SET007 Axioms: SET007+717.ax
%------------------------------------------------------------------------------
% File : SET007+717 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Ordering of Bags
% 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 : bagorder [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 93 ( 4 unt; 0 def)
% Number of atoms : 807 ( 76 equ)
% Maximal formula atoms : 33 ( 8 avg)
% Number of connectives : 807 ( 93 ~; 2 |; 467 &)
% ( 27 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-3 aty)
% Number of functors : 66 ( 66 usr; 6 con; 0-4 aty)
% Number of variables : 236 ( 226 !; 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_bagorder,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v1_seq_1(k7_relat_1(A,B))
& v7_seqm_3(k7_relat_1(A,B)) ) ) ).
fof(fc2_bagorder,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_polynom1(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v1_polynom1(k7_relat_1(A,B)) ) ) ).
fof(fc3_bagorder,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& v7_seqm_3(D)
& m1_pboole(D,A) )
=> ( v1_relat_1(k1_bagorder(A,B,C,D))
& v1_funct_1(k1_bagorder(A,B,C,D))
& v1_seq_1(k1_bagorder(A,B,C,D))
& v7_seqm_3(k1_bagorder(A,B,C,D))
& v1_polynom1(k1_bagorder(A,B,C,D)) ) ) ).
fof(fc4_bagorder,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( v1_relat_1(k1_bagorder(A,B,C,D))
& v1_funct_1(k1_bagorder(A,B,C,D))
& v1_polynom1(k1_bagorder(A,B,C,D)) ) ) ).
fof(fc5_bagorder,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k5_numbers) )
=> ~ v1_xboole_0(k2_bagorder(A,B)) ) ).
fof(rc1_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ? [B] :
( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_1(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A) ) ) ).
fof(fc6_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_relat_1(k17_polynom1(A))
& v1_partfun1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A))
& v3_orders_1(k17_polynom1(A))
& v1_relat_2(k17_polynom1(A))
& v4_relat_2(k17_polynom1(A))
& v8_relat_2(k17_polynom1(A))
& v2_bagorder(k17_polynom1(A),A) ) ) ).
fof(fc7_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_relat_1(k4_bagorder(A))
& v1_partfun1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k4_bagorder(A))
& v4_relat_2(k4_bagorder(A))
& v8_relat_2(k4_bagorder(A))
& v2_bagorder(k4_bagorder(A),A) ) ) ).
fof(fc8_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_relat_1(k6_bagorder(A))
& v1_partfun1(k6_bagorder(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k6_bagorder(A))
& v4_relat_2(k6_bagorder(A))
& v8_relat_2(k6_bagorder(A))
& v2_bagorder(k6_bagorder(A),A) ) ) ).
fof(fc9_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_relat_1(k7_bagorder(A))
& v1_partfun1(k7_bagorder(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k7_bagorder(A))
& v4_relat_2(k7_bagorder(A))
& v8_relat_2(k7_bagorder(A))
& v2_bagorder(k7_bagorder(A),A) ) ) ).
fof(fc10_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k14_bagorder(A))
& v2_orders_2(k14_bagorder(A))
& v3_orders_2(k14_bagorder(A))
& v4_orders_2(k14_bagorder(A)) ) ) ).
fof(fc11_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k14_bagorder(A))
& v2_orders_2(k14_bagorder(A))
& v3_orders_2(k14_bagorder(A))
& v4_orders_2(k14_bagorder(A))
& v16_waybel_0(k14_bagorder(A)) ) ) ).
fof(t1_bagorder,axiom,
! [A,B,C] :
( ( r2_hidden(C,A)
& r2_hidden(C,B) )
=> ( k4_xboole_0(A,k1_tarski(C)) = k4_xboole_0(B,k1_tarski(C))
<=> A = B ) ) ).
fof(t2_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_finseq_1(A))
<=> ( m2_subset_1(k5_real_1(B,np__1),k1_numbers,k5_numbers)
& ~ r1_xreal_0(A,k5_real_1(B,np__1)) ) ) ) ) ).
fof(t3_bagorder,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> k5_relat_1(k9_finseq_1(B),A) = k9_finseq_1(k1_funct_1(A,B)) ) ) ).
fof(t4_bagorder,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( k1_relat_1(A) = k1_relat_1(B)
& r1_tarski(k2_relat_1(A),k1_relat_1(C))
& r1_tarski(k2_relat_1(B),k1_relat_1(C))
& r1_rfinseq(A,B) )
=> r1_rfinseq(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ) ).
fof(t5_bagorder,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ( k9_wsierp_1(A) = np__0
<=> A = k4_finseqop(k5_numbers,k3_finseq_1(A),np__0) ) ) ).
fof(d1_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,k5_binarith(C,B))
=> ( E = k1_bagorder(A,B,C,D)
<=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k5_binarith(C,B))
=> k1_funct_1(E,F) = k1_funct_1(D,k1_nat_1(B,F)) ) ) ) ) ) ) ) ) ).
fof(t6_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,C,D)
<=> ( r6_pboole(k5_binarith(k1_nat_1(B,np__1),np__0),k1_bagorder(A,np__0,k1_nat_1(B,np__1),C),k1_bagorder(A,np__0,k1_nat_1(B,np__1),D))
& r6_pboole(k5_binarith(A,k1_nat_1(B,np__1)),k1_bagorder(A,k1_nat_1(B,np__1),A,C),k1_bagorder(A,k1_nat_1(B,np__1),A,D)) ) ) ) ) ) ) ).
fof(t7_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( B != k1_xboole_0
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ).
fof(t8_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( B != k1_xboole_0
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ).
fof(t9_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v3_wellfnd1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(C,D)
=> ( k8_funct_2(k5_numbers,u1_struct_0(A),B,D) != k8_funct_2(k5_numbers,u1_struct_0(A),B,C)
& r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,C),k8_funct_2(k5_numbers,u1_struct_0(A),B,D)),u1_orders_2(A)) ) ) ) ) ) ) ) ).
fof(d3_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bagorder(B,A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,np__1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) ).
fof(t10_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bagorder(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(C,D)
=> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,C),k8_funct_2(k5_numbers,u1_struct_0(A),B,D)),u1_orders_2(A)) ) ) ) ) ) ) ).
fof(t11_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ~ ( v1_wellfnd1(A)
& v1_bagorder(B,A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& k8_funct_2(k5_numbers,u1_struct_0(A),B,C) != k8_funct_2(k5_numbers,u1_struct_0(A),B,D) ) ) ) ) ) ).
fof(t12_bagorder,axiom,
! [A,B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_partfun1(D,A,A)
& v1_relat_2(D)
& v4_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ( ( C = k1_tarski(B)
& r3_orders_1(D,C) )
=> k2_triang_1(A,C,D) = k9_finseq_1(B) ) ) ) ) ).
fof(d4_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( C = k3_bagorder(A,B)
<=> ? [D] :
( m2_finseq_1(D,k5_numbers)
& C = k9_wsierp_1(D)
& D = k2_polynom2(A,k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),B) ) ) ) ) ) ).
fof(t13_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ! [E] :
( m2_finseq_1(E,k5_numbers)
=> ( ( D = k2_polynom2(A,k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),B)
& E = k2_polynom2(A,k2_triang_1(A,k1_finsub_1(k1_zfmisc_1(A),k1_polynom2(A,B),C),k1_yellow_1(A)),B) )
=> k9_wsierp_1(D) = k9_wsierp_1(E) ) ) ) ) ) ) ).
fof(t14_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> k3_bagorder(A,k9_polynom1(A,B,C)) = k1_nat_1(k3_bagorder(A,B),k3_bagorder(A,C)) ) ) ) ).
fof(t15_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( r3_polynom1(A,C,B)
=> k3_bagorder(A,k10_polynom1(A,B,C)) = k5_real_1(k3_bagorder(A,B),k3_bagorder(A,C)) ) ) ) ) ).
fof(t16_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( k3_bagorder(A,B) = np__0
<=> r6_pboole(A,B,k16_polynom1(A)) ) ) ) ).
fof(t17_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r6_pboole(k5_binarith(B,A),k1_bagorder(C,A,B,k16_polynom1(C)),k16_polynom1(k5_binarith(B,A))) ) ) ) ).
fof(t18_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,C) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,C) )
=> r6_pboole(k5_binarith(B,A),k1_bagorder(C,A,B,k9_polynom1(C,D,E)),k9_polynom1(k5_binarith(B,A),k1_bagorder(C,A,B,D),k1_bagorder(C,A,B,E))) ) ) ) ) ) ).
fof(t19_bagorder,axiom,
! [A] : k1_polynom2(A,k16_polynom1(A)) = k1_xboole_0 ).
fof(t20_bagorder,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( k1_polynom2(A,B) = k1_xboole_0
=> r6_pboole(A,B,k16_polynom1(A)) ) ) ).
fof(t21_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( r2_hidden(B,A)
=> ( v7_seqm_3(k7_relat_1(C,B))
& v1_polynom1(k7_relat_1(C,B))
& m1_pboole(k7_relat_1(C,B),B) ) ) ) ) ) ).
fof(t22_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( r3_polynom1(A,C,B)
=> r1_tarski(k1_polynom2(A,C),k1_polynom2(A,B)) ) ) ) ) ).
fof(d5_bagorder,axiom,
$true ).
fof(d6_bagorder,axiom,
$true ).
fof(d7_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( v2_bagorder(B,A)
<=> ( r7_relat_2(B,k14_polynom1(A))
& ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> r2_hidden(k4_tarski(k16_polynom1(A),C),B) )
& ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(k4_tarski(C,D),B)
=> r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) ) ) ) ) ) ).
fof(t23_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> v2_bagorder(k17_polynom1(A),A) ) ).
fof(t24_bagorder,axiom,
! [A] :
( ( v3_ordinal1(A)
& ~ v1_finset_1(A) )
=> ~ v2_wellord1(k17_polynom1(A)) ) ).
fof(d8_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( B = k4_bagorder(A)
<=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ~ ( ~ r6_pboole(A,C,D)
& ! [E] :
( v3_ordinal1(E)
=> ~ ( r2_hidden(E,A)
& ~ r1_xreal_0(k8_polynom1(D,E),k8_polynom1(C,E))
& ! [F] :
( v3_ordinal1(F)
=> ( ( r2_hidden(E,F)
& r2_hidden(F,A) )
=> k8_polynom1(C,F) = k8_polynom1(D,F) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> v2_bagorder(k4_bagorder(A),A) ) ).
fof(t26_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> v2_wellord1(k4_bagorder(A)) ) ).
fof(d9_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(k4_tarski(C,D),B)
=> r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) )
=> ! [C] :
( ( v1_partfun1(C,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,k14_polynom1(A),k14_polynom1(A)) )
=> ( C = k5_bagorder(A,B)
<=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(k4_tarski(D,E),C)
<=> ~ ( r1_xreal_0(k3_bagorder(A,E),k3_bagorder(A,D))
& ~ ( k3_bagorder(A,D) = k3_bagorder(A,E)
& r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( ( ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(k4_tarski(C,D),B)
=> r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) )
& r7_relat_2(B,k14_polynom1(A)) )
=> v2_bagorder(k5_bagorder(A,B),A) ) ) ) ).
fof(d10_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> k6_bagorder(A) = k5_bagorder(A,k17_polynom1(A)) ) ).
fof(d11_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> k7_bagorder(A) = k5_bagorder(A,k4_bagorder(A)) ) ).
fof(t28_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> v2_bagorder(k6_bagorder(A),A) ) ).
fof(t29_bagorder,axiom,
! [A] :
( ( v3_ordinal1(A)
& ~ v1_finset_1(A) )
=> ~ v2_wellord1(k6_bagorder(A)) ) ).
fof(t30_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> v2_bagorder(k7_bagorder(A),A) ) ).
fof(t31_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> v2_wellord1(k7_bagorder(A)) ) ).
fof(d12_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_partfun1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1))) )
=> ! [D] :
( ( v1_partfun1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))))
& v1_relat_2(D)
& v4_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1)))) )
=> ! [E] :
( ( v1_partfun1(E,k14_polynom1(B),k14_polynom1(B))
& v1_relat_2(E)
& v4_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,k14_polynom1(B),k14_polynom1(B)) )
=> ( E = k8_bagorder(A,B,C,D)
<=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,B) )
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,B) )
=> ( r2_hidden(k4_tarski(F,G),E)
<=> ( ( k1_bagorder(B,np__0,k1_nat_1(A,np__1),F) != k1_bagorder(B,np__0,k1_nat_1(A,np__1),G)
& r2_hidden(k4_tarski(k1_bagorder(B,np__0,k1_nat_1(A,np__1),F),k1_bagorder(B,np__0,k1_nat_1(A,np__1),G)),C) )
| ( r6_pboole(k5_binarith(k1_nat_1(A,np__1),np__0),k1_bagorder(B,np__0,k1_nat_1(A,np__1),F),k1_bagorder(B,np__0,k1_nat_1(A,np__1),G))
& r2_hidden(k4_tarski(k1_bagorder(B,k1_nat_1(A,np__1),B,F),k1_bagorder(B,k1_nat_1(A,np__1),B,G)),D) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_partfun1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1))) )
=> ! [D] :
( ( v1_partfun1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))))
& v1_relat_2(D)
& v4_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1)))) )
=> ( ( v2_bagorder(C,k1_nat_1(A,np__1))
& v2_bagorder(D,k5_binarith(B,k1_nat_1(A,np__1))) )
=> v2_bagorder(k8_bagorder(A,B,C,D),B) ) ) ) ) ) ).
fof(d13_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_orders_2(B)
& l1_orders_2(B) )
=> ( B = k9_bagorder(A)
<=> ( u1_struct_0(B) = k14_polynom1(A)
& ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( r2_hidden(k4_tarski(C,D),u1_orders_2(B))
<=> r3_polynom1(A,C,D) ) ) ) ) ) ) ) ).
fof(t33_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k11_dickson))) = k14_polynom1(A) ) ).
fof(t34_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k9_bagorder(A) = k5_yellow_1(A,k2_pre_circ(A,k11_dickson)) ) ).
fof(t35_bagorder,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( v2_bagorder(B,A)
=> ( r1_tarski(u1_orders_2(k9_bagorder(A)),B)
& v2_wellord1(B) ) ) ) ) ).
fof(d14_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
=> ( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k10_bagorder(A,B)
<=> ( r2_hidden(C,B)
& r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) ).
fof(d15_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
=> ( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k11_bagorder(A,B)
<=> ( r2_hidden(C,B)
& r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) ).
fof(t36_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
=> ( r2_hidden(k1_domain_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)),B,C),k3_tarski(k2_relat_1(k12_bagorder(A))))
<=> ~ ( B != k1_xboole_0
& ~ ( B != k1_xboole_0
& C != k1_xboole_0
& k11_bagorder(A,B) != k11_bagorder(A,C)
& r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k11_bagorder(A,B),k11_bagorder(A,C)),u1_orders_2(A)) )
& ~ ( B != k1_xboole_0
& C != k1_xboole_0
& k11_bagorder(A,B) = k11_bagorder(A,C)
& r2_hidden(k4_tarski(k4_xboole_0(B,k6_domain_1(u1_struct_0(A),k11_bagorder(A,B))),k4_xboole_0(C,k6_domain_1(u1_struct_0(A),k11_bagorder(A,C)))),k3_tarski(k2_relat_1(k12_bagorder(A)))) ) ) ) ) ) ) ).
fof(t37_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
=> ~ ( B != k1_xboole_0
& r2_hidden(k4_tarski(B,k1_xboole_0),k3_tarski(k2_relat_1(k12_bagorder(A)))) ) ) ) ).
fof(t38_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
=> m1_subset_1(k4_xboole_0(B,k6_domain_1(u1_struct_0(A),k11_bagorder(A,B))),k5_finsub_1(u1_struct_0(A))) ) ) ).
fof(t39_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_partfun1(k3_tarski(k2_relat_1(k12_bagorder(A))),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))
& v1_relat_2(k3_tarski(k2_relat_1(k12_bagorder(A))))
& v4_relat_2(k3_tarski(k2_relat_1(k12_bagorder(A))))
& v8_relat_2(k3_tarski(k2_relat_1(k12_bagorder(A))))
& m2_relset_1(k3_tarski(k2_relat_1(k12_bagorder(A))),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) ) ) ).
fof(d17_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> k13_bagorder(A) = k3_tarski(k2_relat_1(k12_bagorder(A))) ) ).
fof(d18_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> k14_bagorder(A) = g1_orders_2(k5_finsub_1(u1_struct_0(A)),k13_bagorder(A)) ) ).
fof(t40_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_bagorder(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k14_bagorder(A)))
=> ( r2_hidden(k1_domain_1(u1_struct_0(k14_bagorder(A)),u1_struct_0(k14_bagorder(A)),B,C),u1_orders_2(k14_bagorder(A)))
<=> ? [D] :
( m1_subset_1(D,k5_finsub_1(u1_struct_0(A)))
& ? [E] :
( m1_subset_1(E,k5_finsub_1(u1_struct_0(A)))
& B = D
& C = E
& ~ ( D != k1_xboole_0
& ~ ( D != k1_xboole_0
& E != k1_xboole_0
& k11_bagorder(A,D) != k11_bagorder(A,E)
& r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k11_bagorder(A,D),k11_bagorder(A,E)),u1_orders_2(A)) )
& ~ ( D != k1_xboole_0
& E != k1_xboole_0
& k11_bagorder(A,D) = k11_bagorder(A,E)
& r2_hidden(k4_tarski(k4_xboole_0(D,k6_domain_1(u1_struct_0(A),k11_bagorder(A,D))),k4_xboole_0(E,k6_domain_1(u1_struct_0(A),k11_bagorder(A,E)))),k13_bagorder(A)) ) ) ) ) ) ) ) ) ).
fof(d19_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( ( v1_wellfnd1(A)
& r1_tarski(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k15_bagorder(A,B)
<=> ( r2_hidden(C,B)
& r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) ).
fof(d20_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( D = k16_bagorder(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,u1_struct_0(A),D,E) = k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(E,C)) ) ) ) ) ) ) ).
fof(t41_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v3_wellfnd1(B,A)
=> v3_wellfnd1(k16_bagorder(A,B,C),A) ) ) ) ) ).
fof(t42_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_wellfnd1(A)
=> v1_wellfnd1(k14_bagorder(A)) ) ) ).
fof(dt_k1_bagorder,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_pboole(D,A) )
=> m1_pboole(k1_bagorder(A,B,C,D),k5_binarith(C,B)) ) ).
fof(dt_k2_bagorder,axiom,
$true ).
fof(dt_k3_bagorder,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> m2_subset_1(k3_bagorder(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k4_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_partfun1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k4_bagorder(A))
& v4_relat_2(k4_bagorder(A))
& v8_relat_2(k4_bagorder(A))
& m2_relset_1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) ).
fof(dt_k5_bagorder,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( v1_partfun1(k5_bagorder(A,B),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k5_bagorder(A,B))
& v4_relat_2(k5_bagorder(A,B))
& v8_relat_2(k5_bagorder(A,B))
& m2_relset_1(k5_bagorder(A,B),k14_polynom1(A),k14_polynom1(A)) ) ) ).
fof(dt_k6_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_partfun1(k6_bagorder(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k6_bagorder(A))
& v4_relat_2(k6_bagorder(A))
& v8_relat_2(k6_bagorder(A))
& m2_relset_1(k6_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) ).
fof(dt_k7_bagorder,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_partfun1(k7_bagorder(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k7_bagorder(A))
& v4_relat_2(k7_bagorder(A))
& v8_relat_2(k7_bagorder(A))
& m2_relset_1(k7_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) ).
fof(dt_k8_bagorder,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& v1_partfun1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m1_relset_1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
& v1_partfun1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))))
& v1_relat_2(D)
& v4_relat_2(D)
& v8_relat_2(D)
& m1_relset_1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1)))) )
=> ( v1_partfun1(k8_bagorder(A,B,C,D),k14_polynom1(B),k14_polynom1(B))
& v1_relat_2(k8_bagorder(A,B,C,D))
& v4_relat_2(k8_bagorder(A,B,C,D))
& v8_relat_2(k8_bagorder(A,B,C,D))
& m2_relset_1(k8_bagorder(A,B,C,D),k14_polynom1(B),k14_polynom1(B)) ) ) ).
fof(dt_k9_bagorder,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_orders_2(k9_bagorder(A))
& l1_orders_2(k9_bagorder(A)) ) ) ).
fof(dt_k10_bagorder,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) )
=> m1_subset_1(k10_bagorder(A,B),u1_struct_0(A)) ) ).
fof(dt_k11_bagorder,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A)
& m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) )
=> m1_subset_1(k11_bagorder(A,B),u1_struct_0(A)) ) ).
fof(dt_k12_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k12_bagorder(A))
& v1_funct_2(k12_bagorder(A),k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))))
& m2_relset_1(k12_bagorder(A),k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))) ) ) ).
fof(dt_k13_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( v1_partfun1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))
& v1_relat_2(k13_bagorder(A))
& v4_relat_2(k13_bagorder(A))
& v8_relat_2(k13_bagorder(A))
& m2_relset_1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) ) ) ).
fof(dt_k14_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ( v2_orders_2(k14_bagorder(A))
& v3_orders_2(k14_bagorder(A))
& v4_orders_2(k14_bagorder(A))
& l1_orders_2(k14_bagorder(A)) ) ) ).
fof(dt_k15_bagorder,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v16_waybel_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B) )
=> m1_subset_1(k15_bagorder(A,B),u1_struct_0(A)) ) ).
fof(dt_k16_bagorder,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> ( v1_funct_1(k16_bagorder(A,B,C))
& v1_funct_2(k16_bagorder(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k16_bagorder(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(d2_bagorder,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> k2_bagorder(A,B) = a_2_0_bagorder(A,B) ) ) ).
fof(d16_bagorder,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))) )
=> ( B = k12_bagorder(A)
<=> ( k4_relset_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B) = k5_numbers
& k8_funct_2(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B,np__0) = a_1_0_bagorder(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B,k1_nat_1(C,np__1)) = a_3_0_bagorder(A,B,C) ) ) ) ) ) ).
fof(fraenkel_a_2_0_bagorder,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_bagorder(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
& A = D
& v1_finset_1(D)
& ~ v1_xboole_0(D)
& r1_tarski(k1_card_1(D),C) ) ) ) ).
fof(fraenkel_a_1_0_bagorder,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v16_waybel_0(B)
& l1_orders_2(B) )
=> ( r2_hidden(A,a_1_0_bagorder(B))
<=> ? [C,D] :
( m1_subset_1(C,k5_finsub_1(u1_struct_0(B)))
& m1_subset_1(D,k5_finsub_1(u1_struct_0(B)))
& A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),C,D)
& ( C = k1_xboole_0
| ( C != k1_xboole_0
& D != k1_xboole_0
& k11_bagorder(B,C) != k11_bagorder(B,D)
& r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),k11_bagorder(B,C),k11_bagorder(B,D)),u1_orders_2(B)) ) ) ) ) ) ).
fof(fraenkel_a_3_0_bagorder,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v16_waybel_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))))
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_3_0_bagorder(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,k5_finsub_1(u1_struct_0(B)))
& m1_subset_1(F,k5_finsub_1(u1_struct_0(B)))
& A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),E,F)
& E != k1_xboole_0
& F != k1_xboole_0
& k11_bagorder(B,E) = k11_bagorder(B,F)
& r2_hidden(k4_tarski(k4_xboole_0(E,k6_domain_1(u1_struct_0(B),k11_bagorder(B,E))),k4_xboole_0(F,k6_domain_1(u1_struct_0(B),k11_bagorder(B,F)))),k8_funct_2(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))),C,D)) ) ) ) ).
%------------------------------------------------------------------------------