SET007 Axioms: SET007+492.ax
%------------------------------------------------------------------------------
% File : SET007+492 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Miscellaneous Facts about Relation Structure
% 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_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 0 unt; 0 def)
% Number of atoms : 641 ( 57 equ)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 614 ( 55 ~; 1 |; 268 &)
% ( 6 <=>; 284 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-3 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-3 aty)
% Number of variables : 266 ( 266 !; 0 ?)
% 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(t1_yellow_5,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))
=> k13_lattice3(A,B,B) = B ) ) ).
fof(t2_yellow_5,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))
=> k12_lattice3(A,B,B) = B ) ) ).
fof(t3_yellow_5,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))
=> ( r1_orders_2(A,k13_lattice3(A,B,C),D)
=> r1_orders_2(A,B,D) ) ) ) ) ) ).
fof(t4_yellow_5,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))
=> ( r1_orders_2(A,D,k12_lattice3(A,B,C))
=> r1_orders_2(A,D,B) ) ) ) ) ) ).
fof(t5_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> r1_orders_2(A,k12_lattice3(A,B,C),k13_lattice3(A,B,D)) ) ) ) ) ).
fof(t6_yellow_5,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))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t7_yellow_5,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))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t8_yellow_5,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))
=> ( r3_orders_2(A,B,C)
=> k13_lattice3(A,B,C) = C ) ) ) ) ).
fof(t9_yellow_5,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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_orders_2(A,B,D)
& r3_orders_2(A,C,D) )
=> r3_orders_2(A,k13_lattice3(A,B,C),D) ) ) ) ) ) ).
fof(t10_yellow_5,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))
=> ( r3_orders_2(A,C,B)
=> k12_lattice3(A,B,C) = C ) ) ) ) ).
fof(t11_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v11_waybel_1(A)
& v1_lattice3(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))
=> ( r6_waybel_1(A,B,C)
<=> C = k7_waybel_1(A,B) ) ) ) ) ).
fof(d1_yellow_5,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_5(A,B,C) = k11_lattice3(A,B,k7_waybel_1(A,C)) ) ) ) ).
fof(d2_yellow_5,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))
=> k2_yellow_5(A,B,C) = k10_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,C,B)) ) ) ) ).
fof(d3_yellow_5,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))
=> ( r1_yellow_5(A,B,C)
<=> k11_lattice3(A,B,C) != k3_yellow_0(A) ) ) ) ) ).
fof(t12_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> ( r1_orders_2(A,B,D)
=> r1_orders_2(A,k1_yellow_5(A,B,C),D) ) ) ) ) ) ).
fof(t13_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> ( r1_orders_2(A,B,C)
=> r1_orders_2(A,k1_yellow_5(A,B,D),k1_yellow_5(A,C,D)) ) ) ) ) ) ).
fof(t14_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> r1_orders_2(A,k1_yellow_5(A,B,C),B) ) ) ) ).
fof(t15_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> r1_orders_2(A,k1_yellow_5(A,B,C),k3_yellow_5(A,B,C)) ) ) ) ).
fof(t16_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> ( ( r3_orders_2(A,k1_yellow_5(A,B,C),D)
& r3_orders_2(A,k1_yellow_5(A,C,B),D) )
=> r3_orders_2(A,k3_yellow_5(A,B,C),D) ) ) ) ) ) ).
fof(t17_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_yellow_5(A,B,B)
<=> B != k3_yellow_0(A) ) ) ) ).
fof(t18_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(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))
=> k12_lattice3(A,B,k1_yellow_5(A,C,D)) = k1_yellow_5(A,k12_lattice3(A,B,C),D) ) ) ) ) ).
fof(t19_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(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))
=> ( k10_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)) = B
=> r1_orders_2(A,B,k10_lattice3(A,C,D)) ) ) ) ) ) ) ).
fof(t20_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(A)
=> ! [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))
=> k13_lattice3(A,B,k12_lattice3(A,C,D)) = k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D)) ) ) ) ) ) ).
fof(t21_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v2_waybel_1(A)
=> ! [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_5(A,k13_lattice3(A,B,C),D) = k13_lattice3(A,k1_yellow_5(A,B,D),k1_yellow_5(A,C,D)) ) ) ) ) ) ).
fof(t22_yellow_5,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,B,k3_yellow_0(A))
=> B = k3_yellow_0(A) ) ) ) ).
fof(t23_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))
=> ( ( r3_orders_2(A,B,C)
& r3_orders_2(A,B,D)
& k12_lattice3(A,C,D) = k3_yellow_0(A) )
=> B = k3_yellow_0(A) ) ) ) ) ) ).
fof(t24_yellow_5,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k13_lattice3(A,B,C) = k3_yellow_0(A)
=> ( B = k3_yellow_0(A)
& C = k3_yellow_0(A) ) ) ) ) ) ).
fof(t25_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))
=> ( ( r1_orders_2(A,B,C)
& k12_lattice3(A,C,D) = k3_yellow_0(A) )
=> k12_lattice3(A,B,D) = k3_yellow_0(A) ) ) ) ) ) ).
fof(t26_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_yellow_5(A,k3_yellow_0(A),B) = k3_yellow_0(A) ) ) ).
fof(t27_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))
=> ( ( r2_yellow_5(A,B,C)
& r1_orders_2(A,C,D) )
=> r2_yellow_5(A,B,D) ) ) ) ) ) ).
fof(t28_yellow_5,axiom,
! [A] :
( ( v4_orders_2(A)
& v1_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k12_lattice3(A,B,k3_yellow_0(A)) = k3_yellow_0(A) ) ) ).
fof(t29_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(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))
=> ( r2_yellow_5(A,B,k12_lattice3(A,C,D))
=> r2_yellow_5(A,B,C) ) ) ) ) ) ).
fof(t30_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(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))
=> ( r2_yellow_5(A,B,k1_yellow_5(A,C,D))
=> r2_yellow_5(A,B,C) ) ) ) ) ) ).
fof(t31_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ r1_yellow_5(A,B,k3_yellow_0(A)) ) ) ).
fof(t32_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))
=> ~ ( ~ r1_yellow_5(A,B,D)
& r1_orders_2(A,C,D)
& r1_yellow_5(A,B,C) ) ) ) ) ) ).
fof(t33_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))
=> ~ ( ~ ( r1_yellow_5(A,B,C)
& r1_yellow_5(A,B,D) )
& r1_yellow_5(A,B,k12_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t34_yellow_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(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))
=> ( ( r3_orders_2(A,B,C)
& r3_orders_2(A,B,D) )
=> ( r1_yellow_5(A,C,D)
| B = k3_yellow_0(A) ) ) ) ) ) ) ).
fof(t35_yellow_5,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(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))
=> ~ ( ~ r1_yellow_5(A,B,C)
& r1_yellow_5(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t36_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> k13_lattice3(A,k13_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,C,D)),k12_lattice3(A,D,B)) = k12_lattice3(A,k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,C,D)),k13_lattice3(A,D,B)) ) ) ) ) ).
fof(t37_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k12_lattice3(A,B,k7_waybel_1(A,B)) = k3_yellow_0(A)
& k13_lattice3(A,B,k7_waybel_1(A,B)) = k4_yellow_0(A) ) ) ) ).
fof(t38_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> ( r3_orders_2(A,k1_yellow_5(A,B,C),D)
=> r3_orders_2(A,B,k13_lattice3(A,C,D)) ) ) ) ) ) ).
fof(t39_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k7_waybel_1(A,k13_lattice3(A,B,C)) = k12_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C))
& k7_waybel_1(A,k12_lattice3(A,B,C)) = k13_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) ) ) ) ) ).
fof(t40_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> r3_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B)) ) ) ) ) ).
fof(t41_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> ( r3_orders_2(A,B,C)
=> r3_orders_2(A,k1_yellow_5(A,D,C),k1_yellow_5(A,D,B)) ) ) ) ) ) ).
fof(t42_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> ( ( r3_orders_2(A,B,C)
& r3_orders_2(A,D,E) )
=> r3_orders_2(A,k1_yellow_5(A,B,E),k1_yellow_5(A,C,D)) ) ) ) ) ) ) ).
fof(t43_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> ( r3_orders_2(A,B,k13_lattice3(A,C,D))
=> ( r3_orders_2(A,k1_yellow_5(A,B,C),D)
& r3_orders_2(A,k1_yellow_5(A,B,D),C) ) ) ) ) ) ) ).
fof(t44_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,k7_waybel_1(A,B),k7_waybel_1(A,k12_lattice3(A,B,C)))
& r3_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,k12_lattice3(A,B,C))) ) ) ) ) ).
fof(t45_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,k7_waybel_1(A,k13_lattice3(A,B,C)),k7_waybel_1(A,B))
& r3_orders_2(A,k7_waybel_1(A,k13_lattice3(A,B,C)),k7_waybel_1(A,C)) ) ) ) ) ).
fof(t46_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,k1_yellow_5(A,C,B))
=> B = k3_yellow_0(A) ) ) ) ) ).
fof(t47_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> C = k13_lattice3(A,B,k1_yellow_5(A,C,B)) ) ) ) ) ).
fof(t48_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,C) = k3_yellow_0(A)
<=> r3_orders_2(A,B,C) ) ) ) ) ).
fof(t49_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> ( ( r3_orders_2(A,B,k13_lattice3(A,C,D))
& k12_lattice3(A,B,D) = k3_yellow_0(A) )
=> r3_orders_2(A,B,C) ) ) ) ) ) ).
fof(t50_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k13_lattice3(A,B,C) = k13_lattice3(A,k1_yellow_5(A,B,C),C) ) ) ) ).
fof(t51_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,k13_lattice3(A,B,C)) = k3_yellow_0(A) ) ) ) ).
fof(t52_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,k12_lattice3(A,B,C)) = k1_yellow_5(A,B,C) ) ) ) ).
fof(t53_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,k1_yellow_5(A,B,C),C) = k3_yellow_0(A) ) ) ) ).
fof(t54_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k13_lattice3(A,B,k1_yellow_5(A,C,B)) = k13_lattice3(A,B,C) ) ) ) ).
fof(t55_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k13_lattice3(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)) = B ) ) ) ).
fof(t56_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,k1_yellow_5(A,C,D)) = k13_lattice3(A,k1_yellow_5(A,B,C),k12_lattice3(A,B,D)) ) ) ) ) ).
fof(t57_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,k1_yellow_5(A,B,C)) = k12_lattice3(A,B,C) ) ) ) ).
fof(t58_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,k13_lattice3(A,B,C),C) = k1_yellow_5(A,B,C) ) ) ) ).
fof(t59_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k12_lattice3(A,B,C) = k3_yellow_0(A)
<=> k1_yellow_5(A,B,C) = B ) ) ) ) ).
fof(t60_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,k13_lattice3(A,C,D)) = k12_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,B,D)) ) ) ) ) ).
fof(t61_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,B,k12_lattice3(A,C,D)) = k13_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,B,D)) ) ) ) ) ).
fof(t62_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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))
=> k12_lattice3(A,B,k1_yellow_5(A,C,D)) = k1_yellow_5(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)) ) ) ) ) ).
fof(t63_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,k13_lattice3(A,B,C),k12_lattice3(A,B,C)) = k13_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,C,B)) ) ) ) ).
fof(t64_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(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_5(A,k1_yellow_5(A,B,C),D) = k1_yellow_5(A,B,k13_lattice3(A,C,D)) ) ) ) ) ).
fof(t65_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A) ) ).
fof(t66_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) ) ).
fof(t67_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_yellow_5(A,B,B) = k3_yellow_0(A) ) ) ).
fof(t68_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_yellow_5(A,B,k3_yellow_0(A)) = B ) ) ).
fof(t69_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k7_waybel_1(A,k1_yellow_5(A,B,C)) = k13_lattice3(A,k7_waybel_1(A,B),C) ) ) ) ).
fof(t70_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r1_yellow_5(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)) ) ) ) ).
fof(t71_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r1_yellow_5(A,k1_yellow_5(A,B,C),C) ) ) ) ).
fof(t72_yellow_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v11_waybel_1(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ r1_yellow_5(A,B,C)
=> k1_yellow_5(A,k13_lattice3(A,B,C),C) = B ) ) ) ) ).
fof(symmetry_r2_yellow_5,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r2_yellow_5(A,B,C)
=> r2_yellow_5(A,C,B) ) ) ).
fof(redefinition_r2_yellow_5,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r2_yellow_5(A,B,C)
<=> r1_yellow_5(A,B,C) ) ) ).
fof(dt_k1_yellow_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_yellow_5(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_yellow_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_yellow_5(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_yellow_5,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k3_yellow_5(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k3_yellow_5,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k3_yellow_5(A,B,C) = k3_yellow_5(A,C,B) ) ).
fof(redefinition_k3_yellow_5,axiom,
! [A,B,C] :
( ( v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k3_yellow_5(A,B,C) = k2_yellow_5(A,B,C) ) ).
%------------------------------------------------------------------------------