SET007 Axioms: SET007+603.ax
%------------------------------------------------------------------------------
% File : SET007+603 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Noetherian Lattices
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : lattice6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 0 unt; 0 def)
% Number of atoms : 584 ( 43 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 613 ( 97 ~; 0 |; 345 &)
% ( 28 <=>; 143 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 47 ( 46 usr; 0 prp; 1-3 aty)
% Number of functors : 27 ( 27 usr; 0 con; 1-3 aty)
% Number of variables : 156 ( 138 !; 18 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_lattice6,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v6_group_1(A) ) ).
fof(cc1_lattice6,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v4_lattice3(A) ) ) ) ).
fof(fc1_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v6_group_1(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k3_lattice3(A))
& v1_orders_2(k3_lattice3(A))
& v2_orders_2(k3_lattice3(A))
& v3_orders_2(k3_lattice3(A))
& v4_orders_2(k3_lattice3(A))
& v1_yellow_0(k3_lattice3(A))
& v2_yellow_0(k3_lattice3(A))
& v3_yellow_0(k3_lattice3(A))
& v24_waybel_0(k3_lattice3(A))
& v25_waybel_0(k3_lattice3(A))
& v1_lattice3(k3_lattice3(A))
& v2_lattice3(k3_lattice3(A))
& v3_lattice3(k3_lattice3(A))
& v1_wellfnd1(k3_lattice3(A)) ) ) ).
fof(rc2_lattice6,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v4_lattice3(A)
& v1_lattice6(A) ) ).
fof(rc3_lattice6,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v4_lattice3(A)
& v2_lattice6(A) ) ).
fof(cc2_lattice6,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v1_lattice6(A) ) ) ) ).
fof(cc3_lattice6,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v2_lattice6(A) ) ) ) ).
fof(rc4_lattice6,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v3_lattices(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v3_realset2(A) ) ).
fof(rc5_lattice6,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v4_lattice3(A)
& v7_lattice6(A) ) ).
fof(fc2_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& v2_lattice6(A)
& l3_lattices(A) )
=> v9_lattice6(k5_lattice6(A),A) ) ).
fof(fc3_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& v1_lattice6(A)
& l3_lattices(A) )
=> v8_lattice6(k6_lattice6(A),A) ) ).
fof(d3_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_lattice6(A)
<=> v1_wellfnd1(k3_lattice3(A)) ) ) ).
fof(d4_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v2_lattice6(A)
<=> v1_wellfnd1(k7_lattice3(k3_lattice3(A))) ) ) ).
fof(t1_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_lattice6(A)
<=> v2_lattice6(k1_lattice2(A)) ) ) ).
fof(d5_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_lattice6(A,B,C)
<=> ( B != C
& r3_lattices(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r3_lattices(A,C,D)
& r3_lattices(A,D,B)
& D != B
& D != C ) ) ) ) ) ) ) ).
fof(t2_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
=> ( C != D
=> ( ( ( r1_lattice6(A,C,B)
& r1_lattice6(A,D,B) )
=> B = k4_lattices(A,D,C) )
& ( ( r1_lattice6(A,B,C)
& r1_lattice6(A,B,D) )
=> B = k3_lattices(A,D,C) ) ) ) ) ) ) ) ).
fof(t3_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v1_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r3_lattices(A,B,C)
& B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r3_lattices(A,D,C)
& r1_lattice6(A,D,B) ) ) ) ) ) ) ).
fof(t4_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v2_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r3_lattices(A,C,B)
& B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r3_lattices(A,C,D)
& r1_lattice6(A,B,D) ) ) ) ) ) ) ).
fof(t5_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ r1_lattice6(A,B,k6_lattices(A)) ) ) ).
fof(t6_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& v1_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k6_lattices(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r1_lattice6(A,C,B) ) ) ) ) ).
fof(t7_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ r1_lattice6(A,k5_lattices(A),B) ) ) ).
fof(t8_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& v2_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k5_lattices(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r1_lattice6(A,B,C) ) ) ) ) ).
fof(d8_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_lattice6(B,A)
<=> k3_lattice6(A,B) != B ) ) ) ).
fof(d9_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_lattice6(B,A)
<=> k4_lattice6(A,B) != B ) ) ) ).
fof(t9_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r3_lattices(A,B,k3_lattice6(A,B))
& r3_lattices(A,k4_lattice6(A,B),B) ) ) ) ).
fof(t10_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( k3_lattice6(A,k6_lattices(A)) = k6_lattices(A)
& v2_waybel_6(k4_lattice3(A,k6_lattices(A)),k3_lattice3(A)) ) ) ).
fof(t11_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( k4_lattice6(A,k5_lattices(A)) = k5_lattices(A)
& v3_waybel_6(k4_lattice3(A,k5_lattices(A)),k3_lattice3(A)) ) ) ).
fof(t12_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_lattice6(B,A)
=> ( r1_lattice6(A,k3_lattice6(A,B),B)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_lattice6(A,C,B)
=> C = k3_lattice6(A,B) ) ) ) ) ) ) ).
fof(t13_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_lattice6(B,A)
=> ( r1_lattice6(A,B,k4_lattice6(A,B))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_lattice6(A,B,C)
=> C = k4_lattice6(A,B) ) ) ) ) ) ) ).
fof(t14_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& v1_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_lattice6(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_lattice6(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice6(A,D,B)
=> D = C ) ) ) ) ) ) ).
fof(t15_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& v2_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_lattice6(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_lattice6(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice6(A,B,D)
=> D = C ) ) ) ) ) ) ).
fof(t16_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_lattice6(B,A)
=> v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) ) ) ) ).
fof(t17_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& v1_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k6_lattices(A)
=> ( v3_lattice6(B,A)
<=> v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) ) ) ) ) ).
fof(t18_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_lattice6(B,A)
=> v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) ) ) ) ).
fof(t19_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& v2_lattice6(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k5_lattices(A)
=> ( v4_lattice6(B,A)
<=> v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) ) ) ) ) ).
fof(t20_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v6_group_1(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( B != k5_lattices(A)
& B != k6_lattices(A)
& ~ ( ( v3_lattice6(B,A)
=> v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) )
& ( v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A))
=> v3_lattice6(B,A) )
& ( v4_lattice6(B,A)
=> v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) )
& ( v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A))
=> v4_lattice6(B,A) ) ) ) ) ) ).
fof(d10_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_lattice6(B,A)
<=> r1_lattice6(A,B,k5_lattices(A)) ) ) ) ).
fof(d11_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v6_lattice6(B,A)
<=> r1_lattice6(A,k6_lattices(A),B) ) ) ) ).
fof(t21_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_lattice6(B,A)
=> v4_lattice6(B,A) ) ) ) ).
fof(t22_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v6_lattice6(B,A)
=> v3_lattice6(B,A) ) ) ) ).
fof(d12_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v7_lattice6(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> v5_lattice6(D,A) ) )
& B = k15_lattice3(A,C) ) ) ) ) ).
fof(d13_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v8_lattice6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
& C = k15_lattice3(A,D) ) ) ) ) ) ).
fof(d14_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v9_lattice6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
& C = k16_lattice3(A,D) ) ) ) ) ) ).
fof(t25_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v9_lattice6(B,A)
<=> v4_waybel_6(k1_lattice6(A,B),k3_lattice3(A)) ) ) ) ).
fof(t26_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v8_lattice6(B,A)
=> r1_tarski(k6_lattice6(A),B) ) ) ) ).
fof(t27_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v9_lattice6(B,A)
=> r1_tarski(k5_lattice6(A),B) ) ) ) ).
fof(dt_k1_lattice6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_lattice6(A,B),k1_zfmisc_1(u1_struct_0(k3_lattice3(A)))) ) ).
fof(dt_k2_lattice6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_lattice3(A)))) )
=> m1_subset_1(k2_lattice6(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k3_lattice6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k3_lattice6(A,B),u1_struct_0(A)) ) ).
fof(dt_k4_lattice6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k4_lattice6(A,B),u1_struct_0(A)) ) ).
fof(dt_k5_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> m1_subset_1(k5_lattice6(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> m1_subset_1(k6_lattice6(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(d1_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_lattice6(A,B) = a_2_0_lattice6(A,B) ) ) ).
fof(d2_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_lattice3(A))))
=> k2_lattice6(A,B) = a_2_1_lattice6(A,B) ) ) ).
fof(d6_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_lattice6(A,B) = k16_lattice3(A,a_2_2_lattice6(A,B)) ) ) ).
fof(d7_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_lattice6(A,B) = k15_lattice3(A,a_2_3_lattice6(A,B)) ) ) ).
fof(t23_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v8_lattice6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C = k15_lattice3(A,a_3_0_lattice6(A,B,C)) ) ) ) ) ).
fof(t24_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v9_lattice6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C = k16_lattice3(A,a_3_1_lattice6(A,B,C)) ) ) ) ) ).
fof(d15_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> k5_lattice6(A) = a_1_0_lattice6(A) ) ).
fof(d16_lattice6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> k6_lattice6(A) = a_1_1_lattice6(A) ) ).
fof(fraenkel_a_2_0_lattice6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_lattice6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k4_lattice3(B,D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_1_lattice6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_lattice3(B)))) )
=> ( r2_hidden(A,a_2_1_lattice6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k3_lattice3(B)))
& A = k5_lattice3(B,D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_2_lattice6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_2_lattice6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_lattices(B,C,D)
& D != C ) ) ) ).
fof(fraenkel_a_2_3_lattice6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_3_lattice6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_lattices(B,D,C)
& D != C ) ) ) ).
fof(fraenkel_a_3_0_lattice6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(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_lattice6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r2_hidden(E,C)
& r3_lattices(B,E,D) ) ) ) ).
fof(fraenkel_a_3_1_lattice6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(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_1_lattice6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r2_hidden(E,C)
& r3_lattices(B,D,E) ) ) ) ).
fof(fraenkel_a_1_0_lattice6,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_1_0_lattice6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = C
& v3_lattice6(C,B) ) ) ) ).
fof(fraenkel_a_1_1_lattice6,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_1_1_lattice6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = C
& v4_lattice6(C,B) ) ) ) ).
%------------------------------------------------------------------------------