SET007 Axioms: SET007+538.ax
%------------------------------------------------------------------------------
% File : SET007+538 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Scott-Continuous Functions
% 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 : waybel17 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 67 ( 0 unt; 0 def)
% Number of atoms : 1124 ( 53 equ)
% Maximal formula atoms : 32 ( 16 avg)
% Number of connectives : 1123 ( 66 ~; 4 |; 823 &)
% ( 29 <=>; 201 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 14 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 53 ( 52 usr; 0 prp; 1-6 aty)
% Number of functors : 64 ( 64 usr; 20 con; 0-5 aty)
% Number of variables : 250 ( 231 !; 19 ?)
% 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_waybel17,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(C,A,B) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(cc2_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(fc1_waybel17,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))
& v5_waybel_3(k2_funcop_1(A,B)) ) ) ).
fof(fc2_waybel17,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) )
=> ( v1_orders_2(k6_yellow_1(A,B))
& v3_lattice3(k6_yellow_1(A,B)) ) ) ).
fof(fc3_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k2_waybel17(A,B))
& v1_orders_2(k2_waybel17(A,B))
& v4_yellow_0(k2_waybel17(A,B),k7_yellow_1(A,B)) ) ) ).
fof(fc4_waybel17,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_waybel17(A,B,C))
& v2_orders_2(k3_waybel17(A,B,C))
& v3_orders_2(k3_waybel17(A,B,C))
& v4_orders_2(k3_waybel17(A,B,C))
& v6_waybel_0(k3_waybel17(A,B,C),A)
& v7_waybel_0(k3_waybel17(A,B,C)) ) ) ).
fof(fc5_waybel17,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k4_waybel17(A,B))
& v2_orders_2(k4_waybel17(A,B))
& v6_waybel_0(k4_waybel17(A,B),A)
& v7_waybel_0(k4_waybel17(A,B)) ) ) ).
fof(fc6_waybel17,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k4_waybel17(A,B))
& v2_orders_2(k4_waybel17(A,B))
& v3_orders_2(k4_waybel17(A,B))
& v6_waybel_0(k4_waybel17(A,B),A)
& v7_waybel_0(k4_waybel17(A,B)) ) ) ).
fof(fc7_waybel17,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k4_waybel17(A,B))
& v2_orders_2(k4_waybel17(A,B))
& v6_waybel_0(k4_waybel17(A,B),A)
& v7_waybel_0(k4_waybel17(A,B))
& v8_waybel_0(k4_waybel17(A,B),A)
& v10_waybel_0(k4_waybel17(A,B),A) ) ) ).
fof(fc8_waybel17,axiom,
! [A,B,C,D] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ~ v3_struct_0(D)
& v8_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( ~ v3_struct_0(k7_waybel_9(A,B,C,D))
& v6_waybel_0(k7_waybel_9(A,B,C,D),B)
& v8_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(cc3_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(cc4_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(C,A,B) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& v5_orders_3(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(d1_waybel17,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,A)
& m2_relset_1(D,k5_numbers,A) )
=> ( D = k1_waybel17(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& E = k2_nat_1(np__2,F) )
=> k8_funct_2(k5_numbers,A,D,E) = B )
& ( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> E != k2_nat_1(np__2,F) )
=> k8_funct_2(k5_numbers,A,D,E) = C ) ) ) ) ) ) ) ) ).
fof(t1_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(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)) )
=> ! [D] :
( ( v12_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v5_orders_3(C,A,B)
=> v12_waybel_0(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ).
fof(t2_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(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)) )
=> ! [D] :
( ( v13_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v5_orders_3(C,A,B)
=> v13_waybel_0(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ).
fof(t3_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(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)) )
=> ( v22_waybel_0(C,A,B)
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t4_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(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_orders_3(C,A,B) ) ) ) ) ).
fof(d2_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_orders_2(C)
& v4_yellow_0(C,k7_yellow_1(A,B))
& m1_yellow_0(C,k7_yellow_1(A,B)) )
=> ( C = k2_waybel17(A,B)
<=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(D,u1_struct_0(C))
<=> v5_pre_topc(D,A,B) ) ) ) ) ) ) ).
fof(d3_waybel17,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))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k3_waybel17(A,B,C)
<=> ( u1_struct_0(D) = k5_numbers
& r4_nattra_1(u1_struct_0(D),u1_struct_0(A),k5_numbers,u1_struct_0(A),u1_waybel_0(A,D),k1_waybel17(u1_struct_0(A),B,C))
& ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( E = G
& F = H )
=> ( r1_orders_2(D,E,F)
<=> r1_xreal_0(G,H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_waybel17,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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel17(A,B,C)))
=> ( k3_waybel_0(A,k3_waybel17(A,B,C),D) = B
| k3_waybel_0(A,k3_waybel17(A,B,C),D) = C ) ) ) ) ) ).
fof(t6_waybel17,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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel17(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_waybel17(A,B,C)))
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( F = D
& G = k1_nat_1(F,np__1)
& G = E )
=> ( ( k3_waybel_0(A,k3_waybel17(A,B,C),D) = B
=> k3_waybel_0(A,k3_waybel17(A,B,C),E) = C )
& ( k3_waybel_0(A,k3_waybel17(A,B,C),D) = C
=> k3_waybel_0(A,k3_waybel17(A,B,C),E) = B ) ) ) ) ) ) ) ) ) ) ).
fof(t7_waybel17,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_waybel11(A,k3_waybel17(A,B,C)) = k12_lattice3(A,B,C) ) ) ) ).
fof(t8_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> k1_waybel11(B,k7_waybel_9(A,B,E,k3_waybel17(A,C,D))) = k12_lattice3(B,k7_yellow_2(u1_struct_0(A),B,E,C),k7_yellow_2(u1_struct_0(A),B,E,D)) ) ) ) ) ) ).
fof(d4_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_waybel17(A,B) = g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),k1_nattra_1(u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B)) ) ) ).
fof(t9_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_waybel17(A,B) = k3_waybel11(A,B,k1_nattra_1(u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B)) ) ) ).
fof(t10_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_waybel11(A,k4_waybel17(A,B)) = k1_yellow_0(A,B) ) ) ).
fof(t11_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_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)) )
=> ( ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> r3_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,k1_waybel11(A,D)),k1_waybel11(B,k7_waybel_9(A,B,C,D))) )
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t15_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_orders_3(D,A,B)
=> ( ( ~ ( r1_yellow_0(A,C)
& r1_yellow_0(B,k4_pre_topc(A,B,D,C)) )
& ~ ( v3_lattice3(A)
& v4_orders_2(A)
& v3_lattice3(B)
& v4_orders_2(B) ) )
| r1_orders_2(B,k1_yellow_0(B,k4_pre_topc(A,B,D,C)),k7_yellow_2(u1_struct_0(A),B,D,k1_yellow_0(A,C))) ) ) ) ) ) ) ).
fof(t16_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_orders_3(D,A,B)
=> ( ( ~ ( r1_yellow_0(A,C)
& r1_yellow_0(B,k4_pre_topc(A,B,D,C)) )
& ~ ( v24_waybel_0(A)
& v24_waybel_0(B) ) )
| r3_orders_2(B,k1_yellow_0(B,k4_pre_topc(A,B,D,C)),k7_yellow_2(u1_struct_0(A),B,D,k1_yellow_0(A,C))) ) ) ) ) ) ) ).
fof(t17_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_orders_3(D,A,B)
=> ( ( ~ ( r2_yellow_0(A,C)
& r2_yellow_0(B,k4_pre_topc(A,B,D,C)) )
& ~ ( v3_lattice3(A)
& v4_orders_2(A)
& v3_lattice3(B)
& v4_orders_2(B) ) )
| r1_orders_2(B,k7_yellow_2(u1_struct_0(A),B,D,k2_yellow_0(A,C)),k2_yellow_0(B,k4_pre_topc(A,B,D,C))) ) ) ) ) ) ) ).
fof(t18_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v1_lattice3(B)
& v2_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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v8_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( v5_orders_3(C,A,B)
=> v8_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ) ) ) ).
fof(t19_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v1_lattice3(B)
& v2_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)) )
=> ( ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> r3_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,k1_waybel11(A,D)),k1_waybel11(B,k7_waybel_9(A,B,C,D))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_yellow_0(B,k4_pre_topc(A,B,C,D)) = k7_yellow_2(u1_struct_0(A),B,C,k1_yellow_0(A,D)) ) ) ) ) ) ).
fof(t21_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)
<=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> r3_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,k1_waybel11(A,D)),k1_waybel11(B,k7_waybel_9(A,B,C,D))) ) ) ) ) ) ).
fof(t22_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)
<=> v22_waybel_0(C,A,B) ) ) ) ) ).
fof(t23_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_waybel_3(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_waybel_3(B,E,k7_yellow_2(u1_struct_0(A),B,C,D))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& r1_waybel_3(A,F,D)
& r1_waybel_3(B,E,k7_yellow_2(u1_struct_0(A),B,C,F)) ) ) ) ) ) ) ) ) ).
fof(t27_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)) )
=> ( ( v2_waybel_8(A)
& v2_waybel_8(B) )
=> ( v5_pre_topc(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,u1_struct_0(k1_waybel_8(B)))
=> ( r3_orders_2(B,E,k7_yellow_2(u1_struct_0(A),B,C,D))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& r2_hidden(F,u1_struct_0(k1_waybel_8(A)))
& r3_orders_2(A,F,D)
& r3_orders_2(B,E,k7_yellow_2(u1_struct_0(A),B,C,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_waybel17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(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] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& l1_waybel_9(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)) )
=> ( v22_waybel_0(C,A,B)
=> v5_pre_topc(C,A,B) ) ) ) ) ).
fof(dt_k1_waybel17,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k1_waybel17(A,B,C))
& v1_funct_2(k1_waybel17(A,B,C),k5_numbers,A)
& m2_relset_1(k1_waybel17(A,B,C),k5_numbers,A) ) ) ).
fof(dt_k2_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(B) )
=> ( v1_orders_2(k2_waybel17(A,B))
& v4_yellow_0(k2_waybel17(A,B),k7_yellow_1(A,B))
& m1_yellow_0(k2_waybel17(A,B),k7_yellow_1(A,B)) ) ) ).
fof(dt_k3_waybel17,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_waybel17(A,B,C))
& v6_waybel_0(k3_waybel17(A,B,C),A)
& l1_waybel_0(k3_waybel17(A,B,C),A) ) ) ).
fof(dt_k4_waybel17,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v6_waybel_0(k4_waybel17(A,B),A)
& l1_waybel_0(k4_waybel17(A,B),A) ) ) ).
fof(t12_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v3_waybel_3(B)
& v1_lattice3(B)
& v2_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)) )
=> ( v22_waybel_0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_0_waybel17(A,B,C,D)) ) ) ) ) ) ).
fof(t13_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& v1_lattice3(B)
& v2_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)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_1_waybel17(A,B,C,D)) )
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t14_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v3_waybel_3(B)
& v1_lattice3(B)
& v2_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)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_2_waybel17(A,B,C,D)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_waybel_3(B,E,k7_yellow_2(u1_struct_0(A),B,C,D))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& r1_waybel_3(A,F,D)
& r1_waybel_3(B,E,k7_yellow_2(u1_struct_0(A),B,C,F)) ) ) ) ) ) ) ) ) ).
fof(t20_waybel17,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] :
( ( 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) )
=> ! [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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k7_waybel_9(A,B,C,D)))
=> ( ( F = E
& v5_orders_3(C,A,B) )
=> r3_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,k2_yellow_0(A,a_3_0_waybel17(A,D,E))),k2_yellow_0(B,a_5_0_waybel17(A,B,C,D,F))) ) ) ) ) ) ) ) ).
fof(t24_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_waybel_3(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_3_waybel17(A,B,C,D)) ) ) ) ) ) ).
fof(t25_waybel17,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( 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) )
=> ! [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)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_4_waybel17(A,B,C,D)) )
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t26_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_5_waybel17(A,B,C,D)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_6_waybel17(A,B,C,D)) ) ) ) ) ) ).
fof(t28_waybel17,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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)) )
=> ( ( v2_waybel_8(A)
& v2_waybel_8(B) )
=> ( v5_pre_topc(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_5_waybel17(A,B,C,D)) ) ) ) ) ) ) ).
fof(s1_waybel17,axiom,
( r1_tarski(u1_struct_0(f2_s1_waybel17),k1_relat_1(f4_s1_waybel17))
=> k9_relat_1(f4_s1_waybel17,a_0_0_waybel17) = a_0_1_waybel17 ) ).
fof(s2_waybel17,axiom,
( r1_tarski(u1_struct_0(f2_s2_waybel17),k1_relat_1(f4_s2_waybel17))
=> k9_relat_1(f4_s2_waybel17,a_0_2_waybel17) = a_0_3_waybel17 ) ).
fof(s3_waybel17,axiom,
( ( r1_tarski(u1_struct_0(f3_s3_waybel17),k1_relat_1(f5_s3_waybel17))
& u1_struct_0(f1_s3_waybel17) = u1_struct_0(f2_s3_waybel17) )
=> k9_relat_1(f5_s3_waybel17,a_0_4_waybel17) = a_0_5_waybel17 ) ).
fof(fraenkel_a_4_0_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v3_waybel_3(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_yellow_0(C)
& v3_waybel_3(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_0_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r1_waybel_3(B,F,E) ) ) ) ).
fof(fraenkel_a_4_1_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_yellow_0(C)
& v24_waybel_0(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_1_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r1_waybel_3(B,F,E) ) ) ) ).
fof(fraenkel_a_4_2_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_yellow_0(C)
& v3_waybel_3(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_2_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r1_waybel_3(B,F,E) ) ) ) ).
fof(fraenkel_a_3_0_waybel17,axiom,
! [A,B,C,D] :
( ( 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(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_waybel17(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_5_0_waybel17,axiom,
! [A,B,C,D,E,F] :
( ( 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)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& ~ v3_struct_0(E)
& v3_orders_2(E)
& v7_waybel_0(E)
& l1_waybel_0(E,B)
& m1_subset_1(F,u1_struct_0(k7_waybel_9(B,C,D,E))) )
=> ( r2_hidden(A,a_5_0_waybel17(B,C,D,E,F))
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(k7_waybel_9(B,C,D,E)))
& A = k3_waybel_0(C,k7_waybel_9(B,C,D,E),G)
& r1_orders_2(k7_waybel_9(B,C,D,E),F,G) ) ) ) ).
fof(fraenkel_a_4_3_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_waybel_3(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_pre_topc(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v3_waybel_3(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_3_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r1_waybel_3(B,F,E) ) ) ) ).
fof(fraenkel_a_4_4_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_4_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r3_orders_2(B,F,E)
& v1_waybel_3(F,B) ) ) ) ).
fof(fraenkel_a_4_5_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_pre_topc(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_5_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r3_orders_2(B,F,E)
& v1_waybel_3(F,B) ) ) ) ).
fof(fraenkel_a_4_6_waybel17,axiom,
! [A,B,C,D,E] :
( ( v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_pre_topc(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_6_waybel17(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r1_waybel_3(B,F,E) ) ) ) ).
fof(fraenkel_a_0_0_waybel17,axiom,
! [A] :
( r2_hidden(A,a_0_0_waybel17)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel17))
& A = f3_s1_waybel17(B)
& p1_s1_waybel17(B) ) ) ).
fof(fraenkel_a_0_1_waybel17,axiom,
! [A] :
( r2_hidden(A,a_0_1_waybel17)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel17))
& A = k1_funct_1(f4_s1_waybel17,f3_s1_waybel17(B))
& p1_s1_waybel17(B) ) ) ).
fof(fraenkel_a_0_2_waybel17,axiom,
! [A] :
( r2_hidden(A,a_0_2_waybel17)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_waybel17))
& A = f3_s2_waybel17(B)
& p1_s2_waybel17(B) ) ) ).
fof(fraenkel_a_0_3_waybel17,axiom,
! [A] :
( r2_hidden(A,a_0_3_waybel17)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_waybel17))
& A = k1_funct_1(f4_s2_waybel17,f3_s2_waybel17(B))
& p1_s2_waybel17(B) ) ) ).
fof(fraenkel_a_0_4_waybel17,axiom,
! [A] :
( r2_hidden(A,a_0_4_waybel17)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s3_waybel17))
& A = f4_s3_waybel17(B)
& p1_s3_waybel17(B) ) ) ).
fof(fraenkel_a_0_5_waybel17,axiom,
! [A] :
( r2_hidden(A,a_0_5_waybel17)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f2_s3_waybel17))
& A = k1_funct_1(f5_s3_waybel17,f4_s3_waybel17(B))
& p1_s3_waybel17(B) ) ) ).
%------------------------------------------------------------------------------