SET007 Axioms: SET007+567.ax
%------------------------------------------------------------------------------
% File : SET007+567 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Concept 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 : conlat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 141 ( 12 unt; 0 def)
% Number of atoms : 842 ( 86 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 885 ( 184 ~; 2 |; 421 &)
% ( 35 <=>; 243 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 1 con; 0-5 aty)
% Number of variables : 306 ( 266 !; 40 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_conlat_1,axiom,
? [A] :
( l1_conlat_1(A)
& v1_conlat_1(A) ) ).
fof(rc2_conlat_1,axiom,
? [A] :
( l1_conlat_1(A)
& v1_conlat_1(A)
& ~ v2_conlat_1(A) ) ).
fof(rc3_conlat_1,axiom,
? [A] :
( l1_conlat_1(A)
& v1_conlat_1(A)
& ~ v3_conlat_1(A) ) ).
fof(rc4_conlat_1,axiom,
? [A] :
( l1_conlat_1(A)
& v1_conlat_1(A)
& v2_conlat_1(A)
& v3_conlat_1(A) ) ).
fof(rc5_conlat_1,axiom,
? [A] :
( l2_conlat_1(A)
& v4_conlat_1(A) ) ).
fof(rc6_conlat_1,axiom,
? [A] :
( l2_conlat_1(A)
& ~ v2_conlat_1(A)
& v4_conlat_1(A) ) ).
fof(rc7_conlat_1,axiom,
? [A] :
( l2_conlat_1(A)
& ~ v3_conlat_1(A)
& v4_conlat_1(A) ) ).
fof(fc1_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ~ v1_xboole_0(u2_conlat_1(A)) ) ).
fof(fc2_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l1_conlat_1(A) )
=> ~ v1_xboole_0(u1_conlat_1(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(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(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(cc1_conlat_1,axiom,
! [A] :
( ( v2_conlat_1(A)
& l1_conlat_1(A) )
=> ! [B] :
( l3_conlat_1(B,A)
=> v7_conlat_1(B,A) ) ) ).
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(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(fc3_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ~ v1_xboole_0(k7_conlat_1(A)) ) ).
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(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(d1_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ( v2_conlat_1(A)
<=> ( v1_xboole_0(u1_conlat_1(A))
& v1_xboole_0(u2_conlat_1(A)) ) ) ) ).
fof(d2_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ( v3_conlat_1(A)
<=> ( v1_xboole_0(u1_conlat_1(A))
| v1_xboole_0(u2_conlat_1(A)) ) ) ) ).
fof(d3_conlat_1,axiom,
$true ).
fof(d4_conlat_1,axiom,
$true ).
fof(d5_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_conlat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_conlat_1(A))
=> ( r1_conlat_1(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u3_conlat_1(A)) ) ) ) ) ).
fof(t3_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),C),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)) ) ) ) ) ).
fof(t4_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B)) ) ) ) ) ).
fof(t5_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> r1_tarski(B,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))) ) ) ).
fof(t6_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> r1_tarski(B,k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))) ) ) ).
fof(t7_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B) = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))) ) ) ).
fof(t8_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B) = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))) ) ) ).
fof(t9_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
=> ( r1_tarski(B,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C))
<=> r1_tarski(k12_mcart_1(u1_conlat_1(A),u2_conlat_1(A),B,C),u3_conlat_1(A)) ) ) ) ) ).
fof(t10_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
=> ( r1_tarski(C,k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))
<=> r1_tarski(k12_mcart_1(u1_conlat_1(A),u2_conlat_1(A),B,C),u3_conlat_1(A)) ) ) ) ) ).
fof(t11_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
=> ( r1_tarski(B,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C))
<=> r1_tarski(C,k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)) ) ) ) ) ).
fof(d8_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k3_conlat_1(A) = k1_conlat_1(A) ) ).
fof(d9_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k4_conlat_1(A) = k2_conlat_1(A) ) ).
fof(d10_conlat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel_1(C,A,B)
=> ( v5_conlat_1(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A))
& C = k1_waybel_1(A,B,D,E)
& v5_waybel_0(D,A,B)
& v5_waybel_0(E,B,A)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(B))
=> ( r1_orders_2(A,F,k1_waybel_0(B,A,E,k1_waybel_0(A,B,D,F)))
& r1_orders_2(B,H,k1_waybel_0(A,B,D,k1_waybel_0(B,A,E,H))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_conlat_1,axiom,
$true ).
fof(t13_conlat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel_1(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( C = k1_waybel_1(A,B,D,E)
=> ( v5_conlat_1(C,A,B)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( r3_orders_2(A,F,k1_waybel_0(B,A,E,G))
<=> r3_orders_2(B,G,k1_waybel_0(A,B,D,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_conlat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel_1(C,A,B)
=> ( v5_conlat_1(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( C = k1_waybel_1(A,B,D,E)
=> ( D = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),D,E),D)
& E = k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),E,D),E) ) ) ) ) ) ) ) ) ).
fof(t15_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> v5_conlat_1(k1_waybel_1(k3_yellow_1(u1_conlat_1(A)),k3_yellow_1(u2_conlat_1(A)),k3_conlat_1(A),k4_conlat_1(A)),k3_yellow_1(u1_conlat_1(A)),k3_yellow_1(u2_conlat_1(A))) ) ).
fof(t16_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k4_subset_1(u1_conlat_1(A),B,C)) = k5_subset_1(u2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),C)) ) ) ) ).
fof(t17_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k4_subset_1(u2_conlat_1(A),B,C)) = k5_subset_1(u1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C)) ) ) ) ).
fof(t18_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k1_funct_1(k1_conlat_1(A),k1_xboole_0) = u2_conlat_1(A) ) ).
fof(t19_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k1_funct_1(k2_conlat_1(A),k1_xboole_0) = u1_conlat_1(A) ) ).
fof(d11_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ! [B] :
( l3_conlat_1(B,A)
=> ( v7_conlat_1(B,A)
<=> ( v1_xboole_0(u4_conlat_1(A,B))
& v1_xboole_0(u5_conlat_1(A,B)) ) ) ) ) ).
fof(d12_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ! [B] :
( l3_conlat_1(B,A)
=> ( v8_conlat_1(B,A)
<=> ( v1_xboole_0(u4_conlat_1(A,B))
| v1_xboole_0(u5_conlat_1(A,B)) ) ) ) ) ).
fof(d13_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( l3_conlat_1(B,A)
=> ( v9_conlat_1(B,A)
<=> ( k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),u4_conlat_1(A,B)) = u5_conlat_1(A,B)
& k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),u5_conlat_1(A,B)) = u4_conlat_1(A,B) ) ) ) ) ).
fof(t20_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ( ~ v7_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),A)
& v9_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),A)
& l3_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A)))
=> ( ( ~ v7_conlat_1(g3_conlat_1(A,C,D),A)
& v9_conlat_1(g3_conlat_1(A,C,D),A)
& l3_conlat_1(g3_conlat_1(A,C,D),A)
& r1_tarski(B,C) )
=> r1_tarski(k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),C) ) ) ) ) ) ) ).
fof(t21_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> ( ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
& ~ v7_conlat_1(g3_conlat_1(A,B,C),A)
& v9_conlat_1(g3_conlat_1(A,B,C),A)
& l3_conlat_1(g3_conlat_1(A,B,C),A) )
<=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)) = B ) ) ) ).
fof(t22_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> ( ~ v7_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))),A)
& v9_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))),A)
& l3_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))),A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A)))
=> ( ( ~ v7_conlat_1(g3_conlat_1(A,C,D),A)
& v9_conlat_1(g3_conlat_1(A,C,D),A)
& l3_conlat_1(g3_conlat_1(A,C,D),A)
& r1_tarski(B,D) )
=> r1_tarski(k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B)),D) ) ) ) ) ) ) ).
fof(t23_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> ( ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
& ~ v7_conlat_1(g3_conlat_1(A,C,B),A)
& v9_conlat_1(g3_conlat_1(A,C,B),A)
& l3_conlat_1(g3_conlat_1(A,C,B),A) )
<=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B)) = B ) ) ) ).
fof(d14_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( l3_conlat_1(B,A)
=> ( v10_conlat_1(B,A)
<=> u4_conlat_1(A,B) = u1_conlat_1(A) ) ) ) ).
fof(d15_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( l3_conlat_1(B,A)
=> ( v11_conlat_1(B,A)
<=> u5_conlat_1(A,B) = u2_conlat_1(A) ) ) ) ).
fof(d16_conlat_1,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)
& v10_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ( B = k5_conlat_1(A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A)))
& B = g3_conlat_1(A,C,D)
& C = k1_funct_1(k2_conlat_1(A),k1_xboole_0)
& D = k1_funct_1(k1_conlat_1(A),k1_funct_1(k2_conlat_1(A),k1_xboole_0)) ) ) ) ) ) ).
fof(d17_conlat_1,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)
& v11_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ( B = k6_conlat_1(A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A)))
& B = g3_conlat_1(A,C,D)
& C = k1_funct_1(k2_conlat_1(A),k1_funct_1(k1_conlat_1(A),k1_xboole_0))
& D = k1_funct_1(k1_conlat_1(A),k1_xboole_0) ) ) ) ) ) ).
fof(t24_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( u4_conlat_1(A,k5_conlat_1(A)) = u1_conlat_1(A)
& u5_conlat_1(A,k6_conlat_1(A)) = u2_conlat_1(A) ) ) ).
fof(t25_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) )
=> ( ( u4_conlat_1(A,B) = k1_xboole_0
=> v11_conlat_1(B,A) )
& ( u5_conlat_1(A,B) = k1_xboole_0
=> v10_conlat_1(B,A) ) ) ) ) ).
fof(t26_conlat_1,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) )
=> ( ( u4_conlat_1(A,B) = k1_xboole_0
=> B = k6_conlat_1(A) )
& ( u5_conlat_1(A,B) = k1_xboole_0
=> B = k5_conlat_1(A) ) ) ) ) ).
fof(t27_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v8_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ~ ( ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A)
& ~ v10_conlat_1(B,A)
& ~ v11_conlat_1(B,A) ) ) ) ).
fof(t28_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v8_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ~ ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A)
& B != k5_conlat_1(A)
& B != k6_conlat_1(A) ) ) ) ).
fof(d18_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( m1_conlat_1(B,A)
<=> ! [C] :
( r2_hidden(C,B)
=> ( ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) ) ) ) ) ) ).
fof(d19_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) )
=> ! [C] :
( ( ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ( r2_conlat_1(A,B,C)
<=> r1_tarski(u4_conlat_1(A,B),u4_conlat_1(A,C)) ) ) ) ) ).
fof(t29_conlat_1,axiom,
$true ).
fof(t30_conlat_1,axiom,
$true ).
fof(t31_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) )
=> ! [C] :
( ( ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ( r2_conlat_1(A,B,C)
<=> r1_tarski(u5_conlat_1(A,C),u5_conlat_1(A,B)) ) ) ) ) ).
fof(t32_conlat_1,axiom,
$true ).
fof(t33_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) )
=> ! [C] :
( ( ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ( r2_conlat_1(A,C,B)
<=> r1_tarski(u5_conlat_1(A,B),u5_conlat_1(A,C)) ) ) ) ) ).
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(t35_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( r2_hidden(B,k8_conlat_1(A))
<=> ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) ) ) ) ).
fof(d21_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A))
& m2_relset_1(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) )
=> ( B = k9_conlat_1(A)
<=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ! [D] :
( ( v6_conlat_1(D,A)
& ~ v7_conlat_1(D,A)
& v9_conlat_1(D,A)
& l3_conlat_1(D,A) )
=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_conlat_1(A)))
& ? [F] :
( m1_subset_1(F,k1_zfmisc_1(u2_conlat_1(A)))
& k1_binop_1(B,C,D) = g3_conlat_1(A,E,F)
& E = k5_subset_1(u1_conlat_1(A),u4_conlat_1(A,C),u4_conlat_1(A,D))
& F = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k4_subset_1(u2_conlat_1(A),u5_conlat_1(A,C),u5_conlat_1(A,D)))) ) ) ) ) ) ) ) ).
fof(d22_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A))
& m2_relset_1(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) )
=> ( B = k10_conlat_1(A)
<=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ! [D] :
( ( v6_conlat_1(D,A)
& ~ v7_conlat_1(D,A)
& v9_conlat_1(D,A)
& l3_conlat_1(D,A) )
=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_conlat_1(A)))
& ? [F] :
( m1_subset_1(F,k1_zfmisc_1(u2_conlat_1(A)))
& k1_binop_1(B,C,D) = g3_conlat_1(A,E,F)
& E = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k4_subset_1(u1_conlat_1(A),u4_conlat_1(A,C),u4_conlat_1(A,D))))
& F = k5_subset_1(u2_conlat_1(A),u5_conlat_1(A,C),u5_conlat_1(A,D)) ) ) ) ) ) ) ) ).
fof(t36_conlat_1,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) )
=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> k1_binop_1(k9_conlat_1(A),B,C) = k1_binop_1(k9_conlat_1(A),C,B) ) ) ) ).
fof(t37_conlat_1,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) )
=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> k1_binop_1(k10_conlat_1(A),B,C) = k1_binop_1(k10_conlat_1(A),C,B) ) ) ) ).
fof(t38_conlat_1,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) )
=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ! [D] :
( ( v6_conlat_1(D,A)
& ~ v7_conlat_1(D,A)
& v9_conlat_1(D,A)
& l3_conlat_1(D,A) )
=> k1_binop_1(k9_conlat_1(A),B,k1_binop_1(k9_conlat_1(A),C,D)) = k1_binop_1(k9_conlat_1(A),k1_binop_1(k9_conlat_1(A),B,C),D) ) ) ) ) ).
fof(t39_conlat_1,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) )
=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> ! [D] :
( ( v6_conlat_1(D,A)
& ~ v7_conlat_1(D,A)
& v9_conlat_1(D,A)
& l3_conlat_1(D,A) )
=> k1_binop_1(k10_conlat_1(A),B,k1_binop_1(k10_conlat_1(A),C,D)) = k1_binop_1(k10_conlat_1(A),k1_binop_1(k10_conlat_1(A),B,C),D) ) ) ) ) ).
fof(t40_conlat_1,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) )
=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> k1_binop_1(k10_conlat_1(A),k1_binop_1(k9_conlat_1(A),B,C),C) = C ) ) ) ).
fof(t41_conlat_1,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) )
=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> k1_binop_1(k9_conlat_1(A),B,k1_binop_1(k10_conlat_1(A),B,C)) = B ) ) ) ).
fof(t42_conlat_1,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_binop_1(k9_conlat_1(A),B,k5_conlat_1(A)) = B ) ) ).
fof(t43_conlat_1,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_binop_1(k10_conlat_1(A),B,k5_conlat_1(A)) = k5_conlat_1(A) ) ) ).
fof(t44_conlat_1,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_binop_1(k10_conlat_1(A),B,k6_conlat_1(A)) = B ) ) ).
fof(t45_conlat_1,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_binop_1(k9_conlat_1(A),B,k6_conlat_1(A)) = k6_conlat_1(A) ) ) ).
fof(d23_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k11_conlat_1(A) = g3_lattices(k8_conlat_1(A),k10_conlat_1(A),k9_conlat_1(A)) ) ).
fof(t46_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& l3_lattices(k11_conlat_1(A)) ) ) ).
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(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(t48_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v4_lattice3(k11_conlat_1(A))
& l3_lattices(k11_conlat_1(A)) ) ) ).
fof(dt_m1_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_conlat_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(existence_m1_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ? [B] : m1_conlat_1(B,A) ) ).
fof(dt_m2_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_conlat_1(B,A) )
=> ! [C] :
( m2_conlat_1(C,A,B)
=> ( ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) ) ) ) ).
fof(existence_m2_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_conlat_1(B,A) )
=> ? [C] : m2_conlat_1(C,A,B) ) ).
fof(redefinition_m2_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_conlat_1(B,A) )
=> ! [C] :
( m2_conlat_1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m3_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ! [C] :
( m3_conlat_1(C,A,B)
=> ( ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) ) ) ) ).
fof(existence_m3_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ? [C] : m3_conlat_1(C,A,B) ) ).
fof(redefinition_m3_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ! [C] :
( m3_conlat_1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_l1_conlat_1,axiom,
$true ).
fof(existence_l1_conlat_1,axiom,
? [A] : l1_conlat_1(A) ).
fof(dt_l2_conlat_1,axiom,
! [A] :
( l2_conlat_1(A)
=> l1_conlat_1(A) ) ).
fof(existence_l2_conlat_1,axiom,
? [A] : l2_conlat_1(A) ).
fof(dt_l3_conlat_1,axiom,
$true ).
fof(existence_l3_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ? [B] : l3_conlat_1(B,A) ) ).
fof(abstractness_v1_conlat_1,axiom,
! [A] :
( l1_conlat_1(A)
=> ( v1_conlat_1(A)
=> A = g1_conlat_1(u1_conlat_1(A),u2_conlat_1(A)) ) ) ).
fof(abstractness_v4_conlat_1,axiom,
! [A] :
( l2_conlat_1(A)
=> ( v4_conlat_1(A)
=> A = g2_conlat_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(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(dt_k1_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k1_conlat_1(A))
& v1_funct_2(k1_conlat_1(A),k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)))
& m2_relset_1(k1_conlat_1(A),k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) ) ) ).
fof(dt_k2_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k2_conlat_1(A))
& v1_funct_2(k2_conlat_1(A),k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)))
& m2_relset_1(k2_conlat_1(A),k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) ) ) ).
fof(dt_k3_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k3_conlat_1(A))
& v1_funct_2(k3_conlat_1(A),u1_struct_0(k3_yellow_1(u1_conlat_1(A))),u1_struct_0(k3_yellow_1(u2_conlat_1(A))))
& m2_relset_1(k3_conlat_1(A),u1_struct_0(k3_yellow_1(u1_conlat_1(A))),u1_struct_0(k3_yellow_1(u2_conlat_1(A)))) ) ) ).
fof(dt_k4_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k4_conlat_1(A))
& v1_funct_2(k4_conlat_1(A),u1_struct_0(k3_yellow_1(u2_conlat_1(A))),u1_struct_0(k3_yellow_1(u1_conlat_1(A))))
& m2_relset_1(k4_conlat_1(A),u1_struct_0(k3_yellow_1(u2_conlat_1(A))),u1_struct_0(k3_yellow_1(u1_conlat_1(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_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_k7_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ~ v1_xboole_0(k7_conlat_1(A)) ) ).
fof(dt_k8_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> m1_conlat_1(k8_conlat_1(A),A) ) ).
fof(redefinition_k8_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k8_conlat_1(A) = k7_conlat_1(A) ) ).
fof(dt_k9_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k9_conlat_1(A))
& v1_funct_2(k9_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A))
& m2_relset_1(k9_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) ) ) ).
fof(dt_k10_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k10_conlat_1(A))
& v1_funct_2(k10_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A))
& m2_relset_1(k10_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) ) ) ).
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_u1_conlat_1,axiom,
$true ).
fof(dt_u2_conlat_1,axiom,
$true ).
fof(dt_u3_conlat_1,axiom,
! [A] :
( l2_conlat_1(A)
=> m2_relset_1(u3_conlat_1(A),u1_conlat_1(A),u2_conlat_1(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(dt_g1_conlat_1,axiom,
! [A,B] :
( v1_conlat_1(g1_conlat_1(A,B))
& l1_conlat_1(g1_conlat_1(A,B)) ) ).
fof(free_g1_conlat_1,axiom,
! [A,B,C,D] :
( g1_conlat_1(A,B) = g1_conlat_1(C,D)
=> ( A = C
& B = D ) ) ).
fof(dt_g2_conlat_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( v4_conlat_1(g2_conlat_1(A,B,C))
& l2_conlat_1(g2_conlat_1(A,B,C)) ) ) ).
fof(free_g2_conlat_1,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ! [D,E,F] :
( g2_conlat_1(A,B,C) = g2_conlat_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
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(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(d6_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)))
& m2_relset_1(B,k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) )
=> ( B = k1_conlat_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),B,C) = a_2_0_conlat_1(A,C) ) ) ) ) ).
fof(d7_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)))
& m2_relset_1(B,k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) )
=> ( B = k2_conlat_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),B,C) = a_2_1_conlat_1(A,C) ) ) ) ) ).
fof(t1_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_conlat_1(A))
=> k1_funct_1(k1_conlat_1(A),k1_tarski(B)) = a_2_2_conlat_1(A,B) ) ) ).
fof(t2_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_conlat_1(A))
=> k1_funct_1(k2_conlat_1(A),k1_tarski(B)) = a_2_3_conlat_1(A,B) ) ) ).
fof(d20_conlat_1,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k7_conlat_1(A) = a_1_0_conlat_1(A) ) ).
fof(fraenkel_a_2_0_conlat_1,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(B))) )
=> ( r2_hidden(A,a_2_0_conlat_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u2_conlat_1(B))
& A = D
& ! [E] :
( m1_subset_1(E,u1_conlat_1(B))
=> ( r2_hidden(E,C)
=> r1_conlat_1(B,E,D) ) ) ) ) ) ).
fof(fraenkel_a_2_1_conlat_1,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(B))) )
=> ( r2_hidden(A,a_2_1_conlat_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_conlat_1(B))
& A = D
& ! [E] :
( m1_subset_1(E,u2_conlat_1(B))
=> ( r2_hidden(E,C)
=> r1_conlat_1(B,D,E) ) ) ) ) ) ).
fof(fraenkel_a_2_2_conlat_1,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& m1_subset_1(C,u1_conlat_1(B)) )
=> ( r2_hidden(A,a_2_2_conlat_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u2_conlat_1(B))
& A = D
& r1_conlat_1(B,C,D) ) ) ) ).
fof(fraenkel_a_2_3_conlat_1,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& m1_subset_1(C,u2_conlat_1(B)) )
=> ( r2_hidden(A,a_2_3_conlat_1(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_conlat_1(B))
& A = D
& r1_conlat_1(B,D,C) ) ) ) ).
fof(fraenkel_a_1_0_conlat_1,axiom,
! [A,B] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B) )
=> ( r2_hidden(A,a_1_0_conlat_1(B))
<=> ? [C,D] :
( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(B)))
& A = g3_conlat_1(B,C,D)
& ~ v7_conlat_1(g3_conlat_1(B,C,D),B)
& k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),C) = D
& k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),D) = C ) ) ) ).
%------------------------------------------------------------------------------