SET007 Axioms: SET007+484.ax
%------------------------------------------------------------------------------
% File : SET007+484 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Properties of Relational Structures, Posets, Lattices and Maps
% 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 : yellow_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 86 ( 1 unt; 0 def)
% Number of atoms : 835 ( 35 equ)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 844 ( 95 ~; 1 |; 510 &)
% ( 12 <=>; 226 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 48 ( 46 usr; 1 prp; 0-4 aty)
% Number of functors : 42 ( 42 usr; 1 con; 0-5 aty)
% Number of variables : 236 ( 231 !; 5 ?)
% 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_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k5_yellow_0(A,B))
& v1_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(fc2_yellow_2,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)) )
=> ( ~ v3_struct_0(k2_yellow_2(A,B,C))
& v1_orders_2(k2_yellow_2(A,B,C))
& v4_yellow_0(k2_yellow_2(A,B,C),B) ) ) ).
fof(cc1_yellow_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(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_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ) ) ).
fof(fc3_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ~ v1_xboole_0(k8_waybel_0(A)) ) ).
fof(fc4_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
& v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v2_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(fc5_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
& v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v1_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(fc6_yellow_2,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(k8_waybel_0(A)))
& v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
& v1_yellow_0(k2_yellow_1(k8_waybel_0(A)))
& v2_yellow_0(k2_yellow_1(k8_waybel_0(A)))
& v3_yellow_0(k2_yellow_1(k8_waybel_0(A)))
& v24_waybel_0(k2_yellow_1(k8_waybel_0(A)))
& v25_waybel_0(k2_yellow_1(k8_waybel_0(A)))
& v1_lattice3(k2_yellow_1(k8_waybel_0(A)))
& v2_lattice3(k2_yellow_1(k8_waybel_0(A)))
& v3_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(fc7_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k3_yellow_2(A))
& v1_funct_1(k3_yellow_2(A))
& v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
& v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ).
fof(fc8_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k4_yellow_2(A))
& v1_funct_1(k4_yellow_2(A))
& v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(t1_yellow_2,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)))
=> ( r1_tarski(C,k6_waybel_0(A,B))
<=> r2_lattice3(A,C,B) ) ) ) ) ).
fof(t2_yellow_2,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)))
=> ( r1_tarski(C,k7_waybel_0(A,B))
<=> r1_lattice3(A,C,B) ) ) ) ) ).
fof(t3_yellow_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r1_yellow_0(A,B)
& r1_yellow_0(A,C) )
=> ( r1_yellow_0(A,k2_xboole_0(B,C))
& k1_yellow_0(A,k2_xboole_0(B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) ).
fof(t4_yellow_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r2_yellow_0(A,B)
& r2_yellow_0(A,C) )
=> ( r2_yellow_0(A,k2_xboole_0(B,C))
& k2_yellow_0(A,k2_xboole_0(B,C)) = k12_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ) ).
fof(t5_yellow_2,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] :
( r1_tarski(B,C)
=> r1_tarski(k2_wellord1(A,B),k2_wellord1(A,C)) ) ) ).
fof(t6_yellow_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> r1_tarski(u1_orders_2(B),u1_orders_2(C)) ) ) ) ) ).
fof(t7_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_yellow_0(C,B) )
=> ( ( ( v1_waybel_0(A,C)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) )
=> ( v1_waybel_0(A,B)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) )
& ( ( v2_waybel_0(A,C)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) )
=> ( v2_waybel_0(A,B)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ).
fof(t8_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
=> ( D = E
=> ( ( v2_waybel_0(D,B)
=> v2_waybel_0(E,C) )
& ( v1_waybel_0(D,B)
=> v1_waybel_0(E,C) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_yellow_2,axiom,
! [A,B] :
( l1_orders_2(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ( r1_yellow_2(A,B,C,D)
<=> ! [E] :
~ ( r2_hidden(E,A)
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ~ ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E)
& r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ).
fof(t9_yellow_2,axiom,
$true ).
fof(t10_yellow_2,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(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_yellow_2(u1_struct_0(A),B,C,D)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_orders_2(B,k1_waybel_0(A,B,C,E),k1_waybel_0(A,B,D,E)) ) ) ) ) ) ) ).
fof(d2_yellow_2,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_yellow_2(A,B,C) = k5_yellow_0(B,k1_yellow_2(A,B,C)) ) ) ) ).
fof(t11_yellow_2,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)) )
=> k1_yellow_2(A,B,C) = u1_struct_0(k2_yellow_2(A,B,C)) ) ) ) ).
fof(t12_yellow_2,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)))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& k1_waybel_0(A,B,C,E) = D ) ) ) ) ) ).
fof(t13_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> v5_orders_3(k7_grcat_1(A),A,A) ) ).
fof(t14_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [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(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v5_orders_3(D,A,B)
& v5_orders_3(E,B,C) )
=> v5_orders_3(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t15_yellow_2,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( v5_orders_3(C,A,B)
& r1_lattice3(A,D,E) )
=> r1_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ).
fof(t16_yellow_2,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( v5_orders_3(C,A,B)
& r2_lattice3(A,D,E) )
=> r2_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ).
fof(t17_yellow_2,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_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v5_orders_3(C,A,B)
=> v1_waybel_0(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ).
fof(t18_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_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)) )
=> ( v22_waybel_0(B,A,A)
=> v5_orders_3(B,A,A) ) ) ) ).
fof(t19_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_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)) )
=> ( v21_waybel_0(B,A,A)
=> v5_orders_3(B,A,A) ) ) ) ).
fof(t20_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(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)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_waybel_0(A,A,B,k1_waybel_0(A,A,B,C)) = k1_waybel_0(A,A,B,C) ) ) ) ) ).
fof(t22_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( 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)) )
=> ( ( v11_quantal1(C)
& r1_tarski(A,k1_yellow_2(B,B,C)) )
=> k4_pre_topc(B,B,C,A) = A ) ) ) ).
fof(t23_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> v11_quantal1(k7_grcat_1(A)) ) ).
fof(t24_yellow_2,axiom,
! [A,B] :
( ( 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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( r2_hidden(C,A)
=> ( r3_orders_2(B,C,k1_yellow_0(B,A))
& r3_orders_2(B,k2_yellow_0(B,A),C) ) ) ) ) ).
fof(t25_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] : r1_yellow_0(A,B)
<=> ! [B] : r2_yellow_0(A,B) ) ) ).
fof(t26_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] : r1_yellow_0(A,B)
=> v3_lattice3(A) ) ) ).
fof(t27_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] : r2_yellow_0(A,B)
=> v3_lattice3(A) ) ) ).
fof(t28_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r2_yellow_0(A,B) )
=> ! [B] :
( r2_yellow_0(A,B)
& k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ) ).
fof(t29_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_yellow_0(A,B) )
=> ! [B] :
( r1_yellow_0(A,B)
& k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ) ).
fof(t30_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r2_yellow_0(A,B) )
=> v3_lattice3(A) ) ) ).
fof(t32_yellow_2,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] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( 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) ) ) ) ).
fof(t33_yellow_2,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] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v8_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( 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) ) ) ) ).
fof(t34_yellow_2,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] :
( ( ~ 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)) )
=> ( v18_waybel_0(C,A,B)
=> v8_yellow_0(k2_yellow_2(A,B,C),B) ) ) ) ) ).
fof(t35_yellow_2,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] :
( ( ~ 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)) )
=> ( v17_waybel_0(C,A,B)
=> v7_yellow_0(k2_yellow_2(A,B,C),B) ) ) ) ) ).
fof(t36_yellow_2,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_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(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)) )
=> ( ( v18_waybel_0(C,A,B)
| v17_waybel_0(C,A,B) )
=> ( v2_orders_2(k2_yellow_2(A,B,C))
& v3_orders_2(k2_yellow_2(A,B,C))
& v4_orders_2(k2_yellow_2(A,B,C))
& v1_lattice3(k2_yellow_2(A,B,C))
& v2_lattice3(k2_yellow_2(A,B,C))
& v3_lattice3(k2_yellow_2(A,B,C))
& l1_orders_2(k2_yellow_2(A,B,C)) ) ) ) ) ) ).
fof(t37_yellow_2,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(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v11_quantal1(B)
& v22_waybel_0(B,A,A) )
=> ( v4_waybel_0(k2_yellow_2(A,A,B),A)
& v2_orders_2(k2_yellow_2(A,A,B))
& v3_orders_2(k2_yellow_2(A,A,B))
& v4_orders_2(k2_yellow_2(A,A,B))
& v1_lattice3(k2_yellow_2(A,A,B))
& v2_lattice3(k2_yellow_2(A,A,B))
& v3_lattice3(k2_yellow_2(A,A,B))
& l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) ).
fof(t38_yellow_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v12_waybel_0(C,A) ) )
=> ( v12_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
& m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t39_yellow_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v13_waybel_0(C,A) ) )
=> ( v13_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
& m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t40_yellow_2,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> ( v12_waybel_0(C,A)
& v1_waybel_0(C,A) ) ) )
=> ( v1_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
& m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t41_yellow_2,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> ( v13_waybel_0(C,A)
& v2_waybel_0(C,A) ) ) )
=> ( v2_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
& m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t42_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(A),B,C))
& v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
& v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
& m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t43_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( m1_subset_1(A,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))
<=> ( ~ v1_xboole_0(A)
& v1_waybel_0(A,B)
& v12_waybel_0(A,B)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ).
fof(t44_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))
=> ( r2_hidden(A,C)
=> m1_subset_1(A,u1_struct_0(B)) ) ) ) ).
fof(t45_yellow_2,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(k2_yellow_1(k8_waybel_0(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> k11_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k3_xboole_0(B,C) ) ) ) ).
fof(t47_yellow_2,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(k8_waybel_0(A))) )
=> ( ~ v1_xboole_0(k1_setfam_1(B))
& v1_waybel_0(k1_setfam_1(B),A)
& v12_waybel_0(k1_setfam_1(B),A)
& m1_subset_1(k1_setfam_1(B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t48_yellow_2,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(k8_waybel_0(A))))) )
=> ( r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B)
& k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k1_setfam_1(B) ) ) ) ).
fof(t49_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0)
& k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0) = k2_pre_topc(A) ) ) ).
fof(t50_yellow_2,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_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ).
fof(d3_yellow_2,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(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) )
=> ( B = k3_yellow_2(A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_funct_1(B,C) = k1_yellow_0(A,C) ) ) ) ) ).
fof(t51_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( k1_relat_1(k3_yellow_2(A)) = k8_waybel_0(A)
& m1_subset_1(k1_yellow_2(k2_yellow_1(k8_waybel_0(A)),A,k3_yellow_2(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(t52_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r2_hidden(A,k1_relat_1(k3_yellow_2(B)))
<=> ( ~ v1_xboole_0(A)
& v1_waybel_0(A,B)
& v12_waybel_0(A,B)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ).
fof(t53_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ).
fof(d4_yellow_2,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)))) )
=> ( B = k4_yellow_2(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C) = k6_waybel_0(A,C) ) ) ) ) ).
fof(t54_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) ) ).
fof(d5_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( v1_relat_1(B)
=> k5_yellow_2(A,B) = k1_yellow_0(A,k2_relat_1(B)) ) ) ).
fof(d6_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( v1_relat_1(B)
=> k6_yellow_2(A,B) = k2_yellow_0(A,k2_relat_1(B)) ) ) ).
fof(t55_yellow_2,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_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m2_relset_1(D,B,u1_struct_0(A)) )
=> ( r3_orders_2(A,k7_yellow_2(B,A,D,C),k5_yellow_2(A,D))
& r3_orders_2(A,k6_yellow_2(A,D),k7_yellow_2(B,A,D,C)) ) ) ) ) ) ).
fof(t56_yellow_2,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] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u1_struct_0(A))
& m2_relset_1(D,C,u1_struct_0(A)) )
=> ( ! [E] :
( m1_subset_1(E,C)
=> r3_orders_2(A,k7_yellow_2(C,A,D,E),B) )
=> r3_orders_2(A,k5_yellow_2(A,D),B) ) ) ) ) ) ).
fof(t57_yellow_2,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] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u1_struct_0(A))
& m2_relset_1(D,C,u1_struct_0(A)) )
=> ( ! [E] :
( m1_subset_1(E,C)
=> r3_orders_2(A,B,k7_yellow_2(C,A,D,E)) )
=> r3_orders_2(A,B,k6_yellow_2(A,D)) ) ) ) ) ) ).
fof(dt_k1_yellow_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(redefinition_k1_yellow_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k1_yellow_2(A,B,C) = k2_relat_1(C) ) ).
fof(dt_k2_yellow_2,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_orders_2(k2_yellow_2(A,B,C))
& v4_yellow_0(k2_yellow_2(A,B,C),B)
& m1_yellow_0(k2_yellow_2(A,B,C),B) ) ) ).
fof(dt_k3_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k3_yellow_2(A))
& v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
& m2_relset_1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) ) ) ).
fof(dt_k4_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k4_yellow_2(A))
& v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& m2_relset_1(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) ).
fof(dt_k5_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v1_relat_1(B) )
=> m1_subset_1(k5_yellow_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k6_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v1_relat_1(B) )
=> m1_subset_1(k6_yellow_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k7_yellow_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B))
& m1_subset_1(D,A) )
=> m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k7_yellow_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B))
& m1_subset_1(D,A) )
=> k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k8_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(redefinition_k8_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> k8_yellow_2(A,B,C) = k2_relat_1(C) ) ).
fof(t21_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(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)
=> k1_yellow_2(A,A,B) = a_2_0_yellow_2(A,B) ) ) ) ).
fof(t31_yellow_2,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(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_yellow_2(A,B)
=> ( v2_orders_2(k5_yellow_0(A,C))
& v3_orders_2(k5_yellow_0(A,C))
& v4_orders_2(k5_yellow_0(A,C))
& v1_lattice3(k5_yellow_0(A,C))
& v2_lattice3(k5_yellow_0(A,C))
& v3_lattice3(k5_yellow_0(A,C))
& l1_orders_2(k5_yellow_0(A,C)) ) ) ) ) ) ) ).
fof(t46_yellow_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& D = a_3_0_yellow_2(A,B,C)
& r1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k2_struct_0(k2_yellow_1(k8_waybel_0(A)),B,C))
& k10_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k4_waybel_0(A,D) ) ) ) ) ).
fof(fraenkel_a_2_0_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(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_yellow_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& D = k1_waybel_0(B,B,C,D) ) ) ) ).
fof(fraenkel_a_2_1_yellow_2,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)
& 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_yellow_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& D = k1_waybel_0(B,B,C,D) ) ) ) ).
fof(fraenkel_a_3_0_yellow_2,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))
& m1_subset_1(D,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) )
=> ( r2_hidden(A,a_3_0_yellow_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ~ ( ~ r2_hidden(E,C)
& ~ r2_hidden(E,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ~ ( r2_hidden(F,C)
& r2_hidden(G,D)
& E = k13_lattice3(B,F,G) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------