SET007 Axioms: SET007+543.ax
%------------------------------------------------------------------------------
% File : SET007+543 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Properties of Product of Relational Structures
% 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 : yellow10 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 0 unt; 0 def)
% Number of atoms : 1059 ( 36 equ)
% Maximal formula atoms : 35 ( 12 avg)
% Number of connectives : 1108 ( 134 ~; 2 |; 681 &)
% ( 10 <=>; 281 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 41 ( 40 usr; 0 prp; 1-3 aty)
% Number of functors : 31 ( 31 usr; 1 con; 0-4 aty)
% Number of variables : 267 ( 267 !; 0 ?)
% 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_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_yellow_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_yellow_0(k3_yellow_3(A,B)) ) ) ).
fof(fc2_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B)) ) ) ).
fof(cc1_yellow10,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)))
=> ( v1_xboole_0(B)
=> v1_waybel_6(B,A) ) ) ) ).
fof(fc3_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_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)))
& v1_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v25_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& ~ v1_yellow_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc4_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v25_waybel_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v25_waybel_0(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(fc5_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& v10_waybel_1(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_yellow_0(B)
& v10_waybel_1(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v1_lattice3(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v2_yellow_0(k3_yellow_3(A,B))
& v3_yellow_0(k3_yellow_3(A,B))
& v10_waybel_1(k3_yellow_3(A,B)) ) ) ).
fof(fc6_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v2_waybel_1(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v1_lattice3(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v2_waybel_1(k3_yellow_3(A,B)) ) ) ).
fof(fc7_yellow10,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_waybel_2(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& v2_waybel_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B))
& v1_waybel_2(k3_yellow_3(A,B))
& v2_waybel_2(k3_yellow_3(A,B)) ) ) ).
fof(fc8_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_waybel_3(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v2_waybel_3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& v25_waybel_0(k3_yellow_3(A,B))
& v2_waybel_3(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(fc9_yellow10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v3_waybel_3(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v25_waybel_0(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& v25_waybel_0(k3_yellow_3(A,B))
& v2_waybel_3(k3_yellow_3(A,B))
& v3_waybel_3(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(fc10_yellow10,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v1_waybel_8(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& v1_waybel_8(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v1_lattice3(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v3_lattice3(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v2_yellow_0(k3_yellow_3(A,B))
& v3_yellow_0(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& v25_waybel_0(k3_yellow_3(A,B))
& v1_waybel_8(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(fc11_yellow10,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v3_lattice3(B)
& v1_yellow_0(B)
& v2_waybel_8(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v1_lattice3(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v3_lattice3(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v2_yellow_0(k3_yellow_3(A,B))
& v3_yellow_0(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& v25_waybel_0(k3_yellow_3(A,B))
& v2_waybel_3(k3_yellow_3(A,B))
& v3_waybel_3(k3_yellow_3(A,B))
& v1_waybel_8(k3_yellow_3(A,B))
& v2_waybel_8(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(fc12_yellow10,axiom,
! [A,B] :
( ( 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)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow_0(B)
& v3_waybel_8(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B))
& v1_lattice3(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B))
& v3_lattice3(k3_yellow_3(A,B))
& v1_yellow_0(k3_yellow_3(A,B))
& v2_yellow_0(k3_yellow_3(A,B))
& v3_yellow_0(k3_yellow_3(A,B))
& v24_waybel_0(k3_yellow_3(A,B))
& v25_waybel_0(k3_yellow_3(A,B))
& v2_waybel_3(k3_yellow_3(A,B))
& v3_waybel_3(k3_yellow_3(A,B))
& v1_waybel_8(k3_yellow_3(A,B))
& v2_waybel_8(k3_yellow_3(A,B))
& v3_waybel_8(k3_yellow_3(A,B))
& ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) ).
fof(t1_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( v2_yellow_0(k3_yellow_3(A,B))
=> ( v2_yellow_0(A)
& v2_yellow_0(B) ) ) ) ) ).
fof(t2_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( v1_yellow_0(k3_yellow_3(A,B))
=> ( v1_yellow_0(A)
& v1_yellow_0(B) ) ) ) ) ).
fof(t3_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> k4_yellow_0(k3_yellow_3(A,B)) = k7_yellow_3(A,B,k4_yellow_0(A),k4_yellow_0(B)) ) ) ).
fof(t4_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> k3_yellow_0(k3_yellow_3(A,B)) = k7_yellow_3(A,B,k3_yellow_0(A),k3_yellow_0(B)) ) ) ).
fof(t5_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( ( v3_lattice3(k3_yellow_3(A,B))
| r1_yellow_0(k3_yellow_3(A,B),C) )
=> k1_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k1_yellow_0(A,k4_yellow_3(A,B,C)),k1_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) ).
fof(t6_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( ( v3_lattice3(k3_yellow_3(A,B))
| r2_yellow_0(k3_yellow_3(A,B),C) )
=> k2_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k2_yellow_0(A,k4_yellow_3(A,B,C)),k2_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) ).
fof(t7_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_lattice3(k3_yellow_3(A,B),k1_struct_0(k3_yellow_3(A,B),D),C)
<=> ( r1_lattice3(A,k1_struct_0(A,k8_yellow_3(A,B,D)),k8_yellow_3(A,B,C))
& r1_lattice3(B,k1_struct_0(B,k9_yellow_3(A,B,D)),k9_yellow_3(A,B,C)) ) ) ) ) ) ) ).
fof(t8_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_lattice3(k3_yellow_3(A,B),k2_struct_0(k3_yellow_3(A,B),D,E),C)
<=> ( r1_lattice3(A,k2_struct_0(A,k8_yellow_3(A,B,D),k8_yellow_3(A,B,E)),k8_yellow_3(A,B,C))
& r1_lattice3(B,k2_struct_0(B,k9_yellow_3(A,B,D),k9_yellow_3(A,B,E)),k9_yellow_3(A,B,C)) ) ) ) ) ) ) ) ).
fof(t9_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r2_lattice3(k3_yellow_3(A,B),k1_struct_0(k3_yellow_3(A,B),D),C)
<=> ( r2_lattice3(A,k1_struct_0(A,k8_yellow_3(A,B,D)),k8_yellow_3(A,B,C))
& r2_lattice3(B,k1_struct_0(B,k9_yellow_3(A,B,D)),k9_yellow_3(A,B,C)) ) ) ) ) ) ) ).
fof(t10_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_yellow_3(A,B)))
=> ( r2_lattice3(k3_yellow_3(A,B),k2_struct_0(k3_yellow_3(A,B),D,E),C)
<=> ( r2_lattice3(A,k2_struct_0(A,k8_yellow_3(A,B,D),k8_yellow_3(A,B,E)),k8_yellow_3(A,B,C))
& r2_lattice3(B,k2_struct_0(B,k9_yellow_3(A,B,D),k9_yellow_3(A,B,E)),k9_yellow_3(A,B,C)) ) ) ) ) ) ) ) ).
fof(t11_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r2_yellow_0(k3_yellow_3(A,B),k2_struct_0(k3_yellow_3(A,B),C,D))
<=> ( r2_yellow_0(A,k2_struct_0(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D)))
& r2_yellow_0(B,k2_struct_0(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D))) ) ) ) ) ) ) ).
fof(t12_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_yellow_0(k3_yellow_3(A,B),k2_struct_0(k3_yellow_3(A,B),C,D))
<=> ( r1_yellow_0(A,k2_struct_0(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D)))
& r1_yellow_0(B,k2_struct_0(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D))) ) ) ) ) ) ) ).
fof(t13_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( k8_yellow_3(A,B,k12_lattice3(k3_yellow_3(A,B),C,D)) = k12_lattice3(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D))
& k9_yellow_3(A,B,k12_lattice3(k3_yellow_3(A,B),C,D)) = k12_lattice3(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D)) ) ) ) ) ) ).
fof(t14_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( k8_yellow_3(A,B,k13_lattice3(k3_yellow_3(A,B),C,D)) = k13_lattice3(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D))
& k9_yellow_3(A,B,k13_lattice3(k3_yellow_3(A,B),C,D)) = k13_lattice3(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D)) ) ) ) ) ) ).
fof(t15_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [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] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k7_yellow_3(A,B,k12_lattice3(A,C,D),k12_lattice3(B,E,F)) = k12_lattice3(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F)) ) ) ) ) ) ) ).
fof(t16_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v1_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] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k7_yellow_3(A,B,k13_lattice3(A,C,D),k13_lattice3(B,E,F)) = k13_lattice3(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F)) ) ) ) ) ) ) ).
fof(t17_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_yellow_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_yellow10(k3_yellow_3(A,B),D,C)
<=> ( r1_yellow10(A,k8_yellow_3(A,B,D),k8_yellow_3(A,B,C))
& r1_yellow10(B,k9_yellow_3(A,B,D),k9_yellow_3(A,B,C)) ) ) ) ) ) ) ).
fof(t18_yellow10,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) )
=> ! [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))
=> ( r1_waybel_3(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F))
=> ( r1_waybel_3(A,C,D)
& r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t19_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [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))
=> ( r1_waybel_3(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F))
<=> ( r1_waybel_3(A,C,D)
& r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t20_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_waybel_3(k3_yellow_3(A,B),C,D)
=> ( r1_waybel_3(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D))
& r1_waybel_3(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D)) ) ) ) ) ) ) ).
fof(t21_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_waybel_3(k3_yellow_3(A,B),C,D)
<=> ( r1_waybel_3(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D))
& r1_waybel_3(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D)) ) ) ) ) ) ) ).
fof(t22_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( v1_waybel_3(C,k3_yellow_3(A,B))
=> ( v1_waybel_3(k8_yellow_3(A,B,C),A)
& v1_waybel_3(k9_yellow_3(A,B,C),B) ) ) ) ) ) ).
fof(t23_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( ( v1_waybel_3(k8_yellow_3(A,B,C),A)
& v1_waybel_3(k9_yellow_3(A,B,C),B) )
=> v1_waybel_3(C,k3_yellow_3(A,B)) ) ) ) ) ).
fof(t24_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( k4_yellow_3(A,B,k4_yellow_4(k3_yellow_3(A,B),C,D)) = k4_yellow_4(A,k4_yellow_3(A,B,C),k4_yellow_3(A,B,D))
& k5_yellow_3(A,B,k4_yellow_4(k3_yellow_3(A,B),C,D)) = k4_yellow_4(B,k5_yellow_3(A,B,C),k5_yellow_3(A,B,D)) ) ) ) ) ) ).
fof(t25_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( k4_yellow_3(A,B,k2_yellow_4(k3_yellow_3(A,B),C,D)) = k2_yellow_4(A,k4_yellow_3(A,B,C),k4_yellow_3(A,B,D))
& k5_yellow_3(A,B,k2_yellow_4(k3_yellow_3(A,B),C,D)) = k2_yellow_4(B,k5_yellow_3(A,B,C),k5_yellow_3(A,B,D)) ) ) ) ) ) ).
fof(t26_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> r1_tarski(k4_waybel_0(k3_yellow_3(A,B),C),k6_yellow_3(A,B,k4_waybel_0(A,k4_yellow_3(A,B,C)),k4_waybel_0(B,k5_yellow_3(A,B,C)))) ) ) ) ).
fof(t27_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> k6_yellow_3(A,B,k4_waybel_0(A,C),k4_waybel_0(B,D)) = k4_waybel_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t28_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( r1_tarski(k4_yellow_3(A,B,k4_waybel_0(k3_yellow_3(A,B),C)),k4_waybel_0(A,k4_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k4_waybel_0(k3_yellow_3(A,B),C)),k4_waybel_0(B,k5_yellow_3(A,B,C))) ) ) ) ) ).
fof(t29_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> k4_yellow_3(A,B,k4_waybel_0(k3_yellow_3(A,B),C)) = k4_waybel_0(A,k4_yellow_3(A,B,C)) ) ) ) ).
fof(t30_yellow10,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> k5_yellow_3(A,B,k4_waybel_0(k3_yellow_3(A,B),C)) = k4_waybel_0(B,k5_yellow_3(A,B,C)) ) ) ) ).
fof(t31_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> r1_tarski(k5_waybel_0(k3_yellow_3(A,B),C),k6_yellow_3(A,B,k5_waybel_0(A,k4_yellow_3(A,B,C)),k5_waybel_0(B,k5_yellow_3(A,B,C)))) ) ) ) ).
fof(t32_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> k6_yellow_3(A,B,k5_waybel_0(A,C),k5_waybel_0(B,D)) = k5_waybel_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t33_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( r1_tarski(k4_yellow_3(A,B,k5_waybel_0(k3_yellow_3(A,B),C)),k5_waybel_0(A,k4_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k5_waybel_0(k3_yellow_3(A,B),C)),k5_waybel_0(B,k5_yellow_3(A,B,C))) ) ) ) ) ).
fof(t34_yellow10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> k4_yellow_3(A,B,k5_waybel_0(k3_yellow_3(A,B),C)) = k5_waybel_0(A,k4_yellow_3(A,B,C)) ) ) ) ).
fof(t35_yellow10,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> k5_yellow_3(A,B,k5_waybel_0(k3_yellow_3(A,B),C)) = k5_waybel_0(B,k5_yellow_3(A,B,C)) ) ) ) ).
fof(t36_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k6_yellow_3(A,B,k6_waybel_0(A,C),k6_waybel_0(B,D)) = k6_waybel_0(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t37_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_tarski(k4_yellow_3(A,B,k6_waybel_0(k3_yellow_3(A,B),C)),k6_waybel_0(A,k8_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k6_waybel_0(k3_yellow_3(A,B),C)),k6_waybel_0(B,k9_yellow_3(A,B,C))) ) ) ) ) ).
fof(t38_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k4_yellow_3(A,B,k6_waybel_0(k3_yellow_3(A,B),C)) = k6_waybel_0(A,k8_yellow_3(A,B,C)) ) ) ) ).
fof(t39_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k5_yellow_3(A,B,k6_waybel_0(k3_yellow_3(A,B),C)) = k6_waybel_0(B,k9_yellow_3(A,B,C)) ) ) ) ).
fof(t40_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k6_yellow_3(A,B,k7_waybel_0(A,C),k7_waybel_0(B,D)) = k7_waybel_0(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t41_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_tarski(k4_yellow_3(A,B,k7_waybel_0(k3_yellow_3(A,B),C)),k7_waybel_0(A,k8_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k7_waybel_0(k3_yellow_3(A,B),C)),k7_waybel_0(B,k9_yellow_3(A,B,C))) ) ) ) ) ).
fof(t42_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k4_yellow_3(A,B,k7_waybel_0(k3_yellow_3(A,B),C)) = k7_waybel_0(A,k8_yellow_3(A,B,C)) ) ) ) ).
fof(t43_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k5_yellow_3(A,B,k7_waybel_0(k3_yellow_3(A,B),C)) = k7_waybel_0(B,k9_yellow_3(A,B,C)) ) ) ) ).
fof(t44_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k13_yellow_3(A,B,k1_waybel_3(A,C),k1_waybel_3(B,D)) = k1_waybel_3(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t45_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_tarski(k4_yellow_3(A,B,k1_waybel_3(k3_yellow_3(A,B),C)),k1_waybel_3(A,k8_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k1_waybel_3(k3_yellow_3(A,B),C)),k1_waybel_3(B,k9_yellow_3(A,B,C))) ) ) ) ) ).
fof(t46_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k4_yellow_3(A,B,k1_waybel_3(k3_yellow_3(A,B),C)) = k1_waybel_3(A,k8_yellow_3(A,B,C)) ) ) ) ).
fof(t47_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k5_yellow_3(A,B,k1_waybel_3(k3_yellow_3(A,B),C)) = k1_waybel_3(B,k9_yellow_3(A,B,C)) ) ) ) ).
fof(t48_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k12_yellow_3(A,B,k2_waybel_3(A,C),k2_waybel_3(B,D)) = k2_waybel_3(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t49_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_tarski(k4_yellow_3(A,B,k2_waybel_3(k3_yellow_3(A,B),C)),k2_waybel_3(A,k8_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k2_waybel_3(k3_yellow_3(A,B),C)),k2_waybel_3(B,k9_yellow_3(A,B,C))) ) ) ) ) ).
fof(t50_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k6_yellow_3(A,B,k2_waybel_8(A,C),k2_waybel_8(B,D)) = k2_waybel_8(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D)) ) ) ) ) ).
fof(t51_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_tarski(k4_yellow_3(A,B,k2_waybel_8(k3_yellow_3(A,B),C)),k2_waybel_8(A,k8_yellow_3(A,B,C)))
& r1_tarski(k5_yellow_3(A,B,k2_waybel_8(k3_yellow_3(A,B),C)),k2_waybel_8(B,k9_yellow_3(A,B,C))) ) ) ) ) ).
fof(t52_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k4_yellow_3(A,B,k2_waybel_8(k3_yellow_3(A,B),C)) = k2_waybel_8(A,k8_yellow_3(A,B,C)) ) ) ) ).
fof(t53_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
=> k5_yellow_3(A,B,k2_waybel_8(k3_yellow_3(A,B),C)) = k2_waybel_8(B,k9_yellow_3(A,B,C)) ) ) ) ).
fof(t54_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( v1_waybel_6(C,k3_yellow_3(A,B))
=> ( v1_waybel_6(k4_yellow_3(A,B,C),A)
& v1_waybel_6(k5_yellow_3(A,B,C),B) ) ) ) ) ) ).
fof(t55_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_waybel_6(C,A)
& v1_waybel_6(D,B) )
=> v1_waybel_6(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B)) ) ) ) ) ) ).
fof(t56_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( v1_waybel11(C,k3_yellow_3(A,B))
=> ( v1_waybel11(k4_yellow_3(A,B,C),A)
& v1_waybel11(k5_yellow_3(A,B,C),B) ) ) ) ) ) ).
fof(t57_yellow10,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) )
=> ! [C] :
( ( v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v13_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( ( v1_waybel11(C,A)
& v1_waybel11(D,B) )
=> v1_waybel11(k12_yellow_3(A,B,C,D),k3_yellow_3(A,B)) ) ) ) ) ) ).
fof(t58_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( v2_waybel11(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
=> ( ( D != k1_xboole_0
=> v2_waybel11(C,A) )
& ( C != k1_xboole_0
=> v2_waybel11(D,B) ) ) ) ) ) ) ) ).
fof(t59_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v2_waybel11(C,A)
& v2_waybel11(D,B) )
=> v2_waybel11(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B)) ) ) ) ) ) ).
fof(t60_yellow10,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( v3_waybel11(C,k3_yellow_3(A,B))
=> ( v3_waybel11(k4_yellow_3(A,B,C),A)
& v3_waybel11(k5_yellow_3(A,B,C),B) ) ) ) ) ) ).
fof(t61_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_waybel11(C,A)
& v3_waybel11(D,B) )
=> v3_waybel11(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B)) ) ) ) ) ) ).
fof(t62_yellow10,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))
& v25_waybel_0(A) )
=> v25_waybel_0(B) ) ) ) ).
fof(t63_yellow10,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) )
=> ( v25_waybel_0(k3_yellow_3(A,B))
=> ( v25_waybel_0(A)
& v25_waybel_0(B) ) ) ) ) ).
fof(t64_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_yellow_0(B)
& l1_orders_2(B) )
=> ( v10_waybel_1(k3_yellow_3(A,B))
=> ( v10_waybel_1(A)
& v10_waybel_1(B) ) ) ) ) ).
fof(t65_yellow10,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( v2_waybel_1(k3_yellow_3(A,B))
=> v2_waybel_1(A) ) ) ) ).
fof(t66_yellow10,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( v2_waybel_1(k3_yellow_3(A,B))
=> v2_waybel_1(B) ) ) ) ).
fof(t67_yellow10,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) )
=> ( v2_waybel_2(k3_yellow_3(A,B))
=> ( v2_waybel_2(A)
& v2_waybel_2(B) ) ) ) ) ).
fof(t68_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ( v3_waybel_3(k3_yellow_3(A,B))
=> ( v3_waybel_3(A)
& v3_waybel_3(B) ) ) ) ) ).
fof(t69_yellow10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ( v2_waybel_8(k3_yellow_3(A,B))
=> ( v2_waybel_8(A)
& v2_waybel_8(B) ) ) ) ) ).
fof(t70_yellow10,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ( v3_waybel_8(k3_yellow_3(A,B))
=> ( v3_waybel_8(A)
& v3_waybel_8(B) ) ) ) ) ).
fof(symmetry_r1_yellow10,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_yellow10(A,B,C)
=> r1_yellow10(A,C,B) ) ) ).
fof(redefinition_r1_yellow10,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_yellow10(A,B,C)
<=> r6_waybel_1(A,B,C) ) ) ).
%------------------------------------------------------------------------------