SET007 Axioms: SET007+483.ax
%------------------------------------------------------------------------------
% File : SET007+483 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Boolean Posets, Posets
% Version : [Urb08] axioms.
% English : Boolean Posets, Posets under Inclusion and Products of Relational
% Structures
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 63 ( 6 unt; 0 def)
% Number of atoms : 341 ( 33 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 330 ( 52 ~; 0 |; 180 &)
% ( 9 <=>; 89 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 0 prp; 1-3 aty)
% Number of functors : 37 ( 37 usr; 1 con; 0-3 aty)
% Number of variables : 119 ( 116 !; 3 ?)
% 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_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k3_lattice3(A))
& v1_orders_2(k3_lattice3(A))
& v2_orders_2(k3_lattice3(A))
& v3_orders_2(k3_lattice3(A))
& v4_orders_2(k3_lattice3(A))
& v1_lattice3(k3_lattice3(A))
& v2_lattice3(k3_lattice3(A)) ) ) ).
fof(fc2_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k3_lattice3(A))
& v1_orders_2(k3_lattice3(A))
& v2_orders_2(k3_lattice3(A))
& v3_orders_2(k3_lattice3(A))
& v4_orders_2(k3_lattice3(A))
& v2_yellow_0(k3_lattice3(A))
& v1_lattice3(k3_lattice3(A))
& v2_lattice3(k3_lattice3(A)) ) ) ).
fof(fc3_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k3_lattice3(A))
& v1_orders_2(k3_lattice3(A))
& v2_orders_2(k3_lattice3(A))
& v3_orders_2(k3_lattice3(A))
& v4_orders_2(k3_lattice3(A))
& v1_yellow_0(k3_lattice3(A))
& v1_lattice3(k3_lattice3(A))
& v2_lattice3(k3_lattice3(A)) ) ) ).
fof(fc4_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k3_lattice3(A))
& v1_orders_2(k3_lattice3(A))
& v2_orders_2(k3_lattice3(A))
& v3_orders_2(k3_lattice3(A))
& v4_orders_2(k3_lattice3(A))
& v1_yellow_0(k3_lattice3(A))
& v2_yellow_0(k3_lattice3(A))
& v3_yellow_0(k3_lattice3(A))
& v1_lattice3(k3_lattice3(A))
& v2_lattice3(k3_lattice3(A))
& v3_lattice3(k3_lattice3(A)) ) ) ).
fof(fc5_yellow_1,axiom,
! [A] :
( v1_orders_2(k2_yellow_1(A))
& v2_orders_2(k2_yellow_1(A))
& v3_orders_2(k2_yellow_1(A))
& v4_orders_2(k2_yellow_1(A)) ) ).
fof(fc6_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k2_yellow_1(A))
& v1_orders_2(k2_yellow_1(A))
& v2_orders_2(k2_yellow_1(A))
& v3_orders_2(k2_yellow_1(A))
& v4_orders_2(k2_yellow_1(A)) ) ) ).
fof(fc7_yellow_1,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A)) ) ).
fof(fc8_yellow_1,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ).
fof(fc9_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A)))
& v1_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v2_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v3_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v4_orders_2(k2_yellow_1(u1_pre_topc(A)))
& v1_yellow_0(k2_yellow_1(u1_pre_topc(A)))
& v2_yellow_0(k2_yellow_1(u1_pre_topc(A)))
& v3_yellow_0(k2_yellow_1(u1_pre_topc(A)))
& v1_lattice3(k2_yellow_1(u1_pre_topc(A)))
& v2_lattice3(k2_yellow_1(u1_pre_topc(A)))
& v3_lattice3(k2_yellow_1(u1_pre_topc(A)))
& ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) ).
fof(cc1_yellow_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_yellow_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_pralg_1(A) ) ) ).
fof(rc1_yellow_1,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v1_yellow_1(B) ) ).
fof(fc10_yellow_1,axiom,
! [A,B] :
( l1_orders_2(B)
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v2_pralg_1(k2_funcop_1(A,B))
& v1_yellow_1(k2_funcop_1(A,B)) ) ) ).
fof(fc11_yellow_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B)) ) ) ).
fof(fc12_yellow_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v2_orders_2(k6_yellow_1(A,B)) ) ) ).
fof(fc13_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A))
& v1_orders_2(k6_yellow_1(k1_xboole_0,A))
& v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ).
fof(fc14_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A))
& v1_orders_2(k6_yellow_1(k1_xboole_0,A))
& v2_orders_2(k6_yellow_1(k1_xboole_0,A))
& v3_orders_2(k6_yellow_1(k1_xboole_0,A))
& v4_orders_2(k6_yellow_1(k1_xboole_0,A))
& v1_yellow_0(k6_yellow_1(k1_xboole_0,A))
& v2_yellow_0(k6_yellow_1(k1_xboole_0,A))
& v3_yellow_0(k6_yellow_1(k1_xboole_0,A))
& v1_lattice3(k6_yellow_1(k1_xboole_0,A))
& v2_lattice3(k6_yellow_1(k1_xboole_0,A))
& v3_lattice3(k6_yellow_1(k1_xboole_0,A))
& v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ).
fof(fc15_yellow_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v3_orders_2(k6_yellow_1(A,B)) ) ) ).
fof(fc16_yellow_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v4_orders_2(k6_yellow_1(A,B)) ) ) ).
fof(fc17_yellow_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v4_orders_2(k6_yellow_1(A,B))
& v2_lattice3(k6_yellow_1(A,B)) ) ) ).
fof(fc18_yellow_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v4_orders_2(k6_yellow_1(A,B))
& v1_lattice3(k6_yellow_1(A,B)) ) ) ).
fof(d1_yellow_1,axiom,
! [A] : k2_yellow_1(A) = g1_orders_2(A,k1_yellow_1(A)) ).
fof(t1_yellow_1,axiom,
! [A] :
( u1_struct_0(k2_yellow_1(A)) = A
& u1_orders_2(k2_yellow_1(A)) = k1_yellow_1(A) ) ).
fof(d2_yellow_1,axiom,
! [A] : k3_yellow_1(A) = k3_lattice3(k1_lattice3(A)) ).
fof(t2_yellow_1,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_1(A)))
=> ( r3_orders_2(k3_yellow_1(A),B,C)
<=> r1_tarski(B,C) ) ) ) ).
fof(t3_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
=> ( r3_orders_2(k2_yellow_1(A),B,C)
<=> r1_tarski(B,C) ) ) ) ) ).
fof(t4_yellow_1,axiom,
! [A] : k3_yellow_1(A) = k2_yellow_1(k1_zfmisc_1(A)) ).
fof(t5_yellow_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( v4_yellow_0(k2_yellow_1(B),k3_yellow_1(A))
& m1_yellow_0(k2_yellow_1(B),k3_yellow_1(A)) ) ) ).
fof(t6_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v1_lattice3(k2_yellow_1(A))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
=> r1_tarski(k2_xboole_0(B,C),k10_lattice3(k2_yellow_1(A),B,C)) ) ) ) ) ).
fof(t7_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v2_lattice3(k2_yellow_1(A))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
=> r1_tarski(k11_lattice3(k2_yellow_1(A),B,C),k3_xboole_0(B,C)) ) ) ) ) ).
fof(t8_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
=> ( r2_hidden(k2_xboole_0(B,C),A)
=> k10_lattice3(k2_yellow_1(A),B,C) = k2_xboole_0(B,C) ) ) ) ) ).
fof(t9_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
=> ( r2_hidden(k3_xboole_0(B,C),A)
=> k11_lattice3(k2_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ) ).
fof(t10_yellow_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> r1_tarski(B,C) ) ) )
=> u1_orders_2(A) = k1_yellow_1(u1_struct_0(A)) ) ) ).
fof(t11_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ! [B,C] :
( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r2_hidden(k2_xboole_0(B,C),A) )
=> v1_lattice3(k2_yellow_1(A)) ) ) ).
fof(t12_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ! [B,C] :
( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r2_hidden(k3_xboole_0(B,C),A) )
=> v2_lattice3(k2_yellow_1(A)) ) ) ).
fof(t13_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( r2_hidden(k1_xboole_0,A)
=> k3_yellow_0(k2_yellow_1(A)) = k1_xboole_0 ) ) ).
fof(t14_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( r2_hidden(k3_tarski(A),A)
=> k4_yellow_0(k2_yellow_1(A)) = k3_tarski(A) ) ) ).
fof(t15_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v2_yellow_0(k2_yellow_1(A))
=> r2_hidden(k3_tarski(A),A) ) ) ).
fof(t16_yellow_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v1_yellow_0(k2_yellow_1(A))
=> r2_hidden(k1_setfam_1(A),A) ) ) ).
fof(t17_yellow_1,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_yellow_1(A)))
=> ( k13_lattice3(k3_yellow_1(A),B,C) = k2_xboole_0(B,C)
& k12_lattice3(k3_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ).
fof(t18_yellow_1,axiom,
! [A] : k3_yellow_0(k3_yellow_1(A)) = k1_xboole_0 ).
fof(t19_yellow_1,axiom,
! [A] : k4_yellow_0(k3_yellow_1(A)) = A ).
fof(t20_yellow_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
=> k2_yellow_0(k3_yellow_1(A),B) = k1_setfam_1(B) ) ).
fof(t21_yellow_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
=> k1_yellow_0(k3_yellow_1(A),B) = k3_tarski(B) ) ).
fof(t22_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A)))))
=> k1_yellow_0(k2_yellow_1(u1_pre_topc(A)),B) = k3_tarski(B) ) ) ).
fof(t23_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> k3_yellow_0(k2_yellow_1(u1_pre_topc(A))) = k1_xboole_0 ) ).
fof(t24_yellow_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> k4_yellow_0(k2_yellow_1(u1_pre_topc(A))) = u1_struct_0(A) ) ).
fof(t25_yellow_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tops_2(B,A)
<=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) ) ) ) ).
fof(d3_yellow_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_yellow_1(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> l1_orders_2(B) ) ) ) ).
fof(d4_yellow_1,axiom,
! [A,B] :
( ( v1_yellow_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_orders_2(C)
& l1_orders_2(C) )
=> ( C = k5_yellow_1(A,B)
<=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( r2_hidden(D,k4_card_3(k12_pralg_1(A,B)))
=> ( r1_orders_2(C,D,E)
<=> ? [F] :
( v1_relat_1(F)
& v1_funct_1(F)
& ? [G] :
( v1_relat_1(G)
& v1_funct_1(G)
& F = D
& G = E
& ! [H] :
~ ( r2_hidden(H,A)
& ! [I] :
( l1_orders_2(I)
=> ! [J] :
( m1_subset_1(J,u1_struct_0(I))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(I))
=> ~ ( I = k1_funct_1(B,H)
& J = k1_funct_1(F,H)
& K = k1_funct_1(G,H)
& r1_orders_2(I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_yellow_1,axiom,
! [A,B] :
( l1_orders_2(B)
=> k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)) ) ).
fof(t26_yellow_1,axiom,
! [A] :
( ( v1_yellow_1(A)
& m1_pboole(A,k1_xboole_0) )
=> k5_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) ).
fof(t27_yellow_1,axiom,
! [A] :
( l1_orders_2(A)
=> k6_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) ).
fof(t28_yellow_1,axiom,
! [A,B] :
( l1_orders_2(B)
=> k1_funct_2(A,u1_struct_0(B)) = u1_struct_0(k6_yellow_1(A,B)) ) ).
fof(d6_yellow_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( v1_orders_2(C)
& v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) )
=> ( C = k7_yellow_1(A,B)
<=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(D,u1_struct_0(C))
<=> ( r2_hidden(D,k1_funct_2(u1_struct_0(A),u1_struct_0(B)))
& v5_orders_3(D,A,B) ) ) ) ) ) ) ) ).
fof(dt_k1_yellow_1,axiom,
! [A] :
( v1_relat_2(k1_yellow_1(A))
& v4_relat_2(k1_yellow_1(A))
& v8_relat_2(k1_yellow_1(A))
& v1_partfun1(k1_yellow_1(A),A,A)
& m2_relset_1(k1_yellow_1(A),A,A) ) ).
fof(redefinition_k1_yellow_1,axiom,
! [A] : k1_yellow_1(A) = k1_wellord2(A) ).
fof(dt_k2_yellow_1,axiom,
! [A] :
( v1_orders_2(k2_yellow_1(A))
& l1_orders_2(k2_yellow_1(A)) ) ).
fof(dt_k3_yellow_1,axiom,
! [A] :
( v1_orders_2(k3_yellow_1(A))
& l1_orders_2(k3_yellow_1(A)) ) ).
fof(dt_k4_yellow_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_yellow_1(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> l1_orders_2(k4_yellow_1(A,B,C)) ) ).
fof(redefinition_k4_yellow_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_yellow_1(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k4_yellow_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k5_yellow_1,axiom,
! [A,B] :
( ( v1_yellow_1(B)
& m1_pboole(B,A) )
=> ( v1_orders_2(k5_yellow_1(A,B))
& l1_orders_2(k5_yellow_1(A,B)) ) ) ).
fof(dt_k6_yellow_1,axiom,
! [A,B] :
( l1_orders_2(B)
=> ( v1_orders_2(k6_yellow_1(A,B))
& l1_orders_2(k6_yellow_1(A,B)) ) ) ).
fof(dt_k7_yellow_1,axiom,
! [A,B] :
( ( l1_orders_2(A)
& l1_orders_2(B) )
=> ( v1_orders_2(k7_yellow_1(A,B))
& v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ).
%------------------------------------------------------------------------------