ) ).
fof(d5_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( r2_waybel_1(A,B)
<=> ( r1_yellow_0(A,B)
& r2_hidden(k1_yellow_0(A,B),B) ) ) ) ).
fof(d6_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r3_waybel_1(A,B,C)
<=> ( r2_yellow_0(A,C)
& B = k2_yellow_0(A,C)
& r2_hidden(k2_yellow_0(A,C),C) ) ) ) ) ).
fof(d7_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r4_waybel_1(A,B,C)
<=> ( r1_yellow_0(A,C)
& B = k1_yellow_0(A,C)
& r2_hidden(k1_yellow_0(A,C),C) ) ) ) ) ).
fof(d8_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( r5_waybel_1(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v23_waybel_0(C,A,B) ) ) ) ) ).
fof(t7_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( r5_waybel_1(A,B)
=> r5_waybel_1(B,A) ) ) ) ).
fof(t8_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( l1_orders_2(C)
=> ( ( r5_waybel_1(A,B)
& r5_waybel_1(B,C) )
=> r5_waybel_1(A,C) ) ) ) ) ).
fof(d9_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_waybel_1(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A))
& C = k4_tarski(D,E) ) ) ) ) ) ).
fof(d10_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel_1(C,A,B)
=> ( v3_waybel_1(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A))
& C = k1_waybel_1(A,B,D,E)
& v5_orders_3(D,A,B)
& v5_orders_3(E,B,A)
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r1_orders_2(B,F,k7_yellow_2(u1_struct_0(A),B,D,G))
<=> r1_orders_2(A,k7_yellow_2(u1_struct_0(B),A,E,F),G) ) ) ) ) ) ) ) ) ) ).
fof(t9_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
<=> ( v5_orders_3(C,A,B)
& v5_orders_3(D,B,A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r3_orders_2(B,E,k7_yellow_2(u1_struct_0(A),B,C,F))
<=> r3_orders_2(A,k7_yellow_2(u1_struct_0(B),A,D,E),F) ) ) ) ) ) ) ) ) ) ).
fof(d11_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v4_waybel_1(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) ) ) ) ) ) ).
fof(d12_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v5_waybel_1(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& v3_waybel_1(k1_waybel_1(A,B,D,C),A,B) ) ) ) ) ) ).
fof(t10_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
=> ( v4_waybel_1(C,A,B)
& v5_waybel_1(D,A,B) ) ) ) ) ) ) ).
fof(t11_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
<=> ( v5_orders_3(C,A,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k7_waybel_0(B,E))) ) ) ) ) ) ) ) ).
fof(t12_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
<=> ( v5_orders_3(D,B,A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k6_waybel_0(A,E))) ) ) ) ) ) ) ) ).
fof(t13_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v4_waybel_1(C,A,B)
=> v17_waybel_0(C,A,B) ) ) ) ) ).
fof(t14_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v5_waybel_1(C,A,B)
=> v18_waybel_0(C,B,A) ) ) ) ) ).
fof(t15_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ~ ( v3_lattice3(A)
& v17_waybel_0(C,A,B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ~ ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k7_waybel_0(B,E))) ) ) ) ) ) ) ) ).
fof(t16_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ~ ( v3_lattice3(B)
& v18_waybel_0(C,B,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)) )
=> ~ ( v3_waybel_1(k1_waybel_1(A,B,D,C),A,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,D,E),k5_pre_topc(B,A,C,k6_waybel_0(A,E))) ) ) ) ) ) ) ) ).
fof(t17_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_lattice3(A)
=> ( v17_waybel_0(C,A,B)
<=> ( v5_orders_3(C,A,B)
& v4_waybel_1(C,A,B) ) ) ) ) ) ) ).
fof(t18_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_lattice3(B)
=> ( v18_waybel_0(C,B,A)
<=> ( v5_orders_3(C,B,A)
& v5_waybel_1(C,A,B) ) ) ) ) ) ) ).
fof(t19_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
=> ( r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A))
& r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) ) ) ).
fof(t20_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v5_orders_3(C,A,B)
& v5_orders_3(D,B,A)
& r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A))
& r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) )
=> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) ) ) ) ) ) ).
fof(t21_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v5_orders_3(C,A,B)
& v5_orders_3(D,B,A)
& r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A))
& r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) )
=> ( D = k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D))
& C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) ) ) ).
fof(t22_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( D = k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D))
& C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) )
=> ( v11_quantal1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C))
& v11_quantal1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)) ) ) ) ) ) ) ).
fof(t23_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k1_struct_0(B,E))) ) ) ) ) ) ) ).
fof(t24_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k1_struct_0(B,E))) )
=> k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C) = k7_grcat_1(B) ) ) ) ) ) ).
fof(t25_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A)
=> ( v2_funct_1(C)
& v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ) ).
fof(t26_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
=> ( v2_funct_2(C,u1_struct_0(A),u1_struct_0(B))
<=> v2_funct_1(D) ) ) ) ) ) ) ).
fof(t27_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
& v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k1_struct_0(A,E))) ) ) ) ) ) ) ).
fof(t28_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k1_struct_0(A,E))) )
=> k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A) ) ) ) ) ) ).
fof(t29_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
=> ( v2_funct_1(C)
<=> v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ) ).
fof(d13_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
<=> ( v11_quantal1(B)
& v5_orders_3(B,A,A) ) ) ) ) ).
fof(d14_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v7_waybel_1(B,A)
<=> ( v6_waybel_1(B,A)
& r1_yellow_2(u1_struct_0(A),A,k7_grcat_1(A),B) ) ) ) ) ).
fof(d15_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_waybel_1(B,A)
<=> ( v6_waybel_1(B,A)
& r1_yellow_2(u1_struct_0(A),A,B,k7_grcat_1(A)) ) ) ) ) ).
fof(t30_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v7_waybel_1(B,A)
& r2_yellow_0(A,C)
& r1_tarski(C,k8_yellow_2(u1_struct_0(A),A,B)) )
=> k2_yellow_0(A,C) = k7_yellow_2(u1_struct_0(A),A,B,k2_yellow_0(A,C)) ) ) ) ) ).
fof(t31_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v8_waybel_1(B,A)
& r1_yellow_0(A,C)
& r1_tarski(C,k8_yellow_2(u1_struct_0(A),A,B)) )
=> k1_yellow_0(A,C) = k7_yellow_2(u1_struct_0(A),A,B,k1_yellow_0(A,C)) ) ) ) ) ).
fof(d16_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k2_waybel_1(A,B,C) = k8_relat_1(u1_struct_0(k2_yellow_2(A,B,C)),C) ) ) ) ).
fof(t32_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k2_waybel_1(A,B,C) = C ) ) ) ).
fof(t33_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_orders_3(C,A,B)
=> v5_orders_3(k2_waybel_1(A,B,C),A,k2_yellow_2(A,B,C)) ) ) ) ) ).
fof(d17_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k3_waybel_1(A,B,C) = k7_grcat_1(k2_yellow_2(A,B,C)) ) ) ) ).
fof(t34_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_yellow_2(A,B,C)))
=> k7_yellow_2(u1_struct_0(k2_yellow_2(A,B,C)),B,k3_waybel_1(A,B,C),D) = D ) ) ) ) ).
fof(t35_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> k7_funct_2(u1_struct_0(A),u1_struct_0(k2_yellow_2(A,A,B)),u1_struct_0(A),k2_waybel_1(A,A,B),k3_waybel_1(A,A,B)) = B ) ) ).
fof(t36_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v11_quantal1(B)
=> k7_funct_2(u1_struct_0(k2_yellow_2(A,A,B)),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,A,B)),k3_waybel_1(A,A,B),k2_waybel_1(A,A,B)) = k7_grcat_1(k2_yellow_2(A,A,B)) ) ) ) ).
fof(t37_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v6_waybel_1(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ~ ( v5_orders_3(D,A,C)
& v2_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& v5_orders_3(E,C,A)
& v2_funct_1(E)
& B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E)
& k7_grcat_1(C) = k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),E,D) ) ) ) ) ) ) ) ).
fof(t38_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ? [C] :
( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C)
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C))
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A))
& v5_orders_3(D,A,C)
& v5_orders_3(E,C,A)
& B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E)
& k7_grcat_1(C) = k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),E,D) ) ) )
=> v6_waybel_1(B,A) ) ) ) ).
fof(t39_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v7_waybel_1(B,A)
=> v3_waybel_1(k1_waybel_1(k2_yellow_2(A,A,B),A,k3_waybel_1(A,A,B),k2_waybel_1(A,A,B)),k2_yellow_2(A,A,B),A) ) ) ) ).
fof(t40_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v7_waybel_1(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ~ ( v3_waybel_1(k1_waybel_1(C,A,D,E),C,A)
& B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),E,D) ) ) ) ) ) ) ) ).
fof(t41_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_orders_3(B,A,A)
=> ( ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ~ ( v3_waybel_1(k1_waybel_1(C,A,D,E),C,A)
& B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),E,D) ) ) ) )
| v7_waybel_1(B,A) ) ) ) ) ).
fof(t42_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_waybel_1(B,A)
=> v3_waybel_1(k1_waybel_1(A,k2_yellow_2(A,A,B),k2_waybel_1(A,A,B),k3_waybel_1(A,A,B)),A,k2_yellow_2(A,A,B)) ) ) ) ).
fof(t43_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v8_waybel_1(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ~ ( v3_waybel_1(k1_waybel_1(A,C,D,E),A,C)
& B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) ) ) ) ) ) ) ) ).
fof(t44_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_orders_3(B,A,A)
=> ( ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ~ ( v3_waybel_1(k1_waybel_1(A,C,D,E),A,C)
& B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) ) ) ) )
| v8_waybel_1(B,A) ) ) ) ) ).
fof(t56_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v7_waybel_1(B,A)
=> v7_yellow_0(k2_yellow_2(A,A,B),A) )
& ( v8_waybel_1(B,A)
=> v8_yellow_0(k2_yellow_2(A,A,B),A) ) ) ) ) ).
fof(t57_waybel_1,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_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> v3_lattice3(k2_yellow_2(A,A,B)) ) ) ) ).
fof(t58_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v7_waybel_1(B,A)
=> ( v18_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(C,u1_struct_0(k2_yellow_2(A,A,B)))
& r1_yellow_0(A,C) )
=> ( r1_yellow_0(k2_yellow_2(A,A,B),C)
& k1_yellow_0(k2_yellow_2(A,A,B),C) = k7_yellow_2(u1_struct_0(A),A,B,k1_yellow_0(A,C)) ) ) ) ) ) ) ) ).
fof(t59_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_waybel_1(B,A)
=> ( v17_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(C,u1_struct_0(k2_yellow_2(A,A,B)))
& r2_yellow_0(A,C) )
=> ( r2_yellow_0(k2_yellow_2(A,A,B),C)
& k2_yellow_0(k2_yellow_2(A,A,B),C) = k7_yellow_2(u1_struct_0(A),A,B,k2_yellow_0(A,C)) ) ) ) ) ) ) ) ).
fof(t60_waybel_1,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) )
=> ( v3_waybel_1(k1_waybel_1(A,k2_yellow_1(k8_waybel_0(A)),k4_yellow_2(A),k3_yellow_2(A)),A,k2_yellow_1(k8_waybel_0(A)))
& v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ).
fof(t61_waybel_1,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) )
=> ( v7_waybel_1(k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),k3_yellow_2(A),k4_yellow_2(A)),k2_yellow_1(k8_waybel_0(A)))
& r5_waybel_1(k2_yellow_2(k2_yellow_1(k8_waybel_0(A)),k2_yellow_1(k8_waybel_0(A)),k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),k3_yellow_2(A),k4_yellow_2(A))),A) ) ) ).
fof(d18_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k4_waybel_1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),A,C,D) = k11_lattice3(A,B,D) ) ) ) ) ) ).
fof(t63_waybel_1,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))
=> v5_orders_3(k4_waybel_1(A,B),A,A) ) ) ).
fof(d19_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
<=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_waybel_1(k4_waybel_1(A,B),A,A) ) ) ) ) ).
fof(d20_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v9_waybel_1(A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k5_waybel_1(A,B)
<=> v3_waybel_1(k1_waybel_1(A,A,C,k4_waybel_1(A,B)),A,A) ) ) ) ) ) ).
fof(t69_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> v2_waybel_1(A) ) ) ).
fof(d21_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_waybel_1(A,B,C) = k7_yellow_2(u1_struct_0(A),A,k5_waybel_1(A,B),C) ) ) ) ).
fof(t70_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_orders_2(A,k11_lattice3(A,C,D),B)
<=> r1_orders_2(A,D,k6_waybel_1(A,C,B)) ) ) ) ) ) ) ).
fof(t71_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> v2_yellow_0(A) ) ) ).
fof(t72_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k4_yellow_0(A) = k6_waybel_1(A,B,C)
<=> r1_orders_2(A,B,C) ) ) ) ) ) ).
fof(t73_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_yellow_0(A) = k6_waybel_1(A,B,B) ) ) ) ).
fof(t74_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( k4_yellow_0(A) = k6_waybel_1(A,B,C)
& k4_yellow_0(A) = k6_waybel_1(A,C,B) )
=> B = C ) ) ) ) ) ).
fof(t75_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_orders_2(A,C,k6_waybel_1(A,B,C)) ) ) ) ) ).
fof(t76_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_yellow_0(A) = k6_waybel_1(A,B,k4_yellow_0(A)) ) ) ) ).
fof(t77_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> B = k6_waybel_1(A,k4_yellow_0(A),B) ) ) ) ).
fof(t78_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k6_waybel_1(A,C,D),k6_waybel_1(A,B,D)) ) ) ) ) ) ) ).
fof(t79_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_orders_2(A,C,D)
=> r1_orders_2(A,k6_waybel_1(A,B,C),k6_waybel_1(A,B,D)) ) ) ) ) ) ) ).
fof(t80_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k11_lattice3(A,B,k6_waybel_1(A,B,C)) = k11_lattice3(A,B,C) ) ) ) ) ).
fof(t81_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k6_waybel_1(A,k10_lattice3(A,B,C),D) = k11_lattice3(A,k6_waybel_1(A,B,D),k6_waybel_1(A,C,D)) ) ) ) ) ) ).
fof(d22_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_1(A,B) = k6_waybel_1(A,B,k3_yellow_0(A)) ) ) ).
fof(t83_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ( v9_waybel_1(A)
& v1_yellow_0(A) )
=> ( k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A)
& k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) ) ) ) ).
fof(t84_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,C,k7_waybel_1(A,B))
<=> r1_orders_2(A,B,k7_waybel_1(A,C)) ) ) ) ) ) ).
fof(t85_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,C,k7_waybel_1(A,B))
<=> k11_lattice3(A,B,C) = k3_yellow_0(A) ) ) ) ) ) ).
fof(t86_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B)) ) ) ) ) ) ).
fof(t87_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k7_waybel_1(A,k10_lattice3(A,B,C)) = k11_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) ) ) ) ) ).
fof(t88_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v9_waybel_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_orders_2(A,k10_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)),k7_waybel_1(A,k11_lattice3(A,B,C))) ) ) ) ) ).
fof(d23_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r6_waybel_1(A,B,C)
<=> ( k10_lattice3(A,B,C) = k4_yellow_0(A)
& k11_lattice3(A,B,C) = k3_yellow_0(A) ) ) ) ) ) ).
fof(d24_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v10_waybel_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r6_waybel_1(A,B,C) ) ) ) ) ).
fof(t89_waybel_1,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ( ( v9_waybel_1(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_1(A,k7_waybel_1(A,B)) = B ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r6_waybel_1(A,B,k7_waybel_1(A,B)) ) ) ) ).
fof(t90_waybel_1,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ( ( ( v2_waybel_1(A)
& v10_waybel_1(A) )
=> ( v9_waybel_1(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_1(A,k7_waybel_1(A,B)) = B ) ) )
& ( ( v9_waybel_1(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_1(A,k7_waybel_1(A,B)) = B ) )
=> ( v2_waybel_1(A)
& v10_waybel_1(A) ) ) ) ) ).
fof(d25_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v11_waybel_1(A)
<=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A) ) ) ) ).
fof(dt_m1_waybel_1,axiom,
$true ).
fof(existence_m1_waybel_1,axiom,
! [A,B] :
( ( l1_orders_2(A)
& l1_orders_2(B) )
=> ? [C] : m1_waybel_1(C,A,B) ) ).
fof(redefinition_v1_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_waybel_1(C,A,B)
<=> v2_funct_1(C) ) ) ).
fof(reflexivity_r5_waybel_1,axiom,
! [A,B] :
( ( l1_orders_2(A)
& l1_orders_2(B) )
=> r5_waybel_1(A,A) ) ).
fof(dt_k1_waybel_1,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> m1_waybel_1(k1_waybel_1(A,B,C,D),A,B) ) ).
fof(redefinition_k1_waybel_1,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> k1_waybel_1(A,B,C,D) = k4_tarski(C,D) ) ).
fof(dt_k2_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k2_waybel_1(A,B,C))
& v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
& m2_relset_1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) ) ) ).
fof(dt_k3_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k3_waybel_1(A,B,C))
& v1_funct_2(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B))
& m2_relset_1(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) ) ) ).
fof(dt_k4_waybel_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k4_waybel_1(A,B))
& v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k5_waybel_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k5_waybel_1(A,B))
& v1_funct_2(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k6_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k6_waybel_1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k7_waybel_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k7_waybel_1(A,B),u1_struct_0(A)) ) ).
fof(t45_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> k8_yellow_2(u1_struct_0(A),A,B) = k3_xboole_0(a_2_0_waybel_1(A,B),a_2_1_waybel_1(A,B)) ) ) ) ).
fof(t46_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ( ~ v1_xboole_0(a_2_0_waybel_1(A,B))
& m1_subset_1(a_2_0_waybel_1(A,B),k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(a_2_1_waybel_1(A,B))
& m1_subset_1(a_2_1_waybel_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t47_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ( k2_relat_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,a_2_0_waybel_1(A,B))) = k8_yellow_2(u1_struct_0(A),A,B)
& k2_relat_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,a_2_1_waybel_1(A,B))) = k8_yellow_2(u1_struct_0(A),A,B) ) ) ) ) ).
fof(t48_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = a_2_0_waybel_1(A,B)
=> ( v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C))
& v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C)))
& m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) ) ) ) ) ) ) ) ).
fof(t49_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = a_2_1_waybel_1(A,B)
=> ( v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C))
& v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C)))
& m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) ) ) ) ) ) ) ).
fof(t50_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = a_2_0_waybel_1(A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C)))
& m2_relset_1(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) )
=> ( D = k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C)
=> v7_waybel_1(D,k5_yellow_0(A,C)) ) ) ) ) ) ) ) ).
fof(t51_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = a_2_1_waybel_1(A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C)))
& m2_relset_1(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) )
=> ( D = k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C)
=> v8_waybel_1(D,k5_yellow_0(A,C)) ) ) ) ) ) ) ) ).
fof(t52_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_orders_3(B,A,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = a_2_0_waybel_1(A,B)
=> v8_yellow_0(k5_yellow_0(A,C),A) ) ) ) ) ) ).
fof(t53_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_orders_3(B,A,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = a_2_1_waybel_1(A,B)
=> v7_yellow_0(k5_yellow_0(A,C),A) ) ) ) ) ) ).
fof(t54_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = a_2_0_waybel_1(A,B)
=> ( ( v17_waybel_0(B,A,A)
=> ( v7_yellow_0(k5_yellow_0(A,C),A)
& v7_yellow_0(k2_yellow_2(A,A,B),A) ) )
& ( v21_waybel_0(B,A,A)
=> ( v3_waybel_0(k5_yellow_0(A,C),A)
& v3_waybel_0(k2_yellow_2(A,A,B),A) ) ) ) ) ) ) ) ) ).
fof(t55_waybel_1,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_waybel_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = a_2_1_waybel_1(A,B)
=> ( ( v18_waybel_0(B,A,A)
=> ( v8_yellow_0(k5_yellow_0(A,C),A)
& v8_yellow_0(k2_yellow_2(A,A,B),A) ) )
& ( v22_waybel_0(B,A,A)
=> ( v4_waybel_0(k5_yellow_0(A,C),A)
& v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) ) ) ) ) ) ) ).
fof(t62_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> a_3_0_waybel_1(A,B,C) = k5_pre_topc(A,A,k4_waybel_1(A,B),k6_waybel_0(A,C)) ) ) ) ).
fof(t64_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k4_pre_topc(A,A,k4_waybel_1(A,B),C) = a_3_1_waybel_1(A,B,C) ) ) ) ).
fof(t65_waybel_1,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))
=> v5_waybel_1(k4_waybel_1(A,B),A,A) )
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_waybel_1(A,a_3_2_waybel_1(A,B,C)) ) ) ) ) ).
fof(t66_waybel_1,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))
=> v5_waybel_1(k4_waybel_1(A,B),A,A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_yellow_0(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_3_waybel_1(A,B,C)) ) ) ) ) ) ).
fof(t67_waybel_1,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] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_waybel_1(k4_waybel_1(A,B),A,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,a_3_4_waybel_1(A,B,C)) ) ) ) ) ).
fof(t68_waybel_1,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_yellow_0(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_5_waybel_1(A,B,C)) ) ) )
=> v2_waybel_1(A) ) ) ).
fof(t82_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ( v9_waybel_1(A)
& v1_yellow_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r4_waybel_1(A,k7_waybel_1(A,B),a_2_2_waybel_1(A,B)) ) ) ) ).
fof(fraenkel_a_2_0_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_waybel_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_orders_2(B,D,k7_yellow_2(u1_struct_0(B),B,C,D)) ) ) ) ).
fof(fraenkel_a_2_1_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_1_waybel_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_orders_2(B,k7_yellow_2(u1_struct_0(B),B,C,D),D) ) ) ) ).
fof(fraenkel_a_3_0_waybel_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_waybel_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r1_orders_2(B,k11_lattice3(B,C,E),D) ) ) ) ).
fof(fraenkel_a_3_1_waybel_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_1_waybel_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k11_lattice3(B,C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_2_waybel_1,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_2_waybel_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r3_orders_2(B,k12_lattice3(B,C,E),D) ) ) ) ).
fof(fraenkel_a_3_3_waybel_1,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(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_3_waybel_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k12_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_3_4_waybel_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(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_4_waybel_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k12_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_3_5_waybel_1,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(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_5_waybel_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k12_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_2_2_waybel_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_2_waybel_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& k11_lattice3(B,C,D) = k3_yellow_0(B) ) ) ) ).
%------------------------------------------------------------------------------