TPTP Problem File: LAT349+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : LAT349+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Representation Theorem for Free Continuous Lattices T12
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Rud96] Rudnicki (1998), Representation Theorem for Free Conti
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t12_waybel22 [Urb08]
% Status : Theorem
% Rating : 0.97 v7.5.0, 1.00 v3.4.0
% Syntax : Number of formulae : 132 ( 23 unt; 0 def)
% Number of atoms : 783 ( 22 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 764 ( 113 ~; 1 |; 510 &)
% ( 12 <=>; 128 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 1 con; 0-4 aty)
% Number of variables : 216 ( 186 !; 30 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Normal version: includes the axioms (which may be theorems from
% other articles) and background that are possibly necessary.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
fof(t12_waybel22,conjecture,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_waybel22(A),u1_struct_0(B))
& m2_relset_1(C,k1_waybel22(A),u1_struct_0(B)) )
=> v5_orders_3(k2_waybel22(A,B,C),k2_yellow_1(k9_waybel_0(k3_yellow_1(A))),B) ) ) ).
fof(abstractness_v1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_orders_2(A)
=> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ) ).
fof(cc10_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ) ) ).
fof(cc11_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_yellow_0(A) ) ) ) ).
fof(cc12_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(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)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc13_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A) ) ) ) ).
fof(cc14_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ) ).
fof(cc1_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc1_setfam_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A) )
=> ! [B] :
( m1_subset_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(cc1_waybel22,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k9_waybel_0(A))))
=> ~ v1_xboole_0(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(cc1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc1_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v1_waybel_5(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ) ).
fof(cc2_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc2_waybel_5,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_waybel_5(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(cc2_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A) ) ) ) ).
fof(cc3_waybel_5,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(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)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(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(cc3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc4_waybel_5,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v9_waybel_1(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(cc4_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_yellow_0(A)
=> ( v1_yellow_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc5_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v16_waybel_0(A) ) ) ) ).
fof(cc5_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v1_yellow_0(A)
& v2_yellow_0(A) )
=> v3_yellow_0(A) ) ) ).
fof(cc9_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v1_lattice3(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(d18_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_0(A,B) = k5_waybel_0(A,k1_struct_0(A,B)) ) ) ).
fof(d24_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> k9_waybel_0(A) = a_1_1_waybel_0(A) ) ).
fof(d2_waybel22,axiom,
! [A] : k1_waybel22(A) = a_1_0_waybel22(A) ).
fof(d3_tarski,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ) ).
fof(d3_waybel22,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_waybel22(A),u1_struct_0(B))
& m2_relset_1(C,k1_waybel22(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))),u1_struct_0(B)) )
=> ( D = k2_waybel22(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))))
=> k1_waybel_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A))),B,D,E) = k1_yellow_0(B,a_4_0_waybel22(A,B,C,E)) ) ) ) ) ) ).
fof(d5_orders_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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)) )
=> ( v5_orders_3(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_orders_2(A,D,E)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( F = k1_funct_1(C,D)
& G = k1_funct_1(C,E) )
=> r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ( v1_orders_2(g1_orders_2(A,B))
& l1_orders_2(g1_orders_2(A,B)) ) ) ).
fof(dt_k1_funct_1,axiom,
$true ).
fof(dt_k1_struct_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k1_tarski,axiom,
$true ).
fof(dt_k1_waybel22,axiom,
! [A] : m1_subset_1(k1_waybel22(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))) ).
fof(dt_k1_waybel_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_waybel22,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k1_waybel22(A),u1_struct_0(B))
& m1_relset_1(C,k1_waybel22(A),u1_struct_0(B)) )
=> ( v1_funct_1(k2_waybel22(A,B,C))
& v1_funct_2(k2_waybel22(A,B,C),u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))),u1_struct_0(B))
& m2_relset_1(k2_waybel22(A,B,C),u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))),u1_struct_0(B)) ) ) ).
fof(dt_k2_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_yellow_1,axiom,
! [A] :
( v1_orders_2(k2_yellow_1(A))
& l1_orders_2(k2_yellow_1(A)) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_yellow_1,axiom,
! [A] :
( v1_orders_2(k3_yellow_1(A))
& l1_orders_2(k3_yellow_1(A)) ) ).
fof(dt_k5_waybel_0,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k7_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k9_waybel_0,axiom,
$true ).
fof(dt_l1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(existence_l1_orders_2,axiom,
? [A] : l1_orders_2(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(fc10_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& 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) ) ) ).
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_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v13_waybel_0(k5_waybel_0(A,B),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(fc14_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> v13_waybel_0(k7_waybel_0(A,B),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(fc17_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_waybel_0(k5_waybel_0(A,B),A)
& v13_waybel_0(k5_waybel_0(A,B),A) ) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ).
fof(fc1_waybel16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ~ v1_xboole_0(k9_waybel_0(A)) ) ).
fof(fc1_waybel22,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k9_waybel_0(A)))
& v1_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v2_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v3_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v4_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v1_yellow_0(k2_yellow_1(k9_waybel_0(A)))
& v2_yellow_0(k2_yellow_1(k9_waybel_0(A)))
& v3_yellow_0(k2_yellow_1(k9_waybel_0(A)))
& v24_waybel_0(k2_yellow_1(k9_waybel_0(A)))
& v25_waybel_0(k2_yellow_1(k9_waybel_0(A)))
& v1_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v2_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v3_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v3_waybel_3(k2_yellow_1(k9_waybel_0(A))) ) ) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0) ).
fof(fc1_yellow_0,axiom,
! [A,B] :
( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
=> ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B))
& v1_orders_2(g1_orders_2(k1_tarski(A),B))
& v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ).
fof(fc2_setfam_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v1_xboole_0(k1_tarski(A))
& v1_setfam_1(k1_tarski(A)) ) ) ).
fof(fc2_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_tarski(A)) ).
fof(fc2_waybel16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k9_waybel_0(A)))
& v1_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v2_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v3_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v4_orders_2(k2_yellow_1(k9_waybel_0(A)))
& v2_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v3_lattice3(k2_yellow_1(k9_waybel_0(A)))
& v1_yellow_0(k2_yellow_1(k9_waybel_0(A)))
& v24_waybel_0(k2_yellow_1(k9_waybel_0(A)))
& v25_waybel_0(k2_yellow_1(k9_waybel_0(A))) ) ) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ).
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_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k5_waybel_0(A,B)) ) ).
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(fraenkel_a_1_0_waybel22,axiom,
! [A,B] :
( r2_hidden(A,a_1_0_waybel22(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_1(B)))
& A = k7_waybel_0(k3_yellow_1(B),C)
& ? [D] :
( m1_subset_1(D,B)
& C = k1_tarski(D) ) ) ) ).
fof(fraenkel_a_1_1_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( r2_hidden(A,a_1_1_waybel_0(B))
<=> ? [C] :
( ~ v1_xboole_0(C)
& v2_waybel_0(C,B)
& v13_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C ) ) ) ).
fof(fraenkel_a_4_0_waybel22,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,k1_waybel22(B),u1_struct_0(C))
& m2_relset_1(D,k1_waybel22(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(B))))) )
=> ( r2_hidden(A,a_4_0_waybel22(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,k1_zfmisc_1(B))
& A = k2_yellow_0(C,a_4_1_waybel22(B,C,D,F))
& r2_hidden(F,E) ) ) ) ).
fof(fraenkel_a_4_1_waybel22,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,k1_waybel22(B),u1_struct_0(C))
& m2_relset_1(D,k1_waybel22(B),u1_struct_0(C))
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_4_1_waybel22(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k3_yellow_1(B)))
& A = k1_funct_1(D,k7_waybel_0(k3_yellow_1(B),F))
& ? [G] :
( m1_subset_1(G,B)
& F = k1_tarski(G)
& r2_hidden(G,E) ) ) ) ) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ! [C,D] :
( g1_orders_2(A,B) = g1_orders_2(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(rc10_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc12_waybel_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A) ) ).
fof(rc13_waybel_0,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)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A) ) ).
fof(rc1_lattice3,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)
& v3_lattice3(A) ) ).
fof(rc1_setfam_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_setfam_1(A) ) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) ) ) ).
fof(rc1_waybel_5,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A) ) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A) ).
fof(rc1_yellow_0,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)
& v3_realset2(A) ) ).
fof(rc1_yellow_7,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)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v1_waybel_5(A)
& v3_realset2(A) ) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) ) ).
fof(rc2_lattice3,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) ) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& v1_xboole_0(B) ) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A) ).
fof(rc2_yellow_0,axiom,
? [A] :
( l1_orders_2(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)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ).
fof(rc3_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(redefinition_k1_struct_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k1_struct_0(A,B) = k1_tarski(B) ) ).
fof(redefinition_k1_waybel_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(A)) )
=> k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(redefinition_r3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_orders_2(A,B,C)
<=> r1_orders_2(A,B,C) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(reflexivity_r3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r3_orders_2(A,B,B) ) ).
fof(t17_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( r1_yellow_0(A,B)
& r2_yellow_0(A,B) ) ) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( v1_xboole_0(B)
| r2_hidden(A,B) ) ) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ) ).
fof(t34_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( ( r1_tarski(B,C)
& r1_yellow_0(A,B)
& r1_yellow_0(A,C) )
=> r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t3_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
=> ( r3_orders_2(k2_yellow_1(A),B,C)
<=> r1_tarski(B,C) ) ) ) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C)) )
=> m1_subset_1(A,C) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
%------------------------------------------------------------------------------