SET007 Axioms: SET007+763.ax
%------------------------------------------------------------------------------
% File : SET007+763 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Morphisms Into Chains. Part I
% 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 : waybel35 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 70 ( 6 unt; 0 def)
% Number of atoms : 547 ( 24 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 534 ( 57 ~; 0 |; 275 &)
% ( 13 <=>; 189 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 0 con; 1-4 aty)
% Number of variables : 220 ( 205 !; 15 ?)
% 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_waybel35,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& v1_realset1(B) ) ).
fof(cc1_waybel35,axiom,
! [A] :
( v1_realset1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_realset1(B) ) ) ).
fof(rc2_waybel35,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_realset1(B) ) ) ).
fof(rc3_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_realset1(B) ) ) ).
fof(rc4_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_realset1(B) ) ) ).
fof(rc5_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_realset1(B) ) ) ).
fof(rc6_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_waybel_4(B,A) ) ) ).
fof(rc7_waybel35,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_waybel_4(B,A)
& v2_waybel_4(B,A) ) ) ).
fof(rc8_waybel35,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v3_waybel_4(B,A) ) ) ).
fof(rc9_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v4_waybel_4(B,A) ) ) ).
fof(cc2_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v1_waybel35(B,A)
=> ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v4_waybel_4(B,A) ) ) ) ) ).
fof(cc3_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v4_waybel_4(B,A) )
=> v1_waybel35(B,A) ) ) ) ).
fof(cc4_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v3_waybel_4(B,A)
& v1_waybel35(B,A) )
=> ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v3_waybel_4(B,A)
& v4_waybel_4(B,A)
& v5_waybel_4(B,A)
& v1_waybel35(B,A) ) ) ) ) ).
fof(cc5_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v5_waybel_4(B,A)
=> ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v4_waybel_4(B,A)
& v1_waybel35(B,A) ) ) ) ) ).
fof(rc10_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v4_waybel_4(B,A)
& v1_waybel35(B,A) ) ) ).
fof(fc1_waybel35,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v2_waybel_4(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_relat_1(k1_waybel35(A,B))
& v1_funct_1(k1_waybel35(A,B))
& v1_funct_2(k1_waybel35(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A))))
& v5_orders_3(k1_waybel35(A,B),A,k2_yellow_1(k4_lattice7(A))) ) ) ).
fof(rc11_waybel35,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ? [C] :
( m1_waybel35(C,A,B)
& ~ v1_xboole_0(C)
& v1_realset1(C) ) ) ).
fof(fc2_waybel35,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& m1_waybel35(C,A,B) )
=> ~ v1_xboole_0(k2_waybel35(A,B,C)) ) ).
fof(cc6_waybel35,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( v1_realset1(C)
=> v3_waybel35(C,A,B) ) ) ) ).
fof(rc12_waybel35,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ? [C] :
( m1_waybel35(C,A,B)
& ~ v1_xboole_0(C)
& v1_realset1(C)
& v3_waybel35(C,A,B) ) ) ).
fof(t1_waybel35,axiom,
! [A] : r1_relat_2(k1_yellow_1(A),A) ).
fof(t2_waybel35,axiom,
! [A] : r8_relat_2(k1_yellow_1(A),A) ).
fof(t3_waybel35,axiom,
! [A] : r4_relat_2(k1_yellow_1(A),A) ).
fof(d1_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( v1_waybel35(B,A)
<=> ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& v4_waybel_4(B,A) ) ) ) ) ).
fof(d2_waybel35,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A))))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A)))) )
=> ( C = k1_waybel35(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_waybel_0(A,k2_yellow_1(k4_lattice7(A)),C,D) = k5_waybel_4(A,D,B) ) ) ) ) ) ).
fof(d3_waybel35,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_waybel35(C,A,B)
<=> ! [D,E] :
~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& ~ r2_hidden(k4_tarski(D,E),B)
& D != E
& ~ r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) ).
fof(t4_waybel35,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( v1_realset1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> m1_waybel35(B,A,C) ) ) ) ).
fof(t5_waybel35,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(D,C)
& r2_hidden(E,C)
& r2_orders_2(A,D,E) )
=> r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) ).
fof(t6_waybel35,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(k4_tarski(C,D),B)
& r2_hidden(k4_tarski(D,C),B) )
=> C = D ) ) ) ) ) ).
fof(t7_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v4_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> m1_waybel35(k2_struct_0(A,k3_yellow_0(A),B),A,C) ) ) ) ).
fof(t8_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> m1_waybel35(k4_subset_1(u1_struct_0(A),C,k1_struct_0(A,k3_yellow_0(A))),A,B) ) ) ) ).
fof(d4_waybel35,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( v2_waybel35(C,A,B)
<=> ! [D] :
( m1_waybel35(D,A,B)
=> ( r1_lattice7(A,C,D)
=> C = D ) ) ) ) ) ) ).
fof(d5_waybel35,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C,D] :
( D = k2_waybel35(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> ( m1_waybel35(E,A,B)
& r1_tarski(C,E) ) ) ) ) ) ).
fof(t9_waybel35,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( r4_orders_1(k1_yellow_1(k2_waybel35(A,B,C)),k2_waybel35(A,B,C))
& ? [D] :
( r6_orders_1(k1_yellow_1(k2_waybel35(A,B,C)),D)
& r1_tarski(C,D) ) ) ) ) ) ).
fof(t10_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ( ( r1_yellow_0(A,C)
& r2_hidden(k1_yellow_0(A,C),B) )
=> ( r1_yellow_0(k5_yellow_0(A,B),C)
& k1_yellow_0(A,C) = k1_yellow_0(k5_yellow_0(A,B),C) ) ) ) ) ) ).
fof(t11_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_waybel35(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(C))
=> ( ( r1_yellow_0(A,D)
& v2_waybel35(C,A,B) )
=> r1_yellow_0(k5_yellow_0(A,C),D) ) ) ) ) ) ).
fof(t12_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_waybel35(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(C))
=> ( ( r2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,k1_yellow_0(A,D)),C))
& r1_yellow_0(A,D)
& v2_waybel35(C,A,B) )
=> ( k1_yellow_0(k5_yellow_0(A,C),D) = k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,k1_yellow_0(A,D)),C))
& ( ~ r2_hidden(k1_yellow_0(A,D),C)
=> r2_orders_2(A,k1_yellow_0(A,D),k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,k1_yellow_0(A,D)),C))) ) ) ) ) ) ) ) ).
fof(t13_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_waybel35(C,A,B) )
=> ( v2_waybel35(C,A,B)
=> v3_lattice3(k5_yellow_0(A,C)) ) ) ) ) ).
fof(t14_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( v2_waybel35(C,A,B)
=> r2_hidden(k3_yellow_0(A),C) ) ) ) ) ).
fof(t15_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( v2_waybel35(C,A,B)
& r4_waybel_1(A,D,C)
& r2_hidden(k4_tarski(D,k4_yellow_0(A)),B) )
=> ( r2_hidden(k4_tarski(k4_yellow_0(A),k4_yellow_0(A)),B)
& D = k4_yellow_0(A) ) ) ) ) ) ) ).
fof(d6_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> ( r1_waybel35(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(k4_tarski(D,E),C)
& D != E
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_hidden(F,B)
& r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(F,E),C)
& D != F ) ) ) ) ) ) ) ) ).
fof(d7_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( v3_waybel35(C,A,B)
<=> r1_waybel35(A,C,B) ) ) ) ) ).
fof(t16_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( ( v1_waybel_4(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( r1_waybel35(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(k4_tarski(D,E),C)
& D != E
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_hidden(F,B)
& r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(F,E),C)
& r2_orders_2(A,D,F) ) ) ) ) ) ) ) ) ).
fof(t17_waybel35,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( ( v2_waybel35(C,A,B)
& v8_waybel_4(B,A) )
=> r1_waybel35(A,C,B) ) ) ) ) ).
fof(d8_waybel35,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] : k3_waybel35(A,B,C) = k3_xboole_0(k10_relat_1(A,k1_tarski(C)),B) ) ).
fof(t18_waybel35,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C,D] :
( r2_hidden(C,k3_waybel35(A,B,D))
<=> ( r2_hidden(k4_tarski(C,D),A)
& r2_hidden(C,B) ) ) ) ).
fof(t19_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C,D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_lattice3(A,k4_waybel35(A,B,C,D),D) ) ) ) ).
fof(t20_waybel35,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_orders_2(A,D,E)
=> r1_lattice7(A,k4_waybel35(A,B,C,D),k4_waybel35(A,B,C,E)) ) ) ) ) ) ) ).
fof(t21_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C,D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(D,C)
& r2_hidden(k4_tarski(D,D),B)
& r1_yellow_0(A,k4_waybel35(A,B,C,D)) )
=> D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) ) ) ).
fof(d9_waybel35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel35(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ( r1_yellow_0(A,C)
=> k1_yellow_0(A,C) = k1_yellow_0(k5_yellow_0(A,B),C) ) ) ) ) ) ).
fof(t22_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel35(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v3_waybel35(C,A,B)
& m1_waybel35(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& r2_orders_2(A,D,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_orders_2(A,D,F)
& r2_hidden(k4_tarski(F,E),B)
& F = k1_yellow_0(A,k4_waybel35(A,B,C,F)) ) ) ) ) ) ) ) ) ).
fof(t23_waybel35,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] :
( ( v1_waybel35(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_waybel35(C,A,B) )
=> ( ( v4_waybel35(C,A)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> r1_yellow_0(A,k4_waybel35(A,B,C,D)) ) )
& r1_waybel35(A,C,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) ) ) ) ) ).
fof(t24_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> ( r1_yellow_0(A,k4_waybel35(A,B,C,D))
& D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) )
=> r1_waybel35(A,C,B) ) ) ) ) ).
fof(d10_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C,D] :
( D = k5_waybel35(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> E = k1_yellow_0(A,k4_waybel35(A,B,C,E)) ) ) ) ) ).
fof(t25_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_yellow_0(A,k4_waybel35(A,B,C,D)) )
=> m1_waybel35(k6_waybel35(A,B,C),A,B) ) ) ) ) ).
fof(t26_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_4(B,A)
& v2_waybel_4(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_yellow_0(A,k4_waybel35(A,B,C,D)) )
=> v4_waybel35(k6_waybel35(A,B,C),A) ) ) ) ) ).
fof(t28_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel35(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v3_waybel35(C,A,B)
& m1_waybel35(C,A,B) )
=> r1_waybel35(A,k6_waybel35(A,B,C),B) ) ) ) ).
fof(t29_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel35(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v3_waybel35(C,A,B)
& m1_waybel35(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& r2_orders_2(A,D,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_hidden(F,k6_waybel35(A,B,C))
& r2_orders_2(A,D,F)
& r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ) ) ).
fof(dt_m1_waybel35,axiom,
! [A,B] :
( ( l1_struct_0(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_waybel35(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_waybel35,axiom,
! [A,B] :
( ( l1_struct_0(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ? [C] : m1_waybel35(C,A,B) ) ).
fof(dt_k1_waybel35,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v2_waybel_4(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_funct_1(k1_waybel35(A,B))
& v1_funct_2(k1_waybel35(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A))))
& m2_relset_1(k1_waybel35(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A)))) ) ) ).
fof(dt_k2_waybel35,axiom,
$true ).
fof(dt_k3_waybel35,axiom,
$true ).
fof(dt_k4_waybel35,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> m1_subset_1(k4_waybel35(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(redefinition_k4_waybel35,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> k4_waybel35(A,B,C,D) = k3_waybel35(B,C,D) ) ).
fof(dt_k5_waybel35,axiom,
$true ).
fof(dt_k6_waybel35,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> m1_subset_1(k6_waybel35(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(redefinition_k6_waybel35,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> k6_waybel35(A,B,C) = k5_waybel35(A,B,C) ) ).
fof(t27_waybel35,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel35(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v3_waybel35(C,A,B)
& m1_waybel35(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k6_waybel35(A,B,C))
=> D = k1_yellow_0(A,a_4_0_waybel35(A,B,C,D)) ) ) ) ) ) ).
fof(fraenkel_a_4_0_waybel35,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& l1_orders_2(B)
& v1_waybel35(C,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B))
& v3_waybel35(D,B,C)
& m1_waybel35(D,B,C)
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_0_waybel35(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = F
& r2_hidden(F,k6_waybel35(B,C,D))
& r2_hidden(k4_tarski(F,E),C) ) ) ) ).
%------------------------------------------------------------------------------