SET007 Axioms: SET007+527.ax
%------------------------------------------------------------------------------
% File : SET007+527 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebraic and Arithmetic Lattices. Part II
% 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 : waybel15 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 42 ( 2 unt; 0 def)
% Number of atoms : 511 ( 16 equ)
% Maximal formula atoms : 30 ( 12 avg)
% Number of connectives : 499 ( 30 ~; 1 |; 338 &)
% ( 18 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 50 ( 48 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 0 con; 1-5 aty)
% Number of variables : 112 ( 102 !; 10 ?)
% 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_waybel15,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))
& v9_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A))
& v11_waybel_1(k3_yellow_1(A))
& v2_waybel_3(k3_yellow_1(A))
& v3_waybel_3(k3_yellow_1(A))
& v1_waybel_8(k3_yellow_1(A))
& v2_waybel_8(k3_yellow_1(A))
& v3_waybel_8(k3_yellow_1(A)) ) ).
fof(cc1_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel15(B,A)
=> v6_waybel_6(B,A) ) ) ) ).
fof(t1_waybel15,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v4_yellow_0(C,B)
& m1_yellow_0(C,B) )
=> ( v4_yellow_0(C,A)
& m1_yellow_0(C,A) ) ) ) ) ).
fof(t2_waybel15,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_struct_0(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)) )
=> ( ( v2_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v2_funct_2(E,u1_struct_0(B),u1_struct_0(C)) )
=> v2_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t3_waybel15,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k4_pre_topc(A,A,k7_grcat_1(A),B) = B ) ) ).
fof(t5_waybel15,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))
=> ( r1_orders_2(A,k4_yellow_0(A),B)
=> B = k4_yellow_0(A) ) ) ) ).
fof(t6_waybel15,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)) )
=> ( ( v2_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) )
=> r5_waybel_1(B,k2_yellow_2(B,A,D)) ) ) ) ) ) ).
fof(t7_waybel15,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] :
( ( ~ 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(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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(G,u1_struct_0(C),u1_struct_0(B)) )
=> ( ( v3_waybel_1(k1_waybel_1(A,B,D,F),A,B)
& v3_waybel_1(k1_waybel_1(B,C,E,G),B,C) )
=> v3_waybel_1(k1_waybel_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),G,F)),A,C) ) ) ) ) ) ) ) ) ).
fof(t8_waybel15,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)) )
=> ( ( D = k2_funct_1(C)
& v23_waybel_0(C,A,B) )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
& v3_waybel_1(k1_waybel_1(B,A,D,C),B,A) ) ) ) ) ) ) ).
fof(t9_waybel15,axiom,
! [A] : v3_waybel_8(k3_yellow_1(A)) ).
fof(t10_waybel15,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_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)) )
=> ( v23_waybel_0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k4_pre_topc(A,B,C,k1_waybel_3(A,D)) = k1_waybel_3(B,k1_waybel_0(A,B,C,D)) ) ) ) ) ) ).
fof(t11_waybel15,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) )
=> ( ( r5_waybel_1(A,B)
& v3_waybel_3(A) )
=> v3_waybel_3(B) ) ) ) ).
fof(t12_waybel15,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v1_yellow_0(A)
& v3_waybel_8(A) )
=> v3_waybel_8(B) ) ) ) ).
fof(t13_waybel15,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] :
( ( ~ 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(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)) )
=> ( ( v22_waybel_0(D,A,B)
& v22_waybel_0(E,B,C) )
=> v22_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t14_waybel15,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(k2_yellow_2(A,B,C))))
=> k4_pre_topc(k2_yellow_2(A,B,C),B,k3_waybel_1(A,B,C),D) = D ) ) ) ) ).
fof(t15_waybel15,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k3_yellow_1(A)))
& m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k3_yellow_1(A))) )
=> ( ( v11_quantal1(B)
& v22_waybel_0(B,k3_yellow_1(A),k3_yellow_1(A)) )
=> v22_waybel_0(k3_waybel_1(k3_yellow_1(A),k3_yellow_1(A),B),k2_yellow_2(k3_yellow_1(A),k3_yellow_1(A),B),k3_yellow_1(A)) ) ) ).
fof(t16_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v22_waybel_0(B,A,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_waybel_3(k2_yellow_2(A,A,B))
& l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) ).
fof(t17_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v22_waybel_0(B,A,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_waybel_3(k2_yellow_2(A,A,B))
& l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) ).
fof(t18_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ? [B] :
( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow_0(B)
& v3_waybel_8(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))
& v2_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v17_waybel_0(C,B,A)
& v22_waybel_0(C,B,A) ) ) ) ) ).
fof(t19_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ? [B] :
( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow_0(B)
& v2_waybel_8(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))
& v2_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v17_waybel_0(C,B,A)
& v22_waybel_0(C,B,A) ) ) ) ) ).
fof(t20_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ ( v3_waybel_3(A)
& ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
& v6_waybel_1(C,k3_yellow_1(B))
& m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) )
=> ~ ( v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B))
& r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) ) ) ) )
& ( ? [B,C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
& v6_waybel_1(C,k3_yellow_1(B))
& m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
& v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B))
& r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) )
=> v3_waybel_3(A) ) ) ) ).
fof(t21_waybel15,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_hidden(B,k4_waybel_6(k7_lattice3(A)))
<=> v6_waybel_6(B,A) ) ) ) ).
fof(d1_waybel15,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel15(B,A)
<=> ( r2_orders_2(A,k3_yellow_0(A),B)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r2_orders_2(A,k3_yellow_0(A),C)
& r1_orders_2(A,C,B) )
=> C = B ) ) ) ) ) ) ).
fof(d2_waybel15,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = k1_waybel15(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
<=> v1_waybel15(C,A) ) ) ) ) ) ).
fof(t22_waybel15,axiom,
$true ).
fof(t23_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel15(B,A)
<=> ( v6_waybel_6(B,A)
& B != k3_yellow_0(A) ) ) ) ) ).
fof(t24_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> k1_waybel15(A) = k4_xboole_0(k4_waybel_6(k7_lattice3(A)),k1_struct_0(A,k3_yellow_0(A))) ) ).
fof(t25_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v1_waybel15(C,A)
=> ( r3_orders_2(A,C,B)
<=> ~ r3_orders_2(A,C,k7_waybel_1(A,B)) ) ) ) ) ) ).
fof(t27_waybel15,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v1_waybel15(B,A)
& v1_waybel15(C,A) )
=> ( B = C
| k12_lattice3(A,B,C) = k3_yellow_0(A) ) ) ) ) ) ).
fof(t28_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v11_waybel_1(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,k1_waybel15(A))
=> ( r2_hidden(B,C)
<=> ( v1_waybel15(B,A)
& r3_orders_2(A,B,k1_yellow_0(A,C)) ) ) ) ) ) ) ).
fof(t29_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,k1_waybel15(A))
& r1_tarski(C,k1_waybel15(A)) )
=> ( r1_tarski(B,C)
<=> r3_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) ) ) ).
fof(t30_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> ? [B] : r5_waybel_1(A,k3_yellow_1(B)) ) ) ).
fof(t31_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> v2_waybel_8(A) ) ) ).
fof(t32_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> v3_waybel_3(A) ) ) ).
fof(t33_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> ( v3_waybel_3(A)
& v3_waybel_3(k7_lattice3(A)) ) ) ) ).
fof(t34_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> v1_waybel_5(A) ) ) ).
fof(t35_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> ( v3_lattice3(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,k1_waybel15(A))
& B = k1_yellow_0(A,C) ) ) ) ) ) ).
fof(dt_k1_waybel15,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m1_subset_1(k1_waybel15(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(t4_waybel15,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> k7_waybel_0(k3_yellow_1(A),B) = a_2_0_waybel15(A,B) ) ).
fof(t26_waybel15,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_0_waybel15(A,B,C)) ) ) ) ).
fof(fraenkel_a_2_0_waybel15,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_1(B)))
=> ( r2_hidden(A,a_2_0_waybel15(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
& A = D
& r1_tarski(C,D) ) ) ) ).
fof(fraenkel_a_3_0_waybel15,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v11_waybel_1(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_waybel15(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k12_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
%------------------------------------------------------------------------------