SET007 Axioms: SET007+698.ax
%------------------------------------------------------------------------------
% File : SET007+698 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Categorial Background for Duality Theory
% 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 : yellow21 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 2 unt; 0 def)
% Number of atoms : 1555 ( 73 equ)
% Maximal formula atoms : 123 ( 20 avg)
% Number of connectives : 1601 ( 123 ~; 0 |;1096 &)
% ( 43 <=>; 339 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 95 ( 93 usr; 1 prp; 0-4 aty)
% Number of functors : 63 ( 63 usr; 16 con; 0-6 aty)
% Number of variables : 323 ( 306 !; 17 ?)
% 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_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ~ v1_xboole_0(k2_yellow21(A)) ) ).
fof(fc2_yellow21,axiom,
! [A] :
( v1_setfam_1(A)
=> v4_orders_3(k2_yellow21(A)) ) ).
fof(cc1_yellow21,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow21(A) ) ) ) ).
fof(cc2_yellow21,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A) ) ) ) ).
fof(rc1_yellow21,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A)
& v2_yellow21(A)
& v3_yellow21(A) ) ).
fof(rc2_yellow21,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A)
& v2_yellow21(A)
& v4_yellow21(A) ) ).
fof(cc3_yellow21,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_wellord1(A) )
=> ( v1_relat_1(A)
& v1_wellord1(A)
& v1_relat_2(A)
& v4_relat_2(A)
& v6_relat_2(A)
& v8_relat_2(A) ) ) ).
fof(rc3_yellow21,axiom,
? [A] :
( v1_relat_1(A)
& v1_wellord1(A)
& v2_wellord1(A)
& v1_relat_2(A)
& v4_relat_2(A)
& v6_relat_2(A)
& v8_relat_2(A) ) ).
fof(fc3_yellow21,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_relat_1(B)
& v1_relat_2(B) )
=> ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
& v1_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) ).
fof(fc4_yellow21,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_relat_1(B)
& v4_relat_2(B) )
=> ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
& v4_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) ).
fof(fc5_yellow21,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_relat_1(B)
& v8_relat_2(B) )
=> ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
& v8_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) ).
fof(rc4_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_relset_1(B,A,A)
& v1_relat_1(B)
& v1_wellord1(B)
& v2_wellord1(B)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& v5_yellow21(B) ) ) ).
fof(fc6_yellow21,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v2_wellord1(B)
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& v5_yellow21(B)
& m1_relset_1(B,A,A) )
=> ( ~ v3_struct_0(g1_orders_2(A,B))
& v1_orders_2(g1_orders_2(A,B))
& v2_orders_2(g1_orders_2(A,B))
& v3_orders_2(g1_orders_2(A,B))
& v4_orders_2(g1_orders_2(A,B))
& v1_yellow_0(g1_orders_2(A,B))
& v2_yellow_0(g1_orders_2(A,B))
& v3_yellow_0(g1_orders_2(A,B))
& v16_waybel_0(g1_orders_2(A,B))
& v24_waybel_0(g1_orders_2(A,B))
& v25_waybel_0(g1_orders_2(A,B))
& v1_waybel_8(g1_orders_2(A,B))
& v2_waybel_8(g1_orders_2(A,B))
& v1_lattice3(g1_orders_2(A,B))
& v2_lattice3(g1_orders_2(A,B))
& v3_lattice3(g1_orders_2(A,B))
& v2_waybel_3(g1_orders_2(A,B))
& v3_waybel_3(g1_orders_2(A,B)) ) ) ).
fof(cc4_yellow21,axiom,
! [A] :
( ~ v1_realset1(A)
=> ( ~ v1_xboole_0(A)
& ~ v2_setfam_1(A) ) ) ).
fof(fc7_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k6_yellow21(A))
& v2_altcat_1(k6_yellow21(A))
& v6_altcat_1(k6_yellow21(A))
& v9_altcat_1(k6_yellow21(A))
& v11_altcat_1(k6_yellow21(A))
& v12_altcat_1(k6_yellow21(A))
& v1_altcat_2(k6_yellow21(A))
& v2_yellow18(k6_yellow21(A))
& v3_yellow18(k6_yellow21(A))
& v4_yellow18(k6_yellow21(A))
& v1_yellow21(k6_yellow21(A))
& v2_yellow21(k6_yellow21(A))
& v3_yellow21(k6_yellow21(A))
& v4_yellow21(k6_yellow21(A)) ) ) ).
fof(fc8_yellow21,axiom,
! [A,B,C] :
( ( ~ v2_setfam_1(A)
& m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
& m1_subset_1(C,u1_struct_0(k6_yellow21(A))) )
=> ~ v1_xboole_0(k1_altcat_1(k6_yellow21(A),B,C)) ) ).
fof(cc5_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v3_yellow18(B) ) ) ) ) ).
fof(cc6_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(B) ) ) ) ) ).
fof(cc7_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B) ) ) ) ) ).
fof(cc8_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v1_yellow21(B) ) ) ) ) ).
fof(cc9_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(B)
& v3_yellow18(B)
& v4_yellow18(B)
& v1_yellow21(B)
& v2_yellow21(B) ) ) ) ) ).
fof(cc10_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& v4_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v2_altcat_2(B,A)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(B)
& v3_yellow18(B)
& v4_yellow18(B)
& v1_yellow21(B)
& v2_yellow21(B)
& v4_yellow21(B) ) ) ) ) ).
fof(cc11_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(B)
& v3_yellow18(B)
& v4_yellow18(B)
& v1_yellow21(B)
& v2_yellow21(B)
& v3_yellow21(B) ) ) ) ) ).
fof(fc9_yellow21,axiom,
! [A,B,C] :
( ( ~ v2_setfam_1(A)
& m1_subset_1(B,u1_struct_0(k7_yellow21(A)))
& m1_subset_1(C,u1_struct_0(k7_yellow21(A))) )
=> ~ v1_xboole_0(k1_altcat_1(k7_yellow21(A),B,C)) ) ).
fof(fc10_yellow21,axiom,
! [A,B,C] :
( ( ~ v2_setfam_1(A)
& m1_subset_1(B,u1_struct_0(k8_yellow21(A)))
& m1_subset_1(C,u1_struct_0(k8_yellow21(A))) )
=> ~ v1_xboole_0(k1_altcat_1(k8_yellow21(A),B,C)) ) ).
fof(d1_yellow21,axiom,
! [A] :
( ( l1_struct_0(A)
=> k1_yellow21(A) = A )
& ( ~ l1_struct_0(A)
=> k1_yellow21(A) = g1_struct_0(A) ) ) ).
fof(d2_yellow21,axiom,
! [A,B] :
( B = k2_yellow21(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v1_orders_2(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C)
& r2_hidden(u1_struct_0(k1_yellow21(C)),A) ) ) ) ).
fof(d3_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v1_yellow21(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( l1_struct_0(C)
& B = C
& k3_yellow18(A,B) = u1_struct_0(C) ) ) ) ) ).
fof(d4_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v2_yellow21(A)
<=> ( v9_altcat_1(A)
& v3_yellow18(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v2_orders_2(E)
& v3_orders_2(E)
& v4_orders_2(E)
& v1_lattice3(E)
& v2_lattice3(E)
& l1_orders_2(E) )
=> ( ( D = B
& E = C )
=> r1_tarski(k1_altcat_1(A,B,C),k1_orders_3(D,E)) ) ) ) ) ) ) ) ) ).
fof(d5_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v3_yellow21(A)
<=> ( v2_yellow21(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) ) ) ) ) ) ).
fof(t1_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_yellow18(A,B) = u1_struct_0(k1_yellow21(B)) ) ) ).
fof(t2_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow18(A)
& v1_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_altcat_1(A,B) = k7_grcat_1(k1_yellow21(B)) ) ) ).
fof(d6_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_yellow21(A,B) = B ) ) ).
fof(d7_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> k5_yellow21(A,B,C,D) = D ) ) ) ) ) ).
fof(t3_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_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_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,D) != k1_xboole_0
& ~ ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,D))
=> k5_altcat_1(A,B,C,D,E,F) = k7_funct_2(u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D)),k5_yellow21(A,B,C,E),k5_yellow21(A,C,D,F)) ) ) ) ) ) ) ) ).
fof(d8_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ( v4_yellow21(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
& m2_relset_1(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) )
=> ( v23_waybel_0(D,k3_yellow21(A,B),k3_yellow21(A,C))
=> r2_hidden(D,k1_altcat_1(A,B,C)) ) ) ) ) ) ) ).
fof(t4_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& v4_yellow21(A)
& l2_altcat_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,k1_altcat_1(A,B,C))
=> ( v23_waybel_0(k5_yellow21(A,B,C,D),k3_yellow21(A,B),k3_yellow21(A,C))
=> v3_altcat_3(D,A,B,C) ) ) ) ) ) ).
fof(t5_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
& v3_altcat_3(D,A,B,C)
& ~ v23_waybel_0(k5_yellow21(A,B,C,D),k3_yellow21(A,B),k3_yellow21(A,C)) ) ) ) ) ) ).
fof(d9_yellow21,axiom,
! [A] :
( v1_relat_1(A)
=> ( v5_yellow21(A)
<=> ? [B] :
! [C] :
( r2_hidden(C,k3_relat_1(A))
=> r2_hidden(k4_tarski(C,B),A) ) ) ) ).
fof(t6_yellow21,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v2_funct_1(C) )
=> ! [D] :
( v1_relat_1(D)
=> ( r2_hidden(k4_tarski(A,B),k5_relat_1(k5_relat_1(C,D),k2_funct_1(C)))
<=> ( r2_hidden(A,k1_relat_1(C))
& r2_hidden(B,k1_relat_1(C))
& r2_hidden(k4_tarski(k1_funct_1(C,A),k1_funct_1(C,B)),D) ) ) ) ) ).
fof(t7_yellow21,axiom,
! [A,B] :
( v3_ordinal1(B)
=> ~ ( r2_wellord2(A,B)
& ! [C] :
( ( v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ~ ( r2_wellord1(C,A)
& k2_wellord2(C) = B ) ) ) ) ).
fof(t8_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v2_yellow_0(A)
<=> v5_yellow21(u1_orders_2(A)) ) ) ).
fof(t9_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( v2_wellord1(u1_orders_2(A))
=> ( v16_waybel_0(A)
& v3_lattice3(A)
& v3_waybel_3(A) ) ) ) ).
fof(t10_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( v2_wellord1(u1_orders_2(A))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_orders_2(A,C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( v1_waybel_3(D,A)
& r3_orders_2(A,C,D)
& r3_orders_2(A,D,B) ) ) ) ) ) ) ) ).
fof(t11_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( v2_wellord1(u1_orders_2(A))
=> v2_waybel_8(A) ) ) ).
fof(d10_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ ! [B] :
( m1_subset_1(B,A)
=> v1_xboole_0(B) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow21(B)
& l2_altcat_1(B) )
=> ( B = k6_yellow21(A)
<=> ( ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> ( v1_orders_2(C)
& v3_lattice3(C)
& r2_hidden(u1_struct_0(C),A) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
& v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
& m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
=> ( r2_hidden(E,k1_altcat_1(B,C,D))
<=> v22_waybel_0(E,k3_yellow21(B,C),k3_yellow21(B,D)) ) ) ) ) ) ) ) ) ) ).
fof(t12_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> r1_tarski(u1_struct_0(k6_yellow21(A)),k2_yellow21(A)) ) ).
fof(t13_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
<=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& r2_hidden(B,k2_yellow21(A)) ) ) ) ).
fof(t14_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( r2_hidden(u1_struct_0(B),A)
=> ( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
<=> ( v1_orders_2(B)
& v3_lattice3(B) ) ) ) ) ) ).
fof(t15_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_yellow21(A)))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(k6_yellow21(A),B,C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k4_yellow21(k6_yellow21(A),B)),u1_struct_0(k4_yellow21(k6_yellow21(A),C)))
& v22_waybel_0(D,k4_yellow21(k6_yellow21(A),B),k4_yellow21(k6_yellow21(A),C))
& m2_relset_1(D,u1_struct_0(k4_yellow21(k6_yellow21(A),B)),u1_struct_0(k4_yellow21(k6_yellow21(A),C))) ) ) ) ) ) ).
fof(t16_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( D = C
=> k3_yellow18(B,D) = k3_yellow18(A,C) ) ) ) ) ) ).
fof(d11_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& v2_altcat_2(B,k6_yellow21(A))
& v3_altcat_2(B,k6_yellow21(A))
& m1_altcat_2(B,k6_yellow21(A)) )
=> ( B = k7_yellow21(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_yellow21(A)))
=> ( m1_subset_1(C,u1_struct_0(B))
<=> v3_waybel_3(k4_yellow21(k6_yellow21(A),C)) ) ) ) ) ) ).
fof(d12_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& v2_altcat_2(B,k7_yellow21(A))
& v3_altcat_2(B,k7_yellow21(A))
& m1_altcat_2(B,k7_yellow21(A)) )
=> ( B = k8_yellow21(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_yellow21(A)))
=> ( m1_subset_1(C,u1_struct_0(B))
<=> v2_waybel_8(k4_yellow21(k7_yellow21(A),C)) ) ) ) ) ) ).
fof(t17_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( r2_hidden(u1_struct_0(B),A)
=> ( m1_subset_1(B,u1_struct_0(k7_yellow21(A)))
<=> ( v1_orders_2(B)
& v3_lattice3(B)
& v3_waybel_3(B) ) ) ) ) ) ).
fof(t18_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( r2_hidden(u1_struct_0(B),A)
=> ( m1_subset_1(B,u1_struct_0(k8_yellow21(A)))
<=> ( v1_orders_2(B)
& v3_lattice3(B)
& v2_waybel_8(B) ) ) ) ) ) ).
fof(t19_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_yellow21(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_yellow21(A)))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(k7_yellow21(A),B,C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k4_yellow21(k7_yellow21(A),B)),u1_struct_0(k4_yellow21(k7_yellow21(A),C)))
& v22_waybel_0(D,k4_yellow21(k7_yellow21(A),B),k4_yellow21(k7_yellow21(A),C))
& m2_relset_1(D,u1_struct_0(k4_yellow21(k7_yellow21(A),B)),u1_struct_0(k4_yellow21(k7_yellow21(A),C))) ) ) ) ) ) ).
fof(t20_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_yellow21(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k8_yellow21(A)))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(k8_yellow21(A),B,C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k4_yellow21(k8_yellow21(A),B)),u1_struct_0(k4_yellow21(k8_yellow21(A),C)))
& v22_waybel_0(D,k4_yellow21(k8_yellow21(A),B),k4_yellow21(k8_yellow21(A),C))
& m2_relset_1(D,u1_struct_0(k4_yellow21(k8_yellow21(A),B)),u1_struct_0(k4_yellow21(k8_yellow21(A),C))) ) ) ) ) ) ).
fof(s1_yellow21,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s1_yellow21)
=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( ( r2_hidden(A,f1_s1_yellow21)
& r2_hidden(B,f1_s1_yellow21)
& r2_hidden(C,f1_s1_yellow21) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( p1_s1_yellow21(A,B,D)
& p1_s1_yellow21(B,C,E) )
=> p1_s1_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,f1_s1_yellow21)
=> p1_s1_yellow21(A,A,k7_grcat_1(A)) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& v2_yellow21(A)
& u1_struct_0(A) = f1_s1_yellow21
& ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v5_orders_3(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C))
<=> ( r2_hidden(B,f1_s1_yellow21)
& r2_hidden(C,f1_s1_yellow21)
& p1_s1_yellow21(B,C,D) ) ) ) ) ) ) ) ).
fof(s2_yellow21,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s2_yellow21)
=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( ( r2_hidden(A,f1_s2_yellow21)
& r2_hidden(B,f1_s2_yellow21)
& r2_hidden(C,f1_s2_yellow21) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( p1_s2_yellow21(A,B,D)
& p1_s2_yellow21(B,C,E) )
=> p1_s2_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,f1_s2_yellow21)
=> p1_s2_yellow21(A,A,k7_grcat_1(A)) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s2_yellow21
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
& v5_orders_3(D,k3_yellow21(A,B),k3_yellow21(A,C))
& m2_relset_1(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) )
=> ( r2_hidden(D,k1_altcat_1(A,B,C))
<=> p1_s2_yellow21(k3_yellow21(A,B),k3_yellow21(A,C),D) ) ) ) ) ) ) ).
fof(s3_yellow21,axiom,
( ( ? [A] :
( v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& p1_s3_yellow21(A)
& r2_hidden(u1_struct_0(A),f1_s3_yellow21) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( ( p1_s3_yellow21(A)
& p1_s3_yellow21(B)
& p1_s3_yellow21(C) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( p2_s3_yellow21(A,B,D)
& p2_s3_yellow21(B,C,E) )
=> p2_s3_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( p1_s3_yellow21(A)
=> p2_s3_yellow21(A,A,k7_grcat_1(A)) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( m1_subset_1(B,u1_struct_0(A))
<=> ( v1_orders_2(B)
& p1_s3_yellow21(B)
& r2_hidden(u1_struct_0(B),f1_s3_yellow21) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
& v5_orders_3(D,k3_yellow21(A,B),k3_yellow21(A,C))
& m2_relset_1(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) )
=> ( r2_hidden(D,k1_altcat_1(A,B,C))
<=> p2_s3_yellow21(k3_yellow21(A,B),k3_yellow21(A,C),D) ) ) ) ) ) ) ).
fof(s4_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow21(B)
& l2_altcat_1(B) )
=> ( ( u1_struct_0(A) = f1_s4_yellow21
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D)))
& v5_orders_3(E,k3_yellow21(A,C),k3_yellow21(A,D))
& m2_relset_1(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D))) )
=> ( r2_hidden(E,k1_altcat_1(A,C,D))
<=> p1_s4_yellow21(C,D,E) ) ) ) )
& u1_struct_0(B) = f1_s4_yellow21
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
& v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
& m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
=> ( r2_hidden(E,k1_altcat_1(B,C,D))
<=> p1_s4_yellow21(C,D,E) ) ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ).
fof(s5_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow21(B)
& l2_altcat_1(B) )
=> ( ( ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( m1_subset_1(C,u1_struct_0(A))
<=> ( v1_orders_2(C)
& p1_s5_yellow21(C)
& r2_hidden(u1_struct_0(C),f1_s5_yellow21) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D)))
& v5_orders_3(E,k3_yellow21(A,C),k3_yellow21(A,D))
& m2_relset_1(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D))) )
=> ( r2_hidden(E,k1_altcat_1(A,C,D))
<=> p2_s5_yellow21(C,D,E) ) ) ) )
& ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> ( v1_orders_2(C)
& p1_s5_yellow21(C)
& r2_hidden(u1_struct_0(C),f1_s5_yellow21) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
& v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
& m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
=> ( r2_hidden(E,k1_altcat_1(B,C,D))
<=> p2_s5_yellow21(C,D,E) ) ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ).
fof(s6_yellow21,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s6_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f1_s6_yellow21))
& r2_hidden(B,u1_struct_0(f1_s6_yellow21))
& p1_s6_yellow21(A,B,C) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s6_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f2_s6_yellow21))
& r2_hidden(B,u1_struct_0(f2_s6_yellow21))
& p2_s6_yellow21(A,B,C) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,u1_struct_0(f1_s6_yellow21))
=> r2_hidden(f3_s6_yellow21(A),u1_struct_0(f2_s6_yellow21)) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( p1_s6_yellow21(A,B,C)
=> ( v1_funct_1(f4_s6_yellow21(A,B,C))
& v1_funct_2(f4_s6_yellow21(A,B,C),u1_struct_0(f3_s6_yellow21(A)),u1_struct_0(f3_s6_yellow21(B)))
& m2_relset_1(f4_s6_yellow21(A,B,C),u1_struct_0(f3_s6_yellow21(A)),u1_struct_0(f3_s6_yellow21(B)))
& p2_s6_yellow21(f3_s6_yellow21(A),f3_s6_yellow21(B),f4_s6_yellow21(A,B,C)) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,u1_struct_0(f1_s6_yellow21))
=> f4_s6_yellow21(A,A,k7_grcat_1(A)) = k7_grcat_1(f3_s6_yellow21(A)) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( p1_s6_yellow21(A,B,D)
& p1_s6_yellow21(B,C,E) )
=> f4_s6_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) = k5_relat_1(f4_s6_yellow21(A,B,D),f4_s6_yellow21(B,C,E)) ) ) ) ) ) ) )
=> ? [A] :
( v9_functor0(A,f1_s6_yellow21,f2_s6_yellow21)
& v15_functor0(A,f1_s6_yellow21,f2_s6_yellow21)
& m2_functor0(A,f1_s6_yellow21,f2_s6_yellow21)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s6_yellow21))
=> k3_functor0(f1_s6_yellow21,f2_s6_yellow21,A,B) = f3_s6_yellow21(k3_yellow21(f1_s6_yellow21,B)) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s6_yellow21))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s6_yellow21))
=> ( k1_altcat_1(f1_s6_yellow21,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s6_yellow21,B,C))
=> k6_functor0(f1_s6_yellow21,f2_s6_yellow21,A,B,C,D) = f4_s6_yellow21(k3_yellow21(f1_s6_yellow21,B),k3_yellow21(f1_s6_yellow21,C),k5_yellow21(f1_s6_yellow21,B,C,D)) ) ) ) ) ) ) ).
fof(s7_yellow21,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s7_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f1_s7_yellow21))
& r2_hidden(B,u1_struct_0(f1_s7_yellow21))
& p1_s7_yellow21(A,B,C) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s7_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f2_s7_yellow21))
& r2_hidden(B,u1_struct_0(f2_s7_yellow21))
& p2_s7_yellow21(A,B,C) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,u1_struct_0(f1_s7_yellow21))
=> r2_hidden(f3_s7_yellow21(A),u1_struct_0(f2_s7_yellow21)) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( p1_s7_yellow21(A,B,C)
=> ( v1_funct_1(f4_s7_yellow21(A,B,C))
& v1_funct_2(f4_s7_yellow21(A,B,C),u1_struct_0(f3_s7_yellow21(B)),u1_struct_0(f3_s7_yellow21(A)))
& m2_relset_1(f4_s7_yellow21(A,B,C),u1_struct_0(f3_s7_yellow21(B)),u1_struct_0(f3_s7_yellow21(A)))
& p2_s7_yellow21(f3_s7_yellow21(B),f3_s7_yellow21(A),f4_s7_yellow21(A,B,C)) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,u1_struct_0(f1_s7_yellow21))
=> f4_s7_yellow21(A,A,k7_grcat_1(A)) = k7_grcat_1(f3_s7_yellow21(A)) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( p1_s7_yellow21(A,B,D)
& p1_s7_yellow21(B,C,E) )
=> f4_s7_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) = k5_relat_1(f4_s7_yellow21(B,C,E),f4_s7_yellow21(A,B,D)) ) ) ) ) ) ) )
=> ? [A] :
( v9_functor0(A,f1_s7_yellow21,f2_s7_yellow21)
& v16_functor0(A,f1_s7_yellow21,f2_s7_yellow21)
& m2_functor0(A,f1_s7_yellow21,f2_s7_yellow21)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s7_yellow21))
=> k3_functor0(f1_s7_yellow21,f2_s7_yellow21,A,B) = f3_s7_yellow21(k3_yellow21(f1_s7_yellow21,B)) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s7_yellow21))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s7_yellow21))
=> ( k1_altcat_1(f1_s7_yellow21,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s7_yellow21,B,C))
=> k8_functor0(f1_s7_yellow21,f2_s7_yellow21,A,B,C,D) = f4_s7_yellow21(k3_yellow21(f1_s7_yellow21,B),k3_yellow21(f1_s7_yellow21,C),k5_yellow21(f1_s7_yellow21,B,C,D)) ) ) ) ) ) ) ).
fof(s8_yellow21,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s8_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f1_s8_yellow21))
& r2_hidden(B,u1_struct_0(f1_s8_yellow21))
& p1_s8_yellow21(A,B,C) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s8_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f2_s8_yellow21))
& r2_hidden(B,u1_struct_0(f2_s8_yellow21))
& p2_s8_yellow21(A,B,C) ) ) ) ) )
& ? [A] :
( v15_functor0(A,f1_s8_yellow21,f2_s8_yellow21)
& m2_functor0(A,f1_s8_yellow21,f2_s8_yellow21)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_yellow21))
=> k3_functor0(f1_s8_yellow21,f2_s8_yellow21,A,B) = f3_s8_yellow21(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_yellow21))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s8_yellow21))
=> ( k1_altcat_1(f1_s8_yellow21,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s8_yellow21,B,C))
=> k6_functor0(f1_s8_yellow21,f2_s8_yellow21,A,B,C,D) = f4_s8_yellow21(B,C,D) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( r2_hidden(A,u1_struct_0(f1_s8_yellow21))
& r2_hidden(B,u1_struct_0(f1_s8_yellow21))
& f3_s8_yellow21(A) = f3_s8_yellow21(B) )
=> A = B ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( 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)) )
=> ( ( p1_s8_yellow21(A,B,C)
& p1_s8_yellow21(A,B,D)
& f4_s8_yellow21(A,B,C) = f4_s8_yellow21(A,B,D) )
=> C = D ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ~ ( p2_s8_yellow21(A,B,C)
& ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v2_orders_2(E)
& v3_orders_2(E)
& v4_orders_2(E)
& v1_lattice3(E)
& v2_lattice3(E)
& l1_orders_2(E) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
=> ~ ( r2_hidden(D,u1_struct_0(f1_s8_yellow21))
& r2_hidden(E,u1_struct_0(f1_s8_yellow21))
& p1_s8_yellow21(D,E,F)
& A = f3_s8_yellow21(D)
& B = f3_s8_yellow21(E)
& C = f4_s8_yellow21(D,E,F) ) ) ) ) ) ) ) ) )
=> r1_functor0(f1_s8_yellow21,f2_s8_yellow21) ) ).
fof(s9_yellow21,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s9_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f1_s9_yellow21))
& r2_hidden(B,u1_struct_0(f1_s9_yellow21))
& p1_s9_yellow21(A,B,C) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s9_yellow21),A,B))
<=> ( r2_hidden(A,u1_struct_0(f2_s9_yellow21))
& r2_hidden(B,u1_struct_0(f2_s9_yellow21))
& p2_s9_yellow21(A,B,C) ) ) ) ) )
& ? [A] :
( v16_functor0(A,f1_s9_yellow21,f2_s9_yellow21)
& m2_functor0(A,f1_s9_yellow21,f2_s9_yellow21)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s9_yellow21))
=> k3_functor0(f1_s9_yellow21,f2_s9_yellow21,A,B) = f3_s9_yellow21(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s9_yellow21))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s9_yellow21))
=> ( k1_altcat_1(f1_s9_yellow21,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s9_yellow21,B,C))
=> k8_functor0(f1_s9_yellow21,f2_s9_yellow21,A,B,C,D) = f4_s9_yellow21(B,C,D) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( r2_hidden(A,u1_struct_0(f1_s9_yellow21))
& r2_hidden(B,u1_struct_0(f1_s9_yellow21))
& f3_s9_yellow21(A) = f3_s9_yellow21(B) )
=> A = B ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( 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)) )
=> ( f4_s9_yellow21(A,B,C) = f4_s9_yellow21(A,B,D)
=> C = D ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ~ ( p2_s9_yellow21(A,B,C)
& ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v2_orders_2(E)
& v3_orders_2(E)
& v4_orders_2(E)
& v1_lattice3(E)
& v2_lattice3(E)
& l1_orders_2(E) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
=> ~ ( r2_hidden(D,u1_struct_0(f1_s9_yellow21))
& r2_hidden(E,u1_struct_0(f1_s9_yellow21))
& p1_s9_yellow21(D,E,F)
& B = f3_s9_yellow21(D)
& A = f3_s9_yellow21(E)
& C = f4_s9_yellow21(D,E,F) ) ) ) ) ) ) ) ) )
=> r2_functor0(f1_s9_yellow21,f2_s9_yellow21) ) ).
fof(s10_yellow21,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s10_yellow21))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow21(f1_s10_yellow21,A)),u1_struct_0(k3_yellow21(f1_s10_yellow21,B)))
& v5_orders_3(C,k3_yellow21(f1_s10_yellow21,A),k3_yellow21(f1_s10_yellow21,B))
& m2_relset_1(C,u1_struct_0(k3_yellow21(f1_s10_yellow21,A)),u1_struct_0(k3_yellow21(f1_s10_yellow21,B))) )
=> ( r2_hidden(C,k1_altcat_1(f1_s10_yellow21,A,B))
<=> p1_s10_yellow21(k3_yellow21(f1_s10_yellow21,A),k3_yellow21(f1_s10_yellow21,B),C) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s10_yellow21))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow21(f2_s10_yellow21,A)),u1_struct_0(k3_yellow21(f2_s10_yellow21,B)))
& v5_orders_3(C,k3_yellow21(f2_s10_yellow21,A),k3_yellow21(f2_s10_yellow21,B))
& m2_relset_1(C,u1_struct_0(k3_yellow21(f2_s10_yellow21,A)),u1_struct_0(k3_yellow21(f2_s10_yellow21,B))) )
=> ( r2_hidden(C,k1_altcat_1(f2_s10_yellow21,A,B))
<=> p2_s10_yellow21(k3_yellow21(f2_s10_yellow21,A),k3_yellow21(f2_s10_yellow21,B),C) ) ) ) )
& ? [A] :
( v15_functor0(A,f1_s10_yellow21,f2_s10_yellow21)
& m2_functor0(A,f1_s10_yellow21,f2_s10_yellow21)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
=> k3_functor0(f1_s10_yellow21,f2_s10_yellow21,A,B) = f3_s10_yellow21(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s10_yellow21))
=> ( k1_altcat_1(f1_s10_yellow21,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s10_yellow21,B,C))
=> k6_functor0(f1_s10_yellow21,f2_s10_yellow21,A,B,C,D) = f5_s10_yellow21(B,C,D) ) ) ) ) )
& ? [A] :
( v15_functor0(A,f2_s10_yellow21,f1_s10_yellow21)
& m2_functor0(A,f2_s10_yellow21,f1_s10_yellow21)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
=> k3_functor0(f2_s10_yellow21,f1_s10_yellow21,A,B) = f4_s10_yellow21(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s10_yellow21))
=> ( k1_altcat_1(f2_s10_yellow21,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f2_s10_yellow21,B,C))
=> k6_functor0(f2_s10_yellow21,f1_s10_yellow21,A,B,C,D) = f6_s10_yellow21(B,C,D) ) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ~ ( r2_hidden(A,u1_struct_0(f1_s10_yellow21))
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(f4_s10_yellow21(f3_s10_yellow21(A))),u1_struct_0(A))
& v5_orders_3(B,f4_s10_yellow21(f3_s10_yellow21(A)),A)
& m2_relset_1(B,u1_struct_0(f4_s10_yellow21(f3_s10_yellow21(A))),u1_struct_0(A)) )
=> ~ ( B = f7_s10_yellow21(A)
& v23_waybel_0(B,f4_s10_yellow21(f3_s10_yellow21(A)),A)
& p1_s10_yellow21(f4_s10_yellow21(f3_s10_yellow21(A)),A,B)
& p1_s10_yellow21(A,f4_s10_yellow21(f3_s10_yellow21(A)),k2_funct_1(B)) ) ) ) )
& ! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ~ ( r2_hidden(A,u1_struct_0(f2_s10_yellow21))
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(f3_s10_yellow21(f4_s10_yellow21(A))))
& v5_orders_3(B,A,f3_s10_yellow21(f4_s10_yellow21(A)))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(f3_s10_yellow21(f4_s10_yellow21(A)))) )
=> ~ ( B = f8_s10_yellow21(A)
& v23_waybel_0(B,A,f3_s10_yellow21(f4_s10_yellow21(A)))
& p2_s10_yellow21(A,f3_s10_yellow21(f4_s10_yellow21(A)),B)
& p2_s10_yellow21(f3_s10_yellow21(f4_s10_yellow21(A)),A,k2_funct_1(B)) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s10_yellow21))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
=> ( k1_altcat_1(f1_s10_yellow21,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s10_yellow21,A,B))
=> k5_relat_1(f6_s10_yellow21(f3_s10_yellow21(A),f3_s10_yellow21(B),f5_s10_yellow21(A,B,C)),f7_s10_yellow21(B)) = k5_relat_1(f7_s10_yellow21(A),k5_yellow21(f1_s10_yellow21,A,B,C)) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s10_yellow21))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
=> ( k1_altcat_1(f2_s10_yellow21,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f2_s10_yellow21,A,B))
=> k5_relat_1(f8_s10_yellow21(A),f5_s10_yellow21(f4_s10_yellow21(A),f4_s10_yellow21(B),f6_s10_yellow21(A,B,C))) = k5_relat_1(k5_yellow21(f2_s10_yellow21,A,B,C),f8_s10_yellow21(B)) ) ) ) ) )
=> r1_yellow18(f1_s10_yellow21,f2_s10_yellow21) ) ).
fof(dt_k1_yellow21,axiom,
! [A] : l1_struct_0(k1_yellow21(A)) ).
fof(dt_k2_yellow21,axiom,
$true ).
fof(dt_k3_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v2_orders_2(k3_yellow21(A,B))
& v3_orders_2(k3_yellow21(A,B))
& v4_orders_2(k3_yellow21(A,B))
& v1_lattice3(k3_yellow21(A,B))
& v2_lattice3(k3_yellow21(A,B))
& l1_orders_2(k3_yellow21(A,B)) ) ) ).
fof(redefinition_k3_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k3_yellow21(A,B) = k1_yellow21(B) ) ).
fof(dt_k4_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v2_orders_2(k4_yellow21(A,B))
& v3_orders_2(k4_yellow21(A,B))
& v4_orders_2(k4_yellow21(A,B))
& v1_lattice3(k4_yellow21(A,B))
& v2_lattice3(k4_yellow21(A,B))
& v3_lattice3(k4_yellow21(A,B))
& l1_orders_2(k4_yellow21(A,B)) ) ) ).
fof(redefinition_k4_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k4_yellow21(A,B) = k1_yellow21(B) ) ).
fof(dt_k5_yellow21,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,k1_altcat_1(A,B,C)) )
=> ( v1_funct_1(k5_yellow21(A,B,C,D))
& v1_funct_2(k5_yellow21(A,B,C,D),u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
& v5_orders_3(k5_yellow21(A,B,C,D),k3_yellow21(A,B),k3_yellow21(A,C))
& m2_relset_1(k5_yellow21(A,B,C,D),u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) ) ) ).
fof(dt_k6_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k6_yellow21(A))
& v2_altcat_1(k6_yellow21(A))
& v6_altcat_1(k6_yellow21(A))
& v11_altcat_1(k6_yellow21(A))
& v12_altcat_1(k6_yellow21(A))
& v2_yellow21(k6_yellow21(A))
& l2_altcat_1(k6_yellow21(A)) ) ) ).
fof(dt_k7_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k7_yellow21(A))
& v2_altcat_1(k7_yellow21(A))
& v6_altcat_1(k7_yellow21(A))
& v2_altcat_2(k7_yellow21(A),k6_yellow21(A))
& v3_altcat_2(k7_yellow21(A),k6_yellow21(A))
& m1_altcat_2(k7_yellow21(A),k6_yellow21(A)) ) ) ).
fof(dt_k8_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k8_yellow21(A))
& v2_altcat_1(k8_yellow21(A))
& v6_altcat_1(k8_yellow21(A))
& v2_altcat_2(k8_yellow21(A),k7_yellow21(A))
& v3_altcat_2(k8_yellow21(A),k7_yellow21(A))
& m1_altcat_2(k8_yellow21(A),k7_yellow21(A)) ) ) ).
%------------------------------------------------------------------------------