TPTP Problem File: LAT339+1.p
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%------------------------------------------------------------------------------
% File : LAT339+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Dual Concept Lattices T05
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Sch01] Schwarzweller (2001), A Characterization of Concept La
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t5_conlat_2 [Urb08]
% Status : Theorem
% Rating : 0.67 v8.2.0, 0.75 v8.1.0, 0.69 v7.5.0, 0.78 v7.4.0, 0.70 v7.3.0, 0.72 v7.1.0, 0.61 v7.0.0, 0.67 v6.4.0, 0.65 v6.3.0, 0.62 v6.2.0, 0.72 v6.1.0, 0.83 v6.0.0, 0.74 v5.5.0, 0.81 v5.4.0, 0.82 v5.3.0, 0.81 v5.2.0, 0.70 v5.1.0, 0.76 v5.0.0, 0.79 v4.1.0, 0.83 v4.0.1, 0.87 v4.0.0, 0.88 v3.7.0, 0.85 v3.5.0, 0.84 v3.4.0
% Syntax : Number of formulae : 120 ( 25 unt; 0 def)
% Number of atoms : 516 ( 25 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 495 ( 99 ~; 1 |; 278 &)
% ( 8 <=>; 109 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 50 ( 48 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 1 con; 0-3 aty)
% Number of variables : 203 ( 171 !; 32 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Normal version: includes the axioms (which may be theorems from
% other articles) and background that are possibly necessary.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
fof(t5_conlat_2,conjecture,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k3_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k6_conlat_1(A)
& k2_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k5_conlat_1(A) ) ) ).
fof(abstractness_v3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( v3_lattices(A)
=> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ).
fof(abstractness_v6_conlat_1,axiom,
! [A,B] :
( ( l1_conlat_1(A)
& l3_conlat_1(B,A) )
=> ( v6_conlat_1(B,A)
=> B = g3_conlat_1(A,u4_conlat_1(A,B),u5_conlat_1(A,B)) ) ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ) ).
fof(cc1_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_partfun1(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B) ) ) ) ).
fof(cc1_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(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) ) ) ) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc2_conlat_1,axiom,
! [A] :
( ( v3_conlat_1(A)
& l1_conlat_1(A) )
=> ! [B] :
( l3_conlat_1(B,A)
=> v8_conlat_1(B,A) ) ) ).
fof(cc2_lattices,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) )
=> ( ~ v3_struct_0(A)
& v10_lattices(A) ) ) ) ).
fof(cc3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v13_lattices(A)
& v14_lattices(A) )
=> ( ~ v3_struct_0(A)
& v15_lattices(A) ) ) ) ).
fof(cc4_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v15_lattices(A) )
=> ( ~ v3_struct_0(A)
& v13_lattices(A)
& v14_lattices(A) ) ) ) ).
fof(cc5_funct_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_partfun1(C,A,B)
& v1_funct_2(C,A,B) ) ) ) ) ).
fof(cc6_funct_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_partfun1(C,A,B)
& v1_funct_2(C,A,B) ) ) ) ) ).
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(d1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k1_conlat_2(A,B) = 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(d24_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k11_conlat_1(A)))
=> k12_conlat_1(A,B) = B ) ) ).
fof(d2_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> k2_conlat_2(A,B) = k16_lattice3(k11_conlat_1(A),B) ) ) ).
fof(d3_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> k3_conlat_2(A,B) = k15_lattice3(k11_conlat_1(A),B) ) ) ).
fof(dt_g3_conlat_1,axiom,
! [A,B,C] :
( ( l1_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
& m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) )
=> ( v6_conlat_1(g3_conlat_1(A,B,C),A)
& l3_conlat_1(g3_conlat_1(A,B,C),A) ) ) ).
fof(dt_g3_lattices,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( v3_lattices(g3_lattices(A,B,C))
& l3_lattices(g3_lattices(A,B,C)) ) ) ).
fof(dt_k11_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& l3_lattices(k11_conlat_1(A)) ) ) ).
fof(dt_k12_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) )
=> ( v6_conlat_1(k12_conlat_1(A,B),A)
& ~ v7_conlat_1(k12_conlat_1(A,B),A)
& v9_conlat_1(k12_conlat_1(A,B),A)
& l3_conlat_1(k12_conlat_1(A,B),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(dt_k1_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> m1_subset_1(k1_conlat_2(A,B),u1_struct_0(k11_conlat_1(A))) ) ).
fof(dt_k1_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( ~ v7_conlat_1(k2_conlat_2(A,B),A)
& v9_conlat_1(k2_conlat_2(A,B),A)
& l3_conlat_1(k2_conlat_2(A,B),A) ) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( ~ v7_conlat_1(k3_conlat_2(A,B),A)
& v9_conlat_1(k3_conlat_2(A,B),A)
& l3_conlat_1(k3_conlat_2(A,B),A) ) ) ).
fof(dt_k5_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v6_conlat_1(k5_conlat_1(A),A)
& ~ v7_conlat_1(k5_conlat_1(A),A)
& v9_conlat_1(k5_conlat_1(A),A)
& v10_conlat_1(k5_conlat_1(A),A)
& l3_conlat_1(k5_conlat_1(A),A) ) ) ).
fof(dt_k5_lattices,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lattices(A) )
=> m1_subset_1(k5_lattices(A),u1_struct_0(A)) ) ).
fof(dt_k6_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v6_conlat_1(k6_conlat_1(A),A)
& ~ v7_conlat_1(k6_conlat_1(A),A)
& v9_conlat_1(k6_conlat_1(A),A)
& v11_conlat_1(k6_conlat_1(A),A)
& l3_conlat_1(k6_conlat_1(A),A) ) ) ).
fof(dt_k6_lattices,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_lattices(A) )
=> m1_subset_1(k6_lattices(A),u1_struct_0(A)) ) ).
fof(dt_l1_conlat_1,axiom,
$true ).
fof(dt_l1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_l2_conlat_1,axiom,
! [A] :
( l2_conlat_1(A)
=> l1_conlat_1(A) ) ).
fof(dt_l2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> l1_struct_0(A) ) ).
fof(dt_l3_conlat_1,axiom,
$true ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l1_lattices(A)
& l2_lattices(A) ) ) ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
fof(dt_u1_conlat_1,axiom,
$true ).
fof(dt_u1_lattices,axiom,
! [A] :
( l1_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))
& m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(dt_u2_conlat_1,axiom,
$true ).
fof(dt_u2_lattices,axiom,
! [A] :
( l2_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))
& m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u4_conlat_1,axiom,
! [A,B] :
( ( l1_conlat_1(A)
& l3_conlat_1(B,A) )
=> m1_subset_1(u4_conlat_1(A,B),k1_zfmisc_1(u1_conlat_1(A))) ) ).
fof(dt_u5_conlat_1,axiom,
! [A,B] :
( ( l1_conlat_1(A)
& l3_conlat_1(B,A) )
=> m1_subset_1(u5_conlat_1(A,B),k1_zfmisc_1(u2_conlat_1(A))) ) ).
fof(existence_l1_conlat_1,axiom,
? [A] : l1_conlat_1(A) ).
fof(existence_l1_lattices,axiom,
? [A] : l1_lattices(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_l2_conlat_1,axiom,
? [A] : l2_conlat_1(A) ).
fof(existence_l2_lattices,axiom,
? [A] : l2_lattices(A) ).
fof(existence_l3_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ? [B] : l3_conlat_1(B,A) ) ).
fof(existence_l3_lattices,axiom,
? [A] : l3_lattices(A) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(fc1_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ~ v1_xboole_0(u2_conlat_1(A)) ) ).
fof(fc1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v13_lattices(k11_conlat_1(A))
& v14_lattices(k11_conlat_1(A))
& v15_lattices(k11_conlat_1(A))
& v4_lattice3(k11_conlat_1(A)) ) ) ).
fof(fc1_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> ( v1_xboole_0(k1_pre_topc(A))
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A)) ) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0) ).
fof(fc2_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ~ v1_xboole_0(u1_conlat_1(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(fc3_lattices,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ~ v3_struct_0(g3_lattices(A,B,C))
& v3_lattices(g3_lattices(A,B,C)) ) ) ).
fof(fc4_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(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(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ).
fof(fc5_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v4_lattice3(k11_conlat_1(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(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(free_g3_conlat_1,axiom,
! [A,B,C] :
( ( l1_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
& m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) )
=> ! [D,E,F] :
( g3_conlat_1(A,B,C) = g3_conlat_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(free_g3_lattices,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D,E,F] :
( g3_lattices(A,B,C) = g3_lattices(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(rc10_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ? [B] :
( l3_conlat_1(B,A)
& v6_conlat_1(B,A) ) ) ).
fof(rc11_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ? [B] :
( l3_conlat_1(B,A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A) ) ) ).
fof(rc11_lattices,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)
& v14_lattices(A)
& v15_lattices(A) ) ).
fof(rc12_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ? [B] :
( l3_conlat_1(B,A)
& v6_conlat_1(B,A)
& v8_conlat_1(B,A) ) ) ).
fof(rc13_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ? [B] :
( l3_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A) ) ) ).
fof(rc14_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ? [B] :
( l3_conlat_1(B,A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A) ) ) ).
fof(rc15_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ? [B] :
( l3_conlat_1(B,A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& v10_conlat_1(B,A) ) ) ).
fof(rc16_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ? [B] :
( l3_conlat_1(B,A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& v11_conlat_1(B,A) ) ) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( m1_relset_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,A,B) ) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) ) ) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A) ).
fof(rc2_partfun1,axiom,
! [A,B] :
? [C] :
( m1_relset_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C) ) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& v1_xboole_0(B) ) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A) ).
fof(rc3_lattices,axiom,
? [A] :
( l3_lattices(A)
& v3_lattices(A) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc6_lattices,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v3_lattices(A) ) ).
fof(rc8_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc9_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc9_lattices,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) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(redefinition_r3_lattices,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_lattices(A,B,C)
<=> r1_lattices(A,B,C) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(reflexivity_r3_lattices,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r3_lattices(A,B,B) ) ).
fof(t1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k5_lattices(k11_conlat_1(A)) = k6_conlat_1(A)
& k6_lattices(k11_conlat_1(A)) = k5_conlat_1(A) ) ) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( v1_xboole_0(B)
| r2_hidden(A,B) ) ) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ) ).
fof(t34_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ( r2_conlat_1(A,B,k5_conlat_1(A))
& r2_conlat_1(A,k6_conlat_1(A),B) ) ) ) ).
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(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t47_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k11_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k11_conlat_1(A)))
=> ( r3_lattices(k11_conlat_1(A),B,C)
<=> r2_conlat_1(A,k12_conlat_1(A,B),k12_conlat_1(A,C)) ) ) ) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C)) )
=> m1_subset_1(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(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
%------------------------------------------------------------------------------