SET007 Axioms: SET007+495.ax
%------------------------------------------------------------------------------
% File : SET007+495 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Duality in Relation 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 : yellow_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 70 ( 0 unt; 0 def)
% Number of atoms : 583 ( 36 equ)
% Maximal formula atoms : 40 ( 8 avg)
% Number of connectives : 557 ( 44 ~; 2 |; 315 &)
% ( 25 <=>; 171 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 50 ( 49 usr; 0 prp; 1-4 aty)
% Number of functors : 33 ( 33 usr; 0 con; 1-6 aty)
% Number of variables : 149 ( 148 !; 1 ?)
% 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_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k7_lattice3(A))
& v2_orders_2(k7_lattice3(A)) ) ) ).
fof(fc2_yellow_7,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k7_lattice3(A))
& v3_orders_2(k7_lattice3(A)) ) ) ).
fof(fc3_yellow_7,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k7_lattice3(A))
& v4_orders_2(k7_lattice3(A)) ) ) ).
fof(fc4_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v16_waybel_0(k7_lattice3(A)) ) ) ).
fof(fc5_yellow_7,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v1_lattice3(k7_lattice3(A)) ) ) ).
fof(fc6_yellow_7,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v2_lattice3(k7_lattice3(A)) ) ) ).
fof(fc7_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v1_lattice3(k7_lattice3(A))
& v2_lattice3(k7_lattice3(A))
& v3_lattice3(k7_lattice3(A))
& v1_yellow_0(k7_lattice3(A))
& v2_yellow_0(k7_lattice3(A))
& v3_yellow_0(k7_lattice3(A)) ) ) ).
fof(fc8_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v2_orders_2(k7_lattice3(A))
& v3_orders_2(k7_lattice3(A))
& v4_orders_2(k7_lattice3(A))
& v1_lattice3(k7_lattice3(A))
& v2_lattice3(k7_lattice3(A))
& v2_waybel_1(k7_lattice3(A)) ) ) ).
fof(fc9_yellow_7,axiom,
! [A] :
( ( v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k7_lattice3(A))
& v2_yellow_0(k7_lattice3(A)) ) ) ).
fof(fc10_yellow_7,axiom,
! [A] :
( ( v2_yellow_0(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k7_lattice3(A))
& v1_yellow_0(k7_lattice3(A)) ) ) ).
fof(fc11_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(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(k7_lattice3(A))
& v1_orders_2(k7_lattice3(A))
& v2_orders_2(k7_lattice3(A))
& v3_orders_2(k7_lattice3(A))
& v4_orders_2(k7_lattice3(A))
& v1_lattice3(k7_lattice3(A))
& v2_lattice3(k7_lattice3(A))
& v1_yellow_0(k7_lattice3(A))
& v2_yellow_0(k7_lattice3(A))
& v3_yellow_0(k7_lattice3(A))
& v10_waybel_1(k7_lattice3(A)) ) ) ).
fof(fc12_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_yellow_7(A))
& v1_funct_1(k1_yellow_7(A))
& v2_funct_1(k1_yellow_7(A))
& v1_funct_2(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A))) ) ) ).
fof(fc13_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k1_yellow_7(A))
& v1_funct_1(k1_yellow_7(A))
& v2_funct_1(k1_yellow_7(A))
& v1_funct_2(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A)))
& v23_waybel_0(k1_yellow_7(A),A,k7_lattice3(A))
& v5_orders_3(k1_yellow_7(A),A,k7_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(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(t1_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
=> ( r1_orders_2(k7_lattice3(A),B,C)
<=> r1_orders_2(A,k9_lattice3(A,C),k9_lattice3(A,B)) ) ) ) ) ).
fof(t2_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
=> ( ( r1_orders_2(A,B,k9_lattice3(A,C))
=> r1_orders_2(k7_lattice3(A),C,k8_lattice3(A,B)) )
& ( r1_orders_2(k7_lattice3(A),C,k8_lattice3(A,B))
=> r1_orders_2(A,B,k9_lattice3(A,C)) )
& ( r1_orders_2(A,k9_lattice3(A,C),B)
=> r1_orders_2(k7_lattice3(A),k8_lattice3(A,B),C) )
& ( r1_orders_2(k7_lattice3(A),k8_lattice3(A,B),C)
=> r1_orders_2(A,k9_lattice3(A,C),B) ) ) ) ) ) ).
fof(t3_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_struct_0(A)
<=> v3_struct_0(k7_lattice3(A)) ) ) ).
fof(t4_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_orders_2(A)
<=> v2_orders_2(k7_lattice3(A)) ) ) ).
fof(t5_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v4_orders_2(A)
<=> v4_orders_2(k7_lattice3(A)) ) ) ).
fof(t6_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_orders_2(A)
<=> v3_orders_2(k7_lattice3(A)) ) ) ).
fof(t7_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v16_waybel_0(A)
<=> v16_waybel_0(k7_lattice3(A)) ) ) ).
fof(t8_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( r1_lattice3(A,C,B)
=> r2_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) )
& ( r2_lattice3(k7_lattice3(A),C,k8_lattice3(A,B))
=> r1_lattice3(A,C,B) )
& ( r2_lattice3(A,C,B)
=> r1_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) )
& ( r1_lattice3(k7_lattice3(A),C,k8_lattice3(A,B))
=> r2_lattice3(A,C,B) ) ) ) ) ).
fof(t9_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
=> ! [C] :
( ( r1_lattice3(k7_lattice3(A),C,B)
=> r2_lattice3(A,C,k9_lattice3(A,B)) )
& ( r2_lattice3(A,C,k9_lattice3(A,B))
=> r1_lattice3(k7_lattice3(A),C,B) )
& ( r2_lattice3(k7_lattice3(A),C,B)
=> r1_lattice3(A,C,k9_lattice3(A,B)) )
& ( r1_lattice3(A,C,k9_lattice3(A,B))
=> r2_lattice3(k7_lattice3(A),C,B) ) ) ) ) ).
fof(t10_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( r1_yellow_0(A,B)
<=> r2_yellow_0(k7_lattice3(A),B) ) ) ).
fof(t11_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( r1_yellow_0(k7_lattice3(A),B)
<=> r2_yellow_0(A,B) ) ) ).
fof(t12_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( r1_yellow_0(A,B)
| r2_yellow_0(k7_lattice3(A),B) )
=> k1_yellow_0(A,B) = k2_yellow_0(k7_lattice3(A),B) ) ) ).
fof(t13_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( r2_yellow_0(A,B)
| r1_yellow_0(k7_lattice3(A),B) )
=> k2_yellow_0(A,B) = k1_yellow_0(k7_lattice3(A),B) ) ) ).
fof(t14_yellow_7,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))
& v2_lattice3(A) )
=> v2_lattice3(B) ) ) ) ).
fof(t15_yellow_7,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))
& v1_lattice3(A) )
=> v1_lattice3(B) ) ) ) ).
fof(t16_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_lattice3(A)
<=> v1_lattice3(k7_lattice3(A)) ) ) ).
fof(t17_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v3_lattice3(A)
<=> v3_lattice3(k7_lattice3(A)) ) ) ).
fof(t18_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
=> ( B = C
=> ( k13_waybel_0(A,B) = k12_waybel_0(k7_lattice3(A),C)
& k12_waybel_0(A,B) = k13_waybel_0(k7_lattice3(A),C) ) ) ) ) ) ).
fof(t19_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
=> ( B = C
=> ( k4_waybel_0(A,B) = k5_waybel_0(k7_lattice3(A),C)
& k5_waybel_0(A,B) = k4_waybel_0(k7_lattice3(A),C) ) ) ) ) ) ).
fof(t20_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
=> ( B = C
=> ( k6_waybel_0(A,B) = k7_waybel_0(k7_lattice3(A),C)
& k7_waybel_0(A,B) = k6_waybel_0(k7_lattice3(A),C) ) ) ) ) ) ).
fof(t21_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,B,C) = k13_lattice3(k7_lattice3(A),k8_lattice3(A,B),k8_lattice3(A,C)) ) ) ) ).
fof(t22_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
=> k12_lattice3(A,k9_lattice3(A,B),k9_lattice3(A,C)) = k13_lattice3(k7_lattice3(A),B,C) ) ) ) ).
fof(t23_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k13_lattice3(A,B,C) = k12_lattice3(k7_lattice3(A),k8_lattice3(A,B),k8_lattice3(A,C)) ) ) ) ).
fof(t24_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
=> k13_lattice3(A,k9_lattice3(A,B),k9_lattice3(A,C)) = k12_lattice3(k7_lattice3(A),B,C) ) ) ) ).
fof(t25_yellow_7,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_1(A)
<=> v2_waybel_1(k7_lattice3(A)) ) ) ).
fof(t26_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> ( v2_waybel_0(B,k7_lattice3(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) ) ) ) ).
fof(t27_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v1_waybel_0(B,k7_lattice3(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) )
<=> ( v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t28_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
<=> ( v13_waybel_0(B,k7_lattice3(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) ) ) ) ).
fof(t29_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v12_waybel_0(B,k7_lattice3(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) )
<=> ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t30_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_yellow_0(A)
<=> v2_yellow_0(k7_lattice3(A)) ) ) ).
fof(t31_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_yellow_0(k7_lattice3(A))
<=> v2_yellow_0(A) ) ) ).
fof(t32_yellow_7,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_yellow_0(A)
<=> v3_yellow_0(k7_lattice3(A)) ) ) ).
fof(t33_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( k8_lattice3(A,k3_yellow_0(A)) = k4_yellow_0(k7_lattice3(A))
& k9_lattice3(A,k4_yellow_0(k7_lattice3(A))) = k3_yellow_0(A) ) ) ).
fof(t34_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( k8_lattice3(A,k4_yellow_0(A)) = k3_yellow_0(k7_lattice3(A))
& k9_lattice3(A,k3_yellow_0(k7_lattice3(A))) = k4_yellow_0(A) ) ) ).
fof(t35_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r6_waybel_1(A,B,C)
<=> r6_waybel_1(k7_lattice3(A),k8_lattice3(A,B),k8_lattice3(A,C)) ) ) ) ) ).
fof(t36_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_yellow_0(A)
& l1_orders_2(A) )
=> ( v10_waybel_1(A)
<=> v10_waybel_1(k7_lattice3(A)) ) ) ).
fof(t37_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_waybel_1(k7_lattice3(A),k8_lattice3(A,B)) = k7_waybel_1(A,B) ) ) ).
fof(d1_yellow_7,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(k7_lattice3(A)))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k7_lattice3(A))) )
=> ( B = k1_yellow_7(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_waybel_0(A,k7_lattice3(A),B,C) = k7_waybel_1(A,C) ) ) ) ) ).
fof(t38_yellow_7,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> r5_waybel_1(A,k7_lattice3(A)) ) ).
fof(t39_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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)) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B)) ) )
& ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B)) )
=> ( 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)) ) )
& ( ( 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)) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) ) )
& ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) )
=> ( 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)) ) )
& ( ( 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)) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) ) )
& ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) )
=> ( 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)) ) ) ) ) ) ).
fof(t40_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) )
=> ( C = D
=> ( ( v5_orders_3(C,A,B)
=> v5_waybel_0(D,A,k7_lattice3(B)) )
& ( v5_waybel_0(D,A,k7_lattice3(B))
=> v5_orders_3(C,A,B) )
& ( v5_waybel_0(C,A,B)
=> v5_orders_3(D,A,k7_lattice3(B)) )
& ( v5_orders_3(D,A,k7_lattice3(B))
=> v5_waybel_0(C,A,B) ) ) ) ) ) ) ) ).
fof(t41_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(B)) )
=> ( C = D
=> ( ( v5_orders_3(C,A,k7_lattice3(B))
=> v5_orders_3(D,k7_lattice3(A),B) )
& ( v5_orders_3(D,k7_lattice3(A),B)
=> v5_orders_3(C,A,k7_lattice3(B)) )
& ( v5_waybel_0(C,A,k7_lattice3(B))
=> v5_waybel_0(D,k7_lattice3(A),B) )
& ( v5_waybel_0(D,k7_lattice3(A),B)
=> v5_waybel_0(C,A,k7_lattice3(B)) ) ) ) ) ) ) ) ).
fof(t42_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) )
=> ( C = D
=> ( ( v5_orders_3(C,A,B)
=> v5_orders_3(D,k7_lattice3(A),k7_lattice3(B)) )
& ( v5_orders_3(D,k7_lattice3(A),k7_lattice3(B))
=> v5_orders_3(C,A,B) )
& ( v5_waybel_0(C,A,B)
=> v5_waybel_0(D,k7_lattice3(A),k7_lattice3(B)) )
& ( v5_waybel_0(D,k7_lattice3(A),k7_lattice3(B))
=> v5_waybel_0(C,A,B) ) ) ) ) ) ) ) ).
fof(t43_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( m1_waybel_1(C,A,B)
=> m1_waybel_1(C,k7_lattice3(A),B) )
& ( m1_waybel_1(C,k7_lattice3(A),B)
=> m1_waybel_1(C,A,B) )
& ( m1_waybel_1(C,A,B)
=> m1_waybel_1(C,A,k7_lattice3(B)) )
& ( m1_waybel_1(C,A,k7_lattice3(B))
=> m1_waybel_1(C,A,B) )
& ( m1_waybel_1(C,A,B)
=> m1_waybel_1(C,k7_lattice3(A),k7_lattice3(B)) )
& ( m1_waybel_1(C,k7_lattice3(A),k7_lattice3(B))
=> m1_waybel_1(C,A,B) ) ) ) ) ).
fof(t44_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(E,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k7_lattice3(B)),u1_struct_0(k7_lattice3(A)))
& m2_relset_1(F,u1_struct_0(k7_lattice3(B)),u1_struct_0(k7_lattice3(A))) )
=> ( ( C = E
& D = F )
=> ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
<=> v3_waybel_1(k1_waybel_1(k7_lattice3(B),k7_lattice3(A),F,E),k7_lattice3(B),k7_lattice3(A)) ) ) ) ) ) ) ) ) ).
fof(t45_yellow_7,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,C,k2_pre_circ(A,B))
=> k2_funct_6(D) = C ) ) ) ).
fof(t46_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( m1_pboole(C,B)
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
<=> m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(k7_lattice3(A)))) ) ) ) ).
fof(t47_yellow_7,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)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> r3_orders_2(A,k5_yellow_2(A,k5_waybel_5(A,D)),k6_yellow_2(A,k4_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D)))) ) ) ) ) ).
fof(t48_yellow_7,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) )
=> ( v1_waybel_5(A)
<=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> k5_yellow_2(A,k5_waybel_5(A,D)) = k6_yellow_2(A,k4_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) ).
fof(t49_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k5_yellow_2(A,B) = k6_yellow_2(k7_lattice3(A),B)
& k6_yellow_2(A,B) = k5_yellow_2(k7_lattice3(A),B) ) ) ) ).
fof(t50_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ( k4_waybel_5(A,B) = k5_waybel_5(k7_lattice3(A),B)
& k5_waybel_5(A,B) = k4_waybel_5(k7_lattice3(A),B) ) ) ) ).
fof(t51_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_waybel_5(A)
<=> v1_waybel_5(k7_lattice3(A)) ) ) ).
fof(dt_k1_yellow_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k1_yellow_7(A))
& v1_funct_2(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A)))
& m2_relset_1(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A))) ) ) ).
fof(dt_k2_yellow_7,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v2_relat_1(C)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m1_subset_1(E,A)
& m1_subset_1(F,k1_funct_1(C,E)) )
=> m1_subset_1(k2_yellow_7(A,B,C,D,E,F),B) ) ).
fof(redefinition_k2_yellow_7,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v2_relat_1(C)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m1_subset_1(E,A)
& m1_subset_1(F,k1_funct_1(C,E)) )
=> k2_yellow_7(A,B,C,D,E,F) = k5_funct_6(D,E,F) ) ).
%------------------------------------------------------------------------------