SET007 Axioms: SET007+297.ax
%------------------------------------------------------------------------------
% File : SET007+297 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Lattice of Natural Numbers and The Sublattice of it.
% 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 : nat_lat [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 116 ( 69 unt; 0 def)
% Number of atoms : 290 ( 46 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 199 ( 25 ~; 0 |; 96 &)
% ( 8 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-4 aty)
% Number of functors : 30 ( 30 usr; 13 con; 0-6 aty)
% Number of variables : 78 ( 75 !; 3 ?)
% 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_nat_lat,axiom,
( ~ v3_struct_0(k6_nat_lat)
& v3_lattices(k6_nat_lat)
& v4_lattices(k6_nat_lat)
& v5_lattices(k6_nat_lat)
& v6_lattices(k6_nat_lat)
& v7_lattices(k6_nat_lat)
& v8_lattices(k6_nat_lat)
& v9_lattices(k6_nat_lat)
& v10_lattices(k6_nat_lat) ) ).
fof(fc2_nat_lat,axiom,
( ~ v1_xboole_0(k7_nat_lat)
& v1_membered(k7_nat_lat)
& v2_membered(k7_nat_lat)
& v3_membered(k7_nat_lat)
& v4_membered(k7_nat_lat)
& v5_membered(k7_nat_lat) ) ).
fof(cc1_nat_lat,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B) ) ) ) ).
fof(cc2_nat_lat,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B) ) ) ) ).
fof(fc3_nat_lat,axiom,
( ~ v3_struct_0(k13_nat_lat)
& v3_lattices(k13_nat_lat)
& v4_lattices(k13_nat_lat)
& v5_lattices(k13_nat_lat)
& v6_lattices(k13_nat_lat)
& v7_lattices(k13_nat_lat)
& v8_lattices(k13_nat_lat)
& v9_lattices(k13_nat_lat)
& v10_lattices(k13_nat_lat) ) ).
fof(rc1_nat_lat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ? [B] :
( m2_nat_lat(B,A)
& ~ v3_struct_0(B)
& v3_lattices(B)
& v4_lattices(B)
& v5_lattices(B)
& v6_lattices(B)
& v7_lattices(B)
& v8_lattices(B)
& v9_lattices(B)
& v10_lattices(B) ) ) ).
fof(d1_nat_lat,axiom,
$true ).
fof(d2_nat_lat,axiom,
$true ).
fof(d3_nat_lat,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )
=> ( A = k1_nat_lat
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k6_nat_1(B,C) ) ) ) ) ).
fof(d4_nat_lat,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )
=> ( A = k2_nat_lat
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k5_nat_1(B,C) ) ) ) ) ).
fof(d5_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> k3_nat_lat(A) = A ) ).
fof(t1_nat_lat,axiom,
$true ).
fof(t2_nat_lat,axiom,
$true ).
fof(t3_nat_lat,axiom,
$true ).
fof(t4_nat_lat,axiom,
$true ).
fof(t5_nat_lat,axiom,
$true ).
fof(t6_nat_lat,axiom,
$true ).
fof(t7_nat_lat,axiom,
$true ).
fof(t8_nat_lat,axiom,
$true ).
fof(t9_nat_lat,axiom,
$true ).
fof(t10_nat_lat,axiom,
$true ).
fof(t11_nat_lat,axiom,
$true ).
fof(t12_nat_lat,axiom,
$true ).
fof(t13_nat_lat,axiom,
$true ).
fof(t14_nat_lat,axiom,
$true ).
fof(t15_nat_lat,axiom,
$true ).
fof(t16_nat_lat,axiom,
$true ).
fof(t17_nat_lat,axiom,
$true ).
fof(t18_nat_lat,axiom,
$true ).
fof(t19_nat_lat,axiom,
$true ).
fof(t20_nat_lat,axiom,
$true ).
fof(t21_nat_lat,axiom,
$true ).
fof(t22_nat_lat,axiom,
$true ).
fof(t23_nat_lat,axiom,
$true ).
fof(t24_nat_lat,axiom,
$true ).
fof(t25_nat_lat,axiom,
$true ).
fof(t26_nat_lat,axiom,
$true ).
fof(t27_nat_lat,axiom,
$true ).
fof(t28_nat_lat,axiom,
$true ).
fof(t29_nat_lat,axiom,
$true ).
fof(t30_nat_lat,axiom,
$true ).
fof(t31_nat_lat,axiom,
$true ).
fof(t32_nat_lat,axiom,
$true ).
fof(t33_nat_lat,axiom,
$true ).
fof(t34_nat_lat,axiom,
$true ).
fof(t35_nat_lat,axiom,
$true ).
fof(t36_nat_lat,axiom,
$true ).
fof(t37_nat_lat,axiom,
$true ).
fof(t38_nat_lat,axiom,
$true ).
fof(t39_nat_lat,axiom,
$true ).
fof(t40_nat_lat,axiom,
$true ).
fof(t41_nat_lat,axiom,
$true ).
fof(t42_nat_lat,axiom,
$true ).
fof(t43_nat_lat,axiom,
$true ).
fof(t44_nat_lat,axiom,
$true ).
fof(t45_nat_lat,axiom,
$true ).
fof(t46_nat_lat,axiom,
$true ).
fof(t47_nat_lat,axiom,
$true ).
fof(t48_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> k1_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,B) = k5_nat_1(k3_nat_lat(A),k3_nat_lat(B)) ) ) ).
fof(t49_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> k2_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,B) = k6_nat_1(k3_nat_lat(A),k3_nat_lat(B)) ) ) ).
fof(t50_nat_lat,axiom,
$true ).
fof(t51_nat_lat,axiom,
$true ).
fof(t52_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> ( r1_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,B)
=> r1_nat_1(k3_nat_lat(A),k3_nat_lat(B)) ) ) ) ).
fof(d6_nat_lat,axiom,
k4_nat_lat = np__1 ).
fof(d7_nat_lat,axiom,
k5_nat_lat = np__0 ).
fof(t53_nat_lat,axiom,
$true ).
fof(t54_nat_lat,axiom,
$true ).
fof(t55_nat_lat,axiom,
k3_nat_lat(k4_nat_lat) = np__1 ).
fof(t56_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> ( k2_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),k4_nat_lat,A) = k4_nat_lat
& k2_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,k4_nat_lat) = k4_nat_lat ) ) ).
fof(d8_nat_lat,axiom,
k6_nat_lat = g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat) ).
fof(t57_nat_lat,axiom,
$true ).
fof(t58_nat_lat,axiom,
$true ).
fof(t59_nat_lat,axiom,
$true ).
fof(t60_nat_lat,axiom,
( ~ v3_struct_0(k6_nat_lat)
& v10_lattices(k6_nat_lat)
& v13_lattices(k6_nat_lat)
& l3_lattices(k6_nat_lat) ) ).
fof(t61_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> k1_binop_1(k2_nat_lat,A,B) = k1_binop_1(k2_nat_lat,B,A) ) ) ).
fof(t62_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> k1_binop_1(k1_nat_lat,A,B) = k1_binop_1(k1_nat_lat,B,A) ) ) ).
fof(t63_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_nat_lat))
=> k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,A,B),C) ) ) ) ).
fof(t64_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_nat_lat))
=> ( k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,B,A),C)
& k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,A,C),B)
& k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,C,B),A)
& k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,C,A),B) ) ) ) ) ).
fof(t65_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_nat_lat))
=> k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) = k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,A,B),C) ) ) ) ).
fof(t66_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_nat_lat))
=> ( k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) = k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,B,A),C)
& k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) = k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,A,C),B)
& k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) = k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,C,B),A)
& k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) = k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,C,A),B) ) ) ) ) ).
fof(t67_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> ( k1_binop_1(k1_nat_lat,A,k1_binop_1(k2_nat_lat,A,B)) = A
& k1_binop_1(k1_nat_lat,k1_binop_1(k2_nat_lat,B,A),A) = A
& k1_binop_1(k1_nat_lat,A,k1_binop_1(k2_nat_lat,B,A)) = A
& k1_binop_1(k1_nat_lat,k1_binop_1(k2_nat_lat,A,B),A) = A ) ) ) ).
fof(t68_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_nat_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_nat_lat))
=> ( k1_binop_1(k2_nat_lat,A,k1_binop_1(k1_nat_lat,A,B)) = A
& k1_binop_1(k2_nat_lat,k1_binop_1(k1_nat_lat,B,A),A) = A
& k1_binop_1(k2_nat_lat,A,k1_binop_1(k1_nat_lat,B,A)) = A
& k1_binop_1(k2_nat_lat,k1_binop_1(k1_nat_lat,A,B),A) = A ) ) ) ).
fof(d9_nat_lat,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ( A = k7_nat_lat
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,A)
<=> ~ r1_xreal_0(B,np__0) ) ) ) ) ).
fof(d10_nat_lat,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> k8_nat_lat(A) = A ) ) ).
fof(d11_nat_lat,axiom,
! [A] :
( m1_nat_lat(A,k1_numbers,k5_numbers,k7_nat_lat)
=> k9_nat_lat(A) = A ) ).
fof(d12_nat_lat,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat)
& m2_relset_1(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) )
=> ( A = k10_nat_lat
<=> ! [B] :
( m1_nat_lat(B,k1_numbers,k5_numbers,k7_nat_lat)
=> ! [C] :
( m1_nat_lat(C,k1_numbers,k5_numbers,k7_nat_lat)
=> k2_binop_1(k7_nat_lat,k7_nat_lat,k7_nat_lat,A,B,C) = k6_nat_1(B,C) ) ) ) ) ).
fof(d13_nat_lat,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat)
& m2_relset_1(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) )
=> ( A = k11_nat_lat
<=> ! [B] :
( m1_nat_lat(B,k1_numbers,k5_numbers,k7_nat_lat)
=> ! [C] :
( m1_nat_lat(C,k1_numbers,k5_numbers,k7_nat_lat)
=> k2_binop_1(k7_nat_lat,k7_nat_lat,k7_nat_lat,A,B,C) = k5_nat_1(B,C) ) ) ) ) ).
fof(d14_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat)))
=> k12_nat_lat(A) = A ) ).
fof(t69_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat)))
=> k1_lattices(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat),A,B) = k5_nat_1(k12_nat_lat(A),k12_nat_lat(B)) ) ) ).
fof(t70_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat)))
=> k2_lattices(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat),A,B) = k6_nat_1(k12_nat_lat(A),k12_nat_lat(B)) ) ) ).
fof(d15_nat_lat,axiom,
k13_nat_lat = g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat) ).
fof(d16_nat_lat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ( m2_nat_lat(B,A)
<=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& u2_lattices(B) = k1_realset1(u2_lattices(A),u1_struct_0(B))
& u1_lattices(B) = k1_realset1(u1_lattices(A),u1_struct_0(B)) ) ) ) ) ).
fof(t71_nat_lat,axiom,
$true ).
fof(t72_nat_lat,axiom,
$true ).
fof(t73_nat_lat,axiom,
$true ).
fof(t74_nat_lat,axiom,
$true ).
fof(t75_nat_lat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> m2_nat_lat(A,A) ) ).
fof(t76_nat_lat,axiom,
m2_nat_lat(k13_nat_lat,k6_nat_lat) ).
fof(dt_m1_nat_lat,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ! [D] :
( m1_nat_lat(D,A,B,C)
=> m2_subset_1(D,A,B) ) ) ).
fof(existence_m1_nat_lat,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ? [D] : m1_nat_lat(D,A,B,C) ) ).
fof(redefinition_m1_nat_lat,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ! [D] :
( m1_nat_lat(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m2_nat_lat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_nat_lat(B,A)
=> ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) ) ) ) ).
fof(existence_m2_nat_lat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ? [B] : m2_nat_lat(B,A) ) ).
fof(dt_k1_nat_lat,axiom,
( v1_funct_1(k1_nat_lat)
& v1_funct_2(k1_nat_lat,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(k1_nat_lat,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) ) ).
fof(dt_k2_nat_lat,axiom,
( v1_funct_1(k2_nat_lat)
& v1_funct_2(k2_nat_lat,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(k2_nat_lat,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) ) ).
fof(dt_k3_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat)))
=> m2_subset_1(k3_nat_lat(A),k1_numbers,k5_numbers) ) ).
fof(dt_k4_nat_lat,axiom,
m1_subset_1(k4_nat_lat,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) ).
fof(dt_k5_nat_lat,axiom,
m1_subset_1(k5_nat_lat,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) ).
fof(dt_k6_nat_lat,axiom,
( ~ v3_struct_0(k6_nat_lat)
& v10_lattices(k6_nat_lat)
& l3_lattices(k6_nat_lat) ) ).
fof(dt_k7_nat_lat,axiom,
m1_subset_1(k7_nat_lat,k1_zfmisc_1(k5_numbers)) ).
fof(dt_k8_nat_lat,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_nat_lat(k8_nat_lat(A),k1_numbers,k5_numbers,k7_nat_lat) ) ).
fof(dt_k9_nat_lat,axiom,
! [A] :
( m1_subset_1(A,k7_nat_lat)
=> m1_nat_lat(k9_nat_lat(A),k1_numbers,k5_numbers,k7_nat_lat) ) ).
fof(dt_k10_nat_lat,axiom,
( v1_funct_1(k10_nat_lat)
& v1_funct_2(k10_nat_lat,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat)
& m2_relset_1(k10_nat_lat,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) ) ).
fof(dt_k11_nat_lat,axiom,
( v1_funct_1(k11_nat_lat)
& v1_funct_2(k11_nat_lat,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat)
& m2_relset_1(k11_nat_lat,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) ) ).
fof(dt_k12_nat_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat)))
=> m1_nat_lat(k12_nat_lat(A),k1_numbers,k5_numbers,k7_nat_lat) ) ).
fof(dt_k13_nat_lat,axiom,
( ~ v3_struct_0(k13_nat_lat)
& v10_lattices(k13_nat_lat)
& l3_lattices(k13_nat_lat) ) ).
%------------------------------------------------------------------------------