SET007 Axioms: SET007+530.ax
%------------------------------------------------------------------------------
% File : SET007+530 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Jonsson Theorem
% 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 : lattice5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 108 ( 12 unt; 0 def)
% Number of atoms : 1425 ( 115 equ)
% Maximal formula atoms : 58 ( 13 avg)
% Number of connectives : 1437 ( 120 ~; 6 |; 937 &)
% ( 25 <=>; 349 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 62 ( 60 usr; 1 prp; 0-6 aty)
% Number of functors : 71 ( 71 usr; 8 con; 0-8 aty)
% Number of variables : 438 ( 404 !; 34 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_lattice5,axiom,
! [A] :
( ~ v3_struct_0(k1_lattice5(A))
& v2_orders_2(k1_lattice5(A))
& v3_orders_2(k1_lattice5(A))
& v4_orders_2(k1_lattice5(A))
& v1_lattice3(k1_lattice5(A))
& v2_lattice3(k1_lattice5(A)) ) ).
fof(fc2_lattice5,axiom,
! [A] :
( ~ v3_struct_0(k1_lattice5(A))
& v2_orders_2(k1_lattice5(A))
& v3_orders_2(k1_lattice5(A))
& v4_orders_2(k1_lattice5(A))
& v1_yellow_0(k1_lattice5(A))
& v2_yellow_0(k1_lattice5(A))
& v3_yellow_0(k1_lattice5(A))
& v1_lattice3(k1_lattice5(A))
& v2_lattice3(k1_lattice5(A))
& v3_lattice3(k1_lattice5(A)) ) ).
fof(rc1_lattice5,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B) ) ) ).
fof(rc2_lattice5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& v1_orders_2(B)
& v5_yellow_0(B,A)
& v6_yellow_0(B,A) ) ) ).
fof(rc3_lattice5,axiom,
! [A,B] :
( ( ~ 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) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_relat_1(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) ) ) ).
fof(fc3_lattice5,axiom,
! [A] : ~ v1_xboole_0(k6_lattice5(A)) ).
fof(fc4_lattice5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v3_ordinal1(B) )
=> ~ v1_xboole_0(k9_lattice5(A,B)) ) ).
fof(fc5_lattice5,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(k14_lattice5(A,B,C)) ) ).
fof(t1_lattice5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ( A = k3_tarski(k2_relat_1(B))
=> k1_relat_1(A) = k3_tarski(k2_relat_1(k2_funct_6(B))) ) ) ) ).
fof(d1_lattice5,axiom,
! [A] : k1_lattice5(A) = k3_lattice3(k2_msualg_5(A)) ).
fof(t4_lattice5,axiom,
! [A,B] :
( r2_hidden(B,u1_struct_0(k1_lattice5(A)))
<=> ( v1_partfun1(B,A,A)
& v3_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,A,A) ) ) ).
fof(t5_lattice5,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k2_msualg_5(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_msualg_5(A)))
=> ( r3_lattices(k2_msualg_5(A),B,C)
<=> r1_tarski(B,C) ) ) ) ).
fof(t6_lattice5,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k1_lattice5(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_lattice5(A)))
=> ( r3_orders_2(k1_lattice5(A),B,C)
<=> r1_tarski(B,C) ) ) ) ).
fof(t7_lattice5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_lattice3(A)))
=> k12_lattice3(k3_lattice3(A),B,C) = k4_lattices(A,k5_lattice3(A,B),k5_lattice3(A,C)) ) ) ) ).
fof(t8_lattice5,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k1_lattice5(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_lattice5(A)))
=> k12_lattice3(k1_lattice5(A),B,C) = k3_xboole_0(B,C) ) ) ).
fof(t9_lattice5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_lattice3(A)))
=> k13_lattice3(k3_lattice3(A),B,C) = k3_lattices(A,k5_lattice3(A,B),k5_lattice3(A,C)) ) ) ) ).
fof(t10_lattice5,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k1_lattice5(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_lattice5(A)))
=> ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ! [E] :
( ( v1_partfun1(E,A,A)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,A,A) )
=> ( ( B = D
& C = E )
=> k13_lattice3(k1_lattice5(A),B,C) = k5_eqrel_1(A,D,E) ) ) ) ) ) ).
fof(d2_lattice5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v3_lattice3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
=> r1_orders_2(A,D,C) ) ) ) ) ) ) ).
fof(d3_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C,D,E] :
( v1_relat_1(E)
=> ! [F] :
( v1_relat_1(F)
=> ( r1_lattice5(A,B,C,D,E,F)
<=> ( k1_funct_1(B,np__1) = C
& k1_funct_1(B,k3_finseq_1(B)) = D
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,G)
=> ( r1_xreal_0(k3_finseq_1(B),G)
| ( ( ~ v1_abian(G)
=> r2_hidden(k4_tarski(k1_funct_1(B,G),k1_funct_1(B,k1_nat_1(G,np__1))),E) )
& ( v1_abian(G)
=> r2_hidden(k4_tarski(k1_funct_1(B,G),k1_funct_1(B,k1_nat_1(G,np__1))),F) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_lattice5,axiom,
$true ).
fof(t12_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( v1_relat_1(D)
=> ! [E] :
( v1_relat_1(E)
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m2_finseq_1(F,A) )
=> ( ( r1_relat_2(D,A)
& r1_relat_2(E,A)
& F = k2_finseq_2(C,B) )
=> r1_lattice5(A,F,B,B,D,E) ) ) ) ) ) ) ).
fof(t13_lattice5,axiom,
$true ).
fof(t14_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C,D] :
( v1_relat_1(D)
=> ! [E] :
( v1_relat_1(E)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(F,G)
& r1_relat_2(D,A)
& r1_relat_2(E,A)
& ? [H] :
( ~ v1_xboole_0(H)
& m2_finseq_1(H,A)
& k3_finseq_1(H) = F
& r1_lattice5(A,H,B,C,D,E) )
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_finseq_1(H,A) )
=> ~ ( k3_finseq_1(H) = G
& r1_lattice5(A,H,B,C,D,E) ) ) ) ) ) ) ) ) ).
fof(d4_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v5_yellow_0(B,k1_lattice5(A))
& v6_yellow_0(B,k1_lattice5(A))
& 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))
& C != k13_cqc_sim1(A) )
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ! [E] :
( ( v1_partfun1(E,A,A)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,A,A) )
=> ! [F,G] :
~ ( r2_hidden(D,u1_struct_0(B))
& r2_hidden(E,u1_struct_0(B))
& r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_finseq_1(H,A) )
=> ~ ( k3_finseq_1(H) = C
& r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) )
& ~ ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( C = k3_lattice5(A,B)
<=> ( ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ! [E] :
( ( v1_partfun1(E,A,A)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,A,A) )
=> ! [F,G] :
~ ( r2_hidden(D,u1_struct_0(B))
& r2_hidden(E,u1_struct_0(B))
& r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_finseq_1(H,A) )
=> ~ ( k3_finseq_1(H) = k1_nat_1(C,np__2)
& r1_lattice5(A,H,F,G,D,E) ) ) ) ) )
& ? [D] :
( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A)
& ? [E] :
( v1_partfun1(E,A,A)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,A,A)
& ? [F,G] :
( r2_hidden(D,u1_struct_0(B))
& r2_hidden(E,u1_struct_0(B))
& r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_finseq_1(H,A) )
=> ~ ( k3_finseq_1(H) = k1_nat_1(C,np__1)
& r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v5_yellow_0(B,k1_lattice5(A))
& v6_yellow_0(B,k1_lattice5(A))
& m1_yellow_0(B,k1_lattice5(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ! [E] :
( ( v1_partfun1(E,A,A)
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,A,A) )
=> ! [F,G] :
~ ( r2_hidden(D,u1_struct_0(B))
& r2_hidden(E,u1_struct_0(B))
& r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_finseq_1(H,A) )
=> ~ ( k3_finseq_1(H) = k1_nat_1(C,np__2)
& r1_lattice5(A,H,F,G,D,E) ) ) ) ) )
=> ( ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ~ ( r2_hidden(D,u1_struct_0(B))
& D != k13_cqc_sim1(A) ) )
| r1_xreal_0(k3_lattice5(A,B),C) ) ) ) ) ) ).
fof(d5_lattice5,axiom,
$true ).
fof(d6_lattice5,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,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k4_lattice5(A,B,C,D,E) = k4_lattice5(A,B,C,E,D) ) ) ) ) ) ) ).
fof(d7_lattice5,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,A)
=> k4_lattice5(A,B,C,D,D) = k3_yellow_0(B) ) ) ) ) ) ).
fof(d8_lattice5,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)) )
=> ( v3_lattice5(C,A,B)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> r1_orders_2(B,k4_lattice5(A,B,C,D,F),k13_lattice3(B,k4_lattice5(A,B,C,D,E),k4_lattice5(A,B,C,E,F))) ) ) ) ) ) ) ) ).
fof(d9_lattice5,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_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(k1_lattice5(A)))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(k1_lattice5(A))) )
=> ( D = k5_lattice5(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( v1_partfun1(F,A,A)
& v3_relat_2(F)
& v8_relat_2(F)
& m2_relset_1(F,A,A)
& F = k7_yellow_2(u1_struct_0(B),k1_lattice5(A),D,E)
& ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ( r2_hidden(k1_domain_1(A,A,G,H),F)
<=> r3_orders_2(B,k4_lattice5(A,B,C,G,H),E) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_lattice5,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)) )
=> v19_waybel_0(k5_lattice5(A,B,C),B,k1_lattice5(A)) ) ) ) ).
fof(t17_lattice5,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)) )
=> ( v2_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
=> v2_funct_1(k5_lattice5(A,B,C)) ) ) ) ) ).
fof(d10_lattice5,axiom,
! [A] : k6_lattice5(A) = k2_xboole_0(A,k1_enumset1(k1_tarski(A),k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(k1_tarski(A))))) ).
fof(d11_lattice5,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(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B)) )
=> ( E = k7_lattice5(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(k1_tarski(k1_tarski(A))),k1_tarski(k1_tarski(k1_tarski(A)))) = k3_yellow_0(B)
& k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(k1_tarski(A)))) = k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
& k1_binop_1(E,k1_tarski(k1_tarski(k1_tarski(A))),k1_tarski(k1_tarski(A))) = k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
& k1_binop_1(E,k1_tarski(A),k1_tarski(k1_tarski(A))) = 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)) = k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)
& k1_binop_1(E,k1_tarski(A),k1_tarski(k1_tarski(k1_tarski(A)))) = 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))
& k1_binop_1(E,k1_tarski(k1_tarski(k1_tarski(A))),k1_tarski(A)) = 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))
& ! [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,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)),k11_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,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)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& k1_binop_1(E,F,k1_tarski(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)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
& k1_binop_1(E,k1_tarski(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)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)) ) ) ) ) ) ) ) ) ) ).
fof(t18_lattice5,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(k7_lattice5(A,B,C,D),k6_lattice5(A),B) ) ) ) ) ) ).
fof(t19_lattice5,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(k7_lattice5(A,B,C,D),k6_lattice5(A),B) ) ) ) ) ) ).
fof(t20_lattice5,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)
& 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(k7_lattice5(A,B,C,D),k6_lattice5(A),B) ) ) ) ) ) ) ).
fof(t21_lattice5,axiom,
! [A] : r1_tarski(A,k6_lattice5(A)) ).
fof(t22_lattice5,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,k7_lattice5(A,B,C,D)) ) ) ) ) ).
fof(t23_lattice5,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)) )
=> k8_lattice5(A,B,C) != k1_xboole_0 ) ) ) ).
fof(d13_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( C = k9_lattice5(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)) = k6_lattice5(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(t24_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k9_lattice5(A,k1_xboole_0) = A ) ).
fof(t25_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> k9_lattice5(A,k1_ordinal1(B)) = k6_lattice5(k9_lattice5(A,B)) ) ) ).
fof(t26_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v5_ordinal1(B) )
=> ! [C] :
( v3_ordinal1(C)
=> ( ( v4_ordinal1(C)
& k1_relat_1(B) = C
& ! [D] :
( v3_ordinal1(D)
=> ( r2_hidden(D,C)
=> k1_funct_1(B,D) = k9_lattice5(A,D) ) ) )
=> ( C = k1_xboole_0
| k9_lattice5(A,C) = k3_tarski(k2_relat_1(B)) ) ) ) ) ) ).
fof(t27_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> r1_tarski(A,k9_lattice5(A,B)) ) ) ).
fof(d15_lattice5,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))
=> k10_lattice5(A,B,C,D,E) = k1_funct_1(D,E) ) ) ) ) ) ) ).
fof(t28_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> ( r2_hidden(C,k8_lattice5(A,B,D))
<=> r2_hidden(C,k1_relat_1(E)) ) ) ) ) ) ) ).
fof(d16_lattice5,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)) )
=> k11_lattice5(A,B,C) = C ) ) ) ).
fof(d17_lattice5,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 = k12_lattice5(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)) = k7_lattice5(k9_lattice5(A,H),B,k11_lattice5(k9_lattice5(A,H),B,k1_funct_1(G,H)),k10_lattice5(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(t29_lattice5,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)
=> k12_lattice5(A,B,C,D,k1_xboole_0) = C ) ) ) ) ).
fof(t30_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> k12_lattice5(A,B,D,E,k1_ordinal1(C)) = k7_lattice5(k9_lattice5(A,C),B,k11_lattice5(k9_lattice5(A,C),B,k12_lattice5(A,B,D,E,C)),k10_lattice5(A,B,D,E,C)) ) ) ) ) ) ).
fof(t31_lattice5,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_relat_1(C)
& v1_funct_1(C)
& v5_ordinal1(C) )
=> ! [D] :
( v3_ordinal1(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [F] :
( m1_lattice5(F,A,B,E)
=> ( ( v4_ordinal1(D)
& k1_relat_1(C) = D
& ! [G] :
( v3_ordinal1(G)
=> ( r2_hidden(G,D)
=> k1_funct_1(C,G) = k12_lattice5(A,B,E,F,G) ) ) )
=> ( D = k1_xboole_0
| k12_lattice5(A,B,E,F,D) = k3_tarski(k2_relat_1(C)) ) ) ) ) ) ) ) ) ).
fof(t32_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( v3_ordinal1(C)
=> ( r1_ordinal1(B,C)
=> r1_tarski(k9_lattice5(A,B),k9_lattice5(A,C)) ) ) ) ) ).
fof(t33_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> ( v1_funct_1(k12_lattice5(A,B,D,E,C))
& v1_funct_2(k12_lattice5(A,B,D,E,C),k2_zfmisc_1(k9_lattice5(A,C),k9_lattice5(A,C)),u1_struct_0(B))
& m2_relset_1(k12_lattice5(A,B,D,E,C),k2_zfmisc_1(k9_lattice5(A,C),k9_lattice5(A,C)),u1_struct_0(B)) ) ) ) ) ) ) ).
fof(t34_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> r1_tarski(D,k13_lattice5(A,B,D,E,C)) ) ) ) ) ) ).
fof(t35_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( v3_ordinal1(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [F] :
( m1_lattice5(F,A,B,E)
=> ( r1_ordinal1(C,D)
=> r1_tarski(k13_lattice5(A,B,E,F,C),k13_lattice5(A,B,E,F,D)) ) ) ) ) ) ) ) ).
fof(t36_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v2_lattice5(D,A,B)
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> v2_lattice5(k13_lattice5(A,B,D,E,C),k9_lattice5(A,C),B) ) ) ) ) ) ) ).
fof(t37_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v1_lattice5(D,A,B)
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> v1_lattice5(k13_lattice5(A,B,D,E,C),k9_lattice5(A,C),B) ) ) ) ) ) ) ).
fof(t38_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( ( v1_lattice5(D,A,B)
& v3_lattice5(D,A,B) )
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> ( r1_ordinal1(C,k8_lattice5(A,B,D))
=> v3_lattice5(k13_lattice5(A,B,D,E,C),k9_lattice5(A,C),B) ) ) ) ) ) ) ) ).
fof(t39_lattice5,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] :
( v3_ordinal1(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(B))
& v1_lattice5(D,A,B)
& v2_lattice5(D,A,B)
& v3_lattice5(D,A,B)
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [E] :
( m1_lattice5(E,A,B,D)
=> ( r1_ordinal1(C,k8_lattice5(A,B,D))
=> ( v1_funct_1(k13_lattice5(A,B,D,E,C))
& v1_funct_2(k13_lattice5(A,B,D,E,C),k2_zfmisc_1(k9_lattice5(A,C),k9_lattice5(A,C)),u1_struct_0(B))
& v1_lattice5(k13_lattice5(A,B,D,E,C),k9_lattice5(A,C),B)
& v2_lattice5(k13_lattice5(A,B,D,E,C),k9_lattice5(A,C),B)
& v3_lattice5(k13_lattice5(A,B,D,E,C),k9_lattice5(A,C),B)
& m2_relset_1(k13_lattice5(A,B,D,E,C),k2_zfmisc_1(k9_lattice5(A,C),k9_lattice5(A,C)),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(d18_lattice5,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)) )
=> k14_lattice5(A,B,C) = k9_lattice5(A,k8_lattice5(A,B,C)) ) ) ) ).
fof(d19_lattice5,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)
=> k15_lattice5(A,B,C,D) = k13_lattice5(A,B,C,D,k8_lattice5(A,B,C)) ) ) ) ) ).
fof(d20_lattice5,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)) )
=> ( r2_lattice5(A,B,C,D,E)
<=> ? [F] :
( m1_lattice5(F,A,B,C)
& D = k14_lattice5(A,B,C)
& E = k16_lattice5(A,B,C,F) ) ) ) ) ) ) ) ).
fof(t40_lattice5,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)) )
=> ( r2_lattice5(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)
=> ! [L] :
( m1_subset_1(L,D)
=> ~ ( k1_binop_1(E,F,J) = H
& k4_lattice5(D,B,E,K,L) = H
& k4_lattice5(D,B,E,J,K) = I
& k1_binop_1(E,L,G) = I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d21_lattice5,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_relat_1(D)
& v1_funct_1(D) )
=> ( m2_lattice5(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))
& r2_lattice5(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(t41_lattice5,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] :
( m2_lattice5(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(t42_lattice5,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] :
( m2_lattice5(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(d22_lattice5,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_lattice5(B,u1_struct_0(A),A)
& v2_lattice5(B,u1_struct_0(A),A)
& v3_lattice5(B,u1_struct_0(A),A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
=> ( B = k17_lattice5(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( C != D
=> k4_lattice5(u1_struct_0(A),A,B,C,D) = k13_lattice3(A,C,D) )
& ( C = D
=> k4_lattice5(u1_struct_0(A),A,B,C,D) = k3_yellow_0(A) ) ) ) ) ) ) ) ).
fof(t43_lattice5,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) )
=> v2_funct_2(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ).
fof(t47_lattice5,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] :
( ~ v1_xboole_0(B)
& ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_lattice5(B)))
& v19_waybel_0(C,A,k1_lattice5(B))
& v20_waybel_0(C,A,k1_lattice5(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_lattice5(B)))
& v2_funct_1(C)
& r1_xreal_0(k3_lattice5(B,k2_lattice5(A,k1_lattice5(B),C)),np__3) ) ) ) ).
fof(s1_lattice5,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
? [C] : p1_s1_lattice5(A,B,C) )
=> ? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& k1_relat_1(A) = k5_numbers
& k1_funct_1(A,np__0) = f1_s1_lattice5
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> p1_s1_lattice5(B,k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1))) ) ) ) ).
fof(dt_m1_lattice5,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)) )
=> ! [D] :
( m1_lattice5(D,A,B,C)
=> m1_ordinal1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B))) ) ) ).
fof(existence_m1_lattice5,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)) )
=> ? [D] : m1_lattice5(D,A,B,C) ) ).
fof(dt_m2_lattice5,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))
& 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] :
( m2_lattice5(D,A,B,C)
=> ( v1_relat_1(D)
& v1_funct_1(D) ) ) ) ).
fof(existence_m2_lattice5,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))
& 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] : m2_lattice5(D,A,B,C) ) ).
fof(dt_k1_lattice5,axiom,
! [A] :
( v2_orders_2(k1_lattice5(A))
& v3_orders_2(k1_lattice5(A))
& v4_orders_2(k1_lattice5(A))
& l1_orders_2(k1_lattice5(A)) ) ).
fof(dt_k2_lattice5,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_orders_2(k2_lattice5(A,B,C))
& v4_yellow_0(k2_lattice5(A,B,C),B)
& v5_yellow_0(k2_lattice5(A,B,C),B)
& v6_yellow_0(k2_lattice5(A,B,C),B)
& m1_yellow_0(k2_lattice5(A,B,C),B) ) ) ).
fof(redefinition_k2_lattice5,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k2_lattice5(A,B,C) = k2_yellow_2(A,B,C) ) ).
fof(dt_k3_lattice5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v5_yellow_0(B,k1_lattice5(A))
& v6_yellow_0(B,k1_lattice5(A))
& m1_yellow_0(B,k1_lattice5(A)) )
=> m2_subset_1(k3_lattice5(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k4_lattice5,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_subset_1(D,A)
& m1_subset_1(E,A) )
=> m1_subset_1(k4_lattice5(A,B,C,D,E),u1_struct_0(B)) ) ).
fof(redefinition_k4_lattice5,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_subset_1(D,A)
& m1_subset_1(E,A) )
=> k4_lattice5(A,B,C,D,E) = k1_binop_1(C,D,E) ) ).
fof(dt_k5_lattice5,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))
& 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)) )
=> ( v1_funct_1(k5_lattice5(A,B,C))
& v1_funct_2(k5_lattice5(A,B,C),u1_struct_0(B),u1_struct_0(k1_lattice5(A)))
& m2_relset_1(k5_lattice5(A,B,C),u1_struct_0(B),u1_struct_0(k1_lattice5(A))) ) ) ).
fof(dt_k6_lattice5,axiom,
$true ).
fof(dt_k7_lattice5,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(k7_lattice5(A,B,C,D))
& v1_funct_2(k7_lattice5(A,B,C,D),k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B))
& m2_relset_1(k7_lattice5(A,B,C,D),k2_zfmisc_1(k6_lattice5(A),k6_lattice5(A)),u1_struct_0(B)) ) ) ).
fof(dt_k8_lattice5,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_card_1(k8_lattice5(A,B,C)) ) ).
fof(dt_k9_lattice5,axiom,
$true ).
fof(dt_k10_lattice5,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(k10_lattice5(A,B,C,D,E),k4_zfmisc_1(k9_lattice5(A,E),k9_lattice5(A,E),u1_struct_0(B),u1_struct_0(B))) ) ).
fof(dt_k11_lattice5,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(k11_lattice5(A,B,C))
& v1_funct_2(k11_lattice5(A,B,C),k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(k11_lattice5(A,B,C),k2_zfmisc_1(A,A),u1_struct_0(B)) ) ) ).
fof(dt_k12_lattice5,axiom,
$true ).
fof(dt_k13_lattice5,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(k13_lattice5(A,B,C,D,E))
& v1_funct_2(k13_lattice5(A,B,C,D,E),k2_zfmisc_1(k9_lattice5(A,E),k9_lattice5(A,E)),u1_struct_0(B))
& m2_relset_1(k13_lattice5(A,B,C,D,E),k2_zfmisc_1(k9_lattice5(A,E),k9_lattice5(A,E)),u1_struct_0(B)) ) ) ).
fof(redefinition_k13_lattice5,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) )
=> k13_lattice5(A,B,C,D,E) = k12_lattice5(A,B,C,D,E) ) ).
fof(dt_k14_lattice5,axiom,
$true ).
fof(dt_k15_lattice5,axiom,
$true ).
fof(dt_k16_lattice5,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))
& 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(k16_lattice5(A,B,C,D))
& v1_funct_2(k16_lattice5(A,B,C,D),k2_zfmisc_1(k14_lattice5(A,B,C),k14_lattice5(A,B,C)),u1_struct_0(B))
& v1_lattice5(k16_lattice5(A,B,C,D),k14_lattice5(A,B,C),B)
& v2_lattice5(k16_lattice5(A,B,C,D),k14_lattice5(A,B,C),B)
& v3_lattice5(k16_lattice5(A,B,C,D),k14_lattice5(A,B,C),B)
& m2_relset_1(k16_lattice5(A,B,C,D),k2_zfmisc_1(k14_lattice5(A,B,C),k14_lattice5(A,B,C)),u1_struct_0(B)) ) ) ).
fof(redefinition_k16_lattice5,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))
& 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) )
=> k16_lattice5(A,B,C,D) = k15_lattice5(A,B,C,D) ) ).
fof(dt_k17_lattice5,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) )
=> ( v1_funct_1(k17_lattice5(A))
& v1_funct_2(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_lattice5(k17_lattice5(A),u1_struct_0(A),A)
& v2_lattice5(k17_lattice5(A),u1_struct_0(A),A)
& v3_lattice5(k17_lattice5(A),u1_struct_0(A),A)
& m2_relset_1(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(t2_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) = k3_tarski(a_2_0_lattice5(A,B)) ) ) ).
fof(t3_lattice5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v6_ordinal1(A)
=> k2_zfmisc_1(k3_tarski(A),k3_tarski(A)) = k3_tarski(a_1_0_lattice5(A)) ) ) ).
fof(d12_lattice5,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] :
( v1_card_1(D)
=> ( D = k8_lattice5(A,B,C)
<=> r2_tarski(D,a_3_0_lattice5(A,B,C)) ) ) ) ) ) ).
fof(d14_lattice5,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_ordinal1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
=> ( m1_lattice5(D,A,B,C)
<=> ( v1_card_1(k1_relat_1(D))
& v2_funct_1(D)
& k2_relat_1(D) = a_3_0_lattice5(A,B,C) ) ) ) ) ) ) ).
fof(t44_lattice5,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_lattice5(B,u1_struct_0(A),A,k17_lattice5(A))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( C = k3_tarski(a_2_1_lattice5(A,B))
=> ( v1_funct_1(k3_tarski(a_2_2_lattice5(A,B)))
& v1_funct_2(k3_tarski(a_2_2_lattice5(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A))
& v1_lattice5(k3_tarski(a_2_2_lattice5(A,B)),C,A)
& v2_lattice5(k3_tarski(a_2_2_lattice5(A,B)),C,A)
& v3_lattice5(k3_tarski(a_2_2_lattice5(A,B)),C,A)
& m2_relset_1(k3_tarski(a_2_2_lattice5(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A)) ) ) ) ) ) ).
fof(t45_lattice5,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_lattice5(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_1_lattice5(A,B))
& D = k3_tarski(a_2_2_lattice5(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)
=> ! [K] :
( m1_subset_1(K,C)
=> ~ ( k4_lattice5(C,A,D,E,I) = G
& k4_lattice5(C,A,D,J,K) = G
& k4_lattice5(C,A,D,I,J) = H
& k4_lattice5(C,A,D,K,F) = H ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_lattice5,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_lattice5(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] :
( m1_subset_1(F,C)
=> ! [G] :
( m1_subset_1(G,C)
=> ! [H] :
( ( v1_partfun1(H,C,C)
& v3_relat_2(H)
& v8_relat_2(H)
& m2_relset_1(H,C,C) )
=> ! [I] :
( ( v1_partfun1(I,C,C)
& v3_relat_2(I)
& v8_relat_2(I)
& m2_relset_1(I,C,C) )
=> ! [J,K] :
~ ( E = k5_lattice5(C,A,D)
& C = k3_tarski(a_2_1_lattice5(A,B))
& D = k3_tarski(a_2_2_lattice5(A,B))
& r2_hidden(H,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E)))
& r2_hidden(I,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E)))
& r2_hidden(k4_tarski(J,K),k5_eqrel_1(C,H,I))
& ! [L] :
( ( ~ v1_xboole_0(L)
& m2_finseq_1(L,C) )
=> ~ ( k3_finseq_1(L) = k1_nat_1(np__3,np__2)
& r1_lattice5(C,L,J,K,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_lattice5,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C) )
=> ( r2_hidden(A,a_2_0_lattice5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,B)
& m1_subset_1(E,C)
& A = k2_zfmisc_1(D,E)
& r2_hidden(D,B)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_1_0_lattice5,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_0_lattice5(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k2_zfmisc_1(C,C)
& r2_hidden(C,B) ) ) ) ).
fof(fraenkel_a_3_0_lattice5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_yellow_0(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),u1_struct_0(C))
& m2_relset_1(D,k2_zfmisc_1(B,B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_lattice5(B,C,D))
<=> ? [E,F,G,H] :
( m1_subset_1(E,B)
& m1_subset_1(F,B)
& m1_subset_1(G,u1_struct_0(C))
& m1_subset_1(H,u1_struct_0(C))
& A = k5_domain_1(B,B,u1_struct_0(C),u1_struct_0(C),E,F,G,H)
& r3_orders_2(C,k4_lattice5(B,C,D,E,F),k13_lattice3(C,G,H)) ) ) ) ).
fof(fraenkel_a_2_1_lattice5,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)
& l1_orders_2(B)
& m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) )
=> ( r2_hidden(A,a_2_1_lattice5(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k1_mcart_1(k1_funct_1(C,D)) ) ) ) ).
fof(fraenkel_a_2_2_lattice5,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)
& l1_orders_2(B)
& m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) )
=> ( r2_hidden(A,a_2_2_lattice5(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_mcart_1(k1_funct_1(C,D)) ) ) ) ).
%------------------------------------------------------------------------------