SET007 Axioms: SET007+486.ax
%------------------------------------------------------------------------------
% File : SET007+486 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Cartesian Products of Relations and 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 : yellow_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 110 ( 4 unt; 0 def)
% Number of atoms : 867 ( 43 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 909 ( 152 ~; 2 |; 426 &)
% ( 26 <=>; 303 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 40 ( 39 usr; 0 prp; 1-4 aty)
% Number of functors : 53 ( 53 usr; 19 con; 0-6 aty)
% Number of variables : 372 ( 350 !; 22 ?)
% 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_3,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_xboole_0(k1_funct_5(A)) ) ).
fof(fc2_yellow_3,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_xboole_0(k2_funct_5(A)) ) ).
fof(fc3_yellow_3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
=> ~ v1_xboole_0(k1_funct_5(C)) ) ).
fof(fc4_yellow_3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
=> ~ v1_xboole_0(k2_funct_5(C)) ) ).
fof(fc5_yellow_3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_xboole_0(k4_waybel_0(A,B)) ) ).
fof(fc6_yellow_3,axiom,
! [A,B] :
( ( 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(fc7_yellow_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B)) ) ) ).
fof(fc8_yellow_3,axiom,
! [A,B] :
( ( v2_orders_2(A)
& l1_orders_2(A)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k3_yellow_3(A,B))
& v2_orders_2(k3_yellow_3(A,B)) ) ) ).
fof(fc9_yellow_3,axiom,
! [A,B] :
( ( v4_orders_2(A)
& l1_orders_2(A)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k3_yellow_3(A,B))
& v4_orders_2(k3_yellow_3(A,B)) ) ) ).
fof(fc10_yellow_3,axiom,
! [A,B] :
( ( v3_orders_2(A)
& l1_orders_2(A)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k3_yellow_3(A,B))
& v3_orders_2(k3_yellow_3(A,B)) ) ) ).
fof(fc11_yellow_3,axiom,
! [A,B] :
( ( v1_lattice3(A)
& l1_orders_2(A)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v1_lattice3(k3_yellow_3(A,B)) ) ) ).
fof(fc12_yellow_3,axiom,
! [A,B] :
( ( v2_lattice3(A)
& l1_orders_2(A)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
& v1_orders_2(k3_yellow_3(A,B))
& v2_lattice3(k3_yellow_3(A,B)) ) ) ).
fof(cc1_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_struct_0(A)
=> v1_yellow_3(A) ) ) ).
fof(rc1_yellow_3,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_yellow_3(A) ) ).
fof(cc2_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ~ v1_yellow_3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc3_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A) )
=> ( ~ v3_struct_0(A)
& ~ v1_yellow_3(A) ) ) ) ).
fof(fc13_yellow_3,axiom,
! [A] :
( ( ~ v1_yellow_3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(u1_orders_2(A))
& v1_relat_1(u1_orders_2(A)) ) ) ).
fof(fc14_yellow_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v3_lattice3(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))
& 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)) ) ) ).
fof(t1_yellow_3,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> r1_tarski(C,k2_zfmisc_1(k1_funct_5(C),k2_funct_5(C))) ) ).
fof(t2_yellow_3,axiom,
! [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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,D)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,k12_lattice3(A,B,C),k12_lattice3(A,D,E)) ) ) ) ) ) ) ).
fof(t3_yellow_3,axiom,
! [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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,D)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,k13_lattice3(A,B,C),k13_lattice3(A,D,E)) ) ) ) ) ) ) ).
fof(t4_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> k12_lattice3(A,k1_yellow_0(A,B),C) = C ) ) ) ) ).
fof(t5_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> k13_lattice3(A,k2_yellow_0(A,B),C) = C ) ) ) ) ).
fof(t6_yellow_3,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(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k4_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) ).
fof(t7_yellow_3,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(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k5_waybel_0(A,B),k5_waybel_0(A,C)) ) ) ) ) ).
fof(t8_yellow_3,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) )
=> ! [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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r3_waybel_0(A,B,C,k2_struct_0(A,D,E))
<=> k1_waybel_0(A,B,C,k12_lattice3(A,D,E)) = k12_lattice3(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ).
fof(t9_yellow_3,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r4_waybel_0(A,B,C,k2_struct_0(A,D,E))
<=> k1_waybel_0(A,B,C,k13_lattice3(A,D,E)) = k13_lattice3(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ).
fof(d1_yellow_3,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( C = k1_yellow_3(A,B)
<=> ! [D,E] :
( r2_hidden(k4_tarski(D,E),C)
<=> ? [F,G,H,I] :
( D = k4_tarski(F,G)
& E = k4_tarski(H,I)
& r2_hidden(k4_tarski(F,H),A)
& r2_hidden(k4_tarski(G,I),B) ) ) ) ) ) ) ).
fof(t10_yellow_3,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( r2_hidden(C,k1_yellow_3(A,B))
<=> ( r2_hidden(k4_tarski(k1_mcart_1(k1_mcart_1(C)),k1_mcart_1(k2_mcart_1(C))),A)
& r2_hidden(k4_tarski(k2_mcart_1(k1_mcart_1(C)),k2_mcart_1(k2_mcart_1(C))),B)
& ? [D,E] : C = k4_tarski(D,E)
& ? [D,E] : k1_mcart_1(C) = k4_tarski(D,E)
& ? [D,E] : k2_mcart_1(C) = k4_tarski(D,E) ) ) ) ) ).
fof(d2_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( v1_orders_2(C)
& l1_orders_2(C) )
=> ( C = k3_yellow_3(A,B)
<=> ( u1_struct_0(C) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))
& u1_orders_2(C) = k2_yellow_3(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)) ) ) ) ) ) ).
fof(t11_yellow_3,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(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_orders_2(A,C,D)
& r1_orders_2(B,E,F) )
<=> r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(t12_yellow_3,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_orders_2(k3_yellow_3(A,B),C,D)
<=> ( r1_orders_2(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D))
& r1_orders_2(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D)) ) ) ) ) ) ) ).
fof(t13_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) ) )
=> D = E ) ) ) ) ) ) ).
fof(t14_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ~ v3_struct_0(k3_yellow_3(A,B))
=> ( ~ v3_struct_0(A)
& ~ v3_struct_0(B) ) ) ) ) ).
fof(t15_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( v2_orders_2(k3_yellow_3(A,B))
=> ( v2_orders_2(A)
& v2_orders_2(B) ) ) ) ) ).
fof(t16_yellow_3,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) )
=> ( v4_orders_2(k3_yellow_3(A,B))
=> ( v4_orders_2(A)
& v4_orders_2(B) ) ) ) ) ).
fof(t17_yellow_3,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) )
=> ( v3_orders_2(k3_yellow_3(A,B))
=> ( v3_orders_2(A)
& v3_orders_2(B) ) ) ) ) ).
fof(t18_yellow_3,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) )
=> ( v1_lattice3(k3_yellow_3(A,B))
=> ( v1_lattice3(A)
& v1_lattice3(B) ) ) ) ) ).
fof(t19_yellow_3,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) )
=> ( v2_lattice3(k3_yellow_3(A,B))
=> ( v2_lattice3(A)
& v2_lattice3(B) ) ) ) ) ).
fof(t20_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v1_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
=> ( v1_waybel_0(C,A)
& v1_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t21_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> ( ~ v1_xboole_0(k4_yellow_3(A,B,C))
& ~ v1_xboole_0(k5_yellow_3(A,B,C)) ) ) ) ) ).
fof(t22_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_yellow_3(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> ( v1_waybel_0(k4_yellow_3(A,B,C),A)
& v1_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) ).
fof(t23_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v2_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
=> ( v2_waybel_0(C,A)
& v2_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t24_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_3(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> ( v2_waybel_0(k4_yellow_3(A,B,C),A)
& v2_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) ).
fof(t25_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v13_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
=> ( v13_waybel_0(C,A)
& v13_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t26_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v13_waybel_0(C,k3_yellow_3(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> ( v13_waybel_0(k4_yellow_3(A,B,C),A)
& v13_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) ).
fof(t27_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v12_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
=> ( v12_waybel_0(C,A)
& v12_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t28_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v12_waybel_0(C,k3_yellow_3(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> ( v12_waybel_0(k4_yellow_3(A,B,C),A)
& v12_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) ).
fof(d3_yellow_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_yellow_3(A)
<=> v1_xboole_0(u1_orders_2(A)) ) ) ).
fof(t29_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F))
=> ( r2_lattice3(A,C,E)
& r2_lattice3(B,D,F) ) ) ) ) ) ) ) ) ).
fof(t30_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r2_lattice3(A,C,E)
& r2_lattice3(B,D,F) )
=> r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F)) ) ) ) ) ) ) ) ).
fof(t31_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_lattice3(k3_yellow_3(A,B),C,k7_yellow_3(A,B,D,E))
<=> ( r2_lattice3(A,k4_yellow_3(A,B,C),D)
& r2_lattice3(B,k5_yellow_3(A,B,C),E) ) ) ) ) ) ) ) ).
fof(t32_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F))
=> ( r1_lattice3(A,C,E)
& r1_lattice3(B,D,F) ) ) ) ) ) ) ) ) ).
fof(t33_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_lattice3(A,C,E)
& r1_lattice3(B,D,F) )
=> r1_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F)) ) ) ) ) ) ) ) ).
fof(t34_yellow_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_lattice3(k3_yellow_3(A,B),C,k7_yellow_3(A,B,D,E))
<=> ( r1_lattice3(A,k4_yellow_3(A,B,C),D)
& r1_lattice3(B,k5_yellow_3(A,B,C),E) ) ) ) ) ) ) ) ).
fof(t35_yellow_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_yellow_0(A,C)
& r1_yellow_0(B,D)
& ! [G] :
( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
=> ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
=> r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,E,F),G) ) ) )
=> ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r2_lattice3(A,C,G)
=> r1_orders_2(A,E,G) ) )
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( r2_lattice3(B,D,G)
=> r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_yellow_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r2_yellow_0(A,C)
& r2_yellow_0(B,D)
& ! [G] :
( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
=> ( r1_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
=> r1_orders_2(k3_yellow_3(A,B),G,k7_yellow_3(A,B,E,F)) ) ) )
=> ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r1_lattice3(A,C,G)
=> r1_orders_2(A,G,E) ) )
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( r1_lattice3(B,D,G)
=> r1_orders_2(B,G,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_yellow_3,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r2_lattice3(A,C,G)
=> r1_orders_2(A,E,G) ) )
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( r2_lattice3(B,D,G)
=> r1_orders_2(B,F,G) ) ) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
=> ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
=> r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,E,F),G) ) ) ) ) ) ) ) ) ) ).
fof(t38_yellow_3,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r2_lattice3(A,C,G)
=> r1_orders_2(A,G,E) ) )
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( r2_lattice3(B,D,G)
=> r1_orders_2(B,G,F) ) ) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
=> ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
=> r1_orders_2(k3_yellow_3(A,B),G,k7_yellow_3(A,B,E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t39_yellow_3,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( ( r1_yellow_0(A,C)
& r1_yellow_0(B,D) )
<=> r1_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) ) ) ) ) ) ).
fof(t40_yellow_3,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( ( r2_yellow_0(A,C)
& r2_yellow_0(B,D) )
<=> r2_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) ) ) ) ) ) ).
fof(t41_yellow_3,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,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( ( r1_yellow_0(A,k4_yellow_3(A,B,C))
& r1_yellow_0(B,k5_yellow_3(A,B,C)) )
<=> r1_yellow_0(k3_yellow_3(A,B),C) ) ) ) ) ).
fof(t42_yellow_3,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,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( ( r2_yellow_0(A,k4_yellow_3(A,B,C))
& r2_yellow_0(B,k5_yellow_3(A,B,C)) )
<=> r2_yellow_0(k3_yellow_3(A,B),C) ) ) ) ) ).
fof(t43_yellow_3,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( ( r1_yellow_0(A,C)
& r1_yellow_0(B,D) )
=> k1_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) = k7_yellow_3(A,B,k1_yellow_0(A,C),k1_yellow_0(B,D)) ) ) ) ) ) ).
fof(t44_yellow_3,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( ( r2_yellow_0(A,C)
& r2_yellow_0(B,D) )
=> k2_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) = k7_yellow_3(A,B,k2_yellow_0(A,C),k2_yellow_0(B,D)) ) ) ) ) ) ).
fof(t45_yellow_3,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) )
=> ( v3_lattice3(k3_yellow_3(A,B))
=> ( v3_lattice3(A)
& v3_lattice3(B) ) ) ) ) ).
fof(t46_yellow_3,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] :
( ( ~ v1_xboole_0(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(t47_yellow_3,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] :
( ( ~ v1_xboole_0(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(t48_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,k3_yellow_3(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> r1_tarski(k6_yellow_3(A,B,k4_yellow_3(A,B,C),k5_yellow_3(A,B,C)),k4_waybel_0(k3_yellow_3(A,B),C)) ) ) ) ).
fof(t49_yellow_3,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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_3(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> r1_tarski(k6_yellow_3(A,B,k4_yellow_3(A,B,C),k5_yellow_3(A,B,C)),k5_waybel_0(k3_yellow_3(A,B),C)) ) ) ) ).
fof(s2_yellow_3,axiom,
( ( ! [A,B] :
( r2_hidden(k4_tarski(A,B),f1_s2_yellow_3)
<=> p1_s2_yellow_3(A,B) )
& ! [A,B] :
( r2_hidden(k4_tarski(A,B),f2_s2_yellow_3)
<=> p1_s2_yellow_3(A,B) ) )
=> f1_s2_yellow_3 = f2_s2_yellow_3 ) ).
fof(s7_yellow_3,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s7_yellow_3))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s7_yellow_3))
=> m1_subset_1(f4_s7_yellow_3(A,B),u1_struct_0(f3_s7_yellow_3)) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k3_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3)),u1_struct_0(f3_s7_yellow_3))
& m2_relset_1(A,u1_struct_0(k3_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3)),u1_struct_0(f3_s7_yellow_3))
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s7_yellow_3))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s7_yellow_3))
=> k1_waybel_0(k3_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3),f3_s7_yellow_3,A,k7_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3,B,C)) = f4_s7_yellow_3(B,C) ) ) ) ) ).
fof(dt_k1_yellow_3,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_relat_1(B) )
=> v1_relat_1(k1_yellow_3(A,B)) ) ).
fof(dt_k2_yellow_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(E,A,B)
& m1_relset_1(F,C,D) )
=> m2_relset_1(k2_yellow_3(A,B,C,D,E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ).
fof(redefinition_k2_yellow_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(E,A,B)
& m1_relset_1(F,C,D) )
=> k2_yellow_3(A,B,C,D,E,F) = k1_yellow_3(E,F) ) ).
fof(dt_k3_yellow_3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& l1_orders_2(B) )
=> ( v1_orders_2(k3_yellow_3(A,B))
& l1_orders_2(k3_yellow_3(A,B)) ) ) ).
fof(dt_k4_yellow_3,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> m1_subset_1(k4_yellow_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(redefinition_k4_yellow_3,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> k4_yellow_3(A,B,C) = k1_funct_5(C) ) ).
fof(dt_k5_yellow_3,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> m1_subset_1(k5_yellow_3(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(redefinition_k5_yellow_3,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> k5_yellow_3(A,B,C) = k2_funct_5(C) ) ).
fof(dt_k6_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> m1_subset_1(k6_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ).
fof(redefinition_k6_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> k6_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ).
fof(dt_k7_yellow_3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k7_yellow_3(A,B,C,D),u1_struct_0(k3_yellow_3(A,B))) ) ).
fof(redefinition_k7_yellow_3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> k7_yellow_3(A,B,C,D) = k4_tarski(C,D) ) ).
fof(dt_k8_yellow_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
=> m1_subset_1(k8_yellow_3(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k8_yellow_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
=> k8_yellow_3(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k9_yellow_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
=> m1_subset_1(k9_yellow_3(A,B,C),u1_struct_0(B)) ) ).
fof(redefinition_k9_yellow_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
=> k9_yellow_3(A,B,C) = k2_mcart_1(C) ) ).
fof(dt_k10_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v1_waybel_0(k10_yellow_3(A,B,C,D),k3_yellow_3(A,B))
& m1_subset_1(k10_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) ).
fof(redefinition_k10_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> k10_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ).
fof(dt_k11_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v2_waybel_0(k11_yellow_3(A,B,C,D),k3_yellow_3(A,B))
& m1_subset_1(k11_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) ).
fof(redefinition_k11_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> k11_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ).
fof(dt_k12_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v13_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v13_waybel_0(k12_yellow_3(A,B,C,D),k3_yellow_3(A,B))
& m1_subset_1(k12_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) ).
fof(redefinition_k12_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v13_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> k12_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ).
fof(dt_k13_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v12_waybel_0(k13_yellow_3(A,B,C,D),k3_yellow_3(A,B))
& m1_subset_1(k13_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) ).
fof(redefinition_k13_yellow_3,axiom,
! [A,B,C,D] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> k13_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ).
fof(s1_yellow_3,axiom,
( ! [A] :
( m1_subset_1(A,f1_s1_yellow_3)
=> ! [B] :
( m1_subset_1(B,f1_s1_yellow_3)
=> r2_hidden(f2_s1_yellow_3(A,B),f1_s1_yellow_3) ) )
=> m1_subset_1(a_0_0_yellow_3,k1_zfmisc_1(f1_s1_yellow_3)) ) ).
fof(s3_yellow_3,axiom,
r1_orders_2(f1_s3_yellow_3,k2_yellow_0(f1_s3_yellow_3,k3_tarski(a_0_1_yellow_3)),k2_yellow_0(f1_s3_yellow_3,a_0_2_yellow_3)) ).
fof(s4_yellow_3,axiom,
k2_yellow_0(f1_s4_yellow_3,a_0_3_yellow_3) = k2_yellow_0(f1_s4_yellow_3,k3_tarski(a_0_4_yellow_3)) ).
fof(s5_yellow_3,axiom,
r1_orders_2(f1_s5_yellow_3,k1_yellow_0(f1_s5_yellow_3,a_0_5_yellow_3),k1_yellow_0(f1_s5_yellow_3,k3_tarski(a_0_6_yellow_3))) ).
fof(s6_yellow_3,axiom,
k1_yellow_0(f1_s6_yellow_3,a_0_7_yellow_3) = k1_yellow_0(f1_s6_yellow_3,k3_tarski(a_0_8_yellow_3)) ).
fof(fraenkel_a_0_0_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_0_yellow_3)
<=> ? [B,C] :
( m1_subset_1(B,f1_s1_yellow_3)
& m1_subset_1(C,f1_s1_yellow_3)
& A = f2_s1_yellow_3(B,C)
& p1_s1_yellow_3(B,C) ) ) ).
fof(fraenkel_a_0_1_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_1_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s3_yellow_3)))
& A = B
& p1_s3_yellow_3(B) ) ) ).
fof(fraenkel_a_0_2_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_2_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s3_yellow_3)))
& A = k2_yellow_0(f1_s3_yellow_3,B)
& p1_s3_yellow_3(B) ) ) ).
fof(fraenkel_a_0_3_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_3_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s4_yellow_3)))
& A = k2_yellow_0(f1_s4_yellow_3,B)
& p1_s4_yellow_3(B) ) ) ).
fof(fraenkel_a_0_4_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_4_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s4_yellow_3)))
& A = B
& p1_s4_yellow_3(B) ) ) ).
fof(fraenkel_a_0_5_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_5_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s5_yellow_3)))
& A = k1_yellow_0(f1_s5_yellow_3,B)
& p1_s5_yellow_3(B) ) ) ).
fof(fraenkel_a_0_6_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_6_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s5_yellow_3)))
& A = B
& p1_s5_yellow_3(B) ) ) ).
fof(fraenkel_a_0_7_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_7_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s6_yellow_3)))
& A = k1_yellow_0(f1_s6_yellow_3,B)
& p1_s6_yellow_3(B) ) ) ).
fof(fraenkel_a_0_8_yellow_3,axiom,
! [A] :
( r2_hidden(A,a_0_8_yellow_3)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s6_yellow_3)))
& A = B
& p1_s6_yellow_3(B) ) ) ).
%------------------------------------------------------------------------------