SET007 Axioms: SET007+815.ax
%------------------------------------------------------------------------------
% File : SET007+815 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Class of Series-Parallel Graphs. Part III
% 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 : neckla_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 66 ( 4 unt; 0 def)
% Number of atoms : 402 ( 35 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 403 ( 67 ~; 8 |; 183 &)
% ( 8 <=>; 137 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 36 ( 35 usr; 0 prp; 1-4 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-8 aty)
% Number of variables : 153 ( 151 !; 2 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_neckla_3,axiom,
! [A,B] :
( ( v1_realset1(A)
& v1_realset1(B) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( v1_finset_1(C)
& v1_realset1(C) ) ) ) ).
fof(cc2_neckla_3,axiom,
! [A] :
( v1_realset1(A)
=> ! [B] :
( m1_relset_1(B,A,A)
=> ( v1_relat_2(B)
& v3_relat_2(B)
& v7_relat_2(B)
& v8_relat_2(B)
& v1_finset_1(B)
& v1_realset1(B) ) ) ) ).
fof(rc1_neckla_3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v1_necklace(A)
& v3_necklace(A)
& v6_group_1(A) ) ).
fof(cc3_neckla_3,axiom,
! [A] :
( ( v3_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v3_necklace(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc4_neckla_3,axiom,
! [A] :
( ( v1_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v1_necklace(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(fc1_neckla_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k1_neckla_2(A,B))
& v1_orders_2(k1_neckla_2(A,B)) ) ) ).
fof(fc2_neckla_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k2_neckla_2(A,B))
& v1_orders_2(k2_neckla_2(A,B)) ) ) ).
fof(fc3_neckla_3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k1_neckla_2(A,B))
& v1_orders_2(k1_neckla_2(A,B)) ) ) ).
fof(fc4_neckla_3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k2_neckla_2(A,B))
& v1_orders_2(k2_neckla_2(A,B)) ) ) ).
fof(fc5_neckla_3,axiom,
! [A,B] :
( ( v6_group_1(A)
& l1_orders_2(A)
& v6_group_1(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k1_neckla_2(A,B))
& v6_group_1(k1_neckla_2(A,B)) ) ) ).
fof(fc6_neckla_3,axiom,
! [A,B] :
( ( v6_group_1(A)
& l1_orders_2(A)
& v6_group_1(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k2_neckla_2(A,B))
& v6_group_1(k2_neckla_2(A,B)) ) ) ).
fof(fc7_neckla_3,axiom,
! [A,B] :
( ( v1_necklace(A)
& l1_orders_2(A)
& v1_necklace(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k1_neckla_2(A,B))
& v1_necklace(k1_neckla_2(A,B)) ) ) ).
fof(fc8_neckla_3,axiom,
! [A,B] :
( ( v1_necklace(A)
& l1_orders_2(A)
& v1_necklace(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k2_neckla_2(A,B))
& v1_necklace(k2_neckla_2(A,B)) ) ) ).
fof(fc9_neckla_3,axiom,
! [A,B] :
( ( v3_necklace(A)
& l1_orders_2(A)
& v3_necklace(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k1_neckla_2(A,B))
& v3_necklace(k1_neckla_2(A,B)) ) ) ).
fof(fc10_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_orders_2(k3_necklace(A))
& v3_necklace(k3_necklace(A)) ) ) ).
fof(fc11_neckla_3,axiom,
! [A] :
( ( v1_necklace(A)
& l1_orders_2(A) )
=> ( v1_orders_2(k3_necklace(A))
& v1_necklace(k3_necklace(A))
& v3_necklace(k3_necklace(A)) ) ) ).
fof(cc5_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v1_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v1_neckla_2(A) ) ) ) ).
fof(cc6_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_struct_0(A)
=> v1_neckla_3(A) ) ) ).
fof(cc7_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v16_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v1_neckla_3(A) ) ) ) ).
fof(cc8_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v1_neckla_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v16_waybel_0(A)
& v1_neckla_3(A) ) ) ) ).
fof(fc12_neckla_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ~ v1_xboole_0(k1_neckla_3(A,B)) ) ).
fof(t1_neckla_3,axiom,
! [A,B] : k2_partfun1(A,A,k6_partfun1(A),B) = k3_xboole_0(k6_partfun1(A),k2_zfmisc_1(B,B)) ).
fof(t2_neckla_3,axiom,
! [A,B,C,D] : k6_partfun1(k2_enumset1(A,B,C,D)) = k2_enumset1(k4_tarski(A,A),k4_tarski(B,B),k4_tarski(C,C),k4_tarski(D,D)) ).
fof(t3_neckla_3,axiom,
! [A,B,C,D,E,F,G,H] : k2_zfmisc_1(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) = k2_xboole_0(k6_enumset1(k4_tarski(A,E),k4_tarski(A,F),k4_tarski(B,E),k4_tarski(B,F),k4_tarski(A,G),k4_tarski(A,H),k4_tarski(B,G),k4_tarski(B,H)),k6_enumset1(k4_tarski(C,E),k4_tarski(C,F),k4_tarski(D,E),k4_tarski(D,F),k4_tarski(C,G),k4_tarski(C,H),k4_tarski(D,G),k4_tarski(D,H))) ).
fof(t4_neckla_3,axiom,
! [A] :
( v1_realset1(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ~ ( ~ v1_xboole_0(B)
& ! [C] : B != k1_tarski(k4_tarski(C,C)) ) ) ) ).
fof(t5_neckla_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_realset1(A) )
=> ! [B] :
( m2_relset_1(B,A,A)
=> r3_relat_2(B,A) ) ) ).
fof(t6_neckla_3,axiom,
! [A] :
( ( v1_necklace(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ~ ( k1_card_1(u1_struct_0(A)) = np__2
& ! [B,C] :
~ ( u1_struct_0(A) = k2_tarski(B,C)
& ( u1_orders_2(A) = k2_tarski(k4_tarski(B,C),k4_tarski(C,B))
| u1_orders_2(A) = k1_xboole_0 ) ) ) ) ).
fof(t7_neckla_3,axiom,
! [A] :
( ( v3_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v3_necklace(B)
& l1_orders_2(B) )
=> ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B))
=> v3_necklace(k2_neckla_2(A,B)) ) ) ) ).
fof(t8_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( k1_neckla_2(A,B) = k1_neckla_2(B,A)
& k2_neckla_2(A,B) = k2_neckla_2(B,A) ) ) ) ).
fof(t9_neckla_3,axiom,
! [A] :
( ( v3_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( l1_orders_2(C)
=> ( ( A = k1_neckla_2(B,C)
| A = k2_neckla_2(B,C) )
=> ( v3_necklace(B)
& v3_necklace(C) ) ) ) ) ) ).
fof(t10_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( l1_orders_2(C)
=> ( r1_xboole_0(u1_struct_0(B),u1_struct_0(C))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) != k1_neckla_2(B,C)
& g1_orders_2(u1_struct_0(A),u1_orders_2(A)) != k2_neckla_2(B,C) )
| ( v4_yellow_0(B,A)
& m1_yellow_0(B,A)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) ) ) ) ) ) ) ).
fof(t11_neckla_3,axiom,
u1_orders_2(k3_necklace(k4_necklace(np__4))) = k4_enumset1(k4_tarski(np__0,np__2),k4_tarski(np__2,np__0),k4_tarski(np__0,np__3),k4_tarski(np__3,np__0),k4_tarski(np__1,np__3),k4_tarski(np__3,np__1)) ).
fof(t12_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> r1_xboole_0(u1_orders_2(A),u1_orders_2(k3_necklace(A))) ) ).
fof(t13_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> r1_xboole_0(k6_partfun1(u1_struct_0(A)),u1_orders_2(k3_necklace(A))) ) ).
fof(t14_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)) = k2_xboole_0(k3_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A)),u1_orders_2(A)),u1_orders_2(k3_necklace(A))) ) ).
fof(t15_neckla_3,axiom,
! [A] :
( ( v1_orders_2(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ( v3_realset2(A)
=> k3_necklace(A) = A ) ) ).
fof(t16_neckla_3,axiom,
! [A] :
( ( v1_orders_2(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> k3_necklace(k3_necklace(A)) = A ) ).
fof(t17_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B))
=> k3_necklace(k1_neckla_2(A,B)) = k2_neckla_2(k3_necklace(A),k3_necklace(B)) ) ) ) ).
fof(t18_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B))
=> k3_necklace(k2_neckla_2(A,B)) = k1_neckla_2(k3_necklace(A),k3_necklace(B)) ) ) ) ).
fof(t19_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> u1_orders_2(k3_necklace(B)) = k2_wellord1(u1_orders_2(k3_necklace(A)),u1_struct_0(k3_necklace(B))) ) ) ).
fof(t20_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_necklace(A)))
=> ( B = C
=> k3_necklace(k5_yellow_0(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k1_struct_0(A,B)))) = k5_yellow_0(k3_necklace(A),k6_subset_1(u1_struct_0(k3_necklace(A)),k2_pre_topc(k3_necklace(A)),k1_struct_0(k3_necklace(A),C))) ) ) ) ) ).
fof(t21_neckla_3,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(D,E),u1_orders_2(A))
<=> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),u1_orders_2(B)) ) ) ) )
<=> r2_necklace(A,B) ) ) ) ).
fof(t22_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> r3_necklace(B,A) ) ) ).
fof(t23_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_neckla_2(A)
=> v1_neckla_2(B) ) ) ) ).
fof(t24_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ( r3_necklace(k4_necklace(np__4),A)
<=> r3_necklace(k4_necklace(np__4),k3_necklace(A)) ) ) ).
fof(t25_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ( v1_neckla_2(A)
<=> v1_neckla_2(k3_necklace(A)) ) ) ).
fof(d1_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_neckla_3(A)
<=> ! [B,C] :
~ ( r2_hidden(B,u1_struct_0(A))
& r2_hidden(C,u1_struct_0(A))
& B != C
& ~ r1_rewrite1(u1_orders_2(A),B,C)
& ~ r1_rewrite1(u1_orders_2(A),C,B) ) ) ) ).
fof(t26_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rewrite1(u1_orders_2(A),B,C)
=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ).
fof(t27_neckla_3,axiom,
! [A] :
( ( v1_necklace(A)
& l1_orders_2(A) )
=> ! [B,C] :
( ( r2_hidden(B,u1_struct_0(A))
& r2_hidden(C,u1_struct_0(A))
& r1_rewrite1(u1_orders_2(A),B,C) )
=> r1_rewrite1(u1_orders_2(A),C,B) ) ) ).
fof(d2_neckla_3,axiom,
! [A] :
( ( v1_necklace(A)
& l1_orders_2(A) )
=> ( v1_neckla_3(A)
<=> ! [B,C] :
( ( r2_hidden(B,u1_struct_0(A))
& r2_hidden(C,u1_struct_0(A)) )
=> ( B = C
| r1_rewrite1(u1_orders_2(A),B,C) ) ) ) ) ).
fof(d3_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_neckla_3(A,B) = k6_eqrel_1(u1_struct_0(A),k1_msualg_5(u1_struct_0(A),u1_orders_2(A)),B) ) ) ).
fof(t28_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_hidden(B,k1_neckla_3(A,B)) ) ) ).
fof(t29_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r2_hidden(C,k1_neckla_3(A,B))
=> r2_hidden(k4_tarski(B,C),k1_msualg_5(u1_struct_0(A),u1_orders_2(A))) ) ) ) ).
fof(t30_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( C = k1_neckla_3(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> r2_hidden(k4_tarski(B,D),k1_msualg_5(u1_struct_0(A),u1_orders_2(A))) ) ) ) ) ).
fof(t31_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_necklace(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ~ ( ~ v1_neckla_3(A)
& ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& v1_necklace(B)
& v3_necklace(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_orders_2(C)
& v1_necklace(C)
& v3_necklace(C)
& l1_orders_2(C) )
=> ~ ( r1_subset_1(u1_struct_0(B),u1_struct_0(C))
& g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k1_neckla_2(B,C) ) ) ) ) ) ).
fof(t32_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_necklace(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ~ ( ~ v1_neckla_3(k3_necklace(A))
& ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& v1_necklace(B)
& v3_necklace(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_orders_2(C)
& v1_necklace(C)
& v3_necklace(C)
& l1_orders_2(C) )
=> ~ ( r1_subset_1(u1_struct_0(B),u1_struct_0(C))
& g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k2_neckla_2(B,C) ) ) ) ) ) ).
fof(t33_neckla_3,axiom,
! [A] :
( ( v3_necklace(A)
& l1_orders_2(A) )
=> ( r2_hidden(A,k4_neckla_2)
=> r2_hidden(k3_necklace(A),k4_neckla_2) ) ) ).
fof(t34_neckla_3,axiom,
! [A] :
( ( v1_necklace(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ( ( k1_card_1(u1_struct_0(A)) = np__2
& r2_hidden(u1_struct_0(A),k13_classes2) )
=> r2_hidden(g1_orders_2(u1_struct_0(A),u1_orders_2(A)),k4_neckla_2) ) ) ).
fof(t35_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( r2_hidden(A,k4_neckla_2)
=> v1_necklace(A) ) ) ).
fof(t36_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ~ ( A = k1_neckla_2(B,C)
& r1_subset_1(u1_struct_0(B),u1_struct_0(C))
& r2_hidden(k4_tarski(D,E),u1_orders_2(A)) ) ) ) ) ) ) ).
fof(t37_neckla_3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ~ ( A = k2_neckla_2(B,C)
& r2_hidden(k4_tarski(D,E),u1_orders_2(k3_necklace(A))) ) ) ) ) ) ) ).
fof(t38_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ~ ( r1_subset_1(u1_struct_0(C),u1_struct_0(D))
& k5_yellow_0(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k1_struct_0(A,B))) = k1_neckla_2(C,D)
& v1_neckla_3(A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ~ r2_hidden(k4_tarski(E,B),u1_orders_2(A)) ) ) ) ) ) ) ).
fof(t39_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_necklace(A)
& v3_necklace(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))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( F = k2_enumset1(B,C,D,E)
& r2_incproj(B,C,D,E)
& r2_hidden(k4_tarski(B,C),u1_orders_2(A))
& r2_hidden(k4_tarski(C,D),u1_orders_2(A))
& r2_hidden(k4_tarski(D,E),u1_orders_2(A)) )
=> ( r2_hidden(k4_tarski(B,D),u1_orders_2(A))
| r2_hidden(k4_tarski(B,E),u1_orders_2(A))
| r2_hidden(k4_tarski(C,E),u1_orders_2(A))
| r2_necklace(k4_necklace(np__4),k5_yellow_0(A,F)) ) ) ) ) ) ) ) ) ).
fof(t40_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_necklace(A)
& v3_necklace(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ( ( r1_subset_1(u1_struct_0(C),u1_struct_0(D))
& k5_yellow_0(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k1_struct_0(A,B))) = k1_neckla_2(C,D)
& v1_neckla_3(A)
& v1_neckla_3(k3_necklace(A)) )
=> ( v3_realset2(A)
| r3_necklace(k4_necklace(np__4),A) ) ) ) ) ) ) ).
fof(t41_neckla_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_orders_2(A)
& v1_necklace(A)
& v3_necklace(A)
& v6_group_1(A)
& l1_orders_2(A) )
=> ( ( v1_neckla_2(A)
& r2_hidden(u1_struct_0(A),k13_classes2) )
=> r2_hidden(g1_orders_2(u1_struct_0(A),u1_orders_2(A)),k4_neckla_2) ) ) ).
fof(dt_k1_neckla_3,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_neckla_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
%------------------------------------------------------------------------------