SET007 Axioms: SET007+639.ax
%------------------------------------------------------------------------------
% File : SET007+639 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Weights of Continuous Lattices
% 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 : waybel31 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 53 ( 3 unt; 0 def)
% Number of atoms : 517 ( 38 equ)
% Maximal formula atoms : 29 ( 9 avg)
% Number of connectives : 492 ( 28 ~; 1 |; 356 &)
% ( 10 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 48 ( 46 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 7 con; 0-3 aty)
% Number of variables : 111 ( 98 !; 13 ?)
% 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_waybel31,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A)
& v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v1_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v2_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v3_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v4_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v1_yellow_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v2_yellow_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v3_yellow_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v24_waybel_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v25_waybel_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& ~ v1_yellow_3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v1_waybel_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v2_waybel_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v1_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v2_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v1_lattice3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v2_lattice3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v3_lattice3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v2_waybel_3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
& v3_waybel_3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ).
fof(cc1_waybel31,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v6_group_1(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_waybel_8(A)
& v2_waybel_8(A)
& v3_waybel_8(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ) ) ).
fof(rc1_waybel31,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v6_group_1(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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A)
& v2_waybel_2(A)
& v1_waybel_8(A)
& v2_waybel_8(A)
& v3_waybel_8(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v3_realset2(A) ) ).
fof(fc2_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k5_waybel11(A)))
& v1_orders_2(k2_yellow_1(k5_waybel11(A)))
& v2_orders_2(k2_yellow_1(k5_waybel11(A)))
& v3_orders_2(k2_yellow_1(k5_waybel11(A)))
& v4_orders_2(k2_yellow_1(k5_waybel11(A)))
& v2_yellow_0(k2_yellow_1(k5_waybel11(A)))
& v24_waybel_0(k2_yellow_1(k5_waybel11(A)))
& ~ v1_yellow_3(k2_yellow_1(k5_waybel11(A)))
& v1_lattice3(k2_yellow_1(k5_waybel11(A)))
& v2_waybel_3(k2_yellow_1(k5_waybel11(A)))
& v3_waybel_3(k2_yellow_1(k5_waybel11(A))) ) ) ).
fof(t1_waybel31,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_cantor_1(B,A)
=> r1_ordinal1(k2_waybel23(A),k1_card_1(B)) ) ) ).
fof(t2_waybel31,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m1_cantor_1(B,A)
& k1_card_1(B) = k2_waybel23(A) ) ) ).
fof(t3_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> r1_ordinal1(k1_waybel31(A),k1_card_1(B)) ) ) ).
fof(t4_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ? [B] :
( v6_waybel23(B,A)
& m1_waybel23(B,A)
& k1_card_1(B) = k1_waybel31(A) ) ) ).
fof(t5_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> k1_waybel31(A) = k1_card_1(u1_struct_0(k1_waybel_8(A))) ) ).
fof(t6_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( k2_yellow_1(u1_pre_topc(A)) = B
=> ! [C] :
( ( v6_waybel23(C,B)
& m1_waybel23(C,B) )
=> m1_cantor_1(C,A) ) ) ) ) ).
fof(t7_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( k2_yellow_1(u1_pre_topc(A)) = B
=> ! [C] :
( m1_cantor_1(C,A)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> ( v6_waybel23(k12_waybel_0(B,D),B)
& m1_waybel23(k12_waybel_0(B,D),B) ) ) ) ) ) ) ) ).
fof(t8_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( k2_yellow_1(u1_pre_topc(A)) = B
=> ( v6_group_1(A)
| k2_waybel23(A) = k1_waybel31(B) ) ) ) ) ).
fof(t9_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( k2_yellow_1(u1_pre_topc(A)) = B
=> r1_ordinal1(k1_card_1(u1_struct_0(A)),k1_card_1(u1_struct_0(B))) ) ) ) ).
fof(t10_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( v6_group_1(A)
=> k2_waybel23(A) = k1_card_1(u1_struct_0(A)) ) ) ).
fof(t11_waybel31,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( ( k2_yellow_1(u1_pre_topc(A)) = B
& v6_group_1(A) )
=> k1_waybel31(B) = k1_card_1(u1_struct_0(B)) ) ) ) ).
fof(t13_waybel31,axiom,
$true ).
fof(t14_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v6_group_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_hidden(B,k2_waybel_8(A,B)) ) ) ) ).
fof(t15_waybel31,axiom,
! [A] :
( ( v6_group_1(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> v3_waybel_8(A) ) ).
fof(t16_waybel31,axiom,
! [A] :
( ( v6_group_1(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( k1_card_1(B) = k1_waybel31(A)
<=> B = u1_struct_0(k1_waybel_8(A)) ) ) ) ).
fof(d2_waybel31,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)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_waybel31(A,B,C) = k6_subset_1(u1_struct_0(A),k2_waybel_3(A,C),k5_waybel_0(A,B)) ) ) ) ).
fof(t17_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_waybel31(A,k1_pre_topc(A),B) = k2_waybel_3(A,B) ) ) ).
fof(t18_waybel31,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)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k5_waybel_0(A,B))
=> k2_waybel31(A,B,C) = k1_xboole_0 ) ) ) ) ).
fof(t19_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> v1_finset_1(k8_waybel_0(A)) ) ).
fof(t20_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( ~ v6_group_1(A)
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ~ v1_finset_1(B) ) ) ) ).
fof(t21_waybel31,axiom,
$true ).
fof(t22_waybel31,axiom,
$true ).
fof(t23_waybel31,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,u1_struct_0(A))
=> ( v1_waybel_3(B,A)
=> B = k2_yellow_0(A,k2_waybel_3(A,B)) ) ) ) ).
fof(t25_waybel31,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k5_waybel_0(A,B)),A)
& v3_pre_topc(k3_subset_1(u1_struct_0(A),k4_waybel_0(A,B)),A) ) ) ) ).
fof(t29_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> k1_waybel31(A) = k2_waybel23(B) ) ) ).
fof(t30_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_waybel19(B)
& m1_yellow_9(B,A) )
=> k1_waybel31(A) = k2_waybel23(B) ) ) ).
fof(t31_waybel31,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( r5_waybel_1(A,B)
=> k1_card_1(u1_struct_0(A)) = k1_card_1(u1_struct_0(B)) ) ) ) ).
fof(t32_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> ( k1_card_1(B) = k1_waybel31(A)
=> k1_waybel31(A) = k1_waybel31(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ) ).
fof(t33_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> r1_ordinal1(k1_waybel31(A),k1_waybel31(k2_yellow_1(k5_waybel11(A)))) ) ).
fof(t34_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( ~ v6_group_1(A)
=> k1_waybel31(A) = k1_waybel31(k2_yellow_1(k5_waybel11(A))) ) ) ).
fof(dt_k1_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> v1_card_1(k1_waybel31(A)) ) ).
fof(dt_k2_waybel31,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_waybel31(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(d1_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> k1_waybel31(A) = k1_setfam_1(a_1_0_waybel31(A)) ) ).
fof(t12_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v2_pre_topc(C)
& v2_waybel19(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( m1_cantor_1(D,C)
=> m1_cantor_1(a_3_0_waybel31(A,C,D),B) ) ) ) ) ).
fof(t24_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( ~ v6_group_1(A)
=> ! [B] :
( ( v6_waybel23(B,A)
& m1_waybel23(B,A) )
=> r1_ordinal1(k1_card_1(a_2_0_waybel31(A,B)),k1_card_1(B)) ) ) ) ).
fof(t26_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_waybel19(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v6_waybel23(C,A)
& m1_waybel23(C,A) )
=> m1_cantor_1(a_2_0_waybel31(A,C),B) ) ) ) ).
fof(t27_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( m1_cantor_1(C,B)
=> m1_cantor_1(a_3_1_waybel31(A,B,C),B) ) ) ) ).
fof(t28_waybel31,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( m1_cantor_1(C,B)
=> ~ ( ~ v1_finset_1(C)
& v1_finset_1(a_3_2_waybel31(A,B,C)) ) ) ) ) ).
fof(s1_waybel31,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(f1_s1_waybel31))))
=> ( A = a_0_0_waybel31
=> k5_waybel_0(f1_s1_waybel31,k5_setfam_1(u1_struct_0(f1_s1_waybel31),A)) = k3_tarski(a_0_1_waybel31) ) ) ).
fof(s2_waybel31,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(f1_s2_waybel31))))
=> ( A = a_0_2_waybel31
=> k4_waybel_0(f1_s2_waybel31,k5_setfam_1(u1_struct_0(f1_s2_waybel31),A)) = k3_tarski(a_0_3_waybel31) ) ) ).
fof(fraenkel_a_1_0_waybel31,axiom,
! [A,B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( r2_hidden(A,a_1_0_waybel31(B))
<=> ? [C] :
( v6_waybel23(C,B)
& m1_waybel23(C,B)
& A = k1_card_1(C) ) ) ) ).
fof(fraenkel_a_3_0_waybel31,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v2_pre_topc(C)
& v2_waybel19(C)
& m1_yellow_9(C,B)
& m1_cantor_1(D,C) )
=> ( r2_hidden(A,a_3_0_waybel31(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
& A = k5_waybel_0(C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_2_0_waybel31,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v6_waybel23(C,B)
& m1_waybel23(C,B) )
=> ( r2_hidden(A,a_2_0_waybel31(B,C))
<=> ? [D,E] :
( m1_subset_1(D,u1_struct_0(B))
& v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = k2_waybel31(B,E,D)
& r2_hidden(D,C)
& r1_tarski(E,C) ) ) ) ).
fof(fraenkel_a_3_1_waybel31,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v4_waybel11(C)
& m1_yellow_9(C,B)
& m1_cantor_1(D,C) )
=> ( r2_hidden(A,a_3_1_waybel31(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
& A = k2_waybel_3(C,k2_yellow_0(C,E))
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_2_waybel31,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v4_waybel11(C)
& m1_yellow_9(C,B)
& m1_cantor_1(D,C) )
=> ( r2_hidden(A,a_3_2_waybel31(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
& A = k2_yellow_0(C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_0_0_waybel31,axiom,
! [A] :
( r2_hidden(A,a_0_0_waybel31)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel31)))
& A = B
& p1_s1_waybel31(B) ) ) ).
fof(fraenkel_a_0_1_waybel31,axiom,
! [A] :
( r2_hidden(A,a_0_1_waybel31)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel31)))
& A = k5_waybel_0(f1_s1_waybel31,B)
& p1_s1_waybel31(B) ) ) ).
fof(fraenkel_a_0_2_waybel31,axiom,
! [A] :
( r2_hidden(A,a_0_2_waybel31)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s2_waybel31)))
& A = B
& p1_s2_waybel31(B) ) ) ).
fof(fraenkel_a_0_3_waybel31,axiom,
! [A] :
( r2_hidden(A,a_0_3_waybel31)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s2_waybel31)))
& A = k4_waybel_0(f1_s2_waybel31,B)
& p1_s2_waybel31(B) ) ) ).
%------------------------------------------------------------------------------