SET007 Axioms: SET007+537.ax
%------------------------------------------------------------------------------
% File : SET007+537 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Completely-Irreducible 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 : waybel16 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 46 ( 4 unt; 0 def)
% Number of atoms : 421 ( 27 equ)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 417 ( 42 ~; 1 |; 250 &)
% ( 8 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 43 ( 42 usr; 0 prp; 1-3 aty)
% Number of functors : 30 ( 30 usr; 0 con; 1-3 aty)
% Number of variables : 114 ( 107 !; 7 ?)
% 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_waybel16,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) )
=> ~ v1_xboole_0(k9_waybel_0(A)) ) ).
fof(fc2_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k9_waybel_0(A)))
& v1_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v2_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v3_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v4_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v2_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v3_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v1_yellow_0(k2_yellow_1(k9_waybel_0(A)))
& v24_waybel_0(k2_yellow_1(k9_waybel_0(A)))
& v25_waybel_0(k2_yellow_1(k9_waybel_0(A))) ) ) ).
fof(t1_waybel16,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k7_waybel_0(A,C))) = k13_lattice3(A,B,C) ) ) ) ).
fof(t2_waybel16,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_yellow_0(A,k5_subset_1(u1_struct_0(A),k6_waybel_0(A,B),k6_waybel_0(A,C))) = k12_lattice3(A,B,C) ) ) ) ).
fof(t3_waybel16,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))
=> ( r3_waybel_4(A,k4_xboole_0(u1_struct_0(A),k7_waybel_0(A,C)),B)
=> k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)) = k5_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k7_waybel_0(A,C)) ) ) ) ) ).
fof(t4_waybel16,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))
=> ( r5_waybel_4(A,k4_xboole_0(u1_struct_0(A),k6_waybel_0(A,C)),B)
=> k6_subset_1(u1_struct_0(A),k6_waybel_0(A,B),k1_struct_0(A,B)) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,B),k6_waybel_0(A,C)) ) ) ) ) ).
fof(t5_waybel16,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
=> ( ( B = D
& C = E )
=> k2_yellow_4(A,B,C) = k4_yellow_4(k7_lattice3(A),D,E) ) ) ) ) ) ) ).
fof(t6_waybel16,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
=> ( ( B = D
& C = E )
=> k4_yellow_4(A,B,C) = k2_yellow_4(k7_lattice3(A),D,E) ) ) ) ) ) ) ).
fof(t7_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)) ) ).
fof(t8_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k8_waybel_0(A) = k9_waybel_0(k7_lattice3(A)) ) ).
fof(d1_waybel16,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] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(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))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( m1_waybel16(C,A,B)
<=> ( v22_waybel_0(C,A,B)
& v17_waybel_0(C,A,B) ) ) ) ) ) ).
fof(d2_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_waybel16(A,B)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(C))
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ? [E] :
( m1_waybel16(E,A,C)
& k7_relat_1(E,B) = D
& ! [F] :
( m1_waybel16(F,A,C)
=> ( k7_relat_1(F,B) = D
=> F = E ) ) ) ) ) ) ) ) ).
fof(t9_waybel16,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))))) )
=> ( ~ v1_xboole_0(k1_setfam_1(B))
& v2_waybel_0(k1_setfam_1(B),k3_yellow_1(A))
& v13_waybel_0(k1_setfam_1(B),k3_yellow_1(A))
& m1_subset_1(k1_setfam_1(B),k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) ) ) ).
fof(t10_waybel16,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))))) )
=> ( r2_yellow_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A))),B)
& k2_yellow_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A))),B) = k1_setfam_1(B) ) ) ).
fof(t11_waybel16,axiom,
! [A] :
( ~ v1_xboole_0(k1_zfmisc_1(A))
& v2_waybel_0(k1_zfmisc_1(A),k3_yellow_1(A))
& v13_waybel_0(k1_zfmisc_1(A),k3_yellow_1(A))
& m1_subset_1(k1_zfmisc_1(A),k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) ) ).
fof(t12_waybel16,axiom,
! [A] :
( ~ v1_xboole_0(k1_tarski(A))
& v2_waybel_0(k1_tarski(A),k3_yellow_1(A))
& v13_waybel_0(k1_tarski(A),k3_yellow_1(A))
& m1_subset_1(k1_tarski(A),k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) ) ).
fof(t13_waybel16,axiom,
! [A] : v2_yellow_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))) ).
fof(t14_waybel16,axiom,
! [A] : v1_yellow_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))) ).
fof(t15_waybel16,axiom,
! [A] : k4_yellow_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))) = k1_zfmisc_1(A) ).
fof(t16_waybel16,axiom,
! [A] : k3_yellow_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))) = k1_tarski(A) ).
fof(t17_waybel16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) )
=> ( r1_yellow_0(k2_yellow_1(A),B)
=> r1_tarski(k3_tarski(B),k1_yellow_0(k2_yellow_1(A),B)) ) ) ) ).
fof(t18_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> v3_lattice3(k2_yellow_1(k9_waybel_0(A))) ) ).
fof(d3_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel16(B,A)
<=> r1_waybel_1(A,k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B))) ) ) ) ).
fof(t19_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( v1_waybel16(B,A)
& k2_yellow_0(A,k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B))) = B ) ) ) ).
fof(d4_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = k1_waybel16(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
<=> v1_waybel16(C,A) ) ) ) ) ) ).
fof(t20_waybel16,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,u1_struct_0(A))
=> ( v1_waybel16(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_orders_2(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_orders_2(A,B,D)
=> r3_orders_2(A,C,D) ) )
& k7_waybel_0(A,B) = k4_subset_1(u1_struct_0(A),k1_struct_0(A,B),k7_waybel_0(A,C)) ) ) ) ) ).
fof(t21_waybel16,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) )
=> ~ r2_hidden(k4_yellow_0(A),k1_waybel16(A)) ) ).
fof(t22_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> r1_tarski(k1_waybel16(A),k3_waybel_6(A)) ) ).
fof(t23_waybel16,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))
=> ( v1_waybel16(B,A)
=> v2_waybel_6(B,A) ) ) ) ).
fof(t24_waybel16,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,u1_struct_0(A))
=> ( v1_waybel16(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_yellow_0(A,C)
& B = k2_yellow_0(A,C) )
=> r2_hidden(B,C) ) ) ) ) ) ).
fof(t25_waybel16,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)))
=> ( v4_waybel_6(B,A)
=> r1_tarski(k1_waybel16(A),B) ) ) ) ).
fof(t26_waybel16,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r3_waybel_4(A,k4_xboole_0(u1_struct_0(A),k7_waybel_0(A,C)),B) )
=> v1_waybel16(B,A) ) ) ) ).
fof(t27_waybel16,axiom,
! [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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_orders_2(A,B,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_orders_2(A,B,E)
=> r1_orders_2(A,C,E) ) ) )
=> ( r1_orders_2(A,D,B)
| k13_lattice3(A,B,D) = k13_lattice3(A,C,D) ) ) ) ) ) ) ).
fof(t28_waybel16,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_orders_2(A,B,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_orders_2(A,B,E)
=> r3_orders_2(A,C,E) ) )
& ~ r3_orders_2(A,D,B)
& r3_orders_2(A,k12_lattice3(A,D,C),B) ) ) ) ) ) ).
fof(t29_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(k7_lattice3(A))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel16(B,A)
=> ( ~ v1_xboole_0(k4_xboole_0(u1_struct_0(A),k6_waybel_0(A,B)))
& v2_waybel_0(k4_xboole_0(u1_struct_0(A),k6_waybel_0(A,B)),A)
& v13_waybel_0(k4_xboole_0(u1_struct_0(A),k6_waybel_0(A,B)),A)
& v1_waybel_6(k4_xboole_0(u1_struct_0(A),k6_waybel_0(A,B)),A)
& m1_subset_1(k4_xboole_0(u1_struct_0(A),k6_waybel_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t30_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ( v2_waybel_2(k7_lattice3(A))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( v1_waybel16(B,A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,u1_struct_0(k1_waybel_8(A)))
& r3_waybel_4(A,k4_xboole_0(u1_struct_0(A),k7_waybel_0(A,C)),B) ) ) ) ) ) ) ).
fof(t31_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(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))
=> ~ ( v1_waybel16(D,A)
& r3_orders_2(A,B,D)
& ~ r3_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(t32_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ( v4_waybel_6(k1_waybel16(A),A)
& ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_waybel_6(B,A)
=> r1_tarski(k1_waybel16(A),B) ) ) ) ) ).
fof(t33_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> B = k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_waybel16(A))) ) ) ).
fof(t34_waybel16,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v1_waybel16(C,A)
& C = k2_yellow_0(A,B) )
=> r2_hidden(C,B) ) ) ) ) ).
fof(t36_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_hidden(C,u1_struct_0(k1_waybel_8(A)))
& r3_waybel_4(A,k4_xboole_0(u1_struct_0(A),k7_waybel_0(A,C)),B) )
<=> v1_waybel16(B,A) ) ) ) ).
fof(dt_m1_waybel16,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel16(C,A,B)
=> ( 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)) ) ) ) ).
fof(existence_m1_waybel16,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ? [C] : m1_waybel16(C,A,B) ) ).
fof(dt_k1_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m1_subset_1(k1_waybel16(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(t35_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_waybel16(B,A)
=> B = k2_yellow_0(A,a_2_0_waybel16(A,B)) ) ) ) ).
fof(fraenkel_a_2_0_waybel16,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel_8(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_waybel16(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r2_hidden(D,k7_waybel_0(B,C))
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r2_hidden(E,u1_struct_0(k1_waybel_8(B)))
& r3_waybel_4(B,k4_xboole_0(u1_struct_0(B),k7_waybel_0(B,E)),D) ) ) ) ) ).
%------------------------------------------------------------------------------