SET007 Axioms: SET007+663.ax
%------------------------------------------------------------------------------
% File : SET007+663 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The J'onsson Theorem about the Representation of Modular 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 : lattice8 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 71 ( 8 unt; 0 def)
% Number of atoms : 1003 ( 67 equ)
% Maximal formula atoms : 39 ( 14 avg)
% Number of connectives : 1014 ( 82 ~; 5 |; 663 &)
% ( 12 <=>; 252 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-6 aty)
% Number of functors : 57 ( 57 usr; 6 con; 0-5 aty)
% Number of variables : 282 ( 265 !; 17 ?)
% 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_lattice8,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow11(A)
& v2_waybel_1(A)
& v6_group_1(A) ) ).
fof(rc2_lattice8,axiom,
! [A] :
( ~ v1_realset1(A)
=> ? [B] :
( m1_yellow_0(B,k1_lattice5(A))
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_yellow_0(B,k1_lattice5(A))
& v5_yellow_0(B,k1_lattice5(A))
& v6_yellow_0(B,k1_lattice5(A))
& v1_lattice3(B)
& v2_lattice3(B)
& ~ v3_realset2(B)
& v1_lattice8(B) ) ) ).
fof(fc1_lattice8,axiom,
! [A] : ~ v1_xboole_0(k1_lattice8(A)) ).
fof(fc2_lattice8,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v3_ordinal1(B) )
=> ~ v1_xboole_0(k3_lattice8(A,B)) ) ).
fof(fc3_lattice8,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ~ v1_xboole_0(k7_lattice8(A,B,C)) ) ).
fof(d1_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( m2_relset_1(C,A,A)
=> ( r1_lattice8(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(k1_domain_1(A,A,D,E),B)
=> r2_hidden(k1_domain_1(A,A,D,E),C) ) ) ) ) ) ) ) ).
fof(d2_lattice8,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice8(A)
<=> ? [B] :
( ~ v1_xboole_0(B)
& ! [C] :
( r2_hidden(C,u1_struct_0(A))
=> ( v1_partfun1(C,B,B)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,B,B) ) )
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( ( v1_partfun1(D,B,B)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,B,B) )
=> ! [E] :
( ( v1_partfun1(E,B,B)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,B,B) )
=> ! [F,G] :
~ ( r2_hidden(D,u1_struct_0(A))
& r2_hidden(E,u1_struct_0(A))
& r2_hidden(k4_tarski(F,G),k5_eqrel_1(B,D,E))
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_finseq_1(H,B) )
=> ~ ( k3_finseq_1(H) = C
& r1_lattice5(B,H,F,G,D,E) ) ) ) ) ) ) ) ) ) ).
fof(d3_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_lattice8(A,B)
<=> ? [C] :
( ~ v1_realset1(C)
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_lattice5(C)))
& v19_waybel_0(D,A,k1_lattice5(C))
& v20_waybel_0(D,A,k1_lattice5(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k1_lattice5(C)))
& v2_funct_1(D)
& v1_lattice8(k2_lattice5(A,k1_lattice5(C),D))
& ? [E] :
( v1_partfun1(E,C,C)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,C,C)
& r2_hidden(E,u1_struct_0(k2_lattice5(A,k1_lattice5(C),D)))
& E != k6_partfun1(C) )
& r1_xreal_0(k3_lattice5(C,k2_lattice5(A,k1_lattice5(C),D)),B) ) ) ) ) ) ).
fof(t1_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> r1_ordinal1(k1_ordinal1(k1_xboole_0),k8_lattice5(A,B,C)) ) ) ) ).
fof(t2_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v3_realset2(A)
& l1_orders_2(A) )
=> v1_yellow11(A) ) ).
fof(t3_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_yellow_0(B,k1_lattice5(A))
& v6_yellow_0(B,k1_lattice5(A))
& m1_yellow_0(B,k1_lattice5(A)) )
=> ~ ( ~ v3_realset2(B)
& ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ~ ( r2_hidden(C,u1_struct_0(B))
& C != k6_partfun1(A) ) ) ) ) ) ).
fof(t4_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v17_waybel_0(C,A,B)
& v18_waybel_0(C,A,B) )
=> ( v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B) ) ) ) ) ) ).
fof(t5_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v1_yellow11(A) )
=> v1_yellow11(B) ) ) ) ).
fof(t6_lattice8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> v1_yellow_0(k2_yellow_2(A,B,C)) ) ) ) ).
fof(t7_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_lattice5(D)))
& v19_waybel_0(E,A,k1_lattice5(D))
& v20_waybel_0(E,A,k1_lattice5(D))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_lattice5(D))) )
=> ( ( v2_funct_1(E)
& r3_orders_2(k2_yellow_2(A,k1_lattice5(D),E),k1_waybel_0(A,k2_yellow_2(A,k1_lattice5(D),E),k2_waybel_1(A,k1_lattice5(D),E),B),k1_waybel_0(A,k2_yellow_2(A,k1_lattice5(D),E),k2_waybel_1(A,k1_lattice5(D),E),C)) )
=> r3_orders_2(A,B,C) ) ) ) ) ) ) ).
fof(t8_lattice8,axiom,
! [A] :
( ~ v1_realset1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,k1_lattice5(A))
& v5_yellow_0(B,k1_lattice5(A))
& v6_yellow_0(B,k1_lattice5(A))
& v1_lattice8(B)
& m1_yellow_0(B,k1_lattice5(A)) )
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ( ( r2_hidden(C,u1_struct_0(B))
& r1_xreal_0(k3_lattice5(A,B),np__2) )
=> ( C = k6_partfun1(A)
| v1_yellow11(B) ) ) ) ) ) ).
fof(t9_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_lattice8(A,np__2)
=> v1_yellow11(A) ) ) ).
fof(d4_lattice8,axiom,
! [A] : k1_lattice8(A) = k2_xboole_0(A,k2_tarski(k1_tarski(A),k1_tarski(k1_tarski(A)))) ).
fof(d5_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B)) )
=> ( E = k2_lattice8(A,B,C,D)
<=> ( ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> k1_binop_1(E,F,G) = k4_lattice5(A,B,C,F,G) ) )
& k1_binop_1(E,k1_tarski(A),k1_tarski(A)) = k3_yellow_0(B)
& k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(A))) = k3_yellow_0(B)
& k1_binop_1(E,k1_tarski(A),k1_tarski(k1_tarski(A))) = k12_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(A)) = k12_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& ! [F] :
( m1_subset_1(F,A)
=> ( k1_binop_1(E,F,k1_tarski(A)) = k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& k1_binop_1(E,k1_tarski(A),F) = k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& k1_binop_1(E,F,k1_tarski(k1_tarski(A))) = k13_lattice3(B,k4_lattice5(A,B,C,F,k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& k1_binop_1(E,k1_tarski(k1_tarski(A)),F) = k13_lattice3(B,k4_lattice5(A,B,C,F,k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)) ) ) ) ) ) ) ) ) ) ).
fof(t10_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v2_lattice5(C,A,B)
=> ! [D] :
( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
=> v2_lattice5(k2_lattice8(A,B,C,D),k1_lattice8(A),B) ) ) ) ) ) ).
fof(t11_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v1_lattice5(C,A,B)
=> ! [D] :
( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
=> v1_lattice5(k2_lattice8(A,B,C,D),k1_lattice8(A),B) ) ) ) ) ) ).
fof(t12_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( v1_yellow11(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( ( v1_lattice5(C,A,B)
& v3_lattice5(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
=> ( r3_orders_2(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k13_lattice3(B,k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)))
=> v3_lattice5(k2_lattice8(A,B,C,D),k1_lattice8(A),B) ) ) ) ) ) ) ) ).
fof(t13_lattice8,axiom,
! [A] : r1_tarski(A,k1_lattice8(A)) ).
fof(t14_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
=> r1_tarski(C,k2_lattice8(A,B,C,D)) ) ) ) ) ).
fof(d6_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( C = k3_lattice8(A,B)
<=> ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& v5_ordinal1(D)
& C = k1_ordinal2(D)
& k1_relat_1(D) = k1_ordinal1(B)
& k1_funct_1(D,k1_xboole_0) = A
& ! [E] :
( v3_ordinal1(E)
=> ( r2_hidden(k1_ordinal1(E),k1_ordinal1(B))
=> k1_funct_1(D,k1_ordinal1(E)) = k1_lattice8(k1_funct_1(D,E)) ) )
& ! [E] :
( v3_ordinal1(E)
=> ( ( r2_hidden(E,k1_ordinal1(B))
& v4_ordinal1(E) )
=> ( E = k1_xboole_0
| k1_funct_1(D,E) = k3_tarski(k2_relat_1(k2_ordinal1(D,E))) ) ) ) ) ) ) ) ).
fof(t15_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k3_lattice8(A,k1_xboole_0) = A ) ).
fof(t16_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> k3_lattice8(A,k1_ordinal1(B)) = k1_lattice8(k3_lattice8(A,B)) ) ) ).
fof(t17_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v5_ordinal1(C) )
=> ( ( v4_ordinal1(B)
& k1_relat_1(C) = B
& ! [D] :
( v3_ordinal1(D)
=> ( r2_hidden(D,B)
=> k1_funct_1(C,D) = k3_lattice8(A,D) ) ) )
=> ( B = k1_xboole_0
| k3_lattice8(A,B) = k3_tarski(k2_relat_1(C)) ) ) ) ) ) ).
fof(t18_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> r1_tarski(A,k3_lattice8(A,B)) ) ) ).
fof(d7_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> ( r2_hidden(E,k1_relat_1(D))
=> k4_lattice8(A,B,C,D,E) = k1_funct_1(D,E) ) ) ) ) ) ) ).
fof(d8_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> ! [F] :
( F = k5_lattice8(A,B,C,D,E)
<=> ? [G] :
( v1_relat_1(G)
& v1_funct_1(G)
& v5_ordinal1(G)
& F = k1_ordinal2(G)
& k1_relat_1(G) = k1_ordinal1(E)
& k1_funct_1(G,k1_xboole_0) = C
& ! [H] :
( v3_ordinal1(H)
=> ( r2_hidden(k1_ordinal1(H),k1_ordinal1(E))
=> k1_funct_1(G,k1_ordinal1(H)) = k2_lattice8(k3_lattice8(A,H),B,k11_lattice5(k3_lattice8(A,H),B,k1_funct_1(G,H)),k4_lattice8(A,B,C,D,H)) ) )
& ! [H] :
( v3_ordinal1(H)
=> ( ( r2_hidden(H,k1_ordinal1(E))
& v4_ordinal1(H) )
=> ( H = k1_xboole_0
| k1_funct_1(G,H) = k3_tarski(k2_relat_1(k2_ordinal1(G,H))) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> k5_lattice8(A,B,C,D,k1_xboole_0) = C ) ) ) ) ).
fof(t20_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> k5_lattice8(A,B,C,D,k1_ordinal1(E)) = k2_lattice8(k3_lattice8(A,E),B,k11_lattice5(k3_lattice8(A,E),B,k5_lattice8(A,B,C,D,E)),k4_lattice8(A,B,C,D,E)) ) ) ) ) ) ).
fof(t21_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v5_ordinal1(E) )
=> ! [F] :
( v3_ordinal1(F)
=> ( ( v4_ordinal1(F)
& k1_relat_1(E) = F
& ! [G] :
( v3_ordinal1(G)
=> ( r2_hidden(G,F)
=> k1_funct_1(E,G) = k5_lattice8(A,B,C,D,G) ) ) )
=> ( F = k1_xboole_0
| k5_lattice8(A,B,C,D,F) = k3_tarski(k2_relat_1(E)) ) ) ) ) ) ) ) ) ).
fof(t22_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( v3_ordinal1(C)
=> ! [D] :
( v3_ordinal1(D)
=> ( r1_ordinal1(C,D)
=> r1_tarski(k3_lattice8(A,C),k3_lattice8(A,D)) ) ) ) ) ) ).
fof(t23_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> ( v1_funct_1(k5_lattice8(A,B,C,D,E))
& v1_funct_2(k5_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B))
& m2_relset_1(k5_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B)) ) ) ) ) ) ) ).
fof(t24_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> r1_tarski(C,k6_lattice8(A,B,C,D,E)) ) ) ) ) ) ).
fof(t25_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( v3_ordinal1(D)
=> ! [E] :
( v3_ordinal1(E)
=> ! [F] :
( m1_lattice5(F,A,B,C)
=> ( r1_ordinal1(D,E)
=> r1_tarski(k6_lattice8(A,B,C,F,D),k6_lattice8(A,B,C,F,E)) ) ) ) ) ) ) ) ).
fof(t26_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v2_lattice5(C,A,B)
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> v2_lattice5(k6_lattice8(A,B,C,D,E),k3_lattice8(A,E),B) ) ) ) ) ) ) ).
fof(t27_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v1_lattice5(C,A,B)
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> ! [E] :
( v3_ordinal1(E)
=> v1_lattice5(k6_lattice8(A,B,C,D,E),k3_lattice8(A,E),B) ) ) ) ) ) ) ).
fof(t28_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( v1_yellow11(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( ( v1_lattice5(C,A,B)
& v3_lattice5(C,A,B) )
=> ! [D] :
( v3_ordinal1(D)
=> ! [E] :
( m1_lattice5(E,A,B,C)
=> ( r1_ordinal1(D,k8_lattice5(A,B,C))
=> v3_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B) ) ) ) ) ) ) ) ) ).
fof(t29_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( v3_ordinal1(D)
=> ! [E] :
( m1_lattice5(E,A,B,C)
=> ( r1_ordinal1(D,k8_lattice5(A,B,C))
=> ( v1_funct_1(k6_lattice8(A,B,C,E,D))
& v1_funct_2(k6_lattice8(A,B,C,E,D),k2_zfmisc_1(k3_lattice8(A,D),k3_lattice8(A,D)),u1_struct_0(B))
& v1_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B)
& v2_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B)
& v3_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B)
& m2_relset_1(k6_lattice8(A,B,C,E,D),k2_zfmisc_1(k3_lattice8(A,D),k3_lattice8(A,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(d9_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> k7_lattice8(A,B,C) = k3_lattice8(A,k8_lattice5(A,B,C)) ) ) ) ).
fof(d10_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> k8_lattice8(A,B,C,D) = k6_lattice8(A,B,C,D,k8_lattice5(A,B,C)) ) ) ) ) ).
fof(d11_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(D,D),u1_struct_0(B))
& v1_lattice5(E,D,B)
& v2_lattice5(E,D,B)
& v3_lattice5(E,D,B)
& m2_relset_1(E,k2_zfmisc_1(D,D),u1_struct_0(B)) )
=> ( r3_lattice8(A,B,C,D,E)
<=> ? [F] :
( m1_lattice5(F,A,B,C)
& D = k7_lattice8(A,B,C)
& E = k8_lattice8(A,B,C,F) ) ) ) ) ) ) ) ).
fof(t30_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(D,D),u1_struct_0(B))
& v1_lattice5(E,D,B)
& v2_lattice5(E,D,B)
& v3_lattice5(E,D,B)
& m2_relset_1(E,k2_zfmisc_1(D,D),u1_struct_0(B)) )
=> ( r3_lattice8(A,B,C,D,E)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(B))
=> ~ ( r3_orders_2(B,k4_lattice5(A,B,C,F,G),k13_lattice3(B,H,I))
& ! [J] :
( m1_subset_1(J,D)
=> ! [K] :
( m1_subset_1(K,D)
=> ~ ( k1_binop_1(E,F,J) = H
& k4_lattice5(D,B,E,J,K) = k12_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,F,G),H),I)
& k1_binop_1(E,K,G) = H ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( m1_lattice8(D,A,B,C)
<=> ( k1_relat_1(D) = k5_numbers
& k1_funct_1(D,np__0) = k4_tarski(A,C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( ~ v1_xboole_0(F)
& ? [G] :
( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(F,F),u1_struct_0(B))
& v1_lattice5(G,F,B)
& v2_lattice5(G,F,B)
& v3_lattice5(G,F,B)
& m2_relset_1(G,k2_zfmisc_1(F,F),u1_struct_0(B))
& ? [H] :
( ~ v1_xboole_0(H)
& ? [I] :
( v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(H,H),u1_struct_0(B))
& v1_lattice5(I,H,B)
& v2_lattice5(I,H,B)
& v3_lattice5(I,H,B)
& m2_relset_1(I,k2_zfmisc_1(H,H),u1_struct_0(B))
& r3_lattice8(F,B,G,H,I)
& k1_funct_1(D,E) = k4_tarski(F,G)
& k1_funct_1(D,k1_nat_1(E,np__1)) = k4_tarski(H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice8(D,A,B,C)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,F)
=> r1_tarski(k1_mcart_1(k1_funct_1(D,E)),k1_mcart_1(k1_funct_1(D,F))) ) ) ) ) ) ) ) ).
fof(t32_lattice8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice8(D,A,B,C)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,F)
=> r1_tarski(k2_mcart_1(k1_funct_1(D,E)),k2_mcart_1(k1_funct_1(D,F))) ) ) ) ) ) ) ) ).
fof(t36_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow11(A)
& l1_orders_2(A) )
=> r2_lattice8(A,np__2) ) ).
fof(t37_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_lattice8(A,np__2)
<=> v1_yellow11(A) ) ) ).
fof(dt_m1_lattice8,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_lattice8(D,A,B,C)
=> ( v1_relat_1(D)
& v1_funct_1(D) ) ) ) ).
fof(existence_m1_lattice8,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ? [D] : m1_lattice8(D,A,B,C) ) ).
fof(reflexivity_r1_lattice8,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(B,A,A)
& m1_relset_1(C,A,A) )
=> r1_lattice8(A,B,B) ) ).
fof(redefinition_r1_lattice8,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(B,A,A)
& m1_relset_1(C,A,A) )
=> ( r1_lattice8(A,B,C)
<=> r1_tarski(B,C) ) ) ).
fof(dt_k1_lattice8,axiom,
$true ).
fof(dt_k2_lattice8,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B))) )
=> ( v1_funct_1(k2_lattice8(A,B,C,D))
& v1_funct_2(k2_lattice8(A,B,C,D),k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B))
& m2_relset_1(k2_lattice8(A,B,C,D),k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B)) ) ) ).
fof(dt_k3_lattice8,axiom,
$true ).
fof(dt_k4_lattice8,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_lattice5(D,A,B,C)
& v3_ordinal1(E) )
=> m1_subset_1(k4_lattice8(A,B,C,D,E),k4_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E),u1_struct_0(B),u1_struct_0(B))) ) ).
fof(dt_k5_lattice8,axiom,
$true ).
fof(dt_k6_lattice8,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_lattice5(D,A,B,C)
& v3_ordinal1(E) )
=> ( v1_funct_1(k6_lattice8(A,B,C,D,E))
& v1_funct_2(k6_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B))
& m2_relset_1(k6_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B)) ) ) ).
fof(redefinition_k6_lattice8,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_lattice5(D,A,B,C)
& v3_ordinal1(E) )
=> k6_lattice8(A,B,C,D,E) = k5_lattice8(A,B,C,D,E) ) ).
fof(dt_k7_lattice8,axiom,
$true ).
fof(dt_k8_lattice8,axiom,
$true ).
fof(dt_k9_lattice8,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_lattice5(D,A,B,C) )
=> ( v1_funct_1(k9_lattice8(A,B,C,D))
& v1_funct_2(k9_lattice8(A,B,C,D),k2_zfmisc_1(k7_lattice8(A,B,C),k7_lattice8(A,B,C)),u1_struct_0(B))
& v1_lattice5(k9_lattice8(A,B,C,D),k7_lattice8(A,B,C),B)
& v2_lattice5(k9_lattice8(A,B,C,D),k7_lattice8(A,B,C),B)
& v3_lattice5(k9_lattice8(A,B,C,D),k7_lattice8(A,B,C),B)
& m2_relset_1(k9_lattice8(A,B,C,D),k2_zfmisc_1(k7_lattice8(A,B,C),k7_lattice8(A,B,C)),u1_struct_0(B)) ) ) ).
fof(redefinition_k9_lattice8,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(C,A,B)
& v2_lattice5(C,A,B)
& v3_lattice5(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_lattice5(D,A,B,C) )
=> k9_lattice8(A,B,C,D) = k8_lattice8(A,B,C,D) ) ).
fof(t33_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow11(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_lattice8(B,u1_struct_0(A),A,k17_lattice5(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( C = k3_tarski(a_2_0_lattice8(A,B))
=> ( v1_funct_1(k3_tarski(a_2_1_lattice8(A,B)))
& v1_funct_2(k3_tarski(a_2_1_lattice8(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A))
& v1_lattice5(k3_tarski(a_2_1_lattice8(A,B)),C,A)
& v2_lattice5(k3_tarski(a_2_1_lattice8(A,B)),C,A)
& v3_lattice5(k3_tarski(a_2_1_lattice8(A,B)),C,A)
& m2_relset_1(k3_tarski(a_2_1_lattice8(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A)) ) ) ) ) ) ).
fof(t34_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow11(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_lattice8(B,u1_struct_0(A),A,k17_lattice5(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),u1_struct_0(A))
& v1_lattice5(D,C,A)
& v2_lattice5(D,C,A)
& v3_lattice5(D,C,A)
& m2_relset_1(D,k2_zfmisc_1(C,C),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,C)
=> ! [F] :
( m1_subset_1(F,C)
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ~ ( C = k3_tarski(a_2_0_lattice8(A,B))
& D = k3_tarski(a_2_1_lattice8(A,B))
& r3_orders_2(A,k4_lattice5(C,A,D,E,F),k13_lattice3(A,G,H))
& ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( m1_subset_1(J,C)
=> ~ ( k4_lattice5(C,A,D,E,I) = G
& k4_lattice5(C,A,D,I,J) = k12_lattice3(A,k13_lattice3(A,k4_lattice5(C,A,D,E,F),G),H)
& k4_lattice5(C,A,D,J,F) = G ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_lattice8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow11(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_lattice8(B,u1_struct_0(A),A,k17_lattice5(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),u1_struct_0(A))
& v1_lattice5(D,C,A)
& v2_lattice5(D,C,A)
& v3_lattice5(D,C,A)
& m2_relset_1(D,k2_zfmisc_1(C,C),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_lattice5(C)))
& v19_waybel_0(E,A,k1_lattice5(C))
& v20_waybel_0(E,A,k1_lattice5(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_lattice5(C))) )
=> ! [F] :
( ( v1_partfun1(F,C,C)
& v3_relat_2(F)
& v8_relat_2(F)
& m2_relset_1(F,C,C) )
=> ! [G] :
( ( v1_partfun1(G,C,C)
& v3_relat_2(G)
& v8_relat_2(G)
& m2_relset_1(G,C,C) )
=> ! [H,I] :
~ ( E = k5_lattice5(C,A,D)
& C = k3_tarski(a_2_0_lattice8(A,B))
& D = k3_tarski(a_2_1_lattice8(A,B))
& r2_hidden(F,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E)))
& r2_hidden(G,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E)))
& r2_hidden(k4_tarski(H,I),k5_eqrel_1(C,F,G))
& ! [J] :
( ( ~ v1_xboole_0(J)
& m2_finseq_1(J,C) )
=> ~ ( k3_finseq_1(J) = k1_nat_1(np__2,np__2)
& r1_lattice5(C,J,H,I,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_lattice8,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B)
& m1_lattice8(C,u1_struct_0(B),B,k17_lattice5(B)) )
=> ( r2_hidden(A,a_2_0_lattice8(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k1_mcart_1(k1_funct_1(C,D)) ) ) ) ).
fof(fraenkel_a_2_1_lattice8,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow11(B)
& l1_orders_2(B)
& m1_lattice8(C,u1_struct_0(B),B,k17_lattice5(B)) )
=> ( r2_hidden(A,a_2_1_lattice8(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_mcart_1(k1_funct_1(C,D)) ) ) ) ).
%------------------------------------------------------------------------------