SET007 Axioms: SET007+636.ax
%------------------------------------------------------------------------------
% File : SET007+636 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Lim-Inf Convergence
% 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 : waybel28 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 45 ( 0 unt; 0 def)
% Number of atoms : 449 ( 21 equ)
% Maximal formula atoms : 23 ( 9 avg)
% Number of connectives : 469 ( 65 ~; 0 |; 278 &)
% ( 6 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 37 ( 36 usr; 0 prp; 1-3 aty)
% Number of functors : 26 ( 26 usr; 0 con; 1-5 aty)
% Number of variables : 121 ( 116 !; 5 ?)
% 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_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_waybel_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_waybel28(B,A) ) ) ).
fof(rc2_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_waybel28(B,A) ) ) ).
fof(fc1_waybel28,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(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(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
& v3_orders_2(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
& v6_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A)
& v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) ) ) ).
fof(fc2_waybel28,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> ( ~ v3_struct_0(k1_waybel28(A,B,C))
& v3_orders_2(k1_waybel28(A,B,C))
& v6_waybel_0(k1_waybel28(A,B,C),A)
& v7_waybel_0(k1_waybel28(A,B,C)) ) ) ).
fof(rc3_waybel28,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ? [C] :
( m2_yellow_6(C,A,B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v6_waybel_0(C,A)
& v7_waybel_0(C) ) ) ).
fof(t1_waybel28,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] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> r3_orders_2(A,k2_waybel_9(A,B),k1_waybel11(A,B)) ) ) ).
fof(t2_waybel28,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] :
( ( ~ 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))
=> ( ! [D] :
( m2_yellow_6(D,A,B)
=> C = k1_waybel11(A,D) )
=> ( C = k1_waybel11(A,B)
& ! [D] :
( m2_yellow_6(D,A,B)
=> r1_orders_2(A,k2_waybel_9(A,D),C) ) ) ) ) ) ) ).
fof(t3_waybel28,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] :
( ( ~ 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))
=> ( ( r2_hidden(B,k7_yellow_6(A))
& ! [D] :
( m2_yellow_6(D,A,B)
=> ( r2_hidden(D,k7_yellow_6(A))
=> C = k1_waybel11(A,D) ) ) )
=> ( C = k1_waybel11(A,B)
& ! [D] :
( m2_yellow_6(D,A,B)
=> ( r2_hidden(D,k7_yellow_6(A))
=> r1_orders_2(A,k2_waybel_9(A,D),C) ) ) ) ) ) ) ) ).
fof(d1_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_waybel28(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_orders_2(A,C,k3_yellow_6(u1_struct_0(A),A,B,C)) ) ) ) ) ).
fof(t4_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> v1_waybel28(k7_grcat_1(A),A) ) ).
fof(t5_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_waybel_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(A))
& r1_orders_2(A,B,D)
& r1_orders_2(A,C,D) ) ) ) ) ).
fof(t6_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_waybel_0(A)
& l1_orders_2(A) )
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_waybel28(B,A) ) ) ).
fof(d2_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( D = k1_waybel28(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) = k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,u1_waybel_0(A,B)) ) ) ) ) ) ) ).
fof(t7_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [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)) )
=> u1_struct_0(k1_waybel28(A,B,C)) = u1_struct_0(B) ) ) ) ).
fof(t8_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [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)) )
=> k1_waybel28(A,B,C) = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,u1_waybel_0(A,B))) ) ) ) ).
fof(t9_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_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)) )
=> ( ~ v3_struct_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
& v3_orders_2(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
& v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
& l1_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A) ) ) ) ) ).
fof(t10_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [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)) )
=> ( ~ v3_struct_0(k1_waybel28(A,B,C))
& v3_orders_2(k1_waybel28(A,B,C))
& v7_waybel_0(k1_waybel28(A,B,C))
& l1_waybel_0(k1_waybel28(A,B,C),A) ) ) ) ) ).
fof(t11_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [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)) )
=> ( r2_hidden(B,k7_yellow_6(A))
=> r2_hidden(k1_waybel28(A,B,C),k7_yellow_6(A)) ) ) ) ) ).
fof(t12_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) = g1_waybel_0(A,u1_struct_0(C),u1_orders_2(C),u1_waybel_0(A,C))
=> m2_yellow_6(C,A,B) ) ) ) ) ).
fof(t13_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& v1_waybel28(C,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> m2_yellow_6(k1_waybel28(A,B,C),A,B) ) ) ) ).
fof(t14_waybel28,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] :
( ( ~ 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))
=> ( ( r2_hidden(B,k7_yellow_6(A))
& C = k1_waybel11(A,B)
& ! [D] :
( m2_yellow_6(D,A,B)
=> ( r2_hidden(D,k7_yellow_6(A))
=> r1_orders_2(A,k2_waybel_9(A,D),C) ) ) )
=> ( C = k1_waybel11(A,B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(B))
& v1_waybel28(D,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
=> r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,B,D)),C) ) ) ) ) ) ) ).
fof(t15_waybel28,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] :
( ( ~ 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))
=> ( ( C = k1_waybel11(A,B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(B))
& v1_waybel28(D,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
=> r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,B,D)),C) ) )
=> ! [D] :
( m2_yellow_6(D,A,B)
=> C = k1_waybel11(A,D) ) ) ) ) ) ).
fof(d3_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( B = k3_waybel28(A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r2_hidden(C,k7_yellow_6(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ! [E] :
( m2_yellow_6(E,A,C)
=> D = k1_waybel11(A,E) ) ) ) ) ) ) ) ) ).
fof(t16_waybel28,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] :
( ( ~ 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))
=> ( r2_hidden(B,k7_yellow_6(A))
=> ( r2_hidden(k4_tarski(B,C),k3_waybel28(A))
<=> ! [D] :
( m2_yellow_6(D,A,B)
=> ( r2_hidden(D,k7_yellow_6(A))
=> C = k1_waybel11(A,D) ) ) ) ) ) ) ) ).
fof(t17_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> ! [C] :
( m2_yellow_6(C,A,B)
=> ( v1_yellow_6(C,A)
& k5_yellow_6(A,B) = k5_yellow_6(A,C) ) ) ) ) ).
fof(d4_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> k4_waybel28(A) = u1_pre_topc(k14_yellow_6(A,k3_waybel28(A))) ) ).
fof(t18_waybel28,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) )
=> v4_yellow_6(k3_waybel28(A),A) ) ).
fof(t19_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> v5_yellow_6(k3_waybel28(A),A) ) ).
fof(t20_waybel28,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> v6_yellow_6(k3_waybel28(A),A) ) ).
fof(t21_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k3_waybel28(A))
=> r2_hidden(B,k7_yellow_6(A)) ) ) ).
fof(t22_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ! [C] :
( m4_yellow_6(C,A)
=> ( r1_tarski(B,C)
=> r1_tarski(u1_pre_topc(k14_yellow_6(A,C)),u1_pre_topc(k14_yellow_6(A,B))) ) ) ) ) ).
fof(t23_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> r1_tarski(k3_waybel28(A),k2_waybel11(A)) ) ).
fof(t24_waybel28,axiom,
! [A,B] :
( r1_tarski(A,B)
=> r2_hidden(A,k2_yellow_6(B)) ) ).
fof(t25_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(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))) )
=> r2_hidden(k4_waybel17(A,B),k7_yellow_6(A)) ) ) ).
fof(t26_waybel28,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] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_yellow_6(C,A,k4_waybel17(A,B))
=> k1_waybel11(A,C) = k1_yellow_0(A,B) ) ) ) ).
fof(t27_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(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] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_hidden(k4_tarski(k4_waybel17(A,B),k1_yellow_0(A,B)),k3_waybel28(A)) ) ) ).
fof(t28_waybel28,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k4_waybel28(A))
=> v3_waybel11(B,A) ) ) ) ).
fof(t29_waybel28,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)))
=> ( r2_hidden(B,k5_waybel11(A))
=> r2_hidden(B,k4_waybel28(A)) ) ) ) ).
fof(t30_waybel28,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v13_waybel_0(B,A)
& r2_hidden(B,k4_waybel28(A)) )
=> r2_hidden(B,k5_waybel11(A)) ) ) ) ).
fof(t31_waybel28,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
=> ( r2_hidden(k3_subset_1(u1_struct_0(A),B),k4_waybel28(A))
<=> v2_waybel11(B,A) ) ) ) ) ).
fof(dt_k1_waybel28,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> ( ~ v3_struct_0(k1_waybel28(A,B,C))
& v6_waybel_0(k1_waybel28(A,B,C),A)
& l1_waybel_0(k1_waybel28(A,B,C),A) ) ) ).
fof(dt_k2_waybel28,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& v1_waybel28(C,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> ( v6_waybel_0(k2_waybel28(A,B,C),A)
& m2_yellow_6(k2_waybel28(A,B,C),A,B) ) ) ).
fof(redefinition_k2_waybel28,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& v1_waybel28(C,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> k2_waybel28(A,B,C) = k1_waybel28(A,B,C) ) ).
fof(dt_k3_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m4_yellow_6(k3_waybel28(A),A) ) ).
fof(dt_k4_waybel28,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m1_subset_1(k4_waybel28(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
%------------------------------------------------------------------------------