SET007 Axioms: SET007+655.ax
%------------------------------------------------------------------------------
% File : SET007+655 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Order-consistent Topology of Complete and Uncomplete 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 : waybel32 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 63 ( 4 unt; 0 def)
% Number of atoms : 701 ( 28 equ)
% Maximal formula atoms : 19 ( 11 avg)
% Number of connectives : 731 ( 93 ~; 1 |; 491 &)
% ( 15 <=>; 131 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 56 ( 54 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 0 con; 1-4 aty)
% Number of variables : 155 ( 139 !; 16 ?)
% 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_waybel32,axiom,
? [A] :
( l1_waybel_9(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)
& v2_pre_topc(A)
& v1_waybel_9(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ).
fof(cc1_waybel32,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_pre_topc(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_pre_topc(A)
& v1_waybel32(A) ) ) ) ).
fof(rc2_waybel32,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v2_pre_topc(A)
& v2_waybel_3(A)
& v1_waybel_9(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_realset2(A)
& v1_waybel32(A) ) ).
fof(cc2_waybel32,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) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( v4_waybel11(B)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B) ) ) ) ) ).
fof(rc3_waybel32,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) )
=> ? [B] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B)
& v4_waybel11(B) ) ) ).
fof(rc4_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B)
& v1_waybel_9(B)
& v4_waybel11(B) ) ) ).
fof(cc3_waybel32,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) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& ~ v1_yellow_3(B) ) ) ) ).
fof(cc4_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
=> v3_waybel11(B,A) ) ) ) ).
fof(rc5_waybel32,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) )
=> ? [B] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B)
& v2_waybel32(B) ) ) ).
fof(rc6_waybel32,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(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)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel32(A) ) ).
fof(fc1_waybel32,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_waybel32(A,B,C))
& v3_orders_2(k1_waybel32(A,B,C))
& v6_waybel_0(k1_waybel32(A,B,C),A) ) ) ).
fof(fc2_waybel32,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_waybel32(A,B,C))
& v6_waybel_0(k1_waybel32(A,B,C),A)
& v7_waybel_0(k1_waybel32(A,B,C)) ) ) ).
fof(fc3_waybel32,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v3_struct_0(k2_waybel32(A,B))
& v3_orders_2(k2_waybel32(A,B))
& v6_waybel_0(k2_waybel32(A,B),A)
& v7_waybel_0(k2_waybel32(A,B)) ) ) ).
fof(fc4_waybel32,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v3_struct_0(k2_waybel32(A,B))
& v3_orders_2(k2_waybel32(A,B))
& v6_waybel_0(k2_waybel32(A,B),A)
& v7_waybel_0(k2_waybel32(A,B)) ) ) ).
fof(fc5_waybel32,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v3_struct_0(k2_waybel32(A,B))
& v3_orders_2(k2_waybel32(A,B))
& v6_waybel_0(k2_waybel32(A,B),A)
& v7_waybel_0(k2_waybel32(A,B))
& v8_waybel_0(k2_waybel32(A,B),A)
& v10_waybel_0(k2_waybel32(A,B),A) ) ) ).
fof(fc6_waybel32,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v3_struct_0(k2_waybel32(A,B))
& v3_orders_2(k2_waybel32(A,B))
& v6_waybel_0(k2_waybel32(A,B),A)
& v7_waybel_0(k2_waybel32(A,B))
& v8_waybel_0(k2_waybel32(A,B),A)
& v10_waybel_0(k2_waybel32(A,B),A) ) ) ).
fof(d2_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_pre_topc(A)
& l1_waybel_9(A) )
=> ( v2_waybel32(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k6_waybel_0(A,B) = k6_pre_topc(A,k1_struct_0(A,B))
& ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v10_waybel_0(C,A)
& l1_waybel_0(C,A) )
=> ( B = k1_waybel_2(A,C)
=> ! [D] :
( m1_connsp_2(D,A,B)
=> r1_waybel_0(A,C,D) ) ) ) ) ) ) ) ).
fof(t1_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_pre_topc(A)
& v1_waybel32(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> v13_waybel_0(B,A) ) ) ) ).
fof(t2_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_pre_topc(A)
& l1_waybel_9(A) )
=> ( v1_waybel32(A)
=> v2_waybel32(A) ) ) ).
fof(t3_waybel32,axiom,
$true ).
fof(t4_waybel32,axiom,
$true ).
fof(t5_waybel32,axiom,
$true ).
fof(t6_waybel32,axiom,
$true ).
fof(t7_waybel32,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) )
=> ? [B] :
( m1_yellow_9(B,A)
& v4_waybel11(B) ) ) ).
fof(t8_waybel32,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) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( v4_waybel11(B)
=> v2_pre_topc(B) ) ) ) ).
fof(t9_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_pre_topc(A,k1_struct_0(A,B)) = k6_waybel_0(A,B) ) ) ).
fof(t10_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> v2_waybel32(A) ) ).
fof(t12_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(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,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> r3_orders_2(A,k2_yellow_0(A,B),C) ) ) ) ) ).
fof(t13_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v8_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> k1_waybel11(A,B) = k1_waybel_2(A,B) ) ) ).
fof(t14_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))))
<=> ( v1_waybel11(B,A)
& v13_waybel_0(B,A) ) ) ) ) ).
fof(t15_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( u1_pre_topc(B) = k5_waybel11(A)
=> v4_waybel11(B) ) ) ) ).
fof(t16_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> k5_waybel11(A) = u1_pre_topc(B) ) ) ).
fof(t17_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) ) ) ).
fof(t18_waybel32,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) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( ( v13_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( ~ r2_hidden(C,D)
=> m2_connsp_2(k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)),B,D) ) ) ) ) ) ).
fof(t19_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v13_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
& C = k6_setfam_1(u1_struct_0(B),D)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(E,D)
=> m2_connsp_2(E,B,C) ) ) ) ) ) ) ).
fof(t20_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ( v13_waybel_0(B,A)
& v3_waybel11(B,A) ) ) ) ) ).
fof(t21_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(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,B)
=> r3_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) ) ).
fof(t22_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v6_group_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v1_waybel11(B,A) ) ) ).
fof(t23_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> v3_pre_topc(k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)),B) ) ) ) ).
fof(t25_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_waybel_0(A,C) = k6_pre_topc(A,k1_struct_0(A,C)) )
& v3_pre_topc(B,A) )
=> v13_waybel_0(B,A) ) ) ) ).
fof(t26_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_waybel_0(A,C) = k6_pre_topc(A,k1_struct_0(A,C)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(C,A)
=> v12_waybel_0(C,A) ) ) ) ) ) ).
fof(t27_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k1_waybel11(A,k6_waybel_9(A,B,C)) = k1_waybel11(A,B) ) ) ) ).
fof(d3_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k1_waybel32(A,B,C)
<=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& u1_waybel_0(A,D) = C ) ) ) ) ) ) ).
fof(t29_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> k1_waybel_2(A,k2_waybel32(A,B)) = k1_waybel11(A,B) ) ) ).
fof(t30_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k1_waybel_2(A,k2_waybel32(A,B)) = k1_waybel11(A,k6_waybel_9(A,B,C)) ) ) ) ).
fof(t31_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_waybel_0(A,k2_waybel32(A,B),C)
=> r1_waybel_0(A,B,C) ) ) ) ) ).
fof(t32_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_waybel_0(A,B,C)
=> r1_waybel_0(A,k2_waybel32(A,B),C) ) ) ) ) ).
fof(t33_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel32(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,C,k1_waybel11(A,B))
=> r3_waybel_9(A,B,C) ) ) ) ) ).
fof(t34_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel32(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v10_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,C,k1_waybel11(A,B))
<=> r3_waybel_9(A,B,C) ) ) ) ) ).
fof(dt_k1_waybel32,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_waybel32(A,B,C))
& v6_waybel_0(k1_waybel32(A,B,C),A)
& l1_waybel_0(k1_waybel32(A,B,C),A) ) ) ).
fof(dt_k2_waybel32,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v3_struct_0(k2_waybel32(A,B))
& v6_waybel_0(k2_waybel32(A,B),A)
& v7_waybel_0(k2_waybel32(A,B))
& l1_waybel_0(k2_waybel32(A,B),A) ) ) ).
fof(d1_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_waybel_9(A) )
=> ( v1_waybel32(A)
<=> m2_cantor_1(a_1_0_waybel32(A),A) ) ) ).
fof(t11_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = a_2_0_waybel32(A,B)
=> ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A) ) ) ) ) ) ).
fof(t24_waybel32,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_pre_topc(C,B)
<=> ( C = u1_struct_0(B)
| r2_hidden(C,a_2_1_waybel32(A,B)) ) ) ) ) ) ).
fof(d4_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_waybel_0(C,A)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( C = k2_waybel32(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& C = k1_waybel32(A,B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k3_yellow_6(u1_struct_0(B),A,D,E) = k2_yellow_0(A,a_3_1_waybel32(A,B,E)) ) ) ) ) ) ) ).
fof(t28_waybel32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> k5_relset_1(u1_struct_0(k2_waybel32(A,B)),u1_struct_0(A),u1_waybel_0(A,k2_waybel32(A,B))) = a_2_2_waybel32(A,B) ) ) ).
fof(fraenkel_a_1_0_waybel32,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_0_waybel32(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) ).
fof(fraenkel_a_2_0_waybel32,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v25_waybel_0(B)
& v2_lattice3(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_0_waybel32(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_yellow_0(B,a_3_0_waybel32(B,C,D)) ) ) ) ).
fof(fraenkel_a_3_0_waybel32,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v25_waybel_0(B)
& v2_lattice3(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_waybel32(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
fof(fraenkel_a_2_1_waybel32,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v16_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& v4_waybel11(C)
& m1_yellow_9(C,B) )
=> ( r2_hidden(A,a_2_1_waybel32(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k3_subset_1(u1_struct_0(C),k6_waybel_0(C,D)) ) ) ) ).
fof(fraenkel_a_3_1_waybel32,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_1_waybel32(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
fof(fraenkel_a_2_2_waybel32,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_2_waybel32(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_yellow_0(B,a_3_2_waybel32(B,C,D)) ) ) ) ).
fof(fraenkel_a_3_2_waybel32,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_2_waybel32(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
%------------------------------------------------------------------------------