SET007 Axioms: SET007+496.ax
%------------------------------------------------------------------------------
% File : SET007+496 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Irreducible and Prime Elements
% 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 : waybel_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 61 ( 0 unt; 0 def)
% Number of atoms : 722 ( 31 equ)
% Maximal formula atoms : 22 ( 11 avg)
% Number of connectives : 729 ( 68 ~; 0 |; 458 &)
% ( 32 <=>; 171 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 55 ( 54 usr; 0 prp; 1-3 aty)
% Number of functors : 42 ( 42 usr; 7 con; 0-5 aty)
% Number of variables : 179 ( 168 !; 11 ?)
% 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(cc1_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_orders_2(B,A)
=> ( v5_orders_2(B,A)
& v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ) ) ).
fof(rc1_waybel_6,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(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)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ).
fof(rc2_waybel_6,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_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))
& v18_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ).
fof(rc3_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& v1_waybel_6(B,A) ) ) ).
fof(rc4_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& v2_waybel_6(B,A) ) ) ).
fof(rc5_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& v5_waybel_6(B,A) ) ) ).
fof(t1_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( v19_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,k12_lattice3(A,D,E)) = k12_lattice3(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) ).
fof(t2_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_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)) )
=> ( v20_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,k13_lattice3(A,D,E)) = k13_lattice3(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) ).
fof(t3_waybel_6,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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)) )
=> ( ( v2_waybel_1(B)
& v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v2_funct_1(C) )
=> v2_waybel_1(A) ) ) ) ) ).
fof(t4_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v2_waybel_2(B)
& v19_waybel_0(C,A,B)
& v2_funct_1(C) )
=> v2_waybel_2(A) ) ) ) ) ).
fof(d1_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r1_waybel_3(A,D,C) ) ) ) ) ) ) ) ).
fof(t5_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& r1_xboole_0(k1_waybel_3(A,C),B) ) ) ) ) ) ).
fof(t7_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_waybel_6(k2_waybel_3(A,B),A) ) ) ).
fof(t8_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,B,C)
& ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,A)
& v13_waybel_0(D,A)
& v1_waybel_6(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(C,D)
& r1_tarski(D,k2_waybel_3(A,B)) ) ) ) ) ) ) ).
fof(t9_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& v1_waybel_6(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r3_orders_2(A,C,D)
& r3_waybel_4(A,k3_subset_1(u1_struct_0(A),B),D) ) ) ) ) ) ) ).
fof(d2_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( B = k11_lattice3(A,C,D)
& C != B
& D != B ) ) ) ) ) ) ).
fof(d3_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( B = k10_lattice3(A,C,D)
& C != B
& D != B ) ) ) ) ) ) ).
fof(d4_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = k3_waybel_6(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
<=> v2_waybel_6(C,A) ) ) ) ) ) ).
fof(t10_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> v2_waybel_6(k4_yellow_0(A),A) ) ).
fof(t11_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_waybel_6(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = k2_yellow_0(A,C)
=> r2_hidden(B,C) ) ) ) ) ) ).
fof(t12_waybel_6,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_subset_1(B,u1_struct_0(A))
=> ( ( ~ v1_xboole_0(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)))
& v2_waybel_0(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)),A)
& v13_waybel_0(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)),A)
& m1_subset_1(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel_6(B,A) ) ) ) ).
fof(t13_waybel_6,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_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_waybel_4(A,k3_subset_1(u1_struct_0(A),C),B)
=> v2_waybel_6(B,A) ) ) ) ) ).
fof(t14_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ~ r3_orders_2(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( v2_waybel_6(D,A)
& r3_orders_2(A,B,D)
& ~ r3_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(d5_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,C),B))
& C = k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,C),B)) ) ) ) ) ) ).
fof(t15_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
& C = k2_yellow_0(A,D) ) ) ) ) ) ).
fof(t16_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,C)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(C))
=> r2_hidden(k2_yellow_0(A,D),C) ) )
=> u1_struct_0(A) = C ) ) ) ) ) ).
fof(t17_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( ~ r3_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& r3_orders_2(A,C,E)
& ~ r3_orders_2(A,D,E) ) ) ) ) ) ) ) ) ).
fof(t18_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = k6_subset_1(u1_struct_0(A),k3_waybel_6(A),k1_struct_0(A,k4_yellow_0(A)))
=> v4_waybel_6(B,A) ) ) ) ).
fof(t19_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_waybel_6(B,A)
& r1_tarski(B,C) )
=> v4_waybel_6(C,A) ) ) ) ) ).
fof(d6_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_orders_2(A,k11_lattice3(A,C,D),B)
& ~ r1_orders_2(A,C,B)
& ~ r1_orders_2(A,D,B) ) ) ) ) ) ) ).
fof(d7_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = k4_waybel_6(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
<=> v5_waybel_6(C,A) ) ) ) ) ) ).
fof(d8_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v6_waybel_6(B,A)
<=> v5_waybel_6(k8_lattice3(A,B),k7_lattice3(A)) ) ) ) ).
fof(t20_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> v5_waybel_6(k4_yellow_0(A),A) ) ).
fof(t21_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> v6_waybel_6(k3_yellow_0(A),A) ) ).
fof(t22_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_orders_2(A,k2_yellow_0(A,C),B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r1_orders_2(A,D,B) ) ) ) ) ) ) ) ).
fof(t23_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v6_waybel_6(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r3_orders_2(A,B,k1_yellow_0(A,C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r3_orders_2(A,B,D) ) ) ) ) ) ) ) ).
fof(t24_waybel_6,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_subset_1(B,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
=> v2_waybel_6(B,A) ) ) ) ).
fof(t25_waybel_6,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_subset_1(B,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
<=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(C))))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(C)))) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k7_yellow_2(u1_struct_0(A),k3_yellow_1(k1_tarski(C)),D,E) = k1_xboole_0
<=> r3_orders_2(A,E,B) ) )
=> ( v19_waybel_0(D,A,k3_yellow_1(k1_tarski(C)))
& v20_waybel_0(D,A,k3_yellow_1(k1_tarski(C))) ) ) ) ) ) ) ).
fof(t26_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k4_yellow_0(A)
=> ( v5_waybel_6(B,A)
<=> ( ~ v1_xboole_0(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)))
& v2_waybel_0(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A)
& v13_waybel_0(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A)
& m1_subset_1(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t27_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_waybel_6(B,A)
<=> v2_waybel_6(B,A) ) ) ) ).
fof(t28_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> k4_waybel_6(A) = k3_waybel_6(A) ) ).
fof(t29_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k4_yellow_0(A)
=> ( v5_waybel_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_orders_2(A,B,C)
=> C = k4_yellow_0(A) ) ) ) ) ) ) ).
fof(t30_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k4_yellow_0(A)
=> ( v5_waybel_6(B,A)
<=> ? [C] :
( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& v13_waybel_0(C,A)
& v1_waybel_6(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& r3_waybel_4(A,k3_subset_1(u1_struct_0(A),C),B) ) ) ) ) ) ).
fof(t31_waybel_6,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_funct_1(k5_funct_3(B,u1_struct_0(A)))
& v1_funct_2(k5_funct_3(B,u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0))))
& m2_relset_1(k5_funct_3(B,u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0)))) ) ) ) ).
fof(t32_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k8_funct_2(u1_struct_0(A),k2_tarski(np__0,np__1),k5_funct_3(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),u1_struct_0(A)),C) = k1_xboole_0
<=> r1_orders_2(A,C,B) ) ) ) ) ).
fof(t33_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0)))) )
=> ! [C] :
( ( v5_waybel_6(C,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ( k5_funct_3(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,C)),u1_struct_0(A)) = B
=> ( v19_waybel_0(B,A,k3_yellow_1(k1_tarski(k1_xboole_0)))
& v20_waybel_0(B,A,k3_yellow_1(k1_tarski(k1_xboole_0))) ) ) ) ) ) ).
fof(t34_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v4_waybel_6(k4_waybel_6(A),A)
=> ( v2_waybel_1(A)
& v2_waybel_2(A) ) ) ) ).
fof(t35_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(A)
<=> v4_waybel_6(k4_waybel_6(A),A) ) ) ).
fof(t36_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(A)
<=> v9_waybel_1(A) ) ) ).
fof(t37_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& B = k1_yellow_0(A,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> v6_waybel_6(D,A) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> B = k1_yellow_0(A,k3_xboole_0(k1_waybel_3(A,B),k4_waybel_6(k7_lattice3(A)))) ) ) ) ).
fof(t38_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v1_waybel_5(A)
<=> ( v3_waybel_3(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& B = k1_yellow_0(A,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> v6_waybel_6(D,A) ) ) ) ) ) ) ) ).
fof(t39_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v1_waybel_5(A)
<=> ( v2_waybel_1(A)
& v3_waybel_3(A)
& v3_waybel_3(k7_lattice3(A)) ) ) ) ).
fof(s1_waybel_6,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_waybel_6))
=> ~ ( r2_hidden(A,f2_s1_waybel_6)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel_6))
=> ~ ( r2_hidden(B,f3_s1_waybel_6)
& p1_s1_waybel_6(A,B) ) ) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f2_s1_waybel_6,f3_s1_waybel_6)
& m2_relset_1(A,f2_s1_waybel_6,f3_s1_waybel_6)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel_6))
=> ~ ( r2_hidden(B,f2_s1_waybel_6)
& ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s1_waybel_6))
=> ~ ( r2_hidden(C,f3_s1_waybel_6)
& C = k1_funct_1(A,B)
& p1_s1_waybel_6(B,C) ) ) ) ) ) ) ).
fof(dt_k1_waybel_6,axiom,
! [A,B,C,D] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(C)
& v1_funct_2(C,B,B)
& m1_relset_1(C,B,B)
& m1_subset_1(D,k5_numbers) )
=> ( v1_funct_1(k1_waybel_6(A,B,C,D))
& v1_funct_2(k1_waybel_6(A,B,C,D),B,B)
& m2_relset_1(k1_waybel_6(A,B,C,D),B,B) ) ) ).
fof(redefinition_k1_waybel_6,axiom,
! [A,B,C,D] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(C)
& v1_funct_2(C,B,B)
& m1_relset_1(C,B,B)
& m1_subset_1(D,k5_numbers) )
=> k1_waybel_6(A,B,C,D) = k9_funct_7(C,D) ) ).
fof(dt_k2_waybel_6,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(D)
& v1_funct_2(D,B,C)
& m1_relset_1(D,B,C)
& m1_subset_1(E,B) )
=> m1_subset_1(k2_waybel_6(A,B,C,D,E),u1_struct_0(A)) ) ).
fof(redefinition_k2_waybel_6,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(D)
& v1_funct_2(D,B,C)
& m1_relset_1(D,B,C)
& m1_subset_1(E,B) )
=> k2_waybel_6(A,B,C,D,E) = k1_funct_1(D,E) ) ).
fof(dt_k3_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m1_subset_1(k3_waybel_6(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k4_waybel_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m1_subset_1(k4_waybel_6(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(t6_waybel_6,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_waybel_6(B,A)
<=> B = k3_tarski(a_2_0_waybel_6(A,B)) ) ) ) ).
fof(fraenkel_a_2_0_waybel_6,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v13_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_waybel_6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k2_waybel_3(B,D)
& r2_hidden(D,C) ) ) ) ).
%------------------------------------------------------------------------------