SET007 Axioms: SET007+751.ax
%------------------------------------------------------------------------------
% File : SET007+751 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Term Orders
% 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 : termord [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 64 ( 0 unt; 0 def)
% Number of atoms : 1021 ( 37 equ)
% Maximal formula atoms : 28 ( 15 avg)
% Number of connectives : 1007 ( 50 ~; 5 |; 718 &)
% ( 9 <=>; 225 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 13 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 48 ( 47 usr; 0 prp; 1-4 aty)
% Number of functors : 28 ( 28 usr; 2 con; 0-4 aty)
% Number of variables : 256 ( 250 !; 6 ?)
% 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(rc1_termord,axiom,
? [A] :
( l1_rlvect_1(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A) ) ).
fof(rc2_termord,axiom,
? [A] :
( l1_rlvect_1(A)
& ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_algstr_1(A)
& v2_algstr_1(A)
& v3_algstr_1(A)
& v4_algstr_1(A)
& v5_algstr_1(A)
& v6_algstr_1(A)
& ~ v3_realset2(A) ) ).
fof(fc1_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v3_polynom7(C,A,B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v3_polynom7(D,A,B)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_relat_1(k28_polynom1(A,B,C,D))
& v1_funct_1(k28_polynom1(A,B,C,D))
& v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k28_polynom1(A,B,C,D),k14_polynom1(A),B)
& v3_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) ).
fof(fc2_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_vectsp_1(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v4_polynom7(C,A,B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v4_polynom7(D,A,B)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_relat_1(k28_polynom1(A,B,C,D))
& v1_funct_1(k28_polynom1(A,B,C,D))
& v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k28_polynom1(A,B,C,D),k14_polynom1(A),B)
& v3_polynom7(k28_polynom1(A,B,C,D),A,B)
& v4_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) ).
fof(rc3_termord,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)
& v6_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A) ) ) ).
fof(cc1_termord,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
=> ( ( 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) )
=> ( 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)
& v1_wellord1(B) ) ) ) ) ).
fof(fc3_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_realset2(C)
& l2_struct_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_relat_1(k5_termord(A,B,C,D))
& v1_funct_1(k5_termord(A,B,C,D))
& v1_funct_2(k5_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k5_termord(A,B,C,D),k14_polynom1(A),C)
& v1_polynom7(k5_termord(A,B,C,D),A,C)
& v3_polynom7(k5_termord(A,B,C,D),A,C) ) ) ).
fof(fc4_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_realset2(C)
& l2_struct_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> v8_rlvect_1(k4_termord(A,B,C,D),C) ) ).
fof(d1_termord,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( v1_termord(B,A)
<=> B != k16_polynom1(A) ) ) ).
fof(t1_termord,axiom,
! [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,B,C)
<=> ? [D] :
( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A)
& r6_pboole(A,C,k9_polynom1(A,B,D)) ) ) ) ) ).
fof(t2_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> k28_polynom1(A,B,k26_polynom1(A,B),C) = k26_polynom1(A,B) ) ) ) ).
fof(t3_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& v2_vectsp_2(B)
& l3_vectsp_1(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] :
( ( v8_rlvect_1(E,B)
& m1_subset_1(E,u1_struct_0(B)) )
=> ! [F] :
( ( v8_rlvect_1(F,B)
& m1_subset_1(F,u1_struct_0(B)) )
=> k1_polynom7(A,B,k1_group_1(B,E,F),k9_polynom1(A,C,D)) = k28_polynom1(A,B,k1_polynom7(A,B,E,C),k1_polynom7(A,B,F,D)) ) ) ) ) ) ) ).
fof(t4_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& v2_vectsp_2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k4_polynom7(A,B,k1_group_1(B,C,D)) = k28_polynom1(A,B,k4_polynom7(A,B,C),k4_polynom7(A,B,D)) ) ) ) ) ).
fof(d2_termord,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) )
=> ( r1_termord(A,B,C,D)
<=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ) ).
fof(d3_termord,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) )
=> ( r2_termord(A,B,C,D)
<=> ( r1_termord(A,B,C,D)
& C != D ) ) ) ) ) ) ).
fof(d4_termord,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) )
=> ( ( r1_termord(A,B,C,D)
=> k1_termord(A,B,C,D) = C )
& ( ~ r1_termord(A,B,C,D)
=> k1_termord(A,B,C,D) = D ) ) ) ) ) ) ).
fof(d5_termord,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) )
=> ( ( r1_termord(A,B,D,C)
=> k2_termord(A,B,C,D) = C )
& ( ~ r1_termord(A,B,D,C)
=> k2_termord(A,B,C,D) = D ) ) ) ) ) ) ).
fof(t5_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_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) )
=> ( r1_termord(A,B,C,D)
<=> ~ r2_termord(A,B,D,C) ) ) ) ) ) ).
fof(t6_termord,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) )
=> r1_termord(A,B,C,C) ) ) ) ).
fof(t7_termord,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) )
=> ( ( r1_termord(A,B,C,D)
& r1_termord(A,B,D,C) )
=> r6_pboole(A,C,D) ) ) ) ) ) ).
fof(t8_termord,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) )
=> ( ( r1_termord(A,B,C,D)
& r1_termord(A,B,D,E) )
=> r1_termord(A,B,C,E) ) ) ) ) ) ) ).
fof(t9_termord,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)
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> r1_termord(A,B,k16_polynom1(A),C) ) ) ) ).
fof(t10_termord,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)
& v2_bagorder(B,A)
& 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) )
=> ( r3_polynom1(A,C,D)
=> r1_termord(A,B,C,D) ) ) ) ) ) ).
fof(t11_termord,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) )
=> ( r6_pboole(A,k1_termord(A,B,C,D),C)
| r6_pboole(A,k1_termord(A,B,C,D),D) ) ) ) ) ) ).
fof(t12_termord,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) )
=> ( r6_pboole(A,k2_termord(A,B,C,D),C)
| r6_pboole(A,k2_termord(A,B,C,D),D) ) ) ) ) ) ).
fof(t13_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_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) )
=> ( r1_termord(A,B,k1_termord(A,B,C,D),C)
& r1_termord(A,B,k1_termord(A,B,C,D),D) ) ) ) ) ) ).
fof(t14_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_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) )
=> ( r1_termord(A,B,C,k2_termord(A,B,C,D))
& r1_termord(A,B,D,k2_termord(A,B,C,D)) ) ) ) ) ) ).
fof(t15_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_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) )
=> ( r6_pboole(A,k1_termord(A,B,C,D),k1_termord(A,B,D,C))
& r6_pboole(A,k2_termord(A,B,C,D),k2_termord(A,B,D,C)) ) ) ) ) ) ).
fof(t16_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_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) )
=> ( r6_pboole(A,k1_termord(A,B,C,D),C)
<=> r6_pboole(A,k2_termord(A,B,C,D),D) ) ) ) ) ) ).
fof(d6_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m1_polynom1(E,A,k14_polynom1(A))
=> ( E = k3_termord(A,B,C,D)
<=> ( ( k12_polynom1(k14_polynom1(A),C,D) = k1_xboole_0
& r6_pboole(A,E,k16_polynom1(A)) )
| ( r2_hidden(E,k12_polynom1(k14_polynom1(A),C,D))
& ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D))
=> r1_termord(A,B,F,E) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k4_termord(A,B,C,D) = k15_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) ).
fof(d8_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k5_termord(A,B,C,D) = k1_polynom7(A,C,k4_termord(A,B,C,D),k3_termord(A,B,C,D)) ) ) ) ) ).
fof(t17_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k4_termord(A,B,C,D) = k1_rlvect_1(C)
<=> D = k26_polynom1(A,C) ) ) ) ) ) ).
fof(t18_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k15_polynom1(A,C,k5_termord(A,B,C,D),k3_termord(A,B,C,D)) = k15_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) ).
fof(t19_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( E != k3_termord(A,B,C,D)
=> k15_polynom1(A,C,k5_termord(A,B,C,D),E) = k1_rlvect_1(C) ) ) ) ) ) ) ).
fof(t20_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),C,k5_termord(A,B,C,D)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ).
fof(t21_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k12_polynom1(k14_polynom1(A),C,k5_termord(A,B,C,D)) = k1_xboole_0
| k12_polynom1(k14_polynom1(A),C,k5_termord(A,B,C,D)) = k1_tarski(k3_termord(A,B,C,D)) ) ) ) ) ) ).
fof(t22_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( r6_pboole(A,k2_polynom7(A,C,k5_termord(A,B,C,D)),k3_termord(A,B,C,D))
& k3_polynom7(A,C,k5_termord(A,B,C,D)) = k4_termord(A,B,C,D) ) ) ) ) ) ).
fof(t23_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v3_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( r6_pboole(A,k3_termord(A,B,C,D),k2_polynom7(A,C,D))
& k4_termord(A,B,C,D) = k3_polynom7(A,C,D)
& k5_termord(A,B,C,D) = D ) ) ) ) ) ).
fof(t24_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v4_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( r6_pboole(A,k3_termord(A,B,C,D),k16_polynom1(A))
& k4_termord(A,B,C,D) = k15_polynom1(A,C,D,k16_polynom1(A)) ) ) ) ) ) ).
fof(t25_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( r6_pboole(A,k3_termord(A,B,C,k4_polynom7(A,C,D)),k16_polynom1(A))
& k4_termord(A,B,C,k4_polynom7(A,C,D)) = D ) ) ) ) ) ).
fof(t26_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> r6_pboole(A,k3_termord(A,B,C,k5_termord(A,B,C,D)),k3_termord(A,B,C,D)) ) ) ) ) ).
fof(t27_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_realset2(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k4_termord(A,B,C,k5_termord(A,B,C,D)) = k4_termord(A,B,C,D) ) ) ) ) ).
fof(t28_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k5_termord(A,B,C,k5_termord(A,B,C,D)) = k5_termord(A,B,C,D) ) ) ) ) ).
fof(t29_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& v1_algstr_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> r2_hidden(k9_polynom1(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E)),k12_polynom1(k14_polynom1(A),C,k28_polynom1(A,C,D,E))) ) ) ) ) ) ).
fof(t31_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> r6_pboole(A,k3_termord(A,B,C,k28_polynom1(A,C,D,E)),k9_polynom1(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) ).
fof(t32_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> k4_termord(A,B,C,k28_polynom1(A,C,D,E)) = k1_group_1(C,k4_termord(A,B,C,D),k4_termord(A,B,C,E)) ) ) ) ) ) ).
fof(t33_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> k5_termord(A,B,C,k28_polynom1(A,C,D,E)) = k28_polynom1(A,C,k5_termord(A,B,C,D),k5_termord(A,B,C,E)) ) ) ) ) ) ).
fof(t34_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v5_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> r1_termord(A,B,k3_termord(A,B,C,k22_polynom1(A,C,D,E)),k2_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) ).
fof(d9_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k6_termord(A,B,C,D) = k25_polynom1(A,C,D,k5_termord(A,B,C,D)) ) ) ) ) ).
fof(t35_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ).
fof(t36_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)) = k4_xboole_0(k12_polynom1(k14_polynom1(A),C,D),k1_tarski(k3_termord(A,B,C,D))) ) ) ) ) ).
fof(t37_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k12_polynom1(k14_polynom1(A),C,k22_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,D))) = k12_polynom1(k14_polynom1(A),C,D) ) ) ) ) ).
fof(t38_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k22_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,D)) = D ) ) ) ) ).
fof(t39_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k15_polynom1(A,C,k6_termord(A,B,C,D),k3_termord(A,B,C,D)) = k1_rlvect_1(C) ) ) ) ) ).
fof(t40_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(E,k12_polynom1(k14_polynom1(A),C,D))
=> ( E = k3_termord(A,B,C,D)
| k15_polynom1(A,C,k6_termord(A,B,C,D),E) = k15_polynom1(A,C,D,E) ) ) ) ) ) ) ) ).
fof(dt_k1_termord,axiom,
! [A,B,C,D] :
( ( 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))
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A)
& v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( v7_seqm_3(k1_termord(A,B,C,D))
& v1_polynom1(k1_termord(A,B,C,D))
& m1_pboole(k1_termord(A,B,C,D),A) ) ) ).
fof(dt_k2_termord,axiom,
! [A,B,C,D] :
( ( 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))
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A)
& v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( v7_seqm_3(k2_termord(A,B,C,D))
& v1_polynom1(k2_termord(A,B,C,D))
& m1_pboole(k2_termord(A,B,C,D),A) ) ) ).
fof(dt_k3_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& l2_struct_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> m1_polynom1(k3_termord(A,B,C,D),A,k14_polynom1(A)) ) ).
fof(dt_k4_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& l2_struct_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> m1_subset_1(k4_termord(A,B,C,D),u1_struct_0(C)) ) ).
fof(dt_k5_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& l2_struct_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_funct_1(k5_termord(A,B,C,D))
& v1_funct_2(k5_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
& v3_polynom7(k5_termord(A,B,C,D),A,C)
& m2_relset_1(k5_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) ).
fof(dt_k6_termord,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_funct_1(k6_termord(A,B,C,D))
& v1_funct_2(k6_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k6_termord(A,B,C,D),k14_polynom1(A),C)
& m2_relset_1(k6_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) ).
fof(t30_termord,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(D,k14_polynom1(A),B)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,C,D)),a_4_0_termord(A,B,C,D)) ) ) ) ) ).
fof(fraenkel_a_4_0_termord,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(B)
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& l3_vectsp_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(B),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(B),C)
& m2_relset_1(D,k14_polynom1(B),u1_struct_0(C))
& v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(B),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(B),C)
& m2_relset_1(E,k14_polynom1(B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_4_0_termord(B,C,D,E))
<=> ? [F,G] :
( m1_polynom1(F,B,k14_polynom1(B))
& m1_polynom1(G,B,k14_polynom1(B))
& A = k9_polynom1(B,F,G)
& r2_hidden(F,k12_polynom1(k14_polynom1(B),C,D))
& r2_hidden(G,k12_polynom1(k14_polynom1(B),C,E)) ) ) ) ).
%------------------------------------------------------------------------------