SET007 Axioms: SET007+480.ax
%------------------------------------------------------------------------------
% File : SET007+480 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bounds in Posets and Relational Substructures
% 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_0 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 117 ( 0 unt; 0 def)
% Number of atoms : 919 ( 72 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 873 ( 71 ~; 2 |; 362 &)
% ( 34 <=>; 404 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 37 usr; 0 prp; 1-3 aty)
% Number of functors : 27 ( 27 usr; 2 con; 0-3 aty)
% Number of variables : 344 ( 331 !; 13 ?)
% 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(cc1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc2_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A) ) ) ) ).
fof(fc1_yellow_0,axiom,
! [A,B] :
( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
=> ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B))
& v1_orders_2(g1_orders_2(k1_tarski(A),B))
& v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ).
fof(rc1_yellow_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_realset2(A) ) ).
fof(fc2_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ~ v1_xboole_0(k2_pre_topc(A)) ) ).
fof(cc3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc4_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_yellow_0(A)
=> ( v1_yellow_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc5_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v1_yellow_0(A)
& v2_yellow_0(A) )
=> v3_yellow_0(A) ) ) ).
fof(rc2_yellow_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ).
fof(rc3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_yellow_0(B,A)
& v1_orders_2(B)
& v4_yellow_0(B,A) ) ) ).
fof(rc4_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,A) ) ) ).
fof(cc6_yellow_0,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v2_orders_2(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc7_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v3_orders_2(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc8_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v4_orders_2(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc9_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v7_yellow_0(B,A)
=> v5_yellow_0(B,A) ) ) ) ).
fof(cc10_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
=> v6_yellow_0(B,A) ) ) ) ).
fof(rc5_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& v6_yellow_0(B,A)
& v7_yellow_0(B,A)
& v8_yellow_0(B,A) ) ) ).
fof(cc11_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A) )
=> ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A) ) ) ) ) ).
fof(cc12_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A) )
=> ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A) ) ) ) ) ).
fof(d1_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v2_orders_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_orders_2(A,B,B) ) ) ) ).
fof(d2_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_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))
=> ( ( r1_orders_2(A,B,C)
& r1_orders_2(A,C,D) )
=> r1_orders_2(A,B,D) ) ) ) ) ) ) ).
fof(d3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v4_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_orders_2(A,C,B) )
=> B = C ) ) ) ) ) ).
fof(t1_yellow_0,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))
=> ! [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))
=> ( ( C = E
& D = F )
=> ( ( r1_orders_2(A,C,D)
=> r1_orders_2(B,E,F) )
& ( r2_orders_2(A,C,D)
=> r2_orders_2(B,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_yellow_0,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))
=> ! [C,D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( D = E
=> ( ( r2_lattice3(A,C,D)
=> r2_lattice3(B,C,E) )
& ( r1_lattice3(A,C,D)
=> r1_lattice3(B,C,E) ) ) ) ) ) ) ) ) ).
fof(t3_yellow_0,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))
& v3_lattice3(A) )
=> v3_lattice3(B) ) ) ) ).
fof(t4_yellow_0,axiom,
! [A] :
( ( v3_orders_2(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)
=> ! [D] :
( ( r1_lattice3(A,D,C)
=> r1_lattice3(A,D,B) )
& ( r2_lattice3(A,D,B)
=> r2_lattice3(A,D,C) ) ) ) ) ) ) ).
fof(t5_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r2_lattice3(A,B,C)
=> r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) )
& ( r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)
=> r2_lattice3(A,B,C) )
& ( r1_lattice3(A,B,C)
=> r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) )
& ( r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)
=> r1_lattice3(A,B,C) ) ) ) ) ).
fof(t6_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_lattice3(A,k1_xboole_0,B)
& r1_lattice3(A,k1_xboole_0,B) ) ) ) ).
fof(t7_yellow_0,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_lattice3(A,k1_tarski(C),B)
=> r1_orders_2(A,B,C) )
& ( r1_orders_2(A,B,C)
=> r1_lattice3(A,k1_tarski(C),B) )
& ( r2_lattice3(A,k1_tarski(C),B)
=> r1_orders_2(A,C,B) )
& ( r1_orders_2(A,C,B)
=> r2_lattice3(A,k1_tarski(C),B) ) ) ) ) ) ).
fof(t8_yellow_0,axiom,
! [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))
=> ( ( r1_lattice3(A,k2_tarski(C,D),B)
=> ( r1_orders_2(A,B,C)
& r1_orders_2(A,B,D) ) )
& ( ( r1_orders_2(A,B,C)
& r1_orders_2(A,B,D) )
=> r1_lattice3(A,k2_tarski(C,D),B) )
& ( r2_lattice3(A,k2_tarski(C,D),B)
=> ( r1_orders_2(A,C,B)
& r1_orders_2(A,D,B) ) )
& ( ( r1_orders_2(A,C,B)
& r1_orders_2(A,D,B) )
=> r2_lattice3(A,k2_tarski(C,D),B) ) ) ) ) ) ) ).
fof(t9_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( r1_tarski(B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_lattice3(A,C,D)
=> r1_lattice3(A,B,D) )
& ( r2_lattice3(A,C,D)
=> r2_lattice3(A,B,D) ) ) ) ) ) ).
fof(t10_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C,D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( ( r1_lattice3(A,B,D)
& r1_lattice3(A,C,D) )
=> r1_lattice3(A,k2_xboole_0(B,C),D) )
& ( ( r2_lattice3(A,B,D)
& r2_lattice3(A,C,D) )
=> r2_lattice3(A,k2_xboole_0(B,C),D) ) ) ) ) ).
fof(t11_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_lattice3(A,B,C)
& r1_orders_2(A,C,D) )
=> r2_lattice3(A,B,D) ) ) ) ) ).
fof(t12_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_lattice3(A,B,C)
& r1_orders_2(A,D,C) )
=> r1_lattice3(A,B,D) ) ) ) ) ).
fof(d4_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_yellow_0(A)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& r1_lattice3(A,u1_struct_0(A),B) ) ) ) ).
fof(d5_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_yellow_0(A)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& r2_lattice3(A,u1_struct_0(A),B) ) ) ) ).
fof(d6_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_yellow_0(A)
<=> ( v1_yellow_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(t13_yellow_0,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_yellow_0(A)
=> v1_yellow_0(B) )
& ( v2_yellow_0(A)
=> v2_yellow_0(B) ) ) ) ) ) ).
fof(d7_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( r1_yellow_0(A,B)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
=> r1_orders_2(A,C,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_lattice3(A,B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_lattice3(A,B,E)
=> r1_orders_2(A,D,E) ) ) )
=> D = C ) ) ) ) ) ).
fof(d8_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( r2_yellow_0(A,B)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
=> r1_orders_2(A,D,C) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_lattice3(A,B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_lattice3(A,B,E)
=> r1_orders_2(A,E,D) ) ) )
=> D = C ) ) ) ) ) ).
fof(t14_yellow_0,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))
=> ! [C] :
( ( r1_yellow_0(A,C)
=> r1_yellow_0(B,C) )
& ( r2_yellow_0(A,C)
=> r2_yellow_0(B,C) ) ) ) ) ) ).
fof(t15_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( r1_yellow_0(A,B)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
=> r1_orders_2(A,C,D) ) ) ) ) ) ).
fof(t16_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( r2_yellow_0(A,B)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r1_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
=> r1_orders_2(A,D,C) ) ) ) ) ) ).
fof(t17_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( r1_yellow_0(A,B)
& r2_yellow_0(A,B) ) ) ).
fof(t18_yellow_0,axiom,
! [A] :
( ( v4_orders_2(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))
=> ( ( ( D = k10_lattice3(A,B,C)
& r1_yellow_0(A,k2_tarski(B,C)) )
=> ( r1_orders_2(A,B,D)
& r1_orders_2(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,E)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,D,E) ) ) ) )
& ( ( r1_orders_2(A,B,D)
& r1_orders_2(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,E)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,D,E) ) ) )
=> ( D = k10_lattice3(A,B,C)
& r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ) ) ) ).
fof(t19_yellow_0,axiom,
! [A] :
( ( v4_orders_2(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))
=> ( ( ( D = k11_lattice3(A,B,C)
& r2_yellow_0(A,k2_tarski(B,C)) )
=> ( r1_orders_2(A,D,B)
& r1_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,E,B)
& r1_orders_2(A,E,C) )
=> r1_orders_2(A,E,D) ) ) ) )
& ( ( r1_orders_2(A,D,B)
& r1_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,E,B)
& r1_orders_2(A,E,C) )
=> r1_orders_2(A,E,D) ) ) )
=> ( D = k11_lattice3(A,B,C)
& r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ) ) ) ).
fof(t20_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_lattice3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ).
fof(t21_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v2_lattice3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ).
fof(t22_yellow_0,axiom,
! [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))
=> ( D = k13_lattice3(A,B,C)
<=> ( r1_orders_2(A,B,D)
& r1_orders_2(A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,E)
& r1_orders_2(A,C,E) )
=> r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ).
fof(t23_yellow_0,axiom,
! [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))
=> ( D = k12_lattice3(A,B,C)
<=> ( r1_orders_2(A,D,B)
& r1_orders_2(A,D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_orders_2(A,E,B)
& r1_orders_2(A,E,C) )
=> r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ).
fof(t24_yellow_0,axiom,
! [A] :
( ( v2_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))
=> ( B = k13_lattice3(A,B,C)
<=> r1_orders_2(A,C,B) ) ) ) ) ).
fof(t25_yellow_0,axiom,
! [A] :
( ( v2_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))
=> ( B = k12_lattice3(A,B,C)
<=> r3_orders_2(A,B,C) ) ) ) ) ).
fof(d9_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_yellow_0(A,B)
=> ( C = k1_yellow_0(A,B)
<=> ( r2_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
=> r1_orders_2(A,C,D) ) ) ) ) ) ) ) ).
fof(d10_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_yellow_0(A,B)
=> ( C = k2_yellow_0(A,B)
<=> ( r1_lattice3(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
=> r1_orders_2(A,D,C) ) ) ) ) ) ) ) ).
fof(t26_yellow_0,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))
=> ! [C] :
( r1_yellow_0(A,C)
=> k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) ) ).
fof(t27_yellow_0,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))
=> ! [C] :
( r2_yellow_0(A,C)
=> k2_yellow_0(A,C) = k2_yellow_0(B,C) ) ) ) ) ).
fof(t28_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( k1_yellow_0(A,B) = k15_lattice3(k14_lattice3(A),B)
& k2_yellow_0(A,B) = k16_lattice3(k14_lattice3(A),B) ) ) ).
fof(t29_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( k15_lattice3(A,B) = k1_yellow_0(k3_lattice3(A),B)
& k16_lattice3(A,B) = k2_yellow_0(k3_lattice3(A),B) ) ) ).
fof(t30_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ( B = k1_yellow_0(A,C)
& r1_yellow_0(A,C) )
=> ( r2_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,C,D)
=> r1_orders_2(A,B,D) ) ) ) )
& ( ( r2_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,C,D)
=> r1_orders_2(A,B,D) ) ) )
=> ( B = k1_yellow_0(A,C)
& r1_yellow_0(A,C) ) ) ) ) ) ).
fof(t31_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ( B = k2_yellow_0(A,C)
& r2_yellow_0(A,C) )
=> ( r1_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,C,D)
=> r1_orders_2(A,D,B) ) ) ) )
& ( ( r1_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,C,D)
=> r1_orders_2(A,D,B) ) ) )
=> ( B = k2_yellow_0(A,C)
& r2_yellow_0(A,C) ) ) ) ) ) ).
fof(t32_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( B = k1_yellow_0(A,C)
<=> ( r2_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,C,D)
=> r1_orders_2(A,B,D) ) ) ) ) ) ) ).
fof(t33_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( B = k2_yellow_0(A,C)
<=> ( r1_lattice3(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,C,D)
=> r1_orders_2(A,D,B) ) ) ) ) ) ) ).
fof(t34_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( ( r1_tarski(B,C)
& r1_yellow_0(A,B)
& r1_yellow_0(A,C) )
=> r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ).
fof(t35_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( ( r1_tarski(B,C)
& r2_yellow_0(A,B)
& r2_yellow_0(A,C) )
=> r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)) ) ) ).
fof(t36_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r1_yellow_0(A,B)
& r1_yellow_0(A,C)
& r1_yellow_0(A,k2_xboole_0(B,C)) )
=> k1_yellow_0(A,k2_xboole_0(B,C)) = k10_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ).
fof(t37_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r2_yellow_0(A,B)
& r2_yellow_0(A,C)
& r2_yellow_0(A,k2_xboole_0(B,C)) )
=> k2_yellow_0(A,k2_xboole_0(B,C)) = k11_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ).
fof(t38_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r1_yellow_0(A,k1_struct_0(A,B))
& r2_yellow_0(A,k1_struct_0(A,B)) ) ) ) ).
fof(t39_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k1_yellow_0(A,k1_struct_0(A,B)) = B
& k2_yellow_0(A,k1_struct_0(A,B)) = B ) ) ) ).
fof(t40_yellow_0,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))
=> k2_yellow_0(A,k2_struct_0(A,B,C)) = k12_lattice3(A,B,C) ) ) ) ).
fof(t41_yellow_0,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))
=> k1_yellow_0(A,k2_struct_0(A,B,C)) = k13_lattice3(A,B,C) ) ) ) ).
fof(t42_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( r1_yellow_0(A,k1_xboole_0)
& r2_yellow_0(A,u1_struct_0(A)) ) ) ).
fof(t43_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( r2_yellow_0(A,k1_xboole_0)
& r1_yellow_0(A,u1_struct_0(A)) ) ) ).
fof(d11_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> k3_yellow_0(A) = k1_yellow_0(A,k1_xboole_0) ) ).
fof(d12_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> k4_yellow_0(A) = k2_yellow_0(A,k1_xboole_0) ) ).
fof(t44_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_orders_2(A,k3_yellow_0(A),B) ) ) ).
fof(t45_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_orders_2(A,B,k4_yellow_0(A)) ) ) ).
fof(t46_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
<=> r2_lattice3(A,C,D) ) )
& r1_yellow_0(A,B) )
=> r1_yellow_0(A,C) ) ) ).
fof(t47_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r1_yellow_0(A,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_lattice3(A,B,D)
<=> r2_lattice3(A,C,D) ) ) )
=> k1_yellow_0(A,B) = k1_yellow_0(A,C) ) ) ).
fof(t48_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
<=> r1_lattice3(A,C,D) ) )
& r2_yellow_0(A,B) )
=> r2_yellow_0(A,C) ) ) ).
fof(t49_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r2_yellow_0(A,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lattice3(A,B,D)
<=> r1_lattice3(A,C,D) ) ) )
=> k2_yellow_0(A,B) = k2_yellow_0(A,C) ) ) ).
fof(t50_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( r1_yellow_0(A,B)
=> r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
& ( r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))
=> r1_yellow_0(A,B) )
& ( r2_yellow_0(A,B)
=> r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
& ( r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))
=> r2_yellow_0(A,B) ) ) ) ).
fof(t51_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( r1_yellow_0(A,B)
| r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
=> k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ).
fof(t52_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( r2_yellow_0(A,B)
| r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
=> k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ).
fof(t53_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_yellow_0(A,B) )
=> v3_lattice3(A) ) ) ).
fof(t54_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_lattice3(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_yellow_0(A,B) ) ) ) ).
fof(t55_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v2_lattice3(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_yellow_0(A,B) ) ) ) ).
fof(t56_yellow_0,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> B = k1_toler_1(B,A) ) ).
fof(d13_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( m1_yellow_0(B,A)
<=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& r1_tarski(u1_orders_2(B),u1_orders_2(A)) ) ) ) ) ).
fof(d14_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
<=> u1_orders_2(B) = k1_toler_1(u1_orders_2(A),u1_struct_0(B)) ) ) ) ).
fof(t57_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A)
& m1_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A) ) ) ) ).
fof(t58_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( u1_struct_0(B) = u1_struct_0(C)
=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C)) ) ) ) ) ).
fof(d15_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_orders_2(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( C = k5_yellow_0(A,B)
<=> u1_struct_0(C) = B ) ) ) ) ).
fof(t59_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ) ).
fof(t60_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = C
& F = D
& r1_orders_2(B,E,F) )
=> r1_orders_2(A,C,D) ) ) ) ) ) ) ) ).
fof(t61_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = C
& F = D
& r1_orders_2(A,C,D)
& r2_hidden(E,u1_struct_0(B))
& r2_hidden(F,u1_struct_0(B)) )
=> r1_orders_2(B,E,F) ) ) ) ) ) ) ) ).
fof(t62_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C,D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E = D
=> ( ( r1_lattice3(A,C,D)
=> r1_lattice3(B,C,E) )
& ( r2_lattice3(A,C,D)
=> r2_lattice3(B,C,E) ) ) ) ) ) ) ) ).
fof(t63_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E = D
=> ( ( r1_lattice3(B,C,E)
=> r1_lattice3(A,C,D) )
& ( r2_lattice3(B,C,E)
=> r2_lattice3(A,C,D) ) ) ) ) ) ) ) ) ).
fof(d16_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v5_yellow_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,u1_struct_0(B))
& r2_hidden(D,u1_struct_0(B))
& r2_yellow_0(A,k2_struct_0(A,C,D)) )
=> r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ).
fof(d17_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v6_yellow_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,u1_struct_0(B))
& r2_hidden(D,u1_struct_0(B))
& r1_yellow_0(A,k2_struct_0(A,C,D)) )
=> r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ).
fof(d18_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v7_yellow_0(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_yellow_0(A,C)
=> r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ).
fof(d19_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_yellow_0(A,C)
=> r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ).
fof(t64_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r2_yellow_0(A,C)
& r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) )
=> ( r2_yellow_0(B,C)
& k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) ).
fof(t65_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_yellow_0(A,C)
& r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) )
=> ( r1_yellow_0(B,C)
& k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) ).
fof(t66_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( ( r2_yellow_0(A,k2_struct_0(B,C,D))
& r2_hidden(k2_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) )
=> ( r2_yellow_0(B,k2_struct_0(B,C,D))
& k2_yellow_0(B,k2_struct_0(B,C,D)) = k2_yellow_0(A,k2_struct_0(B,C,D)) ) ) ) ) ) ) ).
fof(t67_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( ( r1_yellow_0(A,k2_struct_0(B,C,D))
& r2_hidden(k1_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) )
=> ( r1_yellow_0(B,k2_struct_0(B,C,D))
& k1_yellow_0(B,k2_struct_0(B,C,D)) = k1_yellow_0(A,k2_struct_0(B,C,D)) ) ) ) ) ) ) ).
fof(t68_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(k2_yellow_0(A,C),u1_struct_0(B))
=> k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ).
fof(t69_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(k1_yellow_0(A,C),u1_struct_0(B))
=> k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ).
fof(t70_yellow_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( E = C
& F = D )
=> k12_lattice3(B,C,D) = k12_lattice3(A,E,F) ) ) ) ) ) ) ) ).
fof(t71_yellow_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( E = C
& F = D )
=> k13_lattice3(B,C,D) = k13_lattice3(A,E,F) ) ) ) ) ) ) ) ).
fof(s1_yellow_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& v1_orders_2(A)
& l1_orders_2(A)
& u1_struct_0(A) = f1_s1_yellow_0
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> p1_s1_yellow_0(B,C) ) ) ) ) ).
fof(dt_m1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,A)
=> l1_orders_2(B) ) ) ).
fof(existence_m1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] : m1_yellow_0(B,A) ) ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ).
fof(dt_k4_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> m1_subset_1(k4_yellow_0(A),u1_struct_0(A)) ) ).
fof(dt_k5_yellow_0,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A)
& m1_yellow_0(k5_yellow_0(A,B),A) ) ) ).
%------------------------------------------------------------------------------