SET007 Axioms: SET007+253.ax
%------------------------------------------------------------------------------
% File : SET007+253 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Finite Join and Finite Meet, and Dual 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 : lattice2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 108 ( 9 unt; 0 def)
% Number of atoms : 919 ( 75 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 952 ( 141 ~; 8 |; 451 &)
% ( 8 <=>; 344 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 1 con; 0-6 aty)
% Number of variables : 300 ( 295 !; 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_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ) ).
fof(fc2_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_lattices(A) )
=> ( v1_relat_1(u2_lattices(A))
& v1_funct_1(u2_lattices(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(fc3_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_lattices(A)
& l2_lattices(A) )
=> ( v1_relat_1(u2_lattices(A))
& v1_funct_1(u2_lattices(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v2_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(fc4_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A) )
=> ( v1_relat_1(u1_lattices(A))
& v1_funct_1(u1_lattices(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_binop_1(u1_lattices(A),u1_struct_0(A))
& v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(fc5_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_lattices(A)
& l1_lattices(A) )
=> ( v1_relat_1(u1_lattices(A))
& v1_funct_1(u1_lattices(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v2_binop_1(u1_lattices(A),u1_struct_0(A))
& v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(fc6_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A)) ) ) ).
fof(rc1_lattice2,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)
& v1_lattice2(A) ) ).
fof(cc1_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v1_lattice2(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)
& v3_filter_0(A) ) ) ) ).
fof(cc2_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& v3_filter_0(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_lattice2(A) ) ) ) ).
fof(rc2_lattice2,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)
& v13_lattices(A)
& v3_filter_0(A)
& v1_lattice2(A) ) ).
fof(cc3_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v6_group_1(A)
& v10_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) ) ) ) ).
fof(cc4_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v6_group_1(A)
& v10_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)
& v14_lattices(A) ) ) ) ).
fof(cc5_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v6_group_1(A)
& v10_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) ) ) ) ).
fof(cc6_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v6_group_1(A)
& v10_lattices(A)
& v11_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)
& v3_filter_0(A)
& v1_lattice2(A) ) ) ) ).
fof(t1_lattice2,axiom,
$true ).
fof(t2_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> k1_relat_1(k2_partfun1(A,B,D,C)) = C ) ) ) ).
fof(t3_lattice2,axiom,
$true ).
fof(t4_lattice2,axiom,
$true ).
fof(t5_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( k2_partfun1(A,B,D,C) = k2_partfun1(A,B,E,C)
<=> ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,C)
=> k1_funct_1(E,F) = k1_funct_1(D,F) ) ) ) ) ) ) ) ).
fof(t6_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( v1_funct_1(k1_funct_4(C,k2_partfun1(A,B,D,E)))
& v1_funct_2(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B)
& m2_relset_1(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B) ) ) ) ) ).
fof(t7_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> k1_funct_4(k2_partfun1(A,B,D,C),E) = E ) ) ) ) ).
fof(t8_lattice2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(B,A)
=> k1_funct_4(A,B) = A ) ) ) ).
fof(t9_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> k1_funct_4(D,k2_partfun1(A,B,D,C)) = D ) ) ) ).
fof(t10_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,C)
=> k1_funct_1(D,F) = k1_funct_1(E,F) ) )
=> k1_funct_4(E,k2_partfun1(A,B,D,C)) = E ) ) ) ) ) ).
fof(t11_lattice2,axiom,
$true ).
fof(t12_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(A))
=> k1_funct_4(k2_partfun1(A,B,C,E),D) = D ) ) ) ) ).
fof(t13_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(A))
=> k1_relat_1(k2_partfun1(A,B,C,D)) = D ) ) ) ).
fof(t14_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(A))
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,E)
=> k1_funct_1(C,F) = k1_funct_1(D,F) ) )
=> k1_funct_4(D,k2_partfun1(A,B,C,E)) = D ) ) ) ) ) ).
fof(t15_lattice2,axiom,
$true ).
fof(t16_lattice2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(A))
=> ( k2_partfun1(A,B,C,E) = k2_partfun1(A,B,D,E)
=> k2_funct_2(A,B,C,E) = k2_funct_2(A,B,D,E) ) ) ) ) ) ).
fof(d1_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( r1_lattice2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,D,E)) = D ) ) ) ) ) ) ).
fof(t17_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ( v1_binop_1(u2_lattices(A),u1_struct_0(A))
& v2_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_binop_1(u1_lattices(A),u1_struct_0(A))
& v2_binop_1(u1_lattices(A),u1_struct_0(A))
& r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
& r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) )
=> v10_lattices(A) ) ) ).
fof(d2_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> k1_lattice2(A) = g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) ).
fof(t18_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( u1_struct_0(A) = u1_struct_0(k1_lattice2(A))
& u2_lattices(A) = u1_lattices(k1_lattice2(A))
& u1_lattices(A) = u2_lattices(k1_lattice2(A)) ) ) ).
fof(t19_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_lattices(A)
& l3_lattices(A) )
=> k1_lattice2(k1_lattice2(A)) = A ) ).
fof(t20_lattice2,axiom,
$true ).
fof(t21_lattice2,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))
=> k3_lattices(A,B,C) = C )
=> B = k5_lattices(A) ) ) ) ).
fof(t22_lattice2,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))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = C )
=> B = k5_lattices(A) ) ) ) ).
fof(t23_lattice2,axiom,
$true ).
fof(t24_lattice2,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))
=> k4_lattices(A,B,C) = C )
=> B = k6_lattices(A) ) ) ) ).
fof(t25_lattice2,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))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = C )
=> B = k6_lattices(A) ) ) ) ).
fof(t26_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> v3_binop_1(u2_lattices(A),u1_struct_0(A)) ) ).
fof(t27_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_lattices(A) )
=> v1_binop_1(u2_lattices(A),u1_struct_0(A)) ) ).
fof(t28_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_setwiseo(u2_lattices(A),u1_struct_0(A))
=> k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)) ) ) ).
fof(t29_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_lattices(A)
& l2_lattices(A) )
=> v2_binop_1(u2_lattices(A),u1_struct_0(A)) ) ).
fof(t30_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> v3_binop_1(u1_lattices(A),u1_struct_0(A)) ) ).
fof(t31_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A) )
=> v1_binop_1(u1_lattices(A),u1_struct_0(A)) ) ).
fof(t32_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_lattices(A)
& l1_lattices(A) )
=> v2_binop_1(u1_lattices(A),u1_struct_0(A)) ) ).
fof(t33_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_setwiseo(u1_lattices(A),u1_struct_0(A))
=> k6_lattices(A) = k3_binop_1(u1_struct_0(A),u1_lattices(A)) ) ) ).
fof(t34_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> r6_binop_1(u1_struct_0(A),u2_lattices(A),u2_lattices(A)) ) ).
fof(t35_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A) )
=> r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ).
fof(t36_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
=> v11_lattices(A) ) ) ).
fof(t37_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A) )
=> r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) ) ).
fof(t38_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A))
=> v11_lattices(A) ) ) ).
fof(t39_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> r6_binop_1(u1_struct_0(A),u1_lattices(A),u1_lattices(A)) ) ).
fof(t40_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ).
fof(t41_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) ).
fof(d3_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k2_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u2_lattices(B),C,D) ) ) ) ) ).
fof(d4_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k3_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u1_lattices(B),C,D) ) ) ) ) ).
fof(t42_lattice2,axiom,
$true ).
fof(t43_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u1_struct_0(A))
& m2_relset_1(E,B,u1_struct_0(A)) )
=> ( r2_hidden(C,D)
=> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),E,C),k2_lattice2(B,A,D,E)) ) ) ) ) ) ) ).
fof(t44_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( ? [F] :
( m1_subset_1(F,C)
& r2_hidden(F,D)
& r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) )
=> r3_lattices(A,B,k2_lattice2(C,A,D,E)) ) ) ) ) ) ) ).
fof(t45_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,C)
=> ( r2_hidden(F,D)
=> k8_funct_2(C,u1_struct_0(A),E,F) = B ) )
=> ( D = k1_xboole_0
| k2_lattice2(C,A,D,E) = B ) ) ) ) ) ) ) ).
fof(t46_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( r3_lattices(A,k2_lattice2(C,A,D,E),B)
=> ! [F] :
( m1_subset_1(F,C)
=> ( r2_hidden(F,D)
=> r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) ) ) ) ) ) ) ) ) ).
fof(t47_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,C)
=> ( r2_hidden(F,D)
=> r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) ) )
=> ( D = k1_xboole_0
| r3_lattices(A,k2_lattice2(C,A,D,E),B) ) ) ) ) ) ) ) ).
fof(t48_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m2_relset_1(D,B,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u1_struct_0(A))
& m2_relset_1(E,B,u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,B)
=> ( r2_hidden(F,C)
=> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F)) ) )
=> ( C = k1_xboole_0
| r3_lattices(A,k2_lattice2(B,A,C,D),k2_lattice2(B,A,C,E)) ) ) ) ) ) ) ) ).
fof(t49_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m2_relset_1(D,B,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u1_struct_0(A))
& m2_relset_1(E,B,u1_struct_0(A)) )
=> ( k2_partfun1(B,u1_struct_0(A),D,C) = k2_partfun1(B,u1_struct_0(A),E,C)
=> ( C = k1_xboole_0
| k2_lattice2(B,A,C,D) = k2_lattice2(B,A,C,E) ) ) ) ) ) ) ) ).
fof(t50_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( D != k1_xboole_0
=> k3_lattices(A,B,k2_lattice2(C,A,D,E)) = k2_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u2_lattices(A),B,E)) ) ) ) ) ) ) ).
fof(t51_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(k1_lattice2(B)))
& m2_relset_1(E,A,u1_struct_0(k1_lattice2(B))) )
=> ( D = E
=> ( k2_lattice2(A,B,C,D) = k3_lattice2(A,k1_lattice2(B),C,E)
& k3_lattice2(A,B,C,D) = k2_lattice2(A,k1_lattice2(B),C,E) ) ) ) ) ) ) ) ).
fof(t52_lattice2,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(k1_lattice2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
=> ( ( B = D
& C = E )
=> ( k4_lattices(A,B,C) = k3_lattices(k1_lattice2(A),D,E)
& k3_lattices(A,B,C) = k4_lattices(k1_lattice2(A),D,E) ) ) ) ) ) ) ) ).
fof(t53_lattice2,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)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_lattice2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
=> ( ( B = D
& C = E )
=> r3_lattices(k1_lattice2(A),E,D) ) ) ) ) ) ) ) ).
fof(t54_lattice2,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(k1_lattice2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
=> ( ( r3_lattices(k1_lattice2(A),D,E)
& B = D
& C = E )
=> r3_lattices(A,C,B) ) ) ) ) ) ) ).
fof(t55_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u1_struct_0(A))
& m2_relset_1(E,B,u1_struct_0(A)) )
=> ( r2_hidden(C,D)
=> r3_lattices(A,k3_lattice2(B,A,D,E),k8_funct_2(B,u1_struct_0(A),E,C)) ) ) ) ) ) ) ).
fof(t56_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( ? [F] :
( m1_subset_1(F,C)
& r2_hidden(F,D)
& r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) )
=> r3_lattices(A,k3_lattice2(C,A,D,E),B) ) ) ) ) ) ) ).
fof(t57_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,C)
=> ( r2_hidden(F,D)
=> k8_funct_2(C,u1_struct_0(A),E,F) = B ) )
=> ( D = k1_xboole_0
| k3_lattice2(C,A,D,E) = B ) ) ) ) ) ) ) ).
fof(t58_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( D != k1_xboole_0
=> k4_lattices(A,B,k3_lattice2(C,A,D,E)) = k3_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u1_lattices(A),B,E)) ) ) ) ) ) ) ).
fof(t59_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( r3_lattices(A,B,k3_lattice2(C,A,D,E))
=> ! [F] :
( m1_subset_1(F,C)
=> ( r2_hidden(F,D)
=> r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) ) ) ) ) ) ) ) ) ).
fof(t60_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m2_relset_1(D,B,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u1_struct_0(A))
& m2_relset_1(E,B,u1_struct_0(A)) )
=> ( k2_partfun1(B,u1_struct_0(A),D,C) = k2_partfun1(B,u1_struct_0(A),E,C)
=> ( C = k1_xboole_0
| k3_lattice2(B,A,C,D) = k3_lattice2(B,A,C,E) ) ) ) ) ) ) ) ).
fof(t61_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(C))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,u1_struct_0(A))
& m2_relset_1(E,C,u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,C)
=> ( r2_hidden(F,D)
=> r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) ) )
=> ( D = k1_xboole_0
| r3_lattices(A,B,k3_lattice2(C,A,D,E)) ) ) ) ) ) ) ) ).
fof(t62_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(A))
& m2_relset_1(D,B,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u1_struct_0(A))
& m2_relset_1(E,B,u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,B)
=> ( r2_hidden(F,C)
=> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F)) ) )
=> ( C = k1_xboole_0
| r3_lattices(A,k3_lattice2(B,A,C,D),k3_lattice2(B,A,C,E)) ) ) ) ) ) ) ) ).
fof(t63_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v13_lattices(A)
<=> v14_lattices(k1_lattice2(A)) ) ) ).
fof(t64_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v14_lattices(A)
<=> v13_lattices(k1_lattice2(A)) ) ) ).
fof(t65_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A) )
<=> ( ~ v3_struct_0(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& v11_lattices(k1_lattice2(A))
& l3_lattices(k1_lattice2(A)) ) ) ) ).
fof(t66_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> r3_binop_1(u1_struct_0(A),k5_lattices(A),u2_lattices(A)) ) ).
fof(t67_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> v1_setwiseo(u2_lattices(A),u1_struct_0(A)) ) ).
fof(t68_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)) ) ).
fof(t69_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v13_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ( k2_partfun1(A,u1_struct_0(C),D,B) = k2_partfun1(A,u1_struct_0(C),E,B)
=> k2_lattice2(A,C,B,D) = k2_lattice2(A,C,B,E) ) ) ) ) ) ) ).
fof(t70_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v13_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,B)
=> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),E) ) )
=> r3_lattices(C,k2_lattice2(A,C,B,D),E) ) ) ) ) ) ) ).
fof(t71_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v13_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,B)
=> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F)) ) )
=> r3_lattices(C,k2_lattice2(A,C,B,D),k2_lattice2(A,C,B,E)) ) ) ) ) ) ) ).
fof(t72_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> r3_binop_1(u1_struct_0(A),k6_lattices(A),u1_lattices(A)) ) ).
fof(t73_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> v1_setwiseo(u1_lattices(A),u1_struct_0(A)) ) ).
fof(t74_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> k6_lattices(A) = k3_binop_1(u1_struct_0(A),u1_lattices(A)) ) ).
fof(t75_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v14_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ( k2_partfun1(A,u1_struct_0(C),D,B) = k2_partfun1(A,u1_struct_0(C),E,B)
=> k3_lattice2(A,C,B,D) = k3_lattice2(A,C,B,E) ) ) ) ) ) ) ).
fof(t76_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v14_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,B)
=> r3_lattices(C,E,k8_funct_2(A,u1_struct_0(C),D,F)) ) )
=> r3_lattices(C,E,k3_lattice2(A,C,B,D)) ) ) ) ) ) ) ).
fof(t77_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v14_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,B)
=> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F)) ) )
=> r3_lattices(C,k3_lattice2(A,C,B,D),k3_lattice2(A,C,B,E)) ) ) ) ) ) ) ).
fof(t78_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> k5_lattices(A) = k6_lattices(k1_lattice2(A)) ) ).
fof(t79_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> k6_lattices(A) = k5_lattices(k1_lattice2(A)) ) ).
fof(t80_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) ).
fof(t81_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v11_lattices(C)
& v13_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k2_binop_1(u1_struct_0(C),u1_struct_0(C),u1_struct_0(C),u1_lattices(C),E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)) ) ) ) ) ) ).
fof(t82_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v11_lattices(C)
& v13_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( ! [G] :
( m1_subset_1(G,A)
=> ( r2_hidden(G,B)
=> k8_funct_2(A,u1_struct_0(C),D,G) = k4_lattices(C,F,k8_funct_2(A,u1_struct_0(C),E,G)) ) )
=> k4_lattices(C,F,k2_lattice2(A,C,B,E)) = k2_lattice2(A,C,B,D) ) ) ) ) ) ) ) ).
fof(t83_lattice2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v11_lattices(C)
& v13_lattices(C)
& l3_lattices(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k4_lattices(C,E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)) ) ) ) ) ) ).
fof(d5_lattice2,axiom,
$true ).
fof(d6_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_lattice2(A)
<=> ( v3_filter_0(A)
& v13_lattices(A) ) ) ) ).
fof(t84_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v1_lattice2(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_lattices(A,k4_lattices(A,B,D),C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r3_lattices(A,k4_lattices(A,B,E),C)
=> r3_lattices(A,E,D) ) ) ) ) ) ) ) ).
fof(t85_lattice2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v6_group_1(A)
<=> v6_group_1(k1_lattice2(A)) ) ) ).
fof(dt_k1_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( v3_lattices(k1_lattice2(A))
& l3_lattices(k1_lattice2(A)) ) ) ).
fof(dt_k2_lattice2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_subset_1(C,k5_finsub_1(A))
& v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m1_relset_1(D,A,u1_struct_0(B)) )
=> m1_subset_1(k2_lattice2(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k3_lattice2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_subset_1(C,k5_finsub_1(A))
& v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m1_relset_1(D,A,u1_struct_0(B)) )
=> m1_subset_1(k3_lattice2(A,B,C,D),u1_struct_0(B)) ) ).
%------------------------------------------------------------------------------