SET007 Axioms: SET007+335.ax
%------------------------------------------------------------------------------
% File : SET007+335 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complete 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 : lattice3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 137 ( 4 unt; 0 def)
% Number of atoms : 950 ( 88 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 914 ( 101 ~; 0 |; 496 &)
% ( 52 <=>; 265 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 53 ( 51 usr; 1 prp; 0-3 aty)
% Number of functors : 80 ( 80 usr; 9 con; 0-4 aty)
% Number of variables : 381 ( 346 !; 35 ?)
% 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_lattice3,axiom,
! [A] :
( ~ v3_struct_0(k1_lattice3(A))
& v3_lattices(k1_lattice3(A)) ) ).
fof(fc2_lattice3,axiom,
! [A] :
( ~ v3_struct_0(k1_lattice3(A))
& v3_lattices(k1_lattice3(A))
& v4_lattices(k1_lattice3(A))
& v5_lattices(k1_lattice3(A))
& v6_lattices(k1_lattice3(A))
& v7_lattices(k1_lattice3(A))
& v8_lattices(k1_lattice3(A))
& v9_lattices(k1_lattice3(A))
& v10_lattices(k1_lattice3(A)) ) ).
fof(fc3_lattice3,axiom,
! [A] :
( ~ v3_struct_0(k1_lattice3(A))
& v3_lattices(k1_lattice3(A))
& v4_lattices(k1_lattice3(A))
& v5_lattices(k1_lattice3(A))
& v6_lattices(k1_lattice3(A))
& v7_lattices(k1_lattice3(A))
& v8_lattices(k1_lattice3(A))
& v9_lattices(k1_lattice3(A))
& v10_lattices(k1_lattice3(A))
& v11_lattices(k1_lattice3(A))
& v12_lattices(k1_lattice3(A))
& v13_lattices(k1_lattice3(A))
& v14_lattices(k1_lattice3(A))
& v15_lattices(k1_lattice3(A))
& v16_lattices(k1_lattice3(A))
& v17_lattices(k1_lattice3(A)) ) ).
fof(fc4_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(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)) ) ) ).
fof(fc5_lattice3,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k7_lattice3(A))
& v2_orders_2(k7_lattice3(A))
& v3_orders_2(k7_lattice3(A))
& v4_orders_2(k7_lattice3(A)) ) ) ).
fof(fc6_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A)) ) ) ).
fof(cc1_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc2_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(rc1_lattice3,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)
& v3_lattice3(A) ) ).
fof(rc2_lattice3,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)
& v3_lattice3(A) ) ).
fof(rc3_lattice3,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)
& v4_lattice3(A)
& v5_lattice3(A)
& v6_lattice3(A) ) ).
fof(fc7_lattice3,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_struct_0(k14_lattice3(A))
& v3_lattices(k14_lattice3(A))
& v4_lattices(k14_lattice3(A))
& v5_lattices(k14_lattice3(A))
& v6_lattices(k14_lattice3(A))
& v7_lattices(k14_lattice3(A))
& v8_lattices(k14_lattice3(A))
& v9_lattices(k14_lattice3(A))
& v10_lattices(k14_lattice3(A))
& v4_lattice3(k14_lattice3(A)) ) ) ).
fof(d1_lattice3,axiom,
! [A,B] :
( ( v3_lattices(B)
& l3_lattices(B) )
=> ( B = k1_lattice3(A)
<=> ( u1_struct_0(B) = k1_zfmisc_1(A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( k1_binop_1(u2_lattices(B),C,D) = k4_subset_1(A,C,D)
& k1_binop_1(u1_lattices(B),C,D) = k5_subset_1(A,C,D) ) ) ) ) ) ) ).
fof(t1_lattice3,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k1_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_lattice3(A)))
=> ( k1_lattices(k1_lattice3(A),B,C) = k2_xboole_0(B,C)
& k2_lattices(k1_lattice3(A),B,C) = k3_xboole_0(B,C) ) ) ) ).
fof(t2_lattice3,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k1_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_lattice3(A)))
=> ( r1_lattices(k1_lattice3(A),B,C)
<=> r1_tarski(B,C) ) ) ) ).
fof(t3_lattice3,axiom,
! [A] :
( v13_lattices(k1_lattice3(A))
& k5_lattices(k1_lattice3(A)) = k1_xboole_0 ) ).
fof(t4_lattice3,axiom,
! [A] :
( v14_lattices(k1_lattice3(A))
& k6_lattices(k1_lattice3(A)) = A ) ).
fof(t5_lattice3,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k1_lattice3(A)))
=> k7_lattices(k1_lattice3(A),B) = k4_xboole_0(A,B) ) ).
fof(d2_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)) ) ).
fof(t6_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ( k3_lattice3(A) = k3_lattice3(B)
=> g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) ).
fof(d3_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_lattice3(A,B) = B ) ) ).
fof(d4_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_lattice3(A)))
=> k5_lattice3(A,B) = B ) ) ).
fof(t7_lattice3,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))
=> ( r3_lattices(A,B,C)
<=> r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) ) ) ) ) ).
fof(d5_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> k7_lattice3(A) = g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))) ) ).
fof(t8_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> k7_lattice3(k7_lattice3(A)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ).
fof(d6_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_lattice3(A,B) = B ) ) ).
fof(d7_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
=> k9_lattice3(A,B) = B ) ) ).
fof(t9_lattice3,axiom,
! [A] :
( l1_orders_2(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(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B)) ) ) ) ) ).
fof(d8_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_lattice3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,B)
=> r1_orders_2(A,C,D) ) ) ) ) ) ).
fof(d9_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_lattice3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,B)
=> r1_orders_2(A,D,C) ) ) ) ) ) ).
fof(d10_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice3(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,D)
& r1_orders_2(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,E)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,D,E) ) ) ) ) ) ) ) ).
fof(d11_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_lattice3(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,D,B)
& r1_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,E,B)
& r1_orders_2(A,E,C) )
=> r1_orders_2(A,E,D) ) ) ) ) ) ) ) ).
fof(t10_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice3(A)
<=> v2_lattice3(k7_lattice3(A)) ) ) ).
fof(t11_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_lattice3(k3_lattice3(A))
& v2_lattice3(k3_lattice3(A)) ) ) ).
fof(d12_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_lattice3(A)
<=> ! [B] :
? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
=> r1_orders_2(A,C,D) ) ) ) ) ) ).
fof(t12_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v3_lattice3(A)
=> ( v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(d13_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v4_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,D)
& r1_orders_2(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,E)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,D,E) ) ) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( D = k10_lattice3(A,B,C)
<=> ( r1_orders_2(A,B,D)
& r1_orders_2(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,E)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ) ) ).
fof(d14_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v4_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,D,B)
& r1_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,E,B)
& r1_orders_2(A,E,C) )
=> r1_orders_2(A,E,D) ) ) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( D = k11_lattice3(A,B,C)
<=> ( r1_orders_2(A,D,B)
& r1_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,E,B)
& r1_orders_2(A,E,C) )
=> r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_lattice3,axiom,
! [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))
=> k10_lattice3(A,B,C) = k10_lattice3(A,C,B) ) ) ) ).
fof(t14_lattice3,axiom,
! [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))
=> ( v3_orders_2(A)
=> k10_lattice3(A,k10_lattice3(A,B,C),D) = k10_lattice3(A,B,k10_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t15_lattice3,axiom,
! [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))
=> k11_lattice3(A,B,C) = k11_lattice3(A,C,B) ) ) ) ).
fof(t16_lattice3,axiom,
! [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))
=> ( v3_orders_2(A)
=> k11_lattice3(A,k11_lattice3(A,B,C),D) = k11_lattice3(A,B,k11_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t17_lattice3,axiom,
! [A] :
( ( v2_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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k13_lattice3(A,k12_lattice3(A,B,C),C) = C ) ) ) ).
fof(t18_lattice3,axiom,
! [A] :
( ( v2_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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,B,k13_lattice3(A,B,C)) = B ) ) ) ).
fof(t19_lattice3,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] :
( ~ v3_struct_0(B)
& v3_lattices(B)
& v10_lattices(B)
& l3_lattices(B)
& g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) ) ) ).
fof(d15_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_lattices(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ( B = k14_lattice3(A)
<=> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) ) ) ) ) ).
fof(t20_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( k6_lattice3(u1_struct_0(A),k2_lattice3(A)) = k2_lattice3(k1_lattice2(A))
& k7_lattice3(k3_lattice3(A)) = k3_lattice3(k1_lattice2(A)) ) ) ).
fof(d16_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r3_lattice3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> r1_lattices(A,B,D) ) ) ) ) ) ).
fof(d17_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r4_lattice3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> r1_lattices(A,D,B) ) ) ) ) ) ).
fof(t21_lattice3,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))
=> ( r3_lattice3(A,B,k2_struct_0(A,C,D))
<=> r3_lattices(A,B,k4_lattices(A,C,D)) ) ) ) ) ) ).
fof(t22_lattice3,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))
=> ( r4_lattice3(A,B,k2_struct_0(A,C,D))
<=> r3_lattices(A,k3_lattices(A,C,D),B) ) ) ) ) ) ).
fof(d18_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( v4_lattice3(A)
<=> ! [B] :
? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r4_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r4_lattice3(A,D,B)
=> r1_lattices(A,C,D) ) ) ) ) ) ).
fof(t25_lattice3,axiom,
! [A] : v4_lattice3(k1_lattice3(A)) ).
fof(t26_lattice3,axiom,
! [A] : v5_lattice3(k1_lattice3(A)) ).
fof(t27_lattice3,axiom,
! [A] : v6_lattice3(k1_lattice3(A)) ).
fof(t28_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( r3_lattice3(B,C,A)
<=> r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) ).
fof(t29_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_lattice3(B)))
=> ( r1_lattice3(k3_lattice3(B),A,C)
<=> r3_lattice3(B,k5_lattice3(B,C),A) ) ) ) ).
fof(t30_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( r4_lattice3(B,C,A)
<=> r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) ).
fof(t31_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_lattice3(B)))
=> ( r2_lattice3(k3_lattice3(B),A,C)
<=> r4_lattice3(B,k5_lattice3(B,C),A) ) ) ) ).
fof(d21_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k15_lattice3(A,B)
<=> ( r4_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r4_lattice3(A,D,B)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ).
fof(t34_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( B = k16_lattice3(A,C)
<=> ( r3_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattice3(A,D,C)
=> r3_lattices(A,D,B) ) ) ) ) ) ) ).
fof(t38_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r2_hidden(B,C)
=> ( r3_lattices(A,B,k15_lattice3(A,C))
& r3_lattices(A,k16_lattice3(A,C),B) ) ) ) ) ).
fof(t39_lattice3,axiom,
$true ).
fof(t40_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r3_lattice3(A,B,C)
=> r3_lattices(A,B,k16_lattice3(A,C)) ) ) ) ).
fof(t41_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( r2_hidden(B,C)
& r4_lattice3(A,B,C) )
=> k15_lattice3(A,C) = B ) ) ) ).
fof(t42_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( r2_hidden(B,C)
& r3_lattice3(A,B,C) )
=> k16_lattice3(A,C) = B ) ) ) ).
fof(t43_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k15_lattice3(A,k1_struct_0(A,B)) = B
& k16_lattice3(A,k1_struct_0(A,B)) = B ) ) ) ).
fof(t44_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_lattices(A,B,C) = k15_lattice3(A,k2_struct_0(A,B,C))
& k4_lattices(A,B,C) = k16_lattice3(A,k2_struct_0(A,B,C)) ) ) ) ) ).
fof(t46_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B,C] :
( r1_tarski(B,C)
=> ( r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C))
& r3_lattices(A,k16_lattice3(A,C),k16_lattice3(A,B)) ) ) ) ).
fof(t48_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B,C] :
( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r3_lattices(A,D,E)
& r2_hidden(E,C) ) ) ) )
=> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)) ) ) ).
fof(t50_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A)
& k5_lattices(A) = k15_lattice3(A,k1_xboole_0) ) ) ).
fof(t51_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A)
& k6_lattices(A) = k15_lattice3(A,u1_struct_0(A)) ) ) ).
fof(t53_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> v5_lattice3(A) ) ) ).
fof(t56_lattice3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_zfmisc_1(A),A)
& m2_relset_1(B,k1_zfmisc_1(A),A) )
=> ~ ( ! [C] :
( m1_subset_1(C,A)
=> k8_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)) = C )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> k8_funct_2(k1_zfmisc_1(A),A,B,k10_relset_1(k1_zfmisc_1(A),A,B,C)) = k1_funct_1(B,k3_tarski(C)) )
& ! [C] :
( ( ~ v3_struct_0(C)
& v3_lattices(C)
& v10_lattices(C)
& v4_lattice3(C)
& l3_lattices(C) )
=> ~ ( u1_struct_0(C) = A
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
=> k15_lattice3(C,D) = k1_funct_1(B,D) ) ) ) ) ) ) ).
fof(dt_k1_lattice3,axiom,
! [A] :
( v3_lattices(k1_lattice3(A))
& l3_lattices(k1_lattice3(A)) ) ).
fof(dt_k2_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_relat_2(k2_lattice3(A))
& v4_relat_2(k2_lattice3(A))
& v8_relat_2(k2_lattice3(A))
& v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(redefinition_k2_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k2_lattice3(A) = k9_filter_1(A) ) ).
fof(dt_k3_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
& l1_orders_2(k3_lattice3(A)) ) ) ).
fof(dt_k4_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k4_lattice3(A,B),u1_struct_0(k3_lattice3(A))) ) ).
fof(dt_k5_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(k3_lattice3(A))) )
=> m1_subset_1(k5_lattice3(A,B),u1_struct_0(A)) ) ).
fof(dt_k6_lattice3,axiom,
! [A,B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A) )
=> ( v1_relat_2(k6_lattice3(A,B))
& v4_relat_2(k6_lattice3(A,B))
& v8_relat_2(k6_lattice3(A,B))
& v1_partfun1(k6_lattice3(A,B),A,A)
& m2_relset_1(k6_lattice3(A,B),A,A) ) ) ).
fof(involutiveness_k6_lattice3,axiom,
! [A,B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A) )
=> k6_lattice3(A,k6_lattice3(A,B)) = B ) ).
fof(redefinition_k6_lattice3,axiom,
! [A,B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A) )
=> k6_lattice3(A,B) = k4_relat_1(B) ) ).
fof(dt_k7_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_orders_2(k7_lattice3(A))
& l1_orders_2(k7_lattice3(A)) ) ) ).
fof(dt_k8_lattice3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))) ) ).
fof(dt_k9_lattice3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(k7_lattice3(A))) )
=> m1_subset_1(k9_lattice3(A,B),u1_struct_0(A)) ) ).
fof(dt_k10_lattice3,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k11_lattice3,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k12_lattice3,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k12_lattice3,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k12_lattice3(A,B,C) = k12_lattice3(A,C,B) ) ).
fof(redefinition_k12_lattice3,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k12_lattice3(A,B,C) = k11_lattice3(A,B,C) ) ).
fof(dt_k13_lattice3,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k13_lattice3,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) ).
fof(redefinition_k13_lattice3,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) ).
fof(dt_k14_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ~ v3_struct_0(k14_lattice3(A))
& v3_lattices(k14_lattice3(A))
& v10_lattices(k14_lattice3(A))
& l3_lattices(k14_lattice3(A)) ) ) ).
fof(dt_k15_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)) ) ).
fof(dt_k16_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)) ) ).
fof(d19_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( v5_lattice3(A)
<=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r4_lattice3(A,C,B)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r4_lattice3(A,F,B)
=> r1_lattices(A,C,F) ) )
& r4_lattice3(A,E,a_3_0_lattice3(A,B,D))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r4_lattice3(A,F,a_3_0_lattice3(A,B,D))
=> r1_lattices(A,E,F) ) ) )
=> r1_lattices(A,k2_lattices(A,D,C),E) ) ) ) ) ) ) ).
fof(d20_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( v6_lattice3(A)
<=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r3_lattice3(A,C,B)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r3_lattice3(A,F,B)
=> r1_lattices(A,F,C) ) )
& r3_lattice3(A,E,a_3_1_lattice3(A,B,D))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r3_lattice3(A,F,a_3_1_lattice3(A,B,D))
=> r1_lattices(A,F,E) ) ) )
=> r1_lattices(A,E,k1_lattices(A,D,C)) ) ) ) ) ) ) ).
fof(t23_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v17_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( r4_lattice3(B,C,A)
<=> r3_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) ) ) ) ).
fof(t24_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v17_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( r3_lattice3(B,C,A)
<=> r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) ) ) ) ).
fof(d22_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] : k16_lattice3(A,B) = k15_lattice3(A,a_2_1_lattice3(A,B)) ) ).
fof(t32_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] : r3_lattices(A,k15_lattice3(A,a_3_2_lattice3(A,B,C)),k4_lattices(A,B,k15_lattice3(A,C))) ) ) ).
fof(t33_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( v5_lattice3(A)
<=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_lattices(A,k4_lattices(A,C,k15_lattice3(A,B)),k15_lattice3(A,a_3_3_lattice3(A,B,C))) ) ) ) ).
fof(t35_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] : r3_lattices(A,k3_lattices(A,B,k16_lattice3(A,C)),k16_lattice3(A,a_3_4_lattice3(A,B,C))) ) ) ).
fof(t36_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( v6_lattice3(A)
<=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_lattices(A,k16_lattice3(A,a_3_5_lattice3(A,B,C)),k3_lattices(A,C,k16_lattice3(A,B))) ) ) ) ).
fof(t37_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] : k15_lattice3(A,B) = k16_lattice3(A,a_2_2_lattice3(A,B)) ) ).
fof(t45_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k15_lattice3(A,a_2_3_lattice3(A,B))
& B = k16_lattice3(A,a_2_4_lattice3(A,B)) ) ) ) ).
fof(t47_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( k15_lattice3(A,B) = k15_lattice3(A,a_2_5_lattice3(A,B))
& k16_lattice3(A,B) = k16_lattice3(A,a_2_6_lattice3(A,B)) ) ) ).
fof(t49_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( r1_tarski(B,k1_zfmisc_1(u1_struct_0(A)))
=> k15_lattice3(A,k3_tarski(B)) = k15_lattice3(A,a_2_7_lattice3(A,B)) ) ) ).
fof(t52_lattice3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> k4_filter_0(A,B,C) = k15_lattice3(A,a_3_6_lattice3(A,B,C)) ) ) ) ) ).
fof(t54_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& v5_lattice3(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k4_lattices(B,C,k15_lattice3(B,A)) = k15_lattice3(B,a_3_7_lattice3(A,B,C))
& k4_lattices(B,k15_lattice3(B,A),C) = k15_lattice3(B,a_3_8_lattice3(A,B,C)) ) ) ) ).
fof(t55_lattice3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& v6_lattice3(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k3_lattices(B,C,k16_lattice3(B,A)) = k16_lattice3(B,a_3_9_lattice3(A,B,C))
& k3_lattices(B,k16_lattice3(B,A),C) = k16_lattice3(B,a_3_10_lattice3(A,B,C)) ) ) ) ).
fof(s1_lattice3,axiom,
( ? [A] :
( m1_subset_1(A,f2_s1_lattice3)
& p1_s1_lattice3(A) )
=> a_0_0_lattice3 = k1_tarski(f1_s1_lattice3) ) ).
fof(s2_lattice3,axiom,
( r1_tarski(f2_s2_lattice3,k1_relat_1(f4_s2_lattice3))
=> k9_relat_1(f4_s2_lattice3,a_0_1_lattice3) = a_0_2_lattice3 ) ).
fof(fraenkel_a_3_0_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l3_lattices(B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k2_lattices(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_3_1_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l3_lattices(B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k1_lattices(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_2_0_lattice3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v17_lattices(C)
& l3_lattices(C) )
=> ( r2_hidden(A,a_2_0_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k7_lattices(C,D)
& r2_hidden(D,B) ) ) ) ).
fof(fraenkel_a_2_1_lattice3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_2_1_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_lattice3(B,D,C) ) ) ) ).
fof(fraenkel_a_3_2_lattice3,axiom,
! [A,B,C,D] :
( ( ~ 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_3_2_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k4_lattices(B,C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_3_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_3_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k4_lattices(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_3_4_lattice3,axiom,
! [A,B,C,D] :
( ( ~ 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_3_4_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k3_lattices(B,C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_5_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_5_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k3_lattices(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_2_2_lattice3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_2_2_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r4_lattice3(B,D,C) ) ) ) ).
fof(fraenkel_a_2_3_lattice3,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_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_lattices(B,D,C) ) ) ) ).
fof(fraenkel_a_2_4_lattice3,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_4_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_lattices(B,C,D) ) ) ) ).
fof(fraenkel_a_2_5_lattice3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_2_5_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r3_lattices(B,D,E)
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_6_lattice3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_2_6_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r3_lattices(B,E,D)
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_7_lattice3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B) )
=> ( r2_hidden(A,a_2_7_lattice3(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = k15_lattice3(B,D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_3_6_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v4_lattice3(B)
& l3_lattices(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_6_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r3_lattices(B,k4_lattices(B,C,E),D) ) ) ) ).
fof(fraenkel_a_3_7_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v4_lattice3(C)
& v5_lattice3(C)
& l3_lattices(C)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_7_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k4_lattices(C,D,E)
& r2_hidden(E,B) ) ) ) ).
fof(fraenkel_a_3_8_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v4_lattice3(C)
& v5_lattice3(C)
& l3_lattices(C)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_8_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k4_lattices(C,E,D)
& r2_hidden(E,B) ) ) ) ).
fof(fraenkel_a_3_9_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v4_lattice3(C)
& v6_lattice3(C)
& l3_lattices(C)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_9_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_lattices(C,D,E)
& r2_hidden(E,B) ) ) ) ).
fof(fraenkel_a_3_10_lattice3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v4_lattice3(C)
& v6_lattice3(C)
& l3_lattices(C)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_10_lattice3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_lattices(C,E,D)
& r2_hidden(E,B) ) ) ) ).
fof(fraenkel_a_0_0_lattice3,axiom,
! [A] :
( r2_hidden(A,a_0_0_lattice3)
<=> ? [B] :
( m1_subset_1(B,f2_s1_lattice3)
& A = f1_s1_lattice3
& p1_s1_lattice3(B) ) ) ).
fof(fraenkel_a_0_1_lattice3,axiom,
! [A] :
( r2_hidden(A,a_0_1_lattice3)
<=> ? [B] :
( m1_subset_1(B,f1_s2_lattice3)
& A = f3_s2_lattice3(B)
& p1_s2_lattice3(B) ) ) ).
fof(fraenkel_a_0_2_lattice3,axiom,
! [A] :
( r2_hidden(A,a_0_2_lattice3)
<=> ? [B] :
( m1_subset_1(B,f1_s2_lattice3)
& A = k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B))
& p1_s2_lattice3(B) ) ) ).
%------------------------------------------------------------------------------