SET007 Axioms: SET007+498.ax
%------------------------------------------------------------------------------
% File : SET007+498 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebraic 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 : waybel_8 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 3 unt; 0 def)
% Number of atoms : 596 ( 24 equ)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 595 ( 61 ~; 0 |; 394 &)
% ( 16 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 0 con; 1-4 aty)
% Number of variables : 120 ( 116 !; 4 ?)
% 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_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k1_waybel_8(A))
& v1_orders_2(k1_waybel_8(A))
& v2_orders_2(k1_waybel_8(A))
& v4_orders_2(k1_waybel_8(A))
& v4_yellow_0(k1_waybel_8(A),A) ) ) ).
fof(fc2_waybel_8,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ~ v1_xboole_0(k2_waybel_8(A,B)) ) ).
fof(cc1_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_8(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ) ) ).
fof(cc2_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_waybel_8(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v1_waybel_8(A) ) ) ) ).
fof(fc3_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k1_waybel_8(A))
& v2_orders_2(k1_waybel_8(A))
& v3_orders_2(k1_waybel_8(A))
& v4_orders_2(k1_waybel_8(A))
& v4_yellow_0(k1_waybel_8(A),A)
& v6_yellow_0(k1_waybel_8(A),A) ) ) ).
fof(cc3_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_8(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v1_waybel_8(A)
& v2_waybel_8(A) ) ) ) ).
fof(cc4_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v1_waybel_8(A)
& v2_waybel_8(A)
& v3_waybel_8(A) ) ) ) ).
fof(rc1_waybel_8,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(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)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v3_realset2(A)
& v1_waybel_8(A)
& v2_waybel_8(A)
& v3_waybel_8(A) ) ).
fof(fc4_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc5_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc6_waybel_8,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc7_waybel_8,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc8_waybel_8,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc9_waybel_8,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc10_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc11_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc12_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_8(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(rc2_waybel_8,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_8(A)
& l1_orders_2(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_2(A,A,B))))
& ~ v1_xboole_0(C)
& v1_waybel_0(C,k2_yellow_2(A,A,B)) ) ) ).
fof(fc13_waybel_8,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> ( ~ v1_xboole_0(k2_waybel_8(k3_yellow_1(A),B))
& v1_waybel_0(k2_waybel_8(k3_yellow_1(A),B),k3_yellow_1(A))
& v12_waybel_0(k2_waybel_8(k3_yellow_1(A),B),k3_yellow_1(A)) ) ) ).
fof(fc14_waybel_8,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A))
& v9_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A))
& v11_waybel_1(k3_yellow_1(A))
& v2_waybel_3(k3_yellow_1(A))
& v3_waybel_3(k3_yellow_1(A))
& v1_waybel_8(k3_yellow_1(A))
& v2_waybel_8(k3_yellow_1(A)) ) ).
fof(d1_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_orders_2(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( B = k1_waybel_8(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,u1_struct_0(B))
<=> v1_waybel_3(C,A) ) ) ) ) ) ).
fof(t1_waybel_8,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,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_orders_2(A,B,D)
& r3_orders_2(A,D,C)
& r2_hidden(D,u1_struct_0(k1_waybel_8(A))) )
=> r1_waybel_3(A,B,C) ) ) ) ) ) ).
fof(t2_waybel_8,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,u1_struct_0(A))
=> ( ( ~ v1_xboole_0(k7_waybel_0(A,B))
& v2_waybel_0(k7_waybel_0(A,B),A)
& v13_waybel_0(k7_waybel_0(A,B),A)
& v1_waybel_6(k7_waybel_0(A,B),A)
& m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) )
<=> v1_waybel_3(B,A) ) ) ) ).
fof(t3_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v6_yellow_0(k1_waybel_8(A),A)
& r2_hidden(k3_yellow_0(A),u1_struct_0(k1_waybel_8(A))) ) ) ).
fof(t4_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k2_waybel_8(A,B))
<=> ( r1_orders_2(A,C,B)
& v1_waybel_3(C,A) ) ) ) ) ) ).
fof(t5_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_waybel_8(A,B) = k3_xboole_0(k6_waybel_0(A,B),u1_struct_0(k1_waybel_8(A))) ) ) ).
fof(t6_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_tarski(k2_waybel_8(A,B),k1_waybel_3(A,B)) ) ) ).
fof(d3_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_waybel_8(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> B = k1_yellow_0(A,k2_waybel_8(A,B)) ) ) ) ).
fof(d4_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v2_waybel_8(A)
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ v1_xboole_0(k2_waybel_8(A,B))
& v1_waybel_0(k2_waybel_8(A,B),A) ) )
& v24_waybel_0(A)
& v1_waybel_8(A) ) ) ) ).
fof(t7_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_8(A)
<=> ( v3_waybel_3(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r1_waybel_3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,u1_struct_0(k1_waybel_8(A)))
& r3_orders_2(A,B,D)
& r3_orders_2(A,D,C) ) ) ) ) ) ) ) ) ).
fof(d5_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> ( v2_waybel_8(A)
& v5_yellow_0(k1_waybel_8(A),A) ) ) ) ).
fof(t8_waybel_8,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) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v24_waybel_0(A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( C = E
& D = F
& r1_waybel_3(A,C,D) )
=> r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t9_waybel_8,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) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v24_waybel_0(A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( ( C = D
& v1_waybel_3(C,A) )
=> v1_waybel_3(D,B) ) ) ) ) ) ) ).
fof(t10_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k2_waybel_8(A,C) = k2_waybel_8(B,D) ) ) ) ) ) ) ).
fof(t11_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ~ ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& ~ v3_struct_0(A)
& v3_struct_0(B) ) ) ) ).
fof(t12_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v2_orders_2(A) )
=> v2_orders_2(B) ) ) ) ).
fof(t13_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v3_orders_2(A) )
=> v3_orders_2(B) ) ) ) ).
fof(t14_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v4_orders_2(A) )
=> v4_orders_2(B) ) ) ) ).
fof(t15_waybel_8,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) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v24_waybel_0(A) )
=> v24_waybel_0(B) ) ) ) ).
fof(t16_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v1_waybel_8(A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ v1_xboole_0(k2_waybel_8(A,C))
& v1_waybel_0(k2_waybel_8(A,C),A) ) ) )
=> v1_waybel_8(B) ) ) ) ).
fof(t17_waybel_8,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) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v2_waybel_8(A) )
=> v2_waybel_8(B) ) ) ) ).
fof(t18_waybel_8,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) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v3_waybel_8(A) )
=> v3_waybel_8(B) ) ) ) ).
fof(t19_waybel_8,axiom,
$true ).
fof(t20_waybel_8,axiom,
$true ).
fof(t21_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> ( v2_orders_2(k1_waybel_8(A))
& v3_orders_2(k1_waybel_8(A))
& v4_orders_2(k1_waybel_8(A))
& v1_lattice3(k1_waybel_8(A))
& v2_lattice3(k1_waybel_8(A))
& l1_orders_2(k1_waybel_8(A)) ) ) ) ).
fof(t22_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ( v3_waybel_8(A)
<=> v5_waybel_7(k1_waybel_4(A),A) ) ) ).
fof(t23_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
=> v5_waybel_6(B,A) ) ) ) ).
fof(t24_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_1(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_waybel_7(B,A)
=> v5_waybel_6(B,A) ) )
=> v3_waybel_8(A) ) ) ).
fof(t25_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v22_waybel_0(B,A,A)
=> r1_tarski(k4_pre_topc(A,A,B,k2_pre_topc(k1_waybel_8(A))),k2_pre_topc(k1_waybel_8(k2_yellow_2(A,A,B)))) ) ) ) ).
fof(t26_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v22_waybel_0(B,A,A)
=> ( v2_orders_2(k2_yellow_2(A,A,B))
& v3_orders_2(k2_yellow_2(A,A,B))
& v4_orders_2(k2_yellow_2(A,A,B))
& v1_lattice3(k2_yellow_2(A,A,B))
& v2_lattice3(k2_yellow_2(A,A,B))
& v2_waybel_8(k2_yellow_2(A,A,B))
& l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) ).
fof(t27_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v22_waybel_0(B,A,A)
=> k4_pre_topc(A,A,B,k2_pre_topc(k1_waybel_8(A))) = k2_pre_topc(k1_waybel_8(k2_yellow_2(A,A,B))) ) ) ) ).
fof(t28_waybel_8,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
<=> r1_tarski(B,A) ) ).
fof(t29_waybel_8,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_1(A)))
=> ( r1_waybel_3(k3_yellow_1(A),B,C)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ~ ( r1_tarski(C,k5_setfam_1(A,D))
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(D)) )
=> ~ r1_tarski(B,k3_tarski(E)) ) ) ) ) ) ) ).
fof(t30_waybel_8,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> ( v1_finset_1(B)
<=> v1_waybel_3(B,k3_yellow_1(A)) ) ) ).
fof(t32_waybel_8,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( r2_hidden(B,u1_struct_0(k1_waybel_8(k3_yellow_1(A))))
<=> v1_finset_1(B) ) ) ).
fof(t33_waybel_8,axiom,
! [A] : v2_waybel_8(k3_yellow_1(A)) ).
fof(dt_k1_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k1_waybel_8(A))
& v4_yellow_0(k1_waybel_8(A),A)
& m1_yellow_0(k1_waybel_8(A),A) ) ) ).
fof(dt_k2_waybel_8,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(d2_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_waybel_8(A,B) = a_2_0_waybel_8(A,B) ) ) ).
fof(t31_waybel_8,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> k2_waybel_8(k3_yellow_1(A),B) = a_2_1_waybel_8(A,B) ) ).
fof(fraenkel_a_2_0_waybel_8,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_waybel_8(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r1_orders_2(B,D,C)
& v1_waybel_3(D,B) ) ) ) ).
fof(fraenkel_a_2_1_waybel_8,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_1(B)))
=> ( r2_hidden(A,a_2_1_waybel_8(B,C))
<=> ? [D] :
( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(C))
& A = D ) ) ) ).
%------------------------------------------------------------------------------