SET007 Axioms: SET007+487.ax
%------------------------------------------------------------------------------
% File : SET007+487 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Definitions and Properties of the Join and Meet of Subsets
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 94 ( 0 unt; 0 def)
% Number of atoms : 696 ( 43 equ)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 658 ( 56 ~; 0 |; 316 &)
% ( 10 <=>; 276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 0 prp; 1-3 aty)
% Number of functors : 32 ( 32 usr; 1 con; 0-3 aty)
% Number of variables : 324 ( 314 !; 10 ?)
% 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_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k1_yellow_4(A,B,C)) ) ).
fof(fc2_yellow_4,axiom,
! [A,B,C] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel_0(k1_yellow_4(A,B,C),A) ) ).
fof(fc3_yellow_4,axiom,
! [A,B,C] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel_0(k1_yellow_4(A,B,C),A) ) ).
fof(fc4_yellow_4,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v13_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v13_waybel_0(k1_yellow_4(A,B,C),A) ) ).
fof(fc5_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k3_yellow_4(A,B,C)) ) ).
fof(fc6_yellow_4,axiom,
! [A,B,C] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel_0(k3_yellow_4(A,B,C),A) ) ).
fof(fc7_yellow_4,axiom,
! [A,B,C] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel_0(k3_yellow_4(A,B,C),A) ) ).
fof(fc8_yellow_4,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v12_waybel_0(k3_yellow_4(A,B,C),A) ) ).
fof(t1_yellow_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r1_yellow_0(A,B) )
=> r1_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) ).
fof(t2_yellow_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_yellow_0(A,B) )
=> r1_orders_2(A,k2_yellow_0(A,B),C) ) ) ) ).
fof(d1_yellow_4,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_yellow_4(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,C)
& r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ).
fof(d2_yellow_4,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)))
=> ( r2_yellow_4(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ).
fof(t3_yellow_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_yellow_4(A,k1_pre_topc(A),B) ) ) ).
fof(t4_yellow_4,axiom,
! [A] :
( ( v3_orders_2(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_yellow_4(A,B,C)
& r1_yellow_4(A,C,D) )
=> r1_yellow_4(A,B,D) ) ) ) ) ) ).
fof(t5_yellow_4,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_yellow_4(A,C,B)
& v12_waybel_0(B,A) )
=> r1_tarski(C,B) ) ) ) ) ).
fof(t6_yellow_4,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r2_yellow_4(A,B,k1_pre_topc(A)) ) ) ).
fof(t7_yellow_4,axiom,
! [A] :
( ( v3_orders_2(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_yellow_4(A,C,D)
& r2_yellow_4(A,B,C) )
=> r2_yellow_4(A,B,D) ) ) ) ) ) ).
fof(t8_yellow_4,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)))
=> ( ( r2_yellow_4(A,C,B)
& v13_waybel_0(C,A) )
=> r1_tarski(B,C) ) ) ) ) ).
fof(t9_yellow_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_yellow_4(A,B,k1_pre_topc(A)) = k1_xboole_0 ) ) ).
fof(t10_yellow_4,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(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,C) )
=> r2_hidden(k10_lattice3(A,D,E),k1_yellow_4(A,B,C)) ) ) ) ) ) ) ).
fof(t11_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_yellow_4(A,B,k2_yellow_4(A,B,C)) ) ) ) ).
fof(t12_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(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)))
=> r2_yellow_4(A,B,k2_yellow_4(A,B,C)) ) ) ) ).
fof(t13_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(B,k2_yellow_4(A,B,B)) ) ) ).
fof(t14_yellow_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k2_yellow_4(A,k2_yellow_4(A,B,C),D) = k2_yellow_4(A,B,k2_yellow_4(A,C,D)) ) ) ) ) ).
fof(t16_yellow_4,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(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k1_yellow_4(A,B,k4_subset_1(u1_struct_0(A),C,D)) = k4_subset_1(u1_struct_0(A),k1_yellow_4(A,B,C),k1_yellow_4(A,B,D)) ) ) ) ) ).
fof(t17_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k4_subset_1(u1_struct_0(A),B,k2_yellow_4(A,C,D)),k2_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D))) ) ) ) ) ).
fof(t18_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D)),k4_subset_1(u1_struct_0(A),B,k2_yellow_4(A,C,D))) ) ) ) ) ).
fof(t19_yellow_4,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(A))
=> k1_yellow_4(A,k1_struct_0(A,B),k1_struct_0(A,C)) = k1_struct_0(A,k10_lattice3(A,B,C)) ) ) ) ).
fof(t20_yellow_4,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(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_yellow_4(A,k1_struct_0(A,B),k2_struct_0(A,C,D)) = k2_struct_0(A,k10_lattice3(A,B,C),k10_lattice3(A,B,D)) ) ) ) ) ).
fof(t21_yellow_4,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(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,D)
& r1_tarski(C,E) )
=> r1_tarski(k1_yellow_4(A,B,C),k1_yellow_4(A,D,E)) ) ) ) ) ) ) ).
fof(t22_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v1_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))
=> ( r1_lattice3(A,B,C)
=> k2_yellow_4(A,k1_struct_0(A,C),B) = B ) ) ) ) ).
fof(t23_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_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))
=> r1_lattice3(A,k2_yellow_4(A,k1_struct_0(A,C),B),C) ) ) ) ).
fof(t24_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r2_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,C),B))
& r2_yellow_0(A,B) )
=> r3_orders_2(A,k13_lattice3(A,C,k2_yellow_0(A,B)),k2_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,C),B))) ) ) ) ) ).
fof(t25_yellow_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_lattice3(A,B,k1_yellow_0(A,k2_yellow_4(A,B,C))) ) ) ) ).
fof(t26_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_lattice3(A,D,B)
& r1_lattice3(A,E,C) )
=> r1_lattice3(A,k2_yellow_4(A,D,E),k13_lattice3(A,B,C)) ) ) ) ) ) ) ).
fof(t27_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_lattice3(A,D,B)
& r2_lattice3(A,E,C) )
=> r2_lattice3(A,k2_yellow_4(A,D,E),k13_lattice3(A,B,C)) ) ) ) ) ) ) ).
fof(t28_yellow_4,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] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_yellow_0(A,k2_yellow_4(A,B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) ).
fof(t29_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_tarski(B,k4_waybel_0(A,k2_yellow_4(A,B,C))) ) ) ) ).
fof(t30_yellow_4,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(k2_yellow_1(k8_waybel_0(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( B = D
& C = E )
=> k13_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k4_waybel_0(A,k2_yellow_4(A,D,E)) ) ) ) ) ) ) ).
fof(t32_yellow_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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(k4_waybel_0(A,k2_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))),k4_waybel_0(A,k2_yellow_4(A,B,C))) ) ) ) ).
fof(t33_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k4_waybel_0(A,k2_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))) = k4_waybel_0(A,k2_yellow_4(A,B,C)) ) ) ) ).
fof(t34_yellow_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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(k5_waybel_0(A,k2_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))),k5_waybel_0(A,k2_yellow_4(A,B,C))) ) ) ) ).
fof(t35_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_waybel_0(A,k2_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))) = k5_waybel_0(A,k2_yellow_4(A,B,C)) ) ) ) ).
fof(t36_yellow_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k3_yellow_4(A,B,k1_pre_topc(A)) = k1_xboole_0 ) ) ).
fof(t37_yellow_4,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(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,C) )
=> r2_hidden(k11_lattice3(A,D,E),k3_yellow_4(A,B,C)) ) ) ) ) ) ) ).
fof(t38_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_yellow_4(A,k4_yellow_4(A,B,C),B) ) ) ) ).
fof(t39_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(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_yellow_4(A,k4_yellow_4(A,B,C),B) ) ) ) ).
fof(t40_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(B,k4_yellow_4(A,B,B)) ) ) ).
fof(t41_yellow_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k4_yellow_4(A,k4_yellow_4(A,B,C),D) = k4_yellow_4(A,B,k4_yellow_4(A,C,D)) ) ) ) ) ).
fof(t43_yellow_4,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(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k3_yellow_4(A,B,k4_subset_1(u1_struct_0(A),C,D)) = k4_subset_1(u1_struct_0(A),k3_yellow_4(A,B,C),k3_yellow_4(A,B,D)) ) ) ) ) ).
fof(t44_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k4_subset_1(u1_struct_0(A),B,k4_yellow_4(A,C,D)),k4_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D))) ) ) ) ) ).
fof(t45_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k4_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D)),k4_subset_1(u1_struct_0(A),B,k4_yellow_4(A,C,D))) ) ) ) ) ).
fof(t46_yellow_4,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(A))
=> k3_yellow_4(A,k1_struct_0(A,B),k1_struct_0(A,C)) = k1_struct_0(A,k11_lattice3(A,B,C)) ) ) ) ).
fof(t47_yellow_4,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(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_yellow_4(A,k1_struct_0(A,B),k2_struct_0(A,C,D)) = k2_struct_0(A,k11_lattice3(A,B,C),k11_lattice3(A,B,D)) ) ) ) ) ).
fof(t48_yellow_4,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(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,D)
& r1_tarski(C,E) )
=> r1_tarski(k3_yellow_4(A,B,C),k3_yellow_4(A,D,E)) ) ) ) ) ) ) ).
fof(t49_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(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(k5_subset_1(u1_struct_0(A),B,C),k4_yellow_4(A,B,C)) ) ) ) ).
fof(t50_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_yellow_4(A,B,C) = k5_subset_1(u1_struct_0(A),B,C) ) ) ) ).
fof(t51_yellow_4,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& v2_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_lattice3(A,B,C)
=> k4_yellow_4(A,k1_struct_0(A,C),B) = B ) ) ) ) ).
fof(t52_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_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_lattice3(A,k4_yellow_4(A,k1_struct_0(A,C),B),C) ) ) ) ).
fof(t53_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B))
& r1_yellow_0(A,B) )
=> r3_orders_2(A,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)),k12_lattice3(A,C,k1_yellow_0(A,B))) ) ) ) ) ).
fof(t54_yellow_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_lattice3(A,B,k2_yellow_0(A,k4_yellow_4(A,B,C))) ) ) ) ).
fof(t55_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_lattice3(A,D,B)
& r1_lattice3(A,E,C) )
=> r1_lattice3(A,k4_yellow_4(A,D,E),k12_lattice3(A,B,C)) ) ) ) ) ) ) ).
fof(t56_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_lattice3(A,D,B)
& r2_lattice3(A,E,C) )
=> r2_lattice3(A,k4_yellow_4(A,D,E),k12_lattice3(A,B,C)) ) ) ) ) ) ) ).
fof(t57_yellow_4,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] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_yellow_0(A,k4_yellow_4(A,B,C)) = k12_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ) ).
fof(t58_yellow_4,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(k2_yellow_1(k8_waybel_0(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( B = D
& C = E )
=> k12_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k4_yellow_4(A,D,E) ) ) ) ) ) ) ).
fof(t59_yellow_4,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_tarski(B,k5_waybel_0(A,k4_yellow_4(A,B,C))) ) ) ) ).
fof(t61_yellow_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(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(k4_waybel_0(A,k4_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))),k4_waybel_0(A,k4_yellow_4(A,B,C))) ) ) ) ).
fof(t62_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k4_waybel_0(A,k4_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))) = k4_waybel_0(A,k4_yellow_4(A,B,C)) ) ) ) ).
fof(t63_yellow_4,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(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(k5_waybel_0(A,k4_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))),k5_waybel_0(A,k4_yellow_4(A,B,C))) ) ) ) ).
fof(t64_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_waybel_0(A,k4_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))) = k5_waybel_0(A,k4_yellow_4(A,B,C)) ) ) ) ).
fof(reflexivity_r3_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_yellow_4(A,B,B) ) ).
fof(redefinition_r3_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_yellow_4(A,B,C)
<=> r1_yellow_4(A,B,C) ) ) ).
fof(reflexivity_r4_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_yellow_4(A,C,C) ) ).
fof(redefinition_r4_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r4_yellow_4(A,B,C)
<=> r2_yellow_4(A,B,C) ) ) ).
fof(dt_k1_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_yellow_4,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(commutativity_k2_yellow_4,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_yellow_4(A,B,C) = k2_yellow_4(A,C,B) ) ).
fof(redefinition_k2_yellow_4,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_yellow_4(A,B,C) = k1_yellow_4(A,B,C) ) ).
fof(dt_k3_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k3_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k4_yellow_4,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k4_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(commutativity_k4_yellow_4,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_yellow_4(A,B,C) = k4_yellow_4(A,C,B) ) ).
fof(redefinition_k4_yellow_4,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k4_yellow_4(A,B,C) = k3_yellow_4(A,B,C) ) ).
fof(d3_yellow_4,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(A)))
=> k1_yellow_4(A,B,C) = a_3_0_yellow_4(A,B,C) ) ) ) ).
fof(t15_yellow_4,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,u1_struct_0(A))
=> k1_yellow_4(A,k1_struct_0(A,C),B) = a_3_1_yellow_4(A,B,C) ) ) ) ).
fof(t31_yellow_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> k3_tarski(a_2_0_yellow_4(A,B)) = k1_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) ).
fof(d4_yellow_4,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(A)))
=> k3_yellow_4(A,B,C) = a_3_2_yellow_4(A,B,C) ) ) ) ).
fof(t42_yellow_4,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,u1_struct_0(A))
=> k3_yellow_4(A,k1_struct_0(A,C),B) = a_3_3_yellow_4(A,B,C) ) ) ) ).
fof(t60_yellow_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> k3_tarski(a_2_1_yellow_4(A,B)) = k3_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) ).
fof(fraenkel_a_3_0_yellow_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_yellow_4(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k10_lattice3(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_3_1_yellow_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_yellow_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k10_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_2_0_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
=> ( r2_hidden(A,a_2_0_yellow_4(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k1_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
& r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) ).
fof(fraenkel_a_3_2_yellow_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_2_yellow_4(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k11_lattice3(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_3_3_yellow_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_3_yellow_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k11_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_2_1_yellow_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
=> ( r2_hidden(A,a_2_1_yellow_4(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k3_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
& r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) ).
%------------------------------------------------------------------------------