SET007 Axioms: SET007+545.ax
%------------------------------------------------------------------------------
% File : SET007+545 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Injective Spaces
% 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 : waybel18 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 59 ( 0 unt; 0 def)
% Number of atoms : 430 ( 35 equ)
% Maximal formula atoms : 27 ( 7 avg)
% Number of connectives : 439 ( 68 ~; 1 |; 258 &)
% ( 11 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 54 ( 53 usr; 0 prp; 1-3 aty)
% Number of functors : 41 ( 41 usr; 4 con; 0-5 aty)
% Number of variables : 148 ( 138 !; 10 ?)
% 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_waybel18,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_waybel18(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_pralg_1(A) ) ) ).
fof(rc1_waybel18,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v1_waybel18(B) ) ).
fof(rc2_waybel18,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v4_waybel_3(B)
& v2_pralg_1(B)
& v1_waybel18(B) ) ).
fof(fc1_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k3_waybel18(A,B))
& v1_pre_topc(k3_waybel18(A,B))
& v2_pre_topc(k3_waybel18(A,B)) ) ) ).
fof(fc2_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k3_waybel18(A,B))
& v1_pre_topc(k3_waybel18(A,B))
& v2_pre_topc(k3_waybel18(A,B))
& v1_monoid_0(k3_waybel18(A,B)) ) ) ).
fof(fc3_waybel18,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_pre_topc(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ~ v3_struct_0(k7_waybel18(A,B,C)) ) ).
fof(fc4_waybel18,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_pre_topc(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k8_waybel18(A,B,C))
& v1_funct_1(k8_waybel18(A,B,C))
& v1_funct_2(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C)))
& v2_funct_2(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C))) ) ) ).
fof(fc5_waybel18,axiom,
( ~ v3_struct_0(k9_waybel18)
& v1_pre_topc(k9_waybel18)
& v2_pre_topc(k9_waybel18) ) ).
fof(fc6_waybel18,axiom,
( ~ v3_struct_0(k9_waybel18)
& v1_pre_topc(k9_waybel18)
& v2_pre_topc(k9_waybel18)
& v2_t_0topsp(k9_waybel18) ) ).
fof(fc7_waybel18,axiom,
( ~ v3_struct_0(k9_waybel18)
& v1_pre_topc(k9_waybel18)
& v2_pre_topc(k9_waybel18)
& v2_t_0topsp(k9_waybel18)
& v2_waybel18(k9_waybel18) ) ).
fof(fc8_waybel18,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v4_waybel_3(k2_funcop_1(A,B)) ) ) ).
fof(fc9_waybel18,axiom,
! [A,B] :
( l1_pre_topc(B)
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v2_pralg_1(k2_funcop_1(A,B))
& v1_waybel18(k2_funcop_1(A,B)) ) ) ).
fof(fc10_waybel18,axiom,
! [A,B] :
( ( v2_orders_2(B)
& l1_orders_2(B) )
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v1_yellow_1(k2_funcop_1(A,B))
& v5_waybel_3(k2_funcop_1(A,B))
& v2_pralg_1(k2_funcop_1(A,B)) ) ) ).
fof(fc11_waybel18,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ).
fof(fc12_waybel18,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ).
fof(fc13_waybel18,axiom,
! [A,B] :
( ( ~ v1_xboole_0(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) )
=> ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ).
fof(fc14_waybel18,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_waybel_8(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
& v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ).
fof(t1_waybel18,axiom,
! [A,B,C,D] :
( r1_tarski(D,k1_enumset1(A,B,C))
<=> ~ ( D != k1_xboole_0
& D != k1_tarski(A)
& D != k1_tarski(B)
& D != k1_tarski(C)
& D != k2_tarski(A,B)
& D != k2_tarski(B,C)
& D != k2_tarski(A,C)
& D != k1_enumset1(A,B,C) ) ) ).
fof(t2_waybel18,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( C = k4_xboole_0(B,k1_tarski(k1_xboole_0))
| B = k2_xboole_0(C,k1_tarski(k1_xboole_0)) )
=> k1_cantor_1(A,B) = k1_cantor_1(A,C) ) ) ) ).
fof(t3_waybel18,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( m1_cantor_1(B,A)
<=> m1_cantor_1(k4_xboole_0(B,k1_tarski(k1_xboole_0)),A) ) ) ) ).
fof(d1_waybel18,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_waybel18(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> l1_pre_topc(B) ) ) ) ).
fof(d2_waybel18,axiom,
! [A,B] :
( ( v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B)))))
=> ( C = k2_waybel18(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))
=> ( r2_hidden(D,C)
<=> ? [E,F] :
( l1_pre_topc(F)
& ? [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(F)))
& r2_hidden(E,A)
& v3_pre_topc(G,F)
& F = k1_funct_1(B,E)
& D = k4_card_3(k2_funct_7(k12_pralg_1(A,B),E,G)) ) ) ) ) ) ) ) ).
fof(t4_waybel18,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> v2_pre_topc(g1_pre_topc(A,k1_cantor_1(A,k2_cantor_1(A,B)))) ) ).
fof(d3_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_pre_topc(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( C = k3_waybel18(A,B)
<=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
& m2_cantor_1(k2_waybel18(A,B),C) ) ) ) ) ).
fof(d4_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> k6_waybel18(A,B,C) = k3_pralg_3(k12_pralg_1(A,B),C) ) ) ) ).
fof(t5_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C))))
=> k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),D) = k4_card_3(k2_funct_7(k12_pralg_1(A,B),C,D)) ) ) ) ) ).
fof(t6_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> v5_pre_topc(k6_waybel18(A,B,C),k3_waybel18(A,B),k4_waybel18(A,B,C)) ) ) ) ).
fof(t7_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v4_waybel_3(C)
& v1_waybel18(C)
& m1_pboole(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_waybel18(B,C)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_waybel18(B,C))) )
=> ( v5_pre_topc(D,A,k3_waybel18(B,C))
<=> ! [E] :
( m1_subset_1(E,B)
=> v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(k3_waybel18(B,C)),u1_struct_0(k4_waybel18(B,C,E)),D,k6_waybel18(B,C,E)),A,k4_waybel18(B,C,E)) ) ) ) ) ) ) ).
fof(d5_waybel18,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v2_waybel18(A)
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v5_pre_topc(C,B,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ~ ( m1_pre_topc(B,D)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(A)) )
=> ~ ( v5_pre_topc(E,D,A)
& k7_relat_1(E,u1_struct_0(B)) = C ) ) ) ) ) ) ) ) ) ).
fof(t8_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> v2_waybel18(k4_waybel18(A,B,C)) )
=> v2_waybel18(k3_waybel18(A,B)) ) ) ) ).
fof(t9_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_waybel18(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( r1_borsuk_1(A,B)
=> v2_waybel18(B) ) ) ) ) ).
fof(d6_waybel18,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_pre_topc(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)) )
=> k7_waybel18(A,B,C) = k3_pre_topc(B,k1_yellow_2(A,B,C)) ) ) ) ).
fof(t10_waybel18,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_pre_topc(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)) )
=> u1_struct_0(k7_waybel18(A,B,C)) = k1_yellow_2(A,B,C) ) ) ) ).
fof(d7_waybel18,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(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)) )
=> k8_waybel18(A,B,C) = C ) ) ) ).
fof(t11_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(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)) )
=> ( v5_pre_topc(C,A,B)
=> v5_pre_topc(k8_waybel18(A,B,C),A,k7_waybel18(A,B,C)) ) ) ) ) ).
fof(d8_waybel18,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( r1_waybel18(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B))
& v5_pre_topc(C,B,B)
& k2_monoid_0(u1_struct_0(B),C,C) = C
& r1_t_0topsp(k7_waybel18(B,B,C),A) ) ) ) ) ).
fof(t12_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( v2_waybel18(A)
=> ! [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)) )
=> ( v3_tops_2(k8_waybel18(A,B,C),A,k7_waybel18(A,B,C))
=> r1_waybel18(A,B) ) ) ) ) ) ).
fof(d9_waybel18,axiom,
! [A] :
( ( v1_pre_topc(A)
& l1_pre_topc(A) )
=> ( A = k9_waybel18
<=> ( u1_struct_0(A) = k2_tarski(np__0,np__1)
& u1_pre_topc(A) = k1_enumset1(k1_xboole_0,k1_tarski(np__1),k2_tarski(np__0,np__1)) ) ) ) ).
fof(t13_waybel18,axiom,
! [A] :
( ( v4_waybel11(A)
& m1_yellow_9(A,k3_yellow_1(np__1)) )
=> u1_pre_topc(A) = u1_pre_topc(k9_waybel18) ) ).
fof(t15_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))))
& m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))))
& v23_waybel_0(B,k3_yellow_1(A),k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1))))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k1_funct_1(B,C) = k5_funct_3(C,A) ) ) ) ).
fof(t16_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))) )
=> u1_pre_topc(B) = u1_pre_topc(k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ) ).
fof(t17_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& u1_pre_topc(A) = u1_pre_topc(B)
& v2_waybel18(A) )
=> v2_waybel18(B) ) ) ) ).
fof(t18_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))) )
=> v2_waybel18(B) ) ) ).
fof(t19_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_waybel18(B,k2_pre_circ(B,k9_waybel18))))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_waybel18(B,k2_pre_circ(B,k9_waybel18))))
& v3_tops_2(k8_waybel18(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18)),C),A,k7_waybel18(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18)),C)) ) ) ) ).
fof(t20_waybel18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ~ ( v2_waybel18(A)
& ! [B] :
( ~ v1_xboole_0(B)
=> ~ r1_waybel18(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18))) ) ) ) ).
fof(dt_k1_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> l1_pre_topc(k1_waybel18(A,B,C)) ) ).
fof(redefinition_k1_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k1_waybel18(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k2_waybel18,axiom,
! [A,B] :
( ( v1_waybel18(B)
& m1_pboole(B,A) )
=> m1_subset_1(k2_waybel18(A,B),k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) ) ).
fof(dt_k3_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( v1_pre_topc(k3_waybel18(A,B))
& v2_pre_topc(k3_waybel18(A,B))
& l1_pre_topc(k3_waybel18(A,B)) ) ) ).
fof(dt_k4_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( ~ v3_struct_0(k4_waybel18(A,B,C))
& l1_pre_topc(k4_waybel18(A,B,C)) ) ) ).
fof(redefinition_k4_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k4_waybel18(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k5_waybel18,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
& m1_subset_1(D,A) )
=> m1_subset_1(k5_waybel18(A,B,C,D),u1_struct_0(k4_waybel18(A,B,D))) ) ).
fof(redefinition_k5_waybel18,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
& m1_subset_1(D,A) )
=> k5_waybel18(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k6_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k6_waybel18(A,B,C))
& v1_funct_2(k6_waybel18(A,B,C),u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C)))
& m2_relset_1(k6_waybel18(A,B,C),u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C))) ) ) ).
fof(dt_k7_waybel18,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_pre_topc(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_pre_topc(k7_waybel18(A,B,C),B) ) ).
fof(dt_k8_waybel18,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_pre_topc(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k8_waybel18(A,B,C))
& v1_funct_2(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C)))
& m2_relset_1(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C))) ) ) ).
fof(dt_k9_waybel18,axiom,
( v1_pre_topc(k9_waybel18)
& l1_pre_topc(k9_waybel18) ) ).
fof(t14_waybel18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> m2_cantor_1(a_1_0_waybel18(A),k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ).
fof(fraenkel_a_1_0_waybel18,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_0_waybel18(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k4_card_3(k2_funct_7(k12_pralg_1(B,k2_pre_circ(B,k9_waybel18)),C,k1_tarski(np__1))) ) ) ) ).
%------------------------------------------------------------------------------