%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG434-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:09:27 AM UTC 2026
% Result : Unsatisfiable 81.38s 13.98s
% Output : CNFRefutation 81.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 442
% Syntax : Number of formulae : 3794 (2228 unt; 0 typ; 0 def)
% Number of atoms : 19772 (8749 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 53838 (4716 ~;6000 |; 0 &;43122 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 61 usr; 6 con; 0-5 aty)
% Number of variables : 12268 ( 0 ^;12268 !; 0 ?;12268 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(tp_c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(tp_c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_Polynomial_OpCons,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(tp_c_Polynomial_Opdivmod__rel,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Polynomial_Opoly,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(tp_c_Polynomial_Opoly__gcd,type,
c_Polynomial_Opoly__gcd: $i > $i > $i > $i ).
thf(tp_c_Polynomial_Osmult,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(tp_class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__comm__monoid__add,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Odvd,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(tp_class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
thf(tp_tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
thf(tp_v_a,type,
v_a: $i ).
thf(tp_v_p,type,
v_p: $i ).
thf(tp_v_q,type,
v_q: $i ).
thf(1,axiom,
! [T_1: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_HOL_Ozero @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
thf(2,axiom,
! [T_1: $i] :
( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
thf(3,axiom,
! [T_1: $i] :
( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
thf(4,axiom,
! [T_1: $i] :
( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ofield @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
thf(5,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
thf(6,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
thf(7,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
thf(8,axiom,
! [T_1: $i] :
( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ofield @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(9,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
thf(10,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
thf(11,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
thf(12,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
thf(13,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
thf(14,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
thf(15,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
thf(16,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
thf(17,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
thf(18,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
thf(19,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
thf(20,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
thf(21,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
thf(22,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
thf(23,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
thf(24,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
thf(25,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
thf(26,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
thf(27,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
thf(28,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
thf(29,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
thf(30,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
thf(31,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(32,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
thf(33,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(34,axiom,
! [T_1: $i] :
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(35,axiom,
class_HOL_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(36,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(37,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(38,axiom,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(39,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(40,axiom,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(41,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(42,axiom,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(43,axiom,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(44,axiom,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(45,axiom,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(46,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(47,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
thf(48,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(49,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(50,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(51,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(52,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(53,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(54,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(55,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(56,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(57,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(58,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
thf(59,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(60,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(61,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(62,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(63,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(64,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(65,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(66,axiom,
! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(67,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ v_p @ v_q @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(68,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ v_q @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(69,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ T_a )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_p @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
thf(70,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ v_p @ v_q @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pq_0) ).
thf(71,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).
thf(72,axiom,
! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).
thf(73,axiom,
! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(74,axiom,
! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).
thf(75,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).
thf(76,axiom,
! [T_a: $i,V_b: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_k @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(77,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(78,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(79,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__smult__left_0) ).
thf(80,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(81,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(82,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(83,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(84,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
thf(85,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(86,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_y: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).
thf(87,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).
thf(88,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(89,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(90,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(91,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(92,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(93,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(94,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(95,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_4) ).
thf(96,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_2) ).
thf(97,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_1) ).
thf(98,axiom,
! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_1) ).
thf(99,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_0) ).
thf(100,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd_0) ).
thf(101,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__cancel_0) ).
thf(102,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__left_0) ).
thf(103,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_p @ T_a )
= V_p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
thf(104,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(105,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(106,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(107,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(108,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(109,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(110,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(111,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(112,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__right_0) ).
thf(113,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(114,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(115,axiom,
! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).
thf(116,axiom,
! [T_a: $i,V_k: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).
thf(117,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__right_0) ).
thf(118,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(119,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(120,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(121,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(122,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(123,axiom,
! [T_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_0) ).
thf(124,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).
thf(125,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).
thf(126,axiom,
! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_2) ).
thf(127,axiom,
! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__greatest_0) ).
thf(128,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(129,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
thf(130,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
thf(131,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_d @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(132,axiom,
! [T_a: $i,V_l: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_l @ T_a )
!= ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_l @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(133,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(134,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(135,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(136,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_c @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(137,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__minus__left_0) ).
thf(138,axiom,
! [T_a: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_3) ).
thf(139,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(140,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(141,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(142,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(143,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(144,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(145,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__mult__right_0) ).
thf(146,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(147,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
thf(148,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
thf(149,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__code_1) ).
thf(150,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).
thf(151,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(152,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(153,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(154,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).
thf(155,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(156,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__minus__right_0) ).
thf(157,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(158,axiom,
! [T_a: $i,V_z: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_z @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(159,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(160,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(161,axiom,
! [T_a: $i,V_m: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(162,axiom,
! [T_a: $i,V_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(163,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_n @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
thf(164,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(165,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(166,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(167,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(168,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(169,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).
thf(170,axiom,
! [T_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).
thf(171,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(172,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(173,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(174,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(175,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(176,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(177,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(178,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(179,axiom,
! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(180,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(181,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ V_n @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(182,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(183,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(184,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__left_0) ).
thf(185,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(186,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= V_q )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__poly__eq_0) ).
thf(187,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(188,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(189,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(190,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(191,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(192,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_b @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a_H @ T_a ) @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(193,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(194,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(195,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(196,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(197,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(198,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(199,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(200,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0_0) ).
thf(201,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(202,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(203,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(204,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(205,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(206,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(207,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__left_0) ).
thf(208,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(209,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(210,axiom,
! [T_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_5) ).
thf(211,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_6) ).
thf(212,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Polynomial_Osmult @ V_a @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__right_0) ).
thf(213,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ V_u @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a )
= V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(214,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(216,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(217,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(218,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(219,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(220,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(221,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0_0) ).
thf(222,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(223,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(224,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(225,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(226,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
thf(227,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(228,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(229,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(230,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(231,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(232,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(233,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(234,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(235,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(236,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(237,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(238,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(239,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(240,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(241,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(242,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(243,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(244,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(245,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(246,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(248,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(249,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= V_p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
thf(250,axiom,
! [T_a: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= V_q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
thf(251,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(252,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(253,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(254,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(255,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(256,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_a @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(257,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(258,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= V_y )
| ( V_x
= ( c_HOL_Ouminus__class_Ouminus @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(259,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_q_H: $i,V_r_H: $i,V_r: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q_H @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_r_H @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_q @ V_z @ V_q_H @ V_r_H @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__mult_0) ).
thf(260,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(261,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(262,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(263,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ V_a @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(264,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_c @ V_d @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(265,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(266,axiom,
! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(267,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(268,axiom,
! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(269,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(270,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(271,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(272,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(273,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(274,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(275,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(276,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(277,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(278,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_r: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= V_r )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__poly__eq_0) ).
thf(279,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(280,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(281,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(282,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(283,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__minus__left_0) ).
thf(284,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__minus__right_0) ).
thf(285,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(286,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(287,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_d @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(288,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(289,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(290,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(291,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(292,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(293,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(294,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(295,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(296,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(297,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(298,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(299,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(300,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__left_0) ).
thf(301,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__right_0) ).
thf(302,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(303,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ ( c_Polynomial_Opoly__gcd @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__assoc_0) ).
thf(304,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ ( c_Polynomial_Opoly__gcd @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ ( c_Polynomial_Opoly__gcd @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__left__commute_0) ).
thf(305,axiom,
! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(306,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(307,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(308,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel_0) ).
thf(309,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(310,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(311,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(312,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(313,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(314,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(315,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(316,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_z @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).
thf(317,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(318,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_p @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
thf(319,axiom,
! [T_a: $i,V_x: $i,V_q: $i,V_y: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_0) ).
thf(320,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(321,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(322,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a )
!= ( c_HOL_Otimes__class_Otimes @ V_b @ V_b @ T_a ) )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(323,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(324,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(325,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(326,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(327,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(328,axiom,
! [T_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= V_p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I2_J_0) ).
thf(329,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(330,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(331,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(332,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(333,axiom,
! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_Polynomial_OpCons @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__right_0) ).
thf(334,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__left_0) ).
thf(335,axiom,
! [T_a: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I1_J_0) ).
thf(336,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(337,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(338,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(339,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(340,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(341,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(342,axiom,
! [T_a: $i,V_xa: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(343,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(344,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(345,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(346,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(347,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(348,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(349,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(350,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(351,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_1) ).
thf(352,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_0) ).
thf(353,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(354,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(355,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(356,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__add__left_0) ).
thf(357,axiom,
! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(358,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(359,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(360,axiom,
! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(361,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(362,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(363,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(364,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(365,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(366,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(367,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(368,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
thf(369,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
thf(370,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(371,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(372,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(373,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( V_a
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(374,axiom,
! [T_a: $i,V_d: $i,V_x: $i,V_t: $i,V_k: $i,V_D: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(375,axiom,
! [T_a: $i,V_d: $i,V_x: $i,V_k: $i,V_D: $i,V_t: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(376,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(377,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(378,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(379,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(380,axiom,
! [T_a: $i,V_q: $i,V_x: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_0) ).
thf(381,axiom,
! [T_a: $i,V_r: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).
thf(382,axiom,
! [T_a: $i,V_q: $i,V_y: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).
thf(383,axiom,
! [T_a: $i,V_x: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_1) ).
thf(384,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(385,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(386,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(387,axiom,
! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(388,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_y @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__mult__right_0) ).
thf(389,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) @ T_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(390,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(391,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(392,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(393,axiom,
! [T_a: $i,V_r: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r = V_x )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).
thf(394,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_w @ V_z @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_w @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_w @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(395,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(396,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(397,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(398,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(399,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(400,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(401,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__0__0_0) ).
thf(402,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(403,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(404,axiom,
! [T_a: $i,V_r1: $i,V_r2: $i,V_x: $i,V_y: $i,V_q2: $i,V_q1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r1 = V_r2 )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q2 @ V_r2 @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q1 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_1) ).
thf(405,axiom,
! [T_a: $i,V_q1: $i,V_q2: $i,V_x: $i,V_y: $i,V_r2: $i,V_r1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q1 = V_q2 )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q2 @ V_r2 @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q1 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_0) ).
thf(406,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(407,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(408,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(409,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(410,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(411,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(412,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(413,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(414,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(415,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(416,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(417,axiom,
! [T_a: $i,V_c: $i,V_p: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_c @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
thf(418,axiom,
! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ V_c @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_0) ).
thf(419,axiom,
! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ V_c @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_1) ).
thf(420,axiom,
! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ V_c @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_0) ).
thf(421,axiom,
! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ V_c @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_1) ).
thf(422,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) )
| ( V_p = V_q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
thf(423,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
thf(424,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
thf(425,axiom,
! [T_a: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
thf(426,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
thf(427,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_Polynomial_OpCons @ V_b @ V_p @ T_a ) @ T_a )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
thf(428,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).
thf(429,axiom,
! [T_a: $i,V_c: $i,V_p: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_c @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
thf(430,axiom,
! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pCons_0) ).
thf(431,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__pCons_0) ).
thf(432,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__diff_0) ).
thf(433,axiom,
! [T_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__minus_0) ).
thf(434,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
thf(435,axiom,
! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mult_0) ).
thf(436,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
thf(437,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
thf(438,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
thf(439,axiom,
! [T_a: $i,V_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ V_x @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
thf(440,axiom,
! [T_a: $i,V_p: $i,V_c: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_p @ ( c_Polynomial_Osmult @ V_c @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
!= ( c_Polynomial_OpCons @ V_r @ V_q @ T_a ) )
| ( V_r
= ( c_Polynomial_Opoly @ V_p @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
thf(441,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(442,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[441]) ).
thf(443,negated_conjecture,
~ ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(444,plain,
$false = $false,
inference(unfold_def,[status(thm)],[442]) ).
thf(445,plain,
( ( ! [T_1: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_HOL_Ozero @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(446,plain,
( ( ! [T_1: $i] :
( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(447,plain,
( ( ! [T_1: $i] :
( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(448,plain,
( ( ! [T_1: $i] :
( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ofield @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(449,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(450,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(451,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(452,plain,
( ( ! [T_1: $i] :
( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ofield @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(453,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(454,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(455,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(456,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(457,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(458,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(459,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(460,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(461,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(462,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(463,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(464,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(465,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(466,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(467,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(468,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(469,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(470,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(471,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(472,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(473,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(474,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(475,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(476,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(477,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(478,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(479,plain,
( ( class_HOL_Ozero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(480,plain,
( ( class_Power_Opower @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(481,plain,
( ( class_Int_Onumber__ring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(482,plain,
( ( class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(483,plain,
( ( class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(484,plain,
( ( class_Ring__and__Field_Oring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(485,plain,
( ( class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(486,plain,
( ( class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(487,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(488,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(489,plain,
( ( class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(490,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(491,plain,
( ( class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(492,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(493,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(494,plain,
( ( class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(495,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(496,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(497,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(498,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(499,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(500,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(501,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(502,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(503,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(504,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(505,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(506,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(507,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(508,plain,
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(509,plain,
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(510,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(511,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ v_q @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(512,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_q @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(513,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ T_a )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_p @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(514,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ v_q @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(515,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(516,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(517,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(518,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(519,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(520,plain,
( ( ! [T_a: $i,V_b: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(521,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(522,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(523,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(524,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(525,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(526,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(527,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(528,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(529,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(530,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(531,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(532,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(533,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(534,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(535,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(536,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(537,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(538,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(539,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(540,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(541,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(542,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(543,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(544,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(545,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(546,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(547,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_p @ T_a )
= V_p ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(548,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(549,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(550,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(551,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(552,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(553,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(554,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(555,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(556,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(557,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(558,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(559,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(560,plain,
( ( ! [T_a: $i,V_k: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(561,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(562,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(563,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(564,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(565,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(566,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(567,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(568,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(569,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(570,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(571,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(572,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(573,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(574,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(575,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_d @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(576,plain,
( ( ! [T_a: $i,V_l: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_l @ T_a )
!= ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_l @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(577,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(578,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(579,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(580,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_c @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(581,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(582,plain,
( ( ! [T_a: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(583,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(584,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(585,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(586,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(587,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(588,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(589,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(590,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(591,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(592,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(593,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(594,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(595,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(596,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(597,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(598,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(599,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(600,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(601,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(602,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_z @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(603,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(604,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(605,plain,
( ( ! [T_a: $i,V_m: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(606,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(607,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_n @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(608,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(609,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(610,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(611,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(612,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(613,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(614,plain,
( ( ! [T_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(615,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(616,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(617,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(618,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(619,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(620,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(621,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(622,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(623,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(624,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(625,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ V_n @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(626,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(627,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(628,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(629,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(630,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= V_q )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(631,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(632,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(633,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(634,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(635,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(636,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_b @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a_H @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(637,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(638,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(639,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(640,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(641,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(642,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(643,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(644,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(645,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(646,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(647,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(648,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(649,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(650,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(651,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(652,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(653,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(654,plain,
( ( ! [T_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(655,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(656,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Polynomial_Osmult @ V_a @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(657,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ V_u @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a )
= V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(658,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(659,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(660,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(661,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(662,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(663,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(664,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(665,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(666,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(667,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(668,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(669,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(670,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(671,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(672,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(673,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(674,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(675,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(676,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(677,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(678,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(679,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(680,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(681,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(682,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(683,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(684,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(685,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(686,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(687,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(688,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(689,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(690,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(691,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(692,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(693,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= V_p ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(694,plain,
( ( ! [T_a: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= V_q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(695,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(696,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(697,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(698,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(699,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(700,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_a @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(701,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(702,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= V_y )
| ( V_x
= ( c_HOL_Ouminus__class_Ouminus @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(703,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_q_H: $i,V_r_H: $i,V_r: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q_H @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_r_H @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_q @ V_z @ V_q_H @ V_r_H @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(704,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(705,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(706,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(707,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ V_a @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(708,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_c @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(709,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(710,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(711,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(712,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(713,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(714,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(715,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(716,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(717,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(718,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(719,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(720,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(721,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(722,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_r: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= V_r )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(723,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(724,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(725,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(726,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(727,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(728,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(729,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(730,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(731,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(732,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(733,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(734,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(735,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(736,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(737,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(738,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(739,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(740,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(741,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(742,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(743,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(744,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(745,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(746,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(747,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ ( c_Polynomial_Opoly__gcd @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(748,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ ( c_Polynomial_Opoly__gcd @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ ( c_Polynomial_Opoly__gcd @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(749,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(750,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(751,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(752,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(753,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(754,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(755,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(756,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(757,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(758,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(759,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(760,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_z @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(761,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(762,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_p @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(763,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i,V_y: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(764,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(765,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(766,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a )
!= ( c_HOL_Otimes__class_Otimes @ V_b @ V_b @ T_a ) )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(767,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(768,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(769,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(770,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(771,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(772,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= V_p ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(773,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(774,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(775,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(776,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(777,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_Polynomial_OpCons @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(778,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(779,plain,
( ( ! [T_a: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(780,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(781,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(782,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(783,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(784,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(785,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(786,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(787,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(788,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(789,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(790,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(791,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(792,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(793,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(794,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(795,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(796,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(797,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(798,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(799,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(800,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(801,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(802,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(803,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(804,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(805,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(806,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(807,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(808,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(809,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(810,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(811,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(812,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(813,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(814,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(815,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(816,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(817,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( V_a
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(818,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_t: $i,V_k: $i,V_D: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(819,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_k: $i,V_D: $i,V_t: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(820,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(821,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(822,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(823,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(824,plain,
( ( ! [T_a: $i,V_q: $i,V_x: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(825,plain,
( ( ! [T_a: $i,V_r: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(826,plain,
( ( ! [T_a: $i,V_q: $i,V_y: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(827,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(828,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(829,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(830,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(831,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(832,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_y @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(833,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(834,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(835,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(836,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(837,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r = V_x )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(838,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_w @ V_z @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_w @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_w @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(839,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(840,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(841,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(842,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(843,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(844,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(845,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(846,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(847,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(848,plain,
( ( ! [T_a: $i,V_r1: $i,V_r2: $i,V_x: $i,V_y: $i,V_q2: $i,V_q1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r1 = V_r2 )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q2 @ V_r2 @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q1 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(849,plain,
( ( ! [T_a: $i,V_q1: $i,V_q2: $i,V_x: $i,V_y: $i,V_r2: $i,V_r1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q1 = V_q2 )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q2 @ V_r2 @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q1 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(850,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(851,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(852,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(853,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(854,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(855,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(856,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(857,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(858,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(859,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(860,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(861,plain,
( ( ! [T_a: $i,V_c: $i,V_p: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_c @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(862,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ V_c @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(863,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ V_c @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(864,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ V_c @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(865,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ V_c @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(866,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) )
| ( V_p = V_q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(867,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(868,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(869,plain,
( ( ! [T_a: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(870,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(871,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_Polynomial_OpCons @ V_b @ V_p @ T_a ) @ T_a )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(872,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(873,plain,
( ( ! [T_a: $i,V_c: $i,V_p: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_c @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(874,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(875,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(876,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(877,plain,
( ( ! [T_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(878,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(879,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(880,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(881,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(882,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(883,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ V_x @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(884,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_p @ ( c_Polynomial_Osmult @ V_c @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
!= ( c_Polynomial_OpCons @ V_r @ V_q @ T_a ) )
| ( V_r
= ( c_Polynomial_Opoly @ V_p @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(885,plain,
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(886,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[444]) ).
thf(887,plain,
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(888,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_p @ ( c_Polynomial_Osmult @ V_c @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
!= ( c_Polynomial_OpCons @ V_r @ V_q @ T_a ) )
| ( V_r
= ( c_Polynomial_Opoly @ V_p @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(889,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ V_x @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(890,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(891,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(892,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(893,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(894,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(895,plain,
( ( ! [T_a: $i,V_p: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(896,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ V_p @ V_x @ T_a ) @ ( c_Polynomial_Opoly @ V_q @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(897,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(898,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(899,plain,
( ( ! [T_a: $i,V_c: $i,V_p: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_c @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(900,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(901,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_Polynomial_OpCons @ V_b @ V_p @ T_a ) @ T_a )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(902,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(903,plain,
( ( ! [T_a: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(904,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(905,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(906,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_b: $i,V_q: $i] :
( ~ ( class_HOL_Ozero @ T_a )
| ( ( c_Polynomial_OpCons @ V_a @ V_p @ T_a )
!= ( c_Polynomial_OpCons @ V_b @ V_q @ T_a ) )
| ( V_p = V_q ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(907,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ V_c @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(908,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ V_c @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(909,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ V_c @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(910,plain,
( ( ! [T_a: $i,V_p: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Opoly @ V_p @ ( c_HOL_Ouminus__class_Ouminus @ V_c @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ V_c @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ T_a ) @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(911,plain,
( ( ! [T_a: $i,V_c: $i,V_p: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_c @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(912,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(913,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(914,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(915,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(916,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(917,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(918,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(919,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(920,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(921,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(922,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(923,plain,
( ( ! [T_a: $i,V_q1: $i,V_q2: $i,V_x: $i,V_y: $i,V_r2: $i,V_r1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q1 = V_q2 )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q2 @ V_r2 @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q1 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(924,plain,
( ( ! [T_a: $i,V_r1: $i,V_r2: $i,V_x: $i,V_y: $i,V_q2: $i,V_q1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r1 = V_r2 )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q2 @ V_r2 @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q1 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(925,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(926,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(927,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(928,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(929,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(930,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(931,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(932,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(933,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(934,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_w @ V_z @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_w @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_w @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(935,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r = V_x )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(936,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(937,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(938,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(939,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(940,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_y @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(941,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(942,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(943,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(944,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(945,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(946,plain,
( ( ! [T_a: $i,V_q: $i,V_y: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(947,plain,
( ( ! [T_a: $i,V_r: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(948,plain,
( ( ! [T_a: $i,V_q: $i,V_x: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(949,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(950,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(951,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(952,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(953,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_k: $i,V_D: $i,V_t: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(954,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_t: $i,V_k: $i,V_D: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(955,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( V_a
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(956,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(957,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(958,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(959,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(960,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(961,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(962,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(963,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(964,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(965,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(966,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(967,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(968,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(969,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(970,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(971,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(972,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(973,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(974,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(975,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(976,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(977,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(978,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(979,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(980,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(981,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(982,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(983,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(984,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(985,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(986,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(987,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(988,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(989,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(990,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(991,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(992,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(993,plain,
( ( ! [T_a: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(994,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(995,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_Polynomial_OpCons @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(996,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(997,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(998,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(999,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1000,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= V_p ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1001,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1003,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1004,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1005,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a )
!= ( c_HOL_Otimes__class_Otimes @ V_b @ V_b @ T_a ) )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1007,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1008,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1009,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i,V_y: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1010,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_p @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1011,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_z @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1013,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1014,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1016,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1017,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1020,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1021,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1022,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ ( c_Polynomial_Opoly__gcd @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ ( c_Polynomial_Opoly__gcd @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ ( c_Polynomial_Opoly__gcd @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(1026,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1027,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(1028,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1029,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1030,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1031,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1032,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1033,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1034,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1035,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(1036,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(1037,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1038,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(1039,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1040,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(1041,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1042,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1043,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1044,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1045,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1046,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1047,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1049,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1050,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_r: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= V_r )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1051,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1052,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1053,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1055,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1056,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1057,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1058,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1059,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1060,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1061,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(1062,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1063,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(1064,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_c @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1065,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ V_a @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1066,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(1067,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1068,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(1069,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_q_H: $i,V_r_H: $i,V_r: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q_H @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_r_H @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_q @ V_z @ V_q_H @ V_r_H @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= V_y )
| ( V_x
= ( c_HOL_Ouminus__class_Ouminus @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1071,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(1072,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_a @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1073,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1074,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(1075,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(1076,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(1077,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(1078,plain,
( ( ! [T_a: $i,V_q: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= V_q ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= V_p ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1080,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(1081,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(1082,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1085,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1086,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(1087,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1088,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1089,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1090,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1091,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1092,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1093,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1097,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1098,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1099,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1100,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1101,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(1102,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(1104,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(1105,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(1106,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(1107,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(1108,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1110,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(1111,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(1113,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1114,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ V_p @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_p
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ V_u @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a )
= V_u ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1116,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Polynomial_Osmult @ V_a @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1117,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(1118,plain,
( ( ! [T_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(1119,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(1122,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(1123,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(1124,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(1125,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(1126,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1128,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ V_x @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(1131,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(1134,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_b @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_a_H @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1137,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(1138,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1139,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(1140,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(1142,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= V_q )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1144,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(1145,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(1146,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(1147,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ V_n @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(1148,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(1149,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(1150,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(1151,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(1152,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1155,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(1156,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(1159,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(1160,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(1163,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(1164,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(1165,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_n @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(1166,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(1167,plain,
( ( ! [T_a: $i,V_m: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(1168,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(1169,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(1170,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_z @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= V_y ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(1171,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(1172,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(1173,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(1174,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1175,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(1176,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(1177,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(1178,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(1179,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a )
= ( c_Polynomial_Opoly__gcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1180,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(1181,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(1182,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(1183,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_z @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1184,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(1185,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1186,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(1187,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(1188,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) @ V_b @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1189,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1190,plain,
( ( ! [T_a: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_q @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ V_q @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(1191,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(1192,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_c @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(1193,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1195,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1196,plain,
( ( ! [T_a: $i,V_l: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_l @ T_a )
!= ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_l @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(1197,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_d @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1198,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(1199,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1200,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1201,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(1202,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1203,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_x @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1204,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(1205,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_q
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(1206,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(1207,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(1208,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1209,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1210,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1211,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1212,plain,
( ( ! [T_a: $i,V_k: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1213,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_x @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Polynomial_Opoly__gcd @ V_x @ V_y @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1214,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1215,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1216,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_p @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1217,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1218,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1219,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1220,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1221,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(1222,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(1223,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(1224,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(1225,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_p @ T_a )
= V_p ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(1226,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(1227,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(1228,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(1229,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1230,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1231,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(1232,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(1233,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1234,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1235,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(1236,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1237,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1238,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1239,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1240,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1241,plain,
( ( ! [T_a: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_p @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1242,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i,V_q: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_Polynomial_Opdivmod__rel @ V_x @ V_y @ V_q @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1243,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1244,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1245,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1246,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1247,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(1248,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(1249,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ V_a @ V_x @ T_a ) @ V_y @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(1250,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(1251,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(1252,plain,
( ( ! [T_a: $i,V_b: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1253,plain,
( ( ! [T_a: $i,V_p: $i,V_q: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(1254,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(1255,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(1256,plain,
( ( ! [T_a: $i,V_p: $i,V_a: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_p @ ( c_Polynomial_Osmult @ V_a @ V_q @ T_a ) @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(1257,plain,
( ( ! [T_a: $i,V_a: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ V_a @ V_p @ T_a ) @ V_q @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_Osmult @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ ( tc_Polynomial_Opoly @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(1258,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ v_q @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(1259,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_p: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_a )
| ( ( c_Polynomial_Osmult @ V_a @ ( c_Polynomial_Osmult @ V_b @ V_p @ T_a ) @ T_a )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_p @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(1260,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_q @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1261,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ v_q @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(1262,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(1263,plain,
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1264,plain,
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(1265,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(1266,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1267,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(1268,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1269,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(1270,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(1271,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(1272,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1273,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(1274,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(1275,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(1276,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(1277,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(1278,plain,
( ( class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(1279,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(1280,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1281,plain,
( ( class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1282,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(1283,plain,
( ( class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(1284,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1285,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(1286,plain,
( ( class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(1287,plain,
( ( class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(1288,plain,
( ( class_Ring__and__Field_Oring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(1289,plain,
( ( class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(1290,plain,
( ( class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1291,plain,
( ( class_Int_Onumber__ring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1292,plain,
( ( class_Power_Opower @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(1293,plain,
( ( class_HOL_Ozero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(1294,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(1295,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(1296,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(1297,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(1298,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(1299,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(1300,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(1301,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(1302,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(1303,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(1304,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(1305,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(1306,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(1307,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(1308,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(1309,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(1310,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(1311,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(1312,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(1313,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(1314,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(1315,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(1316,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(1317,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(1318,plain,
( ( ! [T_1: $i] :
( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(1319,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(1320,plain,
( ( ! [T_1: $i] :
( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ofield @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(1321,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(1322,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Oidom @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(1323,plain,
( ( ! [T_1: $i] :
( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(1324,plain,
( ( ! [T_1: $i] :
( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ofield @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(1325,plain,
( ( ! [T_1: $i] :
( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(1326,plain,
( ( ! [T_1: $i] :
( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(1327,plain,
( ( ! [T_1: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ T_1 ) )
| ~ ( class_HOL_Ozero @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(1328,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[886]) ).
thf(1329,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(1330,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1105]) ).
thf(1331,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Divides_Osemiring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1109]) ).
thf(1332,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[912]) ).
thf(1333,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[996]) ).
thf(1334,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1146]) ).
thf(1335,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX4 @ SX0 ) @ SX0 ) )
| ( SX3 = SX4 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(1336,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_HOL_Ozero @ SX0 )
| ( ( c_Polynomial_OpCons @ SX1 @ SX2 @ SX0 )
!= ( c_Polynomial_OpCons @ SX3 @ SX4 @ SX0 ) )
| ( SX2 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1337,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1338,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SX0 )
| ( ( c_HOL_Oabs__class_Oabs @ SX1 @ SX0 )
!= ( c_HOL_Oabs__class_Oabs @ SX2 @ SX0 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1196]) ).
thf(1339,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ( ( c_Polynomial_Opoly @ SX1 @ ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SX2 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SX0 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) @ SX0 ) @ SX0 ) @ SX1 @ ( tc_Polynomial_Opoly @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1340,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(1341,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ SX3 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) @ SX5 @ SX0 ) )
| ( SX3
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 ) @ SX5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1125]) ).
thf(1342,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Divides_Osemiring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ SX4 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX5 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SX5 @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1151]) ).
thf(1343,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1344,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SX0 )
| ( ( c_Polynomial_Osmult @ SX1 @ SX2 @ SX0 )
!= ( c_Polynomial_OpCons @ SX3 @ SX2 @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1345,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1106]) ).
thf(1346,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ( ( c_Polynomial_Opoly__gcd @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[977]) ).
thf(1347,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1059]) ).
thf(1348,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[933]) ).
thf(1349,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(1350,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SX1 @ SX2 @ SX0 ) @ ( c_Polynomial_OpCons @ SX3 @ SX2 @ SX0 ) @ ( tc_Polynomial_Opoly @ SX0 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(1351,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1110]) ).
thf(1352,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(1353,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX0 ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1149]) ).
thf(1354,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_HOL_Ozero @ SX0 )
| ( ( c_Polynomial_OpCons @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(1355,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1104]) ).
thf(1356,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
!= SX1 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[978]) ).
thf(1357,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) )
| ( SX1
= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1006]) ).
thf(1358,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(1359,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Divides_Oring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ SX4 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX5 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SX5 @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1169]) ).
thf(1360,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_HOL_Ozero @ SX0 )
| ( ( c_Polynomial_OpCons @ SX1 @ SX2 @ SX0 )
!= ( c_Polynomial_OpCons @ SX3 @ SX4 @ SX0 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1361,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(1362,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(1363,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ( ( c_Polynomial_Osmult @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1114]) ).
thf(1364,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX3 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1049]) ).
thf(1365,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1057]) ).
thf(1366,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ SX3 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) @ SX5 @ SX0 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX1 @ SX4 @ SX0 ) @ SX2 @ SX0 ) @ SX3 @ SX0 )
= SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1124]) ).
thf(1367,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1058]) ).
thf(1368,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_Polynomial_Osmult @ SX2 @ SX3 @ SX0 ) @ ( tc_Polynomial_Opoly @ SX0 ) )
!= ( c_Polynomial_OpCons @ SX4 @ SX3 @ SX0 ) )
| ( SX4
= ( c_Polynomial_Opoly @ SX1 @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(1369,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX0 ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(1370,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Oone__class_Oone @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1371,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ( ( c_Polynomial_Opoly @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SX0 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) @ SX0 ) @ SX0 ) @ SX1 @ ( tc_Polynomial_Opoly @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1372,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ( ( c_Polynomial_Opoly__gcd @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[976]) ).
thf(1373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Divides_Oring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1136]) ).
thf(1374,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Oplus__class_Oplus @ SX2 @ SX3 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX2 @ SX4 @ SX0 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1115]) ).
thf(1375,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SX0 )
| ( ( c_HOL_Oabs__class_Oabs @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1185]) ).
thf(1376,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Oplus__class_Oplus @ SX2 @ SX3 @ SX0 ) @ SX0 )
!= SX2 )
| ( SX1
= ( c_HOL_Ouminus__class_Ouminus @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1070]) ).
thf(1377,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Divides_Osemiring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ SX4 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX5 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SX5 @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1143]) ).
thf(1378,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1048]) ).
thf(1379,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( SX1
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1380,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
!= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[921]) ).
thf(1381,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_HOL_Ozero @ SX0 )
| ( ( c_Polynomial_OpCons @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SX0 ) ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(1382,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SX0 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
!= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1383,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ v_p @ ( c_Polynomial_Osmult @ v_a @ v_q @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(1384,plain,
! [SV1: $i] :
( ( ! [SY1248: $i,SY1249: $i,SY1250: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV1 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ SY1248 @ SY1249 @ SV1 ) @ SY1250 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SY1248 @ ( c_HOL_Otimes__class_Otimes @ SY1250 @ ( c_Polynomial_Opoly @ SY1249 @ SY1250 @ SV1 ) @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1385,plain,
! [SV2: $i] :
( ( ! [SY1251: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV2 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV2 ) ) @ SY1251 @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1386,plain,
! [SV3: $i] :
( ( ! [SY1252: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV3 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV3 ) ) @ SY1252 @ SV3 )
= ( c_HOL_Ozero__class_Ozero @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1387,plain,
! [SV4: $i] :
( ( ! [SY1253: $i,SY1254: $i,SY1255: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV4 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ SY1253 @ SY1254 @ SV4 ) @ SY1255 @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ SY1253 @ ( c_Polynomial_Opoly @ SY1254 @ SY1255 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1388,plain,
! [SV5: $i] :
( ( ! [SY1256: $i,SY1257: $i,SY1258: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV5 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ SY1256 @ SY1257 @ ( tc_Polynomial_Opoly @ SV5 ) ) @ SY1258 @ SV5 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ SY1256 @ SY1258 @ SV5 ) @ ( c_Polynomial_Opoly @ SY1257 @ SY1258 @ SV5 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1389,plain,
! [SV6: $i] :
( ( ! [SY1259: $i,SY1260: $i,SY1261: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV6 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ SY1259 @ SY1260 @ ( tc_Polynomial_Opoly @ SV6 ) ) @ SY1261 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ SY1259 @ SY1261 @ SV6 ) @ ( c_Polynomial_Opoly @ SY1260 @ SY1261 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1390,plain,
! [SV7: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV7 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ SY1262 @ ( tc_Polynomial_Opoly @ SV7 ) ) @ SY1263 @ SV7 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ SY1262 @ SY1263 @ SV7 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1391,plain,
! [SV8: $i] :
( ( ! [SY1264: $i,SY1265: $i,SY1266: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV8 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ SY1264 @ SY1265 @ ( tc_Polynomial_Opoly @ SV8 ) ) @ SY1266 @ SV8 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ SY1264 @ SY1266 @ SV8 ) @ ( c_Polynomial_Opoly @ SY1265 @ SY1266 @ SV8 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1392,plain,
! [SV9: $i] :
( ( ! [SY1267: $i,SY1268: $i,SY1269: $i,SY1270: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV9 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SY1267 @ SY1268 @ SV9 ) @ ( c_Polynomial_OpCons @ SY1269 @ SY1270 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SY1267 @ SY1269 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SY1268 @ SY1270 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1393,plain,
! [SV10: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV10 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ SY1271 @ SY1272 @ SV10 ) @ ( tc_Polynomial_Opoly @ SV10 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SY1271 @ SV10 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1272 @ ( tc_Polynomial_Opoly @ SV10 ) ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1394,plain,
! [SV11: $i] :
( ( ! [SY1273: $i,SY1274: $i,SY1275: $i,SY1276: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SY1273 @ SY1274 @ SV11 ) @ ( c_Polynomial_OpCons @ SY1275 @ SY1276 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SY1273 @ SY1275 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SY1274 @ SY1276 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1395,plain,
! [SV12: $i] :
( ( ! [SY1277: $i,SY1278: $i,SY1279: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV12 )
| ( ( c_Polynomial_Osmult @ SY1277 @ ( c_Polynomial_OpCons @ SY1278 @ SY1279 @ SV12 ) @ SV12 )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ SY1277 @ SY1278 @ SV12 ) @ ( c_Polynomial_Osmult @ SY1277 @ SY1279 @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1396,plain,
! [SV13: $i] :
( ( ~ ( class_HOL_Ozero @ SV13 )
| ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV13 ) ) @ SV13 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1397,plain,
! [SV14: $i] :
( ( ! [SY1280: $i,SY1281: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV14 )
| ( ( c_Polynomial_Opoly @ SY1280 @ SY1281 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SY1281 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SY1280 @ ( tc_Polynomial_Opoly @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1398,plain,
! [SV15: $i] :
( ( ! [SY1282: $i,SY1283: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV15 )
| ( ( c_Polynomial_Opoly @ SY1282 @ ( c_HOL_Ouminus__class_Ouminus @ SY1283 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SY1283 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SY1282 @ ( tc_Polynomial_Opoly @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1399,plain,
! [SV16: $i] :
( ( ! [SY1284: $i,SY1285: $i] :
( ~ ( class_Divides_Osemiring__div @ SV16 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1284 @ SY1285 @ SV16 ) @ SY1284 @ SV16 )
= SY1285 )
| ( SY1284
= ( c_HOL_Ozero__class_Ozero @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1400,plain,
! [SV17: $i] :
( ( ! [SY1286: $i,SY1287: $i] :
( ~ ( class_Divides_Osemiring__div @ SV17 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1286 @ SY1287 @ SV17 ) @ SY1287 @ SV17 )
= SY1286 )
| ( SY1287
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1401,plain,
! [SV18: $i] :
( ( ! [SY1288: $i,SY1289: $i,SY1290: $i,SY1291: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1288 @ SY1289 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SY1290 @ SY1291 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1288 @ SY1290 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SY1289 @ SY1291 @ SV18 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1402,plain,
! [SV19: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i,SY1295: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1292 @ SY1293 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SY1294 @ SY1295 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SY1292 @ ( c_HOL_Otimes__class_Otimes @ SY1293 @ ( c_HOL_Otimes__class_Otimes @ SY1294 @ SY1295 @ SV19 ) @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1403,plain,
! [SV20: $i] :
( ( ! [SY1296: $i,SY1297: $i,SY1298: $i,SY1299: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1296 @ SY1297 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SY1298 @ SY1299 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SY1298 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1296 @ SY1297 @ SV20 ) @ SY1299 @ SV20 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1404,plain,
! [SV21: $i] :
( ( ! [SY1300: $i,SY1301: $i,SY1302: $i,SY1303: $i,SY1304: $i,SY1305: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SY1300 = SY1301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1302 @ SY1303 @ SY1301 @ SY1304 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1302 @ SY1303 @ SY1300 @ SY1305 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1405,plain,
! [SV22: $i] :
( ( ! [SY1306: $i,SY1307: $i,SY1308: $i,SY1309: $i,SY1310: $i,SY1311: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SY1306 = SY1307 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1308 @ SY1309 @ SY1310 @ SY1307 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1308 @ SY1309 @ SY1311 @ SY1306 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1406,plain,
! [SV23: $i] :
( ( ! [SY1312: $i,SY1313: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SY1312 @ SV23 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SY1313 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1407,plain,
! [SV24: $i] :
( ( ! [SY1314: $i,SY1315: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV24 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1314 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ ( c_HOL_Otimes__class_Otimes @ SY1315 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1408,plain,
! [SV25: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV25 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) @ SV25 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1409,plain,
! [SV26: $i] :
( ( ! [SY1316: $i,SY1317: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV26 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY1316 @ SY1317 @ SV26 ) @ SV26 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY1316 @ SV26 ) @ ( c_HOL_Oabs__class_Oabs @ SY1317 @ SV26 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1410,plain,
! [SV27: $i] :
( ( ! [SY1318: $i,SY1319: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV27 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SY1318 @ SY1319 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SY1318 @ SV27 ) @ SY1319 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1411,plain,
! [SV28: $i] :
( ( ! [SY1320: $i,SY1321: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV28 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SY1320 @ SY1321 @ SV28 ) @ SV28 )
= ( c_HOL_Otimes__class_Otimes @ SY1320 @ ( c_HOL_Ouminus__class_Ouminus @ SY1321 @ SV28 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1412,plain,
! [SV29: $i] :
( ( ! [SY1322: $i,SY1323: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1322 @ ( c_HOL_Otimes__class_Otimes @ SY1322 @ SY1323 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SY1322 @ SY1323 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1413,plain,
! [SV30: $i] :
( ( ! [SY1324: $i,SY1325: $i,SY1326: $i,SY1327: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1324 @ SY1325 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SY1326 @ SY1327 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1324 @ SY1326 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SY1325 @ SY1327 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1327 @ SY1326 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1325 @ SY1324 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1414,plain,
! [SV31: $i] :
( ( ! [SY1328: $i,SY1329: $i,SY1330: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV31 )
| ( SY1328 = SY1329 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1329 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SY1330 @ SY1328 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1415,plain,
! [SV32: $i] :
( ( ! [SY1331: $i,SY1332: $i] :
( ~ ( class_Divides_Osemiring__div @ SV32 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SY1331 @ SV32 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SY1332 @ SV32 ) @ SV32 )
= ( c_HOL_Ozero__class_Ozero @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1416,plain,
! [SV33: $i] :
( ( ! [SY1333: $i,SY1334: $i] :
( ~ ( class_Divides_Osemiring__div @ SV33 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1333 @ SY1334 @ SV33 ) @ SY1333 @ SV33 )
= ( c_Divides_Odiv__class_Omod @ SY1334 @ SY1333 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1417,plain,
! [SV34: $i] :
( ( ! [SY1335: $i,SY1336: $i] :
( ~ ( class_Divides_Osemiring__div @ SV34 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1335 @ SY1336 @ SV34 ) @ SY1336 @ SV34 )
= ( c_Divides_Odiv__class_Omod @ SY1335 @ SY1336 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1418,plain,
! [SV35: $i] :
( ( ! [SY1337: $i,SY1338: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1337 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1337 @ SV35 ) @ SY1338 @ SV35 ) @ SV35 )
= SY1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1419,plain,
! [SV36: $i] :
( ( ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV36 )
| ( ( c_Divides_Odiv__class_Omod @ SY1339 @ ( c_HOL_Otimes__class_Otimes @ SY1340 @ SY1341 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1340 @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ SY1339 @ SY1340 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ SY1341 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( c_Divides_Odiv__class_Omod @ SY1339 @ SY1340 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1420,plain,
! [SV37: $i] :
( ( ! [SY1342: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV37 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1342 @ SY1342 @ SV37 )
= SY1342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1421,plain,
! [SV38: $i] :
( ( ! [SY1343: $i,SY1344: $i,SY1345: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV38 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1343 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SY1344 @ SY1345 @ SV38 )
| ( SY1344
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1422,plain,
! [SV39: $i] :
( ( ! [SY1346: $i,SY1347: $i,SY1348: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV39 )
| ( SY1346
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SY1347 @ SY1346 @ SY1348 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1423,plain,
! [SV40: $i] :
( ( ! [SY1349: $i,SY1350: $i,SY1351: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV40 )
| ( SY1349
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SY1350 @ SY1351 @ SY1349 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1424,plain,
! [SV41: $i] :
( ( ! [SY1352: $i,SY1353: $i,SY1354: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV41 )
| ( SY1352
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1353 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SY1352 @ SY1354 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1425,plain,
! [SV42: $i] :
( ( ! [SY1355: $i,SY1356: $i,SY1357: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SY1355 @ SY1356 @ SV42 ) @ SY1357 @ SV42 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY1355 @ SY1357 @ SV42 ) @ ( c_Power_Opower__class_Opower @ SY1356 @ SY1357 @ SV42 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1426,plain,
! [SV43: $i] :
( ( ! [SY1358: $i,SY1359: $i,SY1360: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV43 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SY1358 @ SY1359 @ SV43 ) @ SY1360 @ SV43 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY1358 @ SY1360 @ SV43 ) @ ( c_Power_Opower__class_Opower @ SY1359 @ SY1360 @ SV43 ) @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1427,plain,
! [SV44: $i] :
( ( ! [SY1361: $i,SY1362: $i,SY1363: $i] :
( ~ ( class_Divides_Osemiring__div @ SV44 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1361 @ ( c_Divides_Odiv__class_Omod @ SY1362 @ SY1363 @ SV44 ) @ SV44 ) @ SY1363 @ SV44 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1361 @ SY1362 @ SV44 ) @ SY1363 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1428,plain,
! [SV45: $i] :
( ( ! [SY1364: $i,SY1365: $i,SY1366: $i] :
( ~ ( class_Divides_Osemiring__div @ SV45 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY1364 @ SY1365 @ SV45 ) @ SY1366 @ SV45 ) @ SY1365 @ SV45 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1364 @ SY1366 @ SV45 ) @ SY1365 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1429,plain,
! [SV46: $i] :
( ( ! [SY1367: $i,SY1368: $i,SY1369: $i,SY1370: $i,SY1371: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV46 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1367 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY1368 @ ( c_HOL_Otimes__class_Otimes @ SY1369 @ SY1370 @ SV46 ) @ SV46 ) @ SY1371 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1367 @ ( c_HOL_Oplus__class_Oplus @ SY1368 @ SY1371 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1367 @ SY1370 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1430,plain,
! [SV47: $i] :
( ( ! [SY1372: $i,SY1373: $i,SY1374: $i,SY1375: $i,SY1376: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV47 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1372 @ ( c_HOL_Oplus__class_Oplus @ SY1373 @ SY1374 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1372 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY1373 @ ( c_HOL_Otimes__class_Otimes @ SY1375 @ SY1376 @ SV47 ) @ SV47 ) @ SY1374 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1372 @ SY1376 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1431,plain,
! [SV48: $i] :
( ( ! [SY1377: $i,SY1378: $i] :
( ~ ( class_Divides_Osemiring__div @ SV48 )
| ( SY1377
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1377 @ SY1378 @ SV48 ) @ SY1378 @ SV48 ) @ ( c_Divides_Odiv__class_Omod @ SY1377 @ SY1378 @ SV48 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1432,plain,
! [SV49: $i] :
( ( ! [SY1379: $i,SY1380: $i] :
( ~ ( class_Divides_Osemiring__div @ SV49 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1379 @ SY1380 @ SV49 ) @ SY1380 @ SV49 ) @ ( c_Divides_Odiv__class_Omod @ SY1379 @ SY1380 @ SV49 ) @ SV49 )
= SY1379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1433,plain,
! [SV50: $i] :
( ( ! [SY1381: $i,SY1382: $i] :
( ~ ( class_Divides_Osemiring__div @ SV50 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1381 @ ( c_Divides_Odiv__class_Odiv @ SY1382 @ SY1381 @ SV50 ) @ SV50 ) @ ( c_Divides_Odiv__class_Omod @ SY1382 @ SY1381 @ SV50 ) @ SV50 )
= SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1434,plain,
! [SV51: $i] :
( ( ! [SY1383: $i] :
( ~ ( class_Int_Onumber__ring @ SV51 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY1383 @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV51 ) @ SY1383 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1435,plain,
! [SV52: $i] :
( ( ! [SY1384: $i,SY1385: $i] :
( ~ ( class_Divides_Oring__div @ SV52 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1384 @ ( c_HOL_Ouminus__class_Ouminus @ SY1385 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SY1384 @ SY1385 @ SV52 ) @ SV52 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1385 @ SY1384 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1436,plain,
! [SV53: $i] :
( ( ! [SY1386: $i,SY1387: $i] :
( ~ ( class_Divides_Oring__div @ SV53 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SY1386 @ SV53 ) @ SY1387 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SY1386 @ SY1387 @ SV53 ) @ SV53 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1387 @ SY1386 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1437,plain,
! [SV54: $i] :
( ( ! [SY1388: $i,SY1389: $i,SY1390: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1388 @ SY1389 @ SV54 ) @ SY1390 @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SY1388 @ ( c_HOL_Otimes__class_Otimes @ SY1389 @ SY1390 @ SV54 ) @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1438,plain,
! [SV55: $i] :
( ( ! [SY1391: $i,SY1392: $i,SY1393: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1391 @ SY1392 @ SV55 ) @ SY1393 @ SV55 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1391 @ SY1393 @ SV55 ) @ SY1392 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1439,plain,
! [SV56: $i] :
( ( ! [SY1394: $i,SY1395: $i,SY1396: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1394 @ SY1395 @ SV56 ) @ SY1396 @ SV56 )
= ( c_HOL_Otimes__class_Otimes @ SY1394 @ ( c_HOL_Otimes__class_Otimes @ SY1395 @ SY1396 @ SV56 ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1440,plain,
! [SV57: $i] :
( ( ! [SY1397: $i,SY1398: $i,SY1399: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1397 @ ( c_HOL_Otimes__class_Otimes @ SY1398 @ SY1399 @ SV57 ) @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1397 @ SY1398 @ SV57 ) @ SY1399 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1441,plain,
! [SV58: $i] :
( ( ! [SY1400: $i,SY1401: $i,SY1402: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV58 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1400 @ ( c_HOL_Otimes__class_Otimes @ SY1401 @ SY1402 @ SV58 ) @ SV58 )
= ( c_HOL_Otimes__class_Otimes @ SY1401 @ ( c_HOL_Otimes__class_Otimes @ SY1400 @ SY1402 @ SV58 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1442,plain,
! [SV59: $i] :
( ( ! [SY1403: $i,SY1404: $i,SY1405: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1403 @ ( c_HOL_Otimes__class_Otimes @ SY1404 @ SY1405 @ SV59 ) @ SV59 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1403 @ SY1404 @ SV59 ) @ SY1405 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1443,plain,
! [SV60: $i] :
( ( ! [SY1406: $i,SY1407: $i,SY1408: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1406 @ SY1407 @ SV60 ) @ SY1408 @ SV60 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1406 @ SY1408 @ SV60 ) @ ( c_HOL_Otimes__class_Otimes @ SY1407 @ SY1408 @ SV60 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1444,plain,
! [SV61: $i] :
( ( ! [SY1409: $i,SY1410: $i,SY1411: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV61 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1409 @ ( c_HOL_Oplus__class_Oplus @ SY1410 @ SY1411 @ SV61 ) @ SV61 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1409 @ SY1410 @ SV61 ) @ ( c_HOL_Otimes__class_Otimes @ SY1409 @ SY1411 @ SV61 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1445,plain,
! [SV62: $i] :
( ( ! [SY1412: $i,SY1413: $i,SY1414: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV62 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1412 @ ( c_HOL_Oplus__class_Oplus @ SY1413 @ SY1414 @ SV62 ) @ SV62 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1412 @ SY1413 @ SV62 ) @ ( c_HOL_Otimes__class_Otimes @ SY1412 @ SY1414 @ SV62 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1446,plain,
! [SV63: $i] :
( ( ! [SY1415: $i,SY1416: $i,SY1417: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV63 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1415 @ SY1416 @ SV63 ) @ SY1417 @ SV63 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1415 @ SY1417 @ SV63 ) @ ( c_HOL_Otimes__class_Otimes @ SY1416 @ SY1417 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1447,plain,
! [SV64: $i] :
( ( ! [SY1418: $i,SY1419: $i,SY1420: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV64 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1418 @ SY1419 @ SV64 ) @ SY1420 @ SV64 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1418 @ SY1420 @ SV64 ) @ ( c_HOL_Otimes__class_Otimes @ SY1419 @ SY1420 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1448,plain,
! [SV65: $i] :
( ( ! [SY1421: $i,SY1422: $i,SY1423: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV65 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1421 @ SY1422 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ SY1423 @ ( tc_Polynomial_Opoly @ SV65 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1421 @ SY1423 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY1422 @ SY1423 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( tc_Polynomial_Opoly @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1449,plain,
! [SV66: $i] :
( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1424 @ ( c_HOL_Oplus__class_Oplus @ SY1425 @ SY1426 @ SV66 ) @ SV66 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1424 @ SY1425 @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SY1424 @ SY1426 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1450,plain,
! [SV67: $i] :
( ( ! [SY1427: $i,SY1428: $i,SY1429: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1427 @ SY1428 @ SV67 ) @ SY1429 @ SV67 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1427 @ SY1429 @ SV67 ) @ ( c_HOL_Otimes__class_Otimes @ SY1428 @ SY1429 @ SV67 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1451,plain,
! [SV68: $i] :
( ( ! [SY1430: $i,SY1431: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV68 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY1430 @ SY1431 @ SV68 ) @ SV68 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY1431 @ SY1430 @ SV68 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1452,plain,
! [SV69: $i] :
( ( ! [SY1432: $i,SY1433: $i] :
( ~ ( class_Divides_Osemiring__div @ SV69 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SY1432 @ SY1433 @ SV69 ) @ SY1432 @ SV69 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SY1433 @ SY1432 @ SV69 ) @ ( c_HOL_Oone__class_Oone @ SV69 ) @ SV69 ) )
| ( SY1432
= ( c_HOL_Ozero__class_Ozero @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1453,plain,
! [SV70: $i] :
( ( ! [SY1434: $i,SY1435: $i] :
( ~ ( class_Divides_Osemiring__div @ SV70 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SY1434 @ SY1435 @ SV70 ) @ SY1435 @ SV70 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SY1434 @ SY1435 @ SV70 ) @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV70 ) )
| ( SY1435
= ( c_HOL_Ozero__class_Ozero @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1454,plain,
! [SV71: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV71 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ SV71 ) @ SV71 )
= ( c_HOL_Oone__class_Oone @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1455,plain,
! [SV72: $i] :
( ( ! [SY1436: $i,SY1437: $i,SY1438: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1436 @ SY1437 @ SV72 ) @ ( c_HOL_Otimes__class_Otimes @ SY1438 @ SY1437 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1436 @ SY1438 @ SV72 ) @ SY1437 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1456,plain,
! [SV73: $i] :
( ( ! [SY1439: $i,SY1440: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV73 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SY1439 @ SV73 ) @ SY1440 @ SV73 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SY1439 @ SY1440 @ SV73 ) @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1457,plain,
! [SV74: $i] :
( ( ! [SY1441: $i,SY1442: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV74 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SY1441 @ SV74 ) @ SY1442 @ SV74 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SY1441 @ SY1442 @ SV74 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1458,plain,
! [SV75: $i] :
( ( ! [SY1443: $i,SY1444: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV75 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1443 @ ( c_HOL_Ouminus__class_Ouminus @ SY1444 @ SV75 ) @ SV75 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SY1443 @ SY1444 @ SV75 ) @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1459,plain,
! [SV76: $i] :
( ( ! [SY1445: $i,SY1446: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV76 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1445 @ ( c_HOL_Ouminus__class_Ouminus @ SY1446 @ SV76 ) @ SV76 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SY1445 @ SY1446 @ SV76 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1460,plain,
! [SV77: $i] :
( ( ! [SY1447: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV77 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SY1447 @ SV77 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1447 @ SV77 ) @ SV77 )
= ( c_HOL_Otimes__class_Otimes @ SY1447 @ SY1447 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1461,plain,
! [SV78: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV78 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SY1448 @ SV78 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1449 @ SV78 ) @ SV78 )
= ( c_HOL_Otimes__class_Otimes @ SY1448 @ SY1449 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1462,plain,
! [SV79: $i] :
( ( ! [SY1450: $i,SY1451: $i,SY1452: $i] :
( ~ ( class_Divides_Osemiring__div @ SV79 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1450 @ SY1451 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SY1450 @ SY1452 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SY1451 @ SY1452 @ SV79 ) )
| ( SY1450
= ( c_HOL_Ozero__class_Ozero @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1463,plain,
! [SV80: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i] :
( ~ ( class_Divides_Osemiring__div @ SV80 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1453 @ SY1454 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SY1455 @ SY1454 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SY1453 @ SY1455 @ SV80 ) )
| ( SY1454
= ( c_HOL_Ozero__class_Ozero @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1464,plain,
! [SV81: $i] :
( ( ! [SY1456: $i,SY1457: $i] :
( ~ ( class_Divides_Oring__div @ SV81 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SY1456 @ SV81 ) @ SY1457 @ SV81 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SY1456 @ SY1457 @ SV81 ) @ SV81 ) @ SY1457 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1465,plain,
! [SV82: $i] :
( ( ! [SY1458: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV82 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SY1458 @ SV82 )
= ( c_HOL_Ouminus__class_Ouminus @ SY1458 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1466,plain,
! [SV83: $i] :
( ( ! [SY1459: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV83 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV83 ) ) @ SY1459 @ ( tc_Polynomial_Opoly @ SV83 ) )
= ( c_HOL_Ouminus__class_Ouminus @ SY1459 @ ( tc_Polynomial_Opoly @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1467,plain,
! [SV84: $i] :
( ( ! [SY1460: $i,SY1461: $i,SY1462: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ SY1460 @ SY1461 @ SV84 ) @ SY1462 @ ( tc_Polynomial_Opoly @ SV84 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SY1460 @ SY1462 @ SV84 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( c_HOL_Otimes__class_Otimes @ SY1461 @ SY1462 @ ( tc_Polynomial_Opoly @ SV84 ) ) @ SV84 ) @ ( tc_Polynomial_Opoly @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1468,plain,
! [SV85: $i] :
( ( ! [SY1463: $i,SY1464: $i,SY1465: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV85 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1463 @ ( c_Polynomial_OpCons @ SY1464 @ SY1465 @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SY1464 @ SY1463 @ SV85 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_HOL_Otimes__class_Otimes @ SY1463 @ SY1465 @ ( tc_Polynomial_Opoly @ SV85 ) ) @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1469,plain,
! [SV86: $i] :
( ( ! [SY1466: $i] :
( ~ ( class_Divides_Osemiring__div @ SV86 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1466 @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1470,plain,
! [SV87: $i] :
( ( ! [SY1467: $i] :
( ~ ( class_Divides_Osemiring__div @ SV87 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SY1467 @ SV87 )
= ( c_HOL_Ozero__class_Ozero @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1471,plain,
! [SV88: $i] :
( ( ! [SY1468: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV88 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1468 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV88 ) ) @ ( tc_Polynomial_Opoly @ SV88 ) )
= SY1468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1472,plain,
! [SV89: $i] :
( ( ! [SY1469: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV89 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1469 @ SY1469 @ SV89 )
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1473,plain,
! [SV90: $i] :
( ( ! [SY1470: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV90 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1470 @ SY1470 @ SV90 )
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1474,plain,
! [SV91: $i] :
( ( ! [SY1471: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV91 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1471 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1475,plain,
! [SV92: $i] :
( ( ! [SY1472: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV92 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1472 @ SY1472 @ SV92 )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1476,plain,
! [SV93: $i] :
( ( ! [SY1473: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV93 )
| ~ ( class_Int_Onumber__ring @ SV93 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1473 @ SY1473 @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1477,plain,
! [SV94: $i] :
( ( ! [SY1474: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV94 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV94 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SY1474 @ SV94 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1478,plain,
! [SV95: $i] :
( ( ! [SY1475: $i,SY1476: $i,SY1477: $i,SY1478: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SY1475
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1476 @ SY1477 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SY1478 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1475 @ SY1477 @ SY1476 @ SY1478 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1479,plain,
! [SV96: $i] :
( ( ! [SY1479: $i,SY1480: $i,SY1481: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV96 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ SY1479 @ SY1480 @ SV96 ) @ SY1481 @ SV96 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SY1479 @ SY1481 @ SV96 ) @ ( c_Polynomial_Osmult @ SY1480 @ SY1481 @ SV96 ) @ ( tc_Polynomial_Opoly @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1480,plain,
! [SV97: $i] :
( ( ! [SY1482: $i,SY1483: $i,SY1484: $i,SY1485: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV97 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1482 @ SY1483 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1484 @ SY1482 @ SV97 ) @ SY1483 @ SV97 ) @ SY1485 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1484 @ SY1483 @ SV97 ) @ SY1485 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1481,plain,
! [SV98: $i] :
( ( ! [SY1486: $i,SY1487: $i,SY1488: $i] :
( ~ ( class_Divides_Osemiring__div @ SV98 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SY1486 @ SY1487 @ SV98 ) @ SY1488 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SY1486 @ SY1488 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SY1487 @ SY1488 @ SV98 ) @ SV98 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1488 @ SY1487 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1488 @ SY1486 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1482,plain,
! [SV99: $i] :
( ( ! [SY1489: $i,SY1490: $i,SY1491: $i] :
( ~ ( class_Divides_Osemiring__div @ SV99 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY1489 @ SY1490 @ SV99 ) @ SY1491 @ SV99 ) @ SY1490 @ SV99 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1489 @ SY1491 @ SV99 ) @ SY1490 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1483,plain,
! [SV100: $i] :
( ( ! [SY1492: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1492 @ ( c_HOL_Oone__class_Oone @ SV100 ) @ SV100 )
= SY1492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1484,plain,
! [SV101: $i] :
( ( ! [SY1493: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SY1493 @ SV101 )
= SY1493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1485,plain,
! [SV102: $i] :
( ( ! [SY1494: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV102 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SY1494 @ SV102 )
= SY1494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1486,plain,
! [SV103: $i] :
( ( ! [SY1495: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SY1495 @ SV103 )
= SY1495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1487,plain,
! [SV104: $i] :
( ( ! [SY1496: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV104 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1496 @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV104 )
= SY1496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1488,plain,
! [SV105: $i] :
( ( ! [SY1497: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV105 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SY1497 @ SV105 )
= SY1497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1489,plain,
! [SV106: $i] :
( ( ! [SY1498: $i,SY1499: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV106 )
| ( c_Polynomial_Opdivmod__rel @ SY1498 @ SY1499 @ ( c_Divides_Odiv__class_Odiv @ SY1498 @ SY1499 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ ( c_Divides_Odiv__class_Omod @ SY1498 @ SY1499 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1490,plain,
! [SV107: $i] :
( ( ! [SY1500: $i] :
( ~ ( class_Divides_Osemiring__div @ SV107 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SY1500 @ SV107 )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1491,plain,
! [SV108: $i] :
( ( ! [SY1501: $i,SY1502: $i,SY1503: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV108 )
| ~ ( class_Int_Onumber__ring @ SV108 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1501 @ SY1502 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY1501 @ SY1503 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1501 @ SY1503 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY1501 @ SY1502 @ SV108 ) @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1492,plain,
! [SV109: $i] :
( ( ! [SY1504: $i,SY1505: $i,SY1506: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV109 )
| ~ ( class_Int_Onumber__ring @ SV109 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1504 @ SY1505 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SY1504 @ SY1506 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1504 @ SY1506 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SY1504 @ SY1505 @ SV109 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1493,plain,
! [SV110: $i] :
( ( ! [SY1507: $i,SY1508: $i,SY1509: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV110 )
| ( ( c_Polynomial_Opoly__gcd @ SY1507 @ ( c_Polynomial_Opoly__gcd @ SY1508 @ SY1509 @ SV110 ) @ SV110 )
= ( c_Polynomial_Opoly__gcd @ SY1508 @ ( c_Polynomial_Opoly__gcd @ SY1507 @ SY1509 @ SV110 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1494,plain,
! [SV111: $i] :
( ( ! [SY1510: $i,SY1511: $i,SY1512: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV111 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ SY1510 @ SY1511 @ SV111 ) @ SY1512 @ SV111 )
= ( c_Polynomial_Opoly__gcd @ SY1510 @ ( c_Polynomial_Opoly__gcd @ SY1511 @ SY1512 @ SV111 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1495,plain,
! [SV112: $i] :
( ( ! [SY1513: $i,SY1514: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV112 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY1513 @ SY1514 @ SV112 ) @ SY1514 @ SV112 )
= SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1496,plain,
! [SV113: $i] :
( ( ! [SY1515: $i,SY1516: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV113 )
| ( ( c_Polynomial_Opoly__gcd @ SY1515 @ ( c_HOL_Ouminus__class_Ouminus @ SY1516 @ ( tc_Polynomial_Opoly @ SV113 ) ) @ SV113 )
= ( c_Polynomial_Opoly__gcd @ SY1515 @ SY1516 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1497,plain,
! [SV114: $i] :
( ( ! [SY1517: $i,SY1518: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV114 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ SY1517 @ ( tc_Polynomial_Opoly @ SV114 ) ) @ SY1518 @ SV114 )
= ( c_Polynomial_Opoly__gcd @ SY1517 @ SY1518 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1498,plain,
! [SV115: $i] :
( ( ! [SY1519: $i,SY1520: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1519 @ SY1520 @ SV115 )
= ( c_HOL_Otimes__class_Otimes @ SY1520 @ SY1519 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1499,plain,
! [SV116: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1500,plain,
! [SV117: $i] :
( ( ! [SY1521: $i,SY1522: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1521 @ SY1522 @ SV117 )
= ( c_HOL_Otimes__class_Otimes @ SY1522 @ SY1521 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1501,plain,
! [SV118: $i] :
( ( ! [SY1523: $i,SY1524: $i,SY1525: $i] :
( ~ ( class_Divides_Osemiring__div @ SV118 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1523 @ SY1524 @ SV118 ) @ SY1525 @ SV118 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY1523 @ SY1525 @ SV118 ) @ ( c_Divides_Odiv__class_Omod @ SY1524 @ SY1525 @ SV118 ) @ SV118 ) @ SY1525 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1502,plain,
! [SV119: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV119 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
= ( c_HOL_Ozero__class_Ozero @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1503,plain,
! [SV120: $i] :
( ( ! [SY1526: $i,SY1527: $i,SY1528: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV120 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1526 @ ( c_HOL_Oplus__class_Oplus @ SY1527 @ SY1528 @ SV120 ) @ SV120 )
= ( c_HOL_Oplus__class_Oplus @ SY1527 @ ( c_HOL_Oplus__class_Oplus @ SY1526 @ SY1528 @ SV120 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1504,plain,
! [SV121: $i] :
( ( ! [SY1529: $i,SY1530: $i,SY1531: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV121 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1529 @ SY1530 @ SV121 ) @ SY1531 @ SV121 )
= ( c_HOL_Oplus__class_Oplus @ SY1529 @ ( c_HOL_Oplus__class_Oplus @ SY1530 @ SY1531 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1505,plain,
! [SV122: $i] :
( ( ! [SY1532: $i,SY1533: $i,SY1534: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1532 @ ( c_HOL_Oplus__class_Oplus @ SY1533 @ SY1534 @ SV122 ) @ SV122 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1532 @ SY1533 @ SV122 ) @ SY1534 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1506,plain,
! [SV123: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV123 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1535 @ ( c_HOL_Oplus__class_Oplus @ SY1536 @ SY1537 @ SV123 ) @ SV123 )
= ( c_HOL_Oplus__class_Oplus @ SY1536 @ ( c_HOL_Oplus__class_Oplus @ SY1535 @ SY1537 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1507,plain,
! [SV124: $i] :
( ( ! [SY1538: $i,SY1539: $i,SY1540: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1538 @ SY1539 @ SV124 ) @ SY1540 @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ SY1538 @ ( c_HOL_Oplus__class_Oplus @ SY1539 @ SY1540 @ SV124 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1508,plain,
! [SV125: $i] :
( ( ! [SY1541: $i,SY1542: $i,SY1543: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1541 @ ( c_HOL_Oplus__class_Oplus @ SY1542 @ SY1543 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1541 @ SY1542 @ SV125 ) @ SY1543 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1509,plain,
! [SV126: $i] :
( ( ! [SY1544: $i,SY1545: $i,SY1546: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1544 @ SY1545 @ SV126 ) @ SY1546 @ SV126 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1544 @ SY1546 @ SV126 ) @ SY1545 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1510,plain,
! [SV127: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1547 @ ( c_HOL_Oplus__class_Oplus @ SY1548 @ SY1549 @ SV127 ) @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ SY1548 @ ( c_HOL_Oplus__class_Oplus @ SY1547 @ SY1549 @ SV127 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1511,plain,
! [SV128: $i] :
( ( ! [SY1550: $i,SY1551: $i,SY1552: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1550 @ SY1551 @ SV128 ) @ SY1552 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ SY1550 @ ( c_HOL_Oplus__class_Oplus @ SY1551 @ SY1552 @ SV128 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1512,plain,
! [SV129: $i] :
( ( ! [SY1553: $i,SY1554: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV129 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1553 @ ( c_HOL_Ouminus__class_Ouminus @ SY1554 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SY1553 @ SY1554 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1513,plain,
! [SV130: $i] :
( ( ! [SY1555: $i,SY1556: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV130 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SY1555 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ SY1556 @ ( tc_Polynomial_Opoly @ SV130 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SY1555 @ SY1556 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ ( tc_Polynomial_Opoly @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1514,plain,
! [SV131: $i] :
( ( ! [SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( class_Divides_Osemiring__div @ SV131 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1557 @ SY1558 @ SV131 ) @ SY1559 @ SV131 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1557 @ ( c_Divides_Odiv__class_Omod @ SY1558 @ SY1559 @ SV131 ) @ SV131 ) @ SY1559 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1515,plain,
! [SV132: $i] :
( ( ! [SY1560: $i,SY1561: $i,SY1562: $i] :
( ~ ( class_Divides_Osemiring__div @ SV132 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1560 @ SY1561 @ SV132 ) @ SY1562 @ SV132 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY1560 @ SY1562 @ SV132 ) @ SY1561 @ SV132 ) @ SY1562 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1516,plain,
! [SV133: $i] :
( ( ! [SY1563: $i,SY1564: $i,SY1565: $i,SY1566: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( ( c_Divides_Odiv__class_Omod @ SY1563 @ SY1564 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SY1565 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1563 @ SY1564 @ SY1566 @ SY1565 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1517,plain,
! [SV134: $i] :
( ( ! [SY1567: $i,SY1568: $i,SY1569: $i,SY1570: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV134 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY1567 @ SY1568 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SY1569 @ SY1570 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1567 @ SY1569 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SY1568 @ SY1570 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1567 @ SY1569 @ SV134 ) @ SY1570 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SY1569 @ ( c_HOL_Ominus__class_Ominus @ SY1568 @ SY1570 @ SV134 ) @ SV134 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1518,plain,
! [SV135: $i] :
( ( ! [SY1571: $i,SY1572: $i,SY1573: $i,SY1574: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1571 @ SY1572 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1573 @ SY1572 @ SV135 ) @ SY1574 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1571 @ SY1573 @ SV135 ) @ SY1572 @ SV135 ) @ SY1574 @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1519,plain,
! [SV136: $i] :
( ( ! [SY1575: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV136 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1575 @ SV136 ) @ SY1575 @ SV136 )
= ( c_HOL_Ozero__class_Ozero @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1520,plain,
! [SV137: $i] :
( ( ! [SY1576: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1576 @ SV137 ) @ SY1576 @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1521,plain,
! [SV138: $i] :
( ( ! [SY1577: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1577 @ ( c_HOL_Ouminus__class_Ouminus @ SY1577 @ SV138 ) @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1522,plain,
! [SV139: $i] :
( ( ! [SY1578: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV139 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1578 @ SV139 ) @ SY1578 @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1523,plain,
! [SV140: $i] :
( ( ! [SY1579: $i,SY1580: $i,SY1581: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV140 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1579 @ ( c_HOL_Ominus__class_Ominus @ SY1580 @ SY1581 @ SV140 ) @ SV140 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY1579 @ SY1580 @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SY1579 @ SY1581 @ SV140 ) @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1524,plain,
! [SV141: $i] :
( ( ! [SY1582: $i,SY1583: $i,SY1584: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV141 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1582 @ ( c_HOL_Ominus__class_Ominus @ SY1583 @ SY1584 @ SV141 ) @ SV141 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY1582 @ SY1583 @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SY1582 @ SY1584 @ SV141 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1525,plain,
! [SV142: $i] :
( ( ! [SY1585: $i,SY1586: $i,SY1587: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1585 @ SY1586 @ SV142 ) @ SY1587 @ SV142 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY1585 @ SY1587 @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY1586 @ SY1587 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1526,plain,
! [SV143: $i] :
( ( ! [SY1588: $i,SY1589: $i,SY1590: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV143 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1588 @ SY1589 @ SV143 ) @ SY1590 @ SV143 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY1588 @ SY1590 @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SY1589 @ SY1590 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1527,plain,
! [SV144: $i] :
( ( ! [SY1591: $i,SY1592: $i,SY1593: $i,SY1594: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV144 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY1591 @ SY1592 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SY1593 @ SY1594 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY1591 @ SY1593 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SY1592 @ SY1594 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1528,plain,
! [SV145: $i] :
( ( ! [SY1595: $i,SY1596: $i,SY1597: $i] :
( ~ ( class_Divides_Osemiring__div @ SV145 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1595 @ SY1596 @ SV145 ) @ SY1597 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1595 @ SY1597 @ SV145 ) @ SY1596 @ SV145 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1596 @ SY1595 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1529,plain,
! [SV146: $i] :
( ( ! [SY1598: $i,SY1599: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SY1598 @ SY1599 @ SV146 ) @ SV146 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SY1598 @ SV146 ) @ SY1599 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1530,plain,
! [SV147: $i] :
( ( ! [SY1600: $i,SY1601: $i,SY1602: $i] :
( ~ ( class_Divides_Osemiring__div @ SV147 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1600 @ SY1601 @ SV147 ) @ SY1602 @ SV147 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1600 @ ( c_Divides_Odiv__class_Omod @ SY1601 @ SY1602 @ SV147 ) @ SV147 ) @ SY1602 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1531,plain,
! [SV148: $i] :
( ( ! [SY1603: $i,SY1604: $i,SY1605: $i] :
( ~ ( class_Divides_Osemiring__div @ SV148 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1603 @ SY1604 @ SV148 ) @ SY1605 @ SV148 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY1603 @ SY1605 @ SV148 ) @ SY1604 @ SV148 ) @ SY1605 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1532,plain,
! [SV149: $i] :
( ( ! [SY1606: $i,SY1607: $i,SY1608: $i,SY1609: $i,SY1610: $i,SY1611: $i,SY1612: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SY1606 @ ( c_HOL_Otimes__class_Otimes @ SY1607 @ SY1608 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY1609 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1607 @ SY1610 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY1611 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1612 @ SY1608 @ SY1609 @ SY1610 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1606 @ SY1607 @ SY1612 @ SY1611 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1533,plain,
! [SV150: $i] :
( ( ! [SY1613: $i,SY1614: $i] :
( ~ ( class_Divides_Osemiring__div @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1613 @ ( c_Divides_Odiv__class_Odiv @ SY1614 @ SY1613 @ SV150 ) @ SV150 )
= SY1614 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1613 @ SY1614 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1534,plain,
! [SV151: $i] :
( ( ! [SY1615: $i,SY1616: $i] :
( ~ ( class_Divides_Osemiring__div @ SV151 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1615 @ SY1616 @ SV151 ) @ SY1616 @ SV151 )
= SY1615 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1616 @ SY1615 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1535,plain,
! [SV152: $i] :
( ( ! [SY1617: $i,SY1618: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV152 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1617 @ ( c_HOL_Ouminus__class_Ouminus @ SY1618 @ SV152 ) @ SV152 )
= ( c_HOL_Oplus__class_Oplus @ SY1617 @ SY1618 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1536,plain,
! [SV153: $i] :
( ( ! [SY1619: $i,SY1620: $i,SY1621: $i] :
( ~ ( class_Divides_Osemiring__div @ SV153 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1619 @ ( c_HOL_Otimes__class_Otimes @ SY1620 @ SY1621 @ SV153 ) @ SV153 ) @ SY1620 @ SV153 )
= ( c_Divides_Odiv__class_Omod @ SY1619 @ SY1620 @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1537,plain,
! [SV154: $i] :
( ( ! [SY1622: $i,SY1623: $i,SY1624: $i] :
( ~ ( class_Divides_Osemiring__div @ SV154 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1622 @ ( c_HOL_Otimes__class_Otimes @ SY1623 @ SY1624 @ SV154 ) @ SV154 ) @ SY1624 @ SV154 )
= ( c_Divides_Odiv__class_Omod @ SY1622 @ SY1624 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1538,plain,
! [SV155: $i] :
( ( ! [SY1625: $i,SY1626: $i,SY1627: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV155 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1625 @ SY1626 @ SV155 )
| ( SY1627
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1625 @ SY1627 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SY1626 @ SY1627 @ SV155 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1539,plain,
! [SV156: $i] :
( ( ! [SY1628: $i,SY1629: $i,SY1630: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV156 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1628 @ SY1629 @ SV156 )
| ( SY1630
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1630 @ SY1628 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SY1630 @ SY1629 @ SV156 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1540,plain,
! [SV157: $i] :
( ( ! [SY1631: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV157 ) ) @ SY1631 @ ( tc_Polynomial_Opoly @ SV157 ) )
= SY1631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1541,plain,
! [SV158: $i] :
( ( ! [SY1632: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV158 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1632 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV158 ) ) @ ( tc_Polynomial_Opoly @ SV158 ) )
= SY1632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1542,plain,
! [SV159: $i] :
( ( ! [SY1633: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV159 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1633 @ ( c_HOL_Ozero__class_Ozero @ SV159 ) @ SV159 )
= SY1633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1543,plain,
! [SV160: $i] :
( ( ! [SY1634: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV160 ) @ SY1634 @ SV160 )
= SY1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1544,plain,
! [SV161: $i] :
( ( ! [SY1635: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV161 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1635 @ ( c_HOL_Ozero__class_Ozero @ SV161 ) @ SV161 )
= SY1635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1545,plain,
! [SV162: $i] :
( ( ! [SY1636: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV162 )
| ~ ( class_Int_Onumber__ring @ SV162 )
| ( SY1636
= ( c_HOL_Oplus__class_Oplus @ SY1636 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1546,plain,
! [SV163: $i] :
( ( ! [SY1637: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV163 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV163 ) @ SY1637 @ SV163 )
= SY1637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1547,plain,
! [SV164: $i] :
( ( ! [SY1638: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV164 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SY1638 @ SV164 )
= SY1638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1548,plain,
! [SV165: $i] :
( ( ! [SY1639: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV165 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1639 @ ( c_HOL_Ozero__class_Ozero @ SV165 ) @ SV165 )
= SY1639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1549,plain,
! [SV166: $i] :
( ( ! [SY1640: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV166 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV166 ) @ SY1640 @ SV166 )
= SY1640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1550,plain,
! [SV167: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV167 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY1641 @ SY1642 @ SV167 ) @ SY1642 @ SV167 )
= SY1641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1551,plain,
! [SV168: $i] :
( ( ! [SY1643: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV168 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY1643 @ SV168 ) @ SV168 )
= SY1643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1552,plain,
! [SV169: $i] :
( ( ! [SY1644: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV169 )
| ( SY1644
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY1644 @ SV169 ) @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1553,plain,
! [SV170: $i] :
( ( ! [SY1645: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV170 )
| ( SY1645
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY1645 @ SV170 ) @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1554,plain,
! [SV171: $i] :
( ( ! [SY1646: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV171 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY1646 @ SV171 ) @ SV171 )
= SY1646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1555,plain,
! [SV172: $i] :
( ( ! [SY1647: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV172 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY1647 @ SV172 ) @ SV172 )
= SY1647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1556,plain,
! [SV173: $i] :
( ( ! [SY1648: $i] :
( ~ ( class_Divides_Osemiring__div @ SV173 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1648 @ ( c_HOL_Oone__class_Oone @ SV173 ) @ SV173 )
= SY1648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1557,plain,
! [SV174: $i] :
( ( ! [SY1649: $i,SY1650: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV174 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SY1649 @ SY1650 @ SV174 ) @ SV174 )
= ( c_HOL_Ominus__class_Ominus @ SY1650 @ SY1649 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1558,plain,
! [SV175: $i] :
( ( ! [SY1651: $i,SY1652: $i,SY1653: $i,SY1654: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1651 @ SY1652 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY1653 @ SY1654 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1651 @ SY1653 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY1652 @ SY1654 @ SV175 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1559,plain,
! [SV176: $i] :
( ( ! [SY1655: $i,SY1656: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV176 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1655 @ SY1656 @ SV176 )
= ( c_HOL_Oplus__class_Oplus @ SY1655 @ ( c_HOL_Ouminus__class_Ouminus @ SY1656 @ SV176 ) @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1560,plain,
! [SV177: $i] :
( ( ! [SY1657: $i,SY1658: $i] :
( ~ ( class_Int_Onumber__ring @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1657 @ SY1658 @ SV177 )
= ( c_HOL_Oplus__class_Oplus @ SY1657 @ ( c_HOL_Ouminus__class_Ouminus @ SY1658 @ SV177 ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1561,plain,
! [SV178: $i] :
( ( ! [SY1659: $i,SY1660: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV178 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1659 @ SY1660 @ SV178 )
= ( c_HOL_Oplus__class_Oplus @ SY1659 @ ( c_HOL_Ouminus__class_Ouminus @ SY1660 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1562,plain,
! [SV179: $i] :
( ( ! [SY1661: $i,SY1662: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV179 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1661 @ SY1662 @ SV179 )
= ( c_HOL_Oplus__class_Oplus @ SY1661 @ ( c_HOL_Ouminus__class_Ouminus @ SY1662 @ SV179 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1563,plain,
! [SV180: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i] :
( ~ ( class_Divides_Oring__div @ SV180 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY1663 @ SY1664 @ SV180 ) @ SY1665 @ SV180 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SY1663 @ SY1665 @ SV180 ) @ ( c_Divides_Odiv__class_Omod @ SY1664 @ SY1665 @ SV180 ) @ SV180 ) @ SY1665 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1564,plain,
! [SV181: $i] :
( ( ! [SY1666: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV181 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ SY1666 @ SV181 ) @ SV181 )
= ( c_HOL_Oabs__class_Oabs @ SY1666 @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1565,plain,
! [SV182: $i] :
( ( ! [SY1667: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV182 )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SY1667 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1566,plain,
! [SV183: $i] :
( ( ! [SY1668: $i,SY1669: $i] :
( ~ ( class_Divides_Osemiring__div @ SV183 )
| ( ( c_Divides_Odiv__class_Omod @ SY1668 @ SY1669 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1669 @ SY1668 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1567,plain,
! [SV184: $i] :
( ( ! [SY1670: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV184 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV184 ) @ SY1670 @ SV184 )
= ( c_HOL_Oone__class_Oone @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1568,plain,
! [SV185: $i] :
( ( ! [SY1671: $i,SY1672: $i,SY1673: $i] :
( ~ ( class_Divides_Oring__div @ SV185 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY1671 @ SY1672 @ SV185 ) @ SY1673 @ SV185 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SY1671 @ SY1673 @ SV185 ) @ SY1672 @ SV185 ) @ SY1673 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1569,plain,
! [SV186: $i] :
( ( ! [SY1674: $i,SY1675: $i,SY1676: $i] :
( ~ ( class_Divides_Oring__div @ SV186 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY1674 @ SY1675 @ SV186 ) @ SY1676 @ SV186 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY1674 @ ( c_Divides_Odiv__class_Omod @ SY1675 @ SY1676 @ SV186 ) @ SV186 ) @ SY1676 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1570,plain,
! [SV187: $i] :
( ( ! [SY1677: $i,SY1678: $i,SY1679: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV187 )
| ( ( c_Divides_Odiv__class_Omod @ SY1677 @ ( c_Polynomial_Osmult @ SY1678 @ SY1679 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SY1677 @ SY1679 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
| ( SY1678
= ( c_HOL_Ozero__class_Ozero @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1571,plain,
! [SV188: $i] :
( ( ! [SY1680: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV188 )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SY1680 @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SY1680 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1572,plain,
! [SV189: $i] :
( ( ! [SY1681: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV189 )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SY1681 @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SY1681 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1573,plain,
! [SV190: $i] :
( ( ! [SY1682: $i,SY1683: $i] :
( ~ ( class_Divides_Osemiring__div @ SV190 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SY1682 @ SY1683 @ SV190 ) @ SY1683 @ SV190 )
= ( c_Divides_Odiv__class_Omod @ SY1682 @ SY1683 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1574,plain,
! [SV191: $i] :
( ( ! [SY1684: $i] :
( ~ ( class_Divides_Osemiring__div @ SV191 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1684 @ SY1684 @ SV191 )
= ( c_HOL_Oone__class_Oone @ SV191 ) )
| ( SY1684
= ( c_HOL_Ozero__class_Ozero @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1575,plain,
! [SV192: $i] :
( ( ! [SY1685: $i,SY1686: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV192 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ SY1685 @ SV192 ) @ SY1686 @ SV192 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SY1685 @ SY1686 @ SV192 ) @ ( tc_Polynomial_Opoly @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1576,plain,
! [SV193: $i] :
( ( ! [SY1687: $i,SY1688: $i,SY1689: $i,SY1690: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV193 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1687 @ SY1688 @ SV193 ) @ SY1689 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1690 @ SY1688 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1687 @ SY1690 @ SV193 ) @ SY1688 @ SV193 ) @ SY1689 @ SV193 ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1577,plain,
! [SV194: $i] :
( ( ! [SY1691: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV194 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SY1691 @ SV194 ) @ SV194 )
= ( c_HOL_Oabs__class_Oabs @ SY1691 @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1578,plain,
! [SV195: $i] :
( ( ! [SY1692: $i,SY1693: $i,SY1694: $i] :
( ~ ( class_Divides_Osemiring__div @ SV195 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1692 @ SY1693 @ SV195 ) @ SY1693 @ SV195 ) @ ( c_Divides_Odiv__class_Omod @ SY1692 @ SY1693 @ SV195 ) @ SV195 ) @ SY1694 @ SV195 )
= ( c_HOL_Oplus__class_Oplus @ SY1692 @ SY1694 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1579,plain,
! [SV196: $i] :
( ( ! [SY1695: $i,SY1696: $i,SY1697: $i] :
( ~ ( class_Divides_Osemiring__div @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1695 @ ( c_Divides_Odiv__class_Odiv @ SY1696 @ SY1695 @ SV196 ) @ SV196 ) @ ( c_Divides_Odiv__class_Omod @ SY1696 @ SY1695 @ SV196 ) @ SV196 ) @ SY1697 @ SV196 )
= ( c_HOL_Oplus__class_Oplus @ SY1696 @ SY1697 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1580,plain,
! [SV197: $i] :
( ( ! [SY1698: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV197 )
| ( c_Polynomial_Opdivmod__rel @ SY1698 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ SY1698 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1581,plain,
! [SV198: $i] :
( ( ! [SY1699: $i] :
( ~ ( class_Divides_Osemiring__div @ SV198 )
| ( ( c_Divides_Odiv__class_Omod @ SY1699 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= SY1699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1582,plain,
! [SV199: $i] :
( ( ! [SY1700: $i] :
( ~ ( class_Divides_Osemiring__div @ SV199 )
| ( ( c_Divides_Odiv__class_Omod @ SY1700 @ SY1700 @ SV199 )
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1583,plain,
! [SV200: $i] :
( ( ! [SY1701: $i,SY1702: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV200 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1701 @ SY1702 @ SV200 )
= ( c_HOL_Oplus__class_Oplus @ SY1702 @ SY1701 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1584,plain,
! [SV201: $i] :
( ( ! [SY1703: $i,SY1704: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1703 @ SY1704 @ SV201 )
= ( c_HOL_Oplus__class_Oplus @ SY1704 @ SY1703 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1585,plain,
! [SV202: $i] :
( ( ! [SY1705: $i,SY1706: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV202 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1705 @ SY1706 @ SV202 )
= ( c_HOL_Oplus__class_Oplus @ SY1706 @ SY1705 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1586,plain,
! [SV203: $i] :
( ( ! [SY1707: $i,SY1708: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV203 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SY1707 @ SV203 ) @ SY1708 @ SV203 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV203 ) @ SV203 ) @ SY1708 @ SV203 ) @ ( c_Power_Opower__class_Opower @ SY1707 @ SY1708 @ SV203 ) @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1587,plain,
! [SV204: $i] :
( ( ! [SY1709: $i,SY1710: $i] :
( ~ ( class_Divides_Osemiring__div @ SV204 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ SY1709 @ SY1710 @ SV204 ) @ SY1710 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1588,plain,
! [SV205: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ~ ( class_Divides_Osemiring__div @ SV205 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1711 @ SY1712 @ SV205 ) @ SY1713 @ SV205 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY1711 @ SY1713 @ SV205 ) @ ( c_Divides_Odiv__class_Omod @ SY1712 @ SY1713 @ SV205 ) @ SV205 ) @ SY1713 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1589,plain,
! [SV206: $i] :
( ( ! [SY1714: $i,SY1715: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV206 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY1714 @ SY1715 @ SV206 ) @ SY1714 @ SV206 )
= ( c_HOL_Otimes__class_Otimes @ SY1714 @ ( c_Power_Opower__class_Opower @ SY1714 @ SY1715 @ SV206 ) @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1590,plain,
! [SV207: $i] :
( ( ! [SY1716: $i,SY1717: $i,SY1718: $i] :
( ~ ( class_Divides_Osemiring__div @ SV207 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SY1716 @ ( c_HOL_Otimes__class_Otimes @ SY1717 @ SY1718 @ SV207 ) @ SV207 ) @ SY1718 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SY1717 @ ( c_Divides_Odiv__class_Odiv @ SY1716 @ SY1718 @ SV207 ) @ SV207 ) )
| ( SY1718
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1591,plain,
! [SV208: $i] :
( ( ! [SY1719: $i,SY1720: $i,SY1721: $i] :
( ~ ( class_Divides_Osemiring__div @ SV208 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SY1719 @ ( c_HOL_Otimes__class_Otimes @ SY1720 @ SY1721 @ SV208 ) @ SV208 ) @ SY1720 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SY1721 @ ( c_Divides_Odiv__class_Odiv @ SY1719 @ SY1720 @ SV208 ) @ SV208 ) )
| ( SY1720
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1592,plain,
! [SV209: $i] :
( ( ! [SY1722: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV209 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1722 @ SY1722 @ SV209 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV209 ) @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV209 ) @ SY1722 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1593,plain,
! [SV210: $i] :
( ( ! [SY1723: $i,SY1724: $i,SY1725: $i,SY1726: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV210 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1723 @ SY1724 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SY1725 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1723 @ SY1724 @ SY1725 @ SY1726 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1594,plain,
! [SV211: $i] :
( ( ! [SY1727: $i,SY1728: $i,SY1729: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV211 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ SY1727 @ SY1728 @ SV211 ) @ SY1729 @ SV211 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SY1727 @ SY1729 @ SV211 ) @ ( c_Polynomial_Osmult @ SY1728 @ SY1729 @ SV211 ) @ ( tc_Polynomial_Opoly @ SV211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1595,plain,
! [SV212: $i] :
( ( ! [SY1730: $i,SY1731: $i,SY1732: $i] :
( ~ ( class_Divides_Osemiring__div @ SV212 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SY1730 @ SY1731 @ SV212 ) @ SY1732 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SY1730 @ SY1732 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SY1731 @ SY1732 @ SV212 ) @ SV212 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1731 @ SY1730 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1596,plain,
! [SV213: $i] :
( ( ! [SY1733: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV213 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY1733 @ SV213 ) @ ( c_HOL_Oabs__class_Oabs @ SY1733 @ SV213 ) @ SV213 )
= ( c_HOL_Otimes__class_Otimes @ SY1733 @ SY1733 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1597,plain,
! [SV214: $i] :
( ( ! [SY1734: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV214 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SY1734 @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1598,plain,
! [SV215: $i] :
( ( ! [SY1735: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV215 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1735 @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1599,plain,
! [SV216: $i] :
( ( ! [SY1736: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SY1736 @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1600,plain,
! [SV217: $i] :
( ( ! [SY1737: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV217 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SY1737 @ SV217 )
= ( c_HOL_Ozero__class_Ozero @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1601,plain,
! [SV218: $i] :
( ( ! [SY1738: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV218 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1738 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1602,plain,
! [SV219: $i] :
( ( ! [SY1739: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV219 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1739 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1603,plain,
! [SV220: $i] :
( ( ! [SY1740: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV220 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) @ SY1740 @ ( tc_Polynomial_Opoly @ SV220 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1604,plain,
! [SV221: $i] :
( ( ! [SY1741: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV221 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1741 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) @ ( tc_Polynomial_Opoly @ SV221 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1605,plain,
! [SV222: $i] :
( ( ! [SY1742: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV222 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SY1742 @ SV222 )
= ( c_HOL_Ozero__class_Ozero @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1606,plain,
! [SV223: $i] :
( ( ! [SY1743: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV223 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SY1743 @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1607,plain,
! [SV224: $i] :
( ( ! [SY1744: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV224 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1744 @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1608,plain,
! [SV225: $i] :
( ( ! [SY1745: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV225 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SY1745 @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1609,plain,
! [SV226: $i] :
( ( ! [SY1746: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV226 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1746 @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 )
= ( c_HOL_Ozero__class_Ozero @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1610,plain,
! [SV227: $i] :
( ( ! [SY1747: $i,SY1748: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV227 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SY1747 @ SV227 ) @ SY1748 @ SV227 ) @ SV227 )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SY1747 @ SY1748 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1611,plain,
! [SV228: $i] :
( ( ! [SY1749: $i,SY1750: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1749 @ SY1750 @ SV228 ) @ SY1750 @ SV228 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1749 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 ) @ SY1750 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1612,plain,
! [SV229: $i] :
( ( ! [SY1751: $i,SY1752: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV229 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1751 @ ( c_HOL_Otimes__class_Otimes @ SY1752 @ SY1751 @ SV229 ) @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1752 @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV229 ) @ SY1751 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1613,plain,
! [SV230: $i] :
( ( ! [SY1753: $i] :
( ~ ( class_Divides_Osemiring__div @ SV230 )
| ( ( c_Divides_Odiv__class_Omod @ SY1753 @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 )
= ( c_HOL_Ozero__class_Ozero @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1614,plain,
! [SV231: $i] :
( ( ! [SY1754: $i,SY1755: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1754 @ SV231 ) @ ( c_HOL_Oplus__class_Oplus @ SY1755 @ SY1754 @ SV231 ) @ SV231 )
= SY1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1615,plain,
! [SV232: $i] :
( ( ! [SY1756: $i,SY1757: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1756 @ SV232 ) @ ( c_HOL_Oplus__class_Oplus @ SY1756 @ SY1757 @ SV232 ) @ SV232 )
= SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1616,plain,
! [SV233: $i] :
( ( ! [SY1758: $i,SY1759: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV233 )
| ( ( c_Divides_Odiv__class_Omod @ SY1758 @ ( c_HOL_Ouminus__class_Ouminus @ SY1759 @ ( tc_Polynomial_Opoly @ SV233 ) ) @ ( tc_Polynomial_Opoly @ SV233 ) )
= ( c_Divides_Odiv__class_Omod @ SY1758 @ SY1759 @ ( tc_Polynomial_Opoly @ SV233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1617,plain,
! [SV234: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV234 )
| ( ( c_HOL_Ozero__class_Ozero @ SV234 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1618,plain,
! [SV235: $i] :
( ( ! [SY1760: $i,SY1761: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV235 )
| ( ( c_Polynomial_Opoly__gcd @ SY1760 @ SY1761 @ SV235 )
= ( c_Polynomial_Opoly__gcd @ SY1761 @ SY1760 @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1619,plain,
! [SV236: $i] :
( ( ! [SY1762: $i,SY1763: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV236 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SY1762 @ SV236 ) @ SY1763 @ SV236 )
= ( c_HOL_Otimes__class_Otimes @ SY1762 @ ( c_HOL_Ouminus__class_Ouminus @ SY1763 @ SV236 ) @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1620,plain,
! [SV237: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV237 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 )
= ( c_HOL_Ozero__class_Ozero @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1621,plain,
! [SV238: $i] :
( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV238 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV238 ) @ SV238 )
= ( c_HOL_Ozero__class_Ozero @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1622,plain,
! [SV239: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV239 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV239 ) ) @ ( tc_Polynomial_Opoly @ SV239 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1623,plain,
! [SV240: $i] :
( ( ! [SY1764: $i,SY1765: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV240 )
| ( ( c_Polynomial_Opoly__gcd @ SY1764 @ SY1765 @ SV240 )
= ( c_Polynomial_Opoly__gcd @ SY1765 @ ( c_Divides_Odiv__class_Omod @ SY1764 @ SY1765 @ ( tc_Polynomial_Opoly @ SV240 ) ) @ SV240 ) )
| ( SY1765
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV240 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1624,plain,
! [SV241: $i] :
( ( ! [SY1766: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV241 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SY1766 @ SV241 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1625,plain,
! [SV242: $i] :
( ( ! [SY1767: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV242 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SY1767 @ SV242 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV242 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1626,plain,
! [SV243: $i] :
( ( ! [SY1768: $i,SY1769: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ SY1768 @ SV243 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1769 @ SV243 ) @ SV243 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SY1768 @ SY1769 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1627,plain,
! [SV244: $i] :
( ( ! [SY1770: $i,SY1771: $i,SY1772: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV244 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1770 @ ( c_HOL_Otimes__class_Otimes @ SY1771 @ SY1772 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ ( tc_Polynomial_Opoly @ SV244 ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ SY1770 @ SY1771 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ SY1772 @ ( tc_Polynomial_Opoly @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1628,plain,
! [SV245: $i] :
( ( ! [SY1773: $i,SY1774: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV245 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SY1773 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SY1774 @ SV245 ) @ SV245 ) @ SV245 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SY1773 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SY1774 @ SV245 ) @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1629,plain,
! [SV246: $i] :
( ( ! [SY1775: $i,SY1776: $i] :
( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1775 @ SY1776 @ SV246 ) @ SY1775 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1630,plain,
! [SV247: $i] :
( ( ! [SY1777: $i,SY1778: $i] :
( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1777 @ SY1778 @ SV247 ) @ SY1778 @ SV247 )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1631,plain,
! [SV248: $i] :
( ( ! [SY1779: $i,SY1780: $i] :
( ~ ( class_Divides_Osemiring__div @ SV248 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY1779 @ SY1780 @ SV248 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1779 @ SY1780 @ SV248 ) @ SY1780 @ SV248 ) @ SV248 )
= SY1779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1632,plain,
! [SV249: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV249 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV249 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV249 ) @ SV249 )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1633,plain,
! [SV250: $i] :
( ( ! [SY1781: $i,SY1782: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV250 )
| ( SY1781
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1782 @ SY1781 @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SY1781 @ SY1782 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1634,plain,
! [SV251: $i] :
( ( ! [SY1783: $i,SY1784: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV251 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SY1783 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ SY1784 @ ( tc_Polynomial_Opoly @ SV251 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SY1783 @ SY1784 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ ( tc_Polynomial_Opoly @ SV251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1635,plain,
! [SV252: $i] :
( ( ! [SY1785: $i,SY1786: $i,SY1787: $i] :
( ~ ( class_Divides_Osemiring__div @ SV252 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1785 @ SY1786 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SY1785 @ SY1787 @ SV252 ) @ SV252 )
= ( c_HOL_Otimes__class_Otimes @ SY1785 @ ( c_Divides_Odiv__class_Omod @ SY1786 @ SY1787 @ SV252 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1636,plain,
! [SV253: $i] :
( ( ! [SY1788: $i,SY1789: $i,SY1790: $i] :
( ~ ( class_Divides_Osemiring__div @ SV253 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1788 @ SY1789 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SY1790 @ SY1789 @ SV253 ) @ SV253 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY1788 @ SY1790 @ SV253 ) @ SY1789 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1637,plain,
! [SV254: $i] :
( ( ! [SY1791: $i,SY1792: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV254 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SY1791 @ SY1792 @ SV254 ) @ SV254 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1792 @ SV254 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1791 @ SV254 ) @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1638,plain,
! [SV255: $i] :
( ( ! [SY1793: $i,SY1794: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV255 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SY1793 @ SY1794 @ SV255 ) @ SV255 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY1793 @ SV255 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1794 @ SV255 ) @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1639,plain,
! [SV256: $i] :
( ( ! [SY1795: $i,SY1796: $i,SY1797: $i,SY1798: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1795 @ SY1796 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SY1797 @ SY1798 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1796 @ SY1798 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1795 @ SY1797 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1640,plain,
! [SV257: $i] :
( ( ! [SY1799: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV257 )
| ( ( c_Polynomial_Osmult @ SY1799 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) @ SV257 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1641,plain,
! [SV258: $i] :
( ( ! [SY1800: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV258 )
| ( ( c_Polynomial_Osmult @ SY1800 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) @ SV258 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1642,plain,
! [SV259: $i] :
( ( ! [SY1801: $i,SY1802: $i,SY1803: $i] :
( ~ ( class_Divides_Osemiring__div @ SV259 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SY1801 @ SY1802 @ SV259 ) @ SY1803 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SY1801 @ SY1803 @ SV259 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1803 @ SY1802 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1643,plain,
! [SV260: $i] :
( ( ! [SY1804: $i,SY1805: $i,SY1806: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV260 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1804 @ ( c_Polynomial_Opoly__gcd @ SY1805 @ SY1806 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1804 @ SY1806 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1804 @ SY1805 @ ( tc_Polynomial_Opoly @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1644,plain,
! [SV261: $i] :
( ( ! [SY1807: $i,SY1808: $i,SY1809: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV261 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1807 @ ( c_Polynomial_Opoly__gcd @ SY1808 @ SY1809 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1807 @ SY1809 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1807 @ SY1808 @ ( tc_Polynomial_Opoly @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1645,plain,
! [SV262: $i] :
( ( ! [SY1810: $i,SY1811: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV262 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SY1810 @ SY1811 @ SV262 ) @ SY1810 @ ( tc_Polynomial_Opoly @ SV262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1646,plain,
! [SV263: $i] :
( ( ! [SY1812: $i,SY1813: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV263 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SY1812 @ SY1813 @ SV263 ) @ SY1813 @ ( tc_Polynomial_Opoly @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1647,plain,
! [SV264: $i] :
( ( ! [SY1814: $i,SY1815: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV264 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SY1814 @ SV264 ) @ SY1815 @ ( tc_Polynomial_Opoly @ SV264 ) )
| ( SY1815
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1648,plain,
! [SV265: $i] :
( ( ! [SY1816: $i,SY1817: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV265 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1816 @ ( c_HOL_Oabs__class_Oabs @ SY1817 @ SV265 ) @ SV265 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1816 @ SY1817 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1649,plain,
! [SV266: $i] :
( ( ! [SY1818: $i,SY1819: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV266 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1818 @ SY1819 @ SV266 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1818 @ ( c_HOL_Oabs__class_Oabs @ SY1819 @ SV266 ) @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1650,plain,
! [SV267: $i] :
( ( ! [SY1820: $i,SY1821: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV267 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SY1820 @ SV267 ) @ SY1821 @ SV267 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1820 @ SY1821 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1651,plain,
! [SV268: $i] :
( ( ! [SY1822: $i,SY1823: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV268 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1822 @ SY1823 @ SV268 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SY1822 @ SV268 ) @ SY1823 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1652,plain,
! [SV269: $i] :
( ( ! [SY1824: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1824 @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1653,plain,
! [SV270: $i] :
( ( ! [SY1825: $i,SY1826: $i,SY1827: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV270 )
| ( ( c_Polynomial_Osmult @ SY1825 @ ( c_HOL_Ominus__class_Ominus @ SY1826 @ SY1827 @ ( tc_Polynomial_Opoly @ SV270 ) ) @ SV270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SY1825 @ SY1826 @ SV270 ) @ ( c_Polynomial_Osmult @ SY1825 @ SY1827 @ SV270 ) @ ( tc_Polynomial_Opoly @ SV270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1654,plain,
! [SV271: $i] :
( ( ! [SY1828: $i,SY1829: $i,SY1830: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV271 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1828 @ SY1829 @ ( tc_Polynomial_Opoly @ SV271 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1828 @ ( c_Polynomial_Opoly__gcd @ SY1830 @ SY1829 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1655,plain,
! [SV272: $i] :
( ( ! [SY1831: $i,SY1832: $i,SY1833: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV272 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1831 @ SY1832 @ ( tc_Polynomial_Opoly @ SV272 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1831 @ ( c_Polynomial_Opoly__gcd @ SY1832 @ SY1833 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1656,plain,
! [SV273: $i] :
( ( ! [SY1834: $i,SY1835: $i,SY1836: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV273 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1834 @ SY1835 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SY1836 @ SY1835 @ SV273 ) @ SV273 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1834 @ SY1836 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1657,plain,
! [SV274: $i] :
( ( ! [SY1837: $i,SY1838: $i,SY1839: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV274 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1837 @ SY1838 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SY1837 @ SY1839 @ SV274 ) @ SV274 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1838 @ SY1839 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1658,plain,
! [SV275: $i] :
( ( ! [SY1840: $i,SY1841: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV275 )
| ( ( c_Polynomial_Osmult @ SY1840 @ ( c_HOL_Ouminus__class_Ouminus @ SY1841 @ ( tc_Polynomial_Opoly @ SV275 ) ) @ SV275 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SY1840 @ SY1841 @ SV275 ) @ ( tc_Polynomial_Opoly @ SV275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1659,plain,
! [SV276: $i] :
( ( ! [SY1842: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
| ( SY1842
= ( c_HOL_Ozero__class_Ozero @ SV276 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SY1842 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1660,plain,
! [SV277: $i] :
( ( ! [SY1843: $i,SY1844: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SY1843 @ SV277 ) @ SY1844 @ SV277 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1843 @ SY1844 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1661,plain,
! [SV278: $i] :
( ( ! [SY1845: $i,SY1846: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1845 @ SY1846 @ SV278 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SY1845 @ SV278 ) @ SY1846 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1662,plain,
! [SV279: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1847 @ ( c_HOL_Ouminus__class_Ouminus @ SY1848 @ SV279 ) @ SV279 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1847 @ SY1848 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1663,plain,
! [SV280: $i] :
( ( ! [SY1849: $i,SY1850: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1849 @ SY1850 @ SV280 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1849 @ ( c_HOL_Ouminus__class_Ouminus @ SY1850 @ SV280 ) @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1664,plain,
! [SV281: $i] :
( ( ! [SY1851: $i,SY1852: $i,SY1853: $i] :
( ~ ( class_Divides_Osemiring__div @ SV281 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SY1851 @ SY1852 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SY1853 @ SY1852 @ SV281 ) @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1851 @ SY1853 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1852 @ SY1853 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1852 @ SY1851 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1665,plain,
! [SV282: $i] :
( ( ! [SY1854: $i,SY1855: $i,SY1856: $i] :
( ~ ( class_Divides_Osemiring__div @ SV282 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1854 @ SY1855 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SY1854 @ SY1856 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SY1855 @ SY1856 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1856 @ SY1855 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1856 @ SY1854 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1666,plain,
! [SV283: $i] :
( ( ! [SY1857: $i,SY1858: $i,SY1859: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1857 @ ( c_HOL_Oplus__class_Oplus @ SY1858 @ SY1859 @ SV283 ) @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1857 @ SY1859 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1857 @ SY1858 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1667,plain,
! [SV284: $i] :
( ( ! [SY1860: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV284 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SY1860 @ SV284 )
= SY1860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1668,plain,
! [SV285: $i] :
( ( ! [SY1861: $i,SY1862: $i,SY1863: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV285 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ SY1861 @ SY1862 @ SV285 ) @ SY1863 @ ( tc_Polynomial_Opoly @ SV285 ) )
= ( c_Polynomial_Osmult @ SY1861 @ ( c_Divides_Odiv__class_Omod @ SY1862 @ SY1863 @ ( tc_Polynomial_Opoly @ SV285 ) ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1669,plain,
! [SV286: $i] :
( ( ! [SY1864: $i,SY1865: $i,SY1866: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV286 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1864 @ SY1865 @ ( tc_Polynomial_Opoly @ SV286 ) )
| ( SY1866
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1864 @ ( c_Polynomial_Osmult @ SY1866 @ SY1865 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1670,plain,
! [SV287: $i] :
( ( ! [SY1867: $i,SY1868: $i,SY1869: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV287 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY1867 @ SY1868 @ SV287 ) @ SY1869 @ ( tc_Polynomial_Opoly @ SV287 ) )
| ( SY1867
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1868 @ SY1869 @ ( tc_Polynomial_Opoly @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1671,plain,
! [SV288: $i] :
( ( ! [SY1870: $i,SY1871: $i,SY1872: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV288 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1870 @ SY1871 @ ( tc_Polynomial_Opoly @ SV288 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1870 @ ( c_Polynomial_Osmult @ SY1872 @ SY1871 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SY1872
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1672,plain,
! [SV289: $i] :
( ( ! [SY1873: $i,SY1874: $i,SY1875: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV289 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1873 @ ( c_Polynomial_Osmult @ SY1874 @ SY1875 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1873 @ SY1875 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SY1874
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1673,plain,
! [SV290: $i] :
( ( ! [SY1876: $i,SY1877: $i,SY1878: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV290 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1876 @ SY1877 @ ( tc_Polynomial_Opoly @ SV290 ) )
| ( SY1878
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY1878 @ SY1876 @ SV290 ) @ SY1877 @ ( tc_Polynomial_Opoly @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1674,plain,
! [SV291: $i] :
( ( ! [SY1879: $i,SY1880: $i,SY1881: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV291 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY1879 @ SY1880 @ SV291 ) @ SY1881 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1880 @ SY1881 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SY1879
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1675,plain,
! [SV292: $i] :
( ( ! [SY1882: $i,SY1883: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV292 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY1882 @ SY1883 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1883 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1676,plain,
! [SV293: $i] :
( ( ! [SY1884: $i,SY1885: $i,SY1886: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1884 @ SY1885 @ SV293 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1886 @ SY1884 @ SV293 ) @ SY1885 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1677,plain,
! [SV294: $i] :
( ( ! [SY1887: $i,SY1888: $i,SY1889: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1887 @ SY1888 @ SV294 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1887 @ SY1889 @ SV294 ) @ SY1888 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1678,plain,
! [SV295: $i] :
( ( ! [SY1890: $i,SY1891: $i,SY1892: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1890 @ ( c_HOL_Otimes__class_Otimes @ SY1891 @ SY1892 @ SV295 ) @ SV295 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1890 @ SY1891 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1679,plain,
! [SV296: $i] :
( ( ! [SY1893: $i,SY1894: $i,SY1895: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1893 @ ( c_HOL_Otimes__class_Otimes @ SY1894 @ SY1895 @ SV296 ) @ SV296 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1893 @ SY1895 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1680,plain,
! [SV297: $i] :
( ( ! [SY1896: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV297 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SY1896 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1681,plain,
! [SV298: $i] :
( ( ! [SY1897: $i,SY1898: $i,SY1899: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1897 @ SY1898 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1899 @ SY1898 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1897 @ SY1899 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1682,plain,
! [SV299: $i] :
( ( ! [SY1900: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV299 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1900 @ SY1900 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1683,plain,
! [SV300: $i] :
( ( ! [SY1901: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV300 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SY1901 @ SV300 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV300 ) ) @ ( tc_Polynomial_Opoly @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1684,plain,
! [SV301: $i] :
( ( ! [SY1902: $i,SY1903: $i,SY1904: $i,SY1905: $i,SY1906: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV301 )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SY1902 @ SY1903 @ SV301 ) @ SY1904 @ ( c_Polynomial_Osmult @ SY1902 @ SY1905 @ SV301 ) @ ( c_Polynomial_Osmult @ SY1902 @ SY1906 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY1903 @ SY1904 @ SY1905 @ SY1906 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1685,plain,
! [SV302: $i] :
( ( ! [SY1907: $i,SY1908: $i,SY1909: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1907 @ ( c_HOL_Ominus__class_Ominus @ SY1908 @ SY1909 @ SV302 ) @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1907 @ SY1909 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1907 @ SY1908 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1686,plain,
! [SV303: $i] :
( ( ! [SY1910: $i,SY1911: $i,SY1912: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV303 )
| ( ( c_Polynomial_Osmult @ SY1910 @ ( c_HOL_Oplus__class_Oplus @ SY1911 @ SY1912 @ ( tc_Polynomial_Opoly @ SV303 ) ) @ SV303 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SY1910 @ SY1911 @ SV303 ) @ ( c_Polynomial_Osmult @ SY1910 @ SY1912 @ SV303 ) @ ( tc_Polynomial_Opoly @ SV303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1687,plain,
! [SV304: $i] :
( ( ! [SY1913: $i,SY1914: $i,SY1915: $i] :
( ~ ( class_Divides_Osemiring__div @ SV304 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1913 @ SY1914 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1913 @ SY1915 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1913 @ ( c_Divides_Odiv__class_Omod @ SY1914 @ SY1915 @ SV304 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1688,plain,
! [SV305: $i] :
( ( ! [SY1916: $i,SY1917: $i,SY1918: $i] :
( ~ ( class_Divides_Osemiring__div @ SV305 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1916 @ ( c_Divides_Odiv__class_Omod @ SY1917 @ SY1918 @ SV305 ) @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1916 @ SY1917 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1916 @ SY1918 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1689,plain,
! [SV306: $i] :
( ( ! [SY1919: $i,SY1920: $i,SY1921: $i] :
( ~ ( class_Divides_Osemiring__div @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1919 @ SY1920 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1919 @ ( c_Divides_Odiv__class_Omod @ SY1920 @ SY1921 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1919 @ SY1921 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1690,plain,
! [SV307: $i] :
( ( ! [SY1922: $i,SY1923: $i,SY1924: $i] :
( ~ ( class_Divides_Osemiring__div @ SV307 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1922 @ ( c_Divides_Odiv__class_Omod @ SY1923 @ SY1924 @ SV307 ) @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1922 @ SY1924 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1922 @ SY1923 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1691,plain,
! [SV308: $i] :
( ( ! [SY1925: $i,SY1926: $i,SY1927: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV308 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ SY1925 @ SY1926 @ SV308 ) @ SY1927 @ ( tc_Polynomial_Opoly @ SV308 ) )
= ( c_Polynomial_Osmult @ SY1925 @ ( c_Divides_Odiv__class_Odiv @ SY1926 @ SY1927 @ ( tc_Polynomial_Opoly @ SV308 ) ) @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1692,plain,
! [SV309: $i] :
( ( ! [SY1928: $i,SY1929: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV309 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1928 @ ( c_HOL_Otimes__class_Otimes @ SY1929 @ SY1928 @ SV309 ) @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1693,plain,
! [SV310: $i] :
( ( ! [SY1930: $i,SY1931: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV310 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1930 @ ( c_HOL_Otimes__class_Otimes @ SY1930 @ SY1931 @ SV310 ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1694,plain,
! [SV311: $i] :
( ( ! [SY1932: $i,SY1933: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV311 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1932 @ ( c_HOL_Otimes__class_Otimes @ SY1932 @ SY1933 @ SV311 ) @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1695,plain,
! [SV312: $i] :
( ( ! [SY1934: $i,SY1935: $i,SY1936: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1934 @ SY1935 @ ( tc_Polynomial_Opoly @ SV312 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY1936 @ SY1934 @ SV312 ) @ SY1935 @ ( tc_Polynomial_Opoly @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1696,plain,
! [SV313: $i] :
( ( ! [SY1937: $i,SY1938: $i,SY1939: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1937 @ ( c_Polynomial_Osmult @ SY1938 @ SY1939 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1937 @ SY1939 @ ( tc_Polynomial_Opoly @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1697,plain,
! [SV314: $i] :
( ( ! [SY1940: $i,SY1941: $i,SY1942: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY1940 @ SY1941 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SY1942 @ SY1941 @ SV314 ) @ SV314 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1940 @ SY1942 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1698,plain,
! [SV315: $i] :
( ( ! [SY1943: $i,SY1944: $i,SY1945: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV315 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1943 @ ( c_Polynomial_Osmult @ SY1944 @ SY1945 @ SV315 ) @ ( tc_Polynomial_Opoly @ SV315 ) )
= ( c_Polynomial_Osmult @ SY1944 @ ( c_HOL_Otimes__class_Otimes @ SY1943 @ SY1945 @ ( tc_Polynomial_Opoly @ SV315 ) ) @ SV315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1699,plain,
! [SV316: $i] :
( ( ! [SY1946: $i,SY1947: $i,SY1948: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV316 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ SY1946 @ SY1947 @ SV316 ) @ SY1948 @ ( tc_Polynomial_Opoly @ SV316 ) )
= ( c_Polynomial_Osmult @ SY1946 @ ( c_HOL_Otimes__class_Otimes @ SY1947 @ SY1948 @ ( tc_Polynomial_Opoly @ SV316 ) ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1700,plain,
! [SV317: $i] :
( ( ! [SY1949: $i,SY1950: $i,SY1951: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV317 )
| ( ( c_Polynomial_Osmult @ SY1949 @ ( c_Polynomial_Osmult @ SY1950 @ SY1951 @ SV317 ) @ SV317 )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ SY1949 @ SY1950 @ SV317 ) @ SY1951 @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1701,plain,
! [SV318: $i] :
( ( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ SV318 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1702,plain,
! [SV319: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ SV319 ) )
| ~ ( class_Ring__and__Field_Oidom @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1703,plain,
! [SV320: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ SV320 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1704,plain,
! [SV321: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ SV321 ) )
| ~ ( class_Ring__and__Field_Oidom @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1705,plain,
! [SV322: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ SV322 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1706,plain,
! [SV323: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ SV323 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1707,plain,
! [SV324: $i] :
( ( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ SV324 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1708,plain,
! [SV325: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ SV325 ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1709,plain,
! [SV326: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ SV326 ) )
| ~ ( class_Ring__and__Field_Oidom @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1710,plain,
! [SV327: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ SV327 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1711,plain,
! [SV328: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ SV328 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1712,plain,
! [SV329: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ SV329 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1713,plain,
! [SV330: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ SV330 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1714,plain,
! [SV331: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ SV331 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1715,plain,
! [SV332: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ SV332 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1716,plain,
! [SV333: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ SV333 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1717,plain,
! [SV334: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ SV334 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1718,plain,
! [SV335: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ SV335 ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1719,plain,
! [SV336: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ SV336 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1720,plain,
! [SV337: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ SV337 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1721,plain,
! [SV338: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ SV338 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1722,plain,
! [SV339: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ SV339 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1723,plain,
! [SV340: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ SV340 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1724,plain,
! [SV341: $i] :
( ( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ SV341 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1725,plain,
! [SV342: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ SV342 ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1726,plain,
! [SV343: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ SV343 ) )
| ~ ( class_OrderedGroup_Oab__group__add @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1727,plain,
! [SV344: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ SV344 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1728,plain,
! [SV345: $i] :
( ( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ SV345 ) )
| ~ ( class_Ring__and__Field_Ofield @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1729,plain,
! [SV346: $i] :
( ( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ SV346 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1730,plain,
! [SV347: $i] :
( ( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ SV347 ) )
| ~ ( class_Ring__and__Field_Oidom @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1731,plain,
! [SV348: $i] :
( ( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ SV348 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1732,plain,
! [SV349: $i] :
( ( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ SV349 ) )
| ~ ( class_Ring__and__Field_Ofield @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1733,plain,
! [SV350: $i] :
( ( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ SV350 ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1734,plain,
! [SV351: $i] :
( ( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ SV351 ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1735,plain,
! [SV352: $i] :
( ( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ SV352 ) )
| ~ ( class_HOL_Ozero @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1736,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1737,plain,
! [SV353: $i] :
( ( ! [SY1952: $i,SY1953: $i,SY1954: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV353 )
| ~ ( class_Int_Onumber__ring @ SV353 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1952 @ SY1953 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SY1952 @ SY1954 @ SV353 ) )
| ( SY1953 = SY1954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1738,plain,
! [SV354: $i] :
( ( ! [SY1955: $i,SY1956: $i,SY1957: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1955 @ SY1956 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SY1955 @ SY1957 @ SV354 ) )
| ( SY1956 = SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1739,plain,
! [SV355: $i] :
( ( ! [SY1958: $i,SY1959: $i] :
( ~ ( class_Divides_Osemiring__div @ SV355 )
| ( ( c_Divides_Odiv__class_Omod @ SY1958 @ SY1959 @ SV355 )
!= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1959 @ SY1958 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1740,plain,
! [SV356: $i] :
( ( ! [SY1960: $i,SY1961: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1960 @ SY1961 @ SV356 )
!= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SY1961
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SY1960
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1741,plain,
! [SV357: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1962 @ SY1963 @ SV357 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SY1962
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SY1963
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1742,plain,
! [SV358: $i] :
( ( ! [SY1964: $i,SY1965: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV358 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1964 @ SY1965 @ SV358 )
!= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
| ( SY1964
= ( c_HOL_Ouminus__class_Ouminus @ SY1965 @ SV358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1743,plain,
! [SV359: $i] :
( ( ! [SY1966: $i,SY1967: $i,SY1968: $i,SY1969: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV359 )
| ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1966 @ ( c_HOL_Otimes__class_Otimes @ SY1967 @ SY1968 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SY1966 @ ( c_HOL_Otimes__class_Otimes @ SY1967 @ SY1969 @ SV359 ) @ SV359 ) )
| ( SY1968 = SY1969 )
| ( SY1967
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1744,plain,
! [SV360: $i] :
( ( ! [SY1970: $i,SY1971: $i,SY1972: $i,SY1973: $i] :
( ~ ( class_HOL_Ozero @ SV360 )
| ( ( c_Polynomial_OpCons @ SY1970 @ SY1971 @ SV360 )
!= ( c_Polynomial_OpCons @ SY1972 @ SY1973 @ SV360 ) )
| ( SY1971 = SY1973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1745,plain,
! [SV361: $i] :
( ( ! [SY1974: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV361 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1974 @ SY1974 @ SV361 )
!= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
| ( SY1974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1746,plain,
! [SV362: $i] :
( ( ! [SY1975: $i,SY1976: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV362 )
| ( ( c_HOL_Oabs__class_Oabs @ SY1975 @ SV362 )
!= ( c_HOL_Oabs__class_Oabs @ SY1976 @ SV362 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1975 @ SY1976 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1747,plain,
! [SV363: $i] :
( ( ! [SY1977: $i,SY1978: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV363 )
| ( ( c_Polynomial_Opoly @ SY1977 @ ( c_HOL_Ouminus__class_Ouminus @ SY1978 @ SV363 ) @ SV363 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SY1978 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SY1977 @ ( tc_Polynomial_Opoly @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1748,plain,
! [SV364: $i] :
( ( ! [SY1979: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV364 )
| ( ( c_HOL_Ozero__class_Ozero @ SV364 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY1979 @ SV364 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= SY1979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1749,plain,
! [SV365: $i] :
( ( ! [SY1980: $i,SY1981: $i,SY1982: $i,SY1983: $i,SY1984: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV365 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1980 @ SY1981 @ SV365 ) @ SY1982 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1983 @ SY1981 @ SV365 ) @ SY1984 @ SV365 ) )
| ( SY1982
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1983 @ SY1980 @ SV365 ) @ SY1981 @ SV365 ) @ SY1984 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1750,plain,
! [SV366: $i] :
( ( ! [SY1985: $i,SY1986: $i,SY1987: $i,SY1988: $i,SY1989: $i] :
( ~ ( class_Divides_Osemiring__div @ SV366 )
| ( ( c_Divides_Odiv__class_Omod @ SY1985 @ SY1986 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY1987 @ SY1986 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY1988 @ SY1986 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY1989 @ SY1986 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1988 @ SY1985 @ SV366 ) @ SY1986 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY1989 @ SY1987 @ SV366 ) @ SY1986 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1751,plain,
! [SV367: $i] :
( ( ! [SY1990: $i,SY1991: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SY1990 @ SY1991 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SY1990
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1752,plain,
! [SV368: $i] :
( ( ! [SY1992: $i,SY1993: $i,SY1994: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
| ( ( c_Polynomial_Osmult @ SY1992 @ SY1993 @ SV368 )
!= ( c_Polynomial_OpCons @ SY1994 @ SY1993 @ SV368 ) )
| ( SY1993
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1753,plain,
! [SV369: $i] :
( ( ! [SY1995: $i,SY1996: $i,SY1997: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1995 @ SY1996 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SY1997 @ SY1996 @ SV369 ) )
| ( SY1995 = SY1997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1754,plain,
! [SV370: $i] :
( ( ! [SY1998: $i,SY1999: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV370 )
| ( ( c_Polynomial_Opoly__gcd @ SY1998 @ SY1999 @ SV370 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
| ( SY1999
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1755,plain,
! [SV371: $i] :
( ( ! [SY2000: $i,SY2001: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV371 )
| ~ ( class_Int_Onumber__ring @ SV371 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2000 @ SY2001 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SY2000 = SY2001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1756,plain,
! [SV372: $i] :
( ( ! [SY2002: $i,SY2003: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 )
| ( ( c_Power_Opower__class_Opower @ SY2002 @ SY2003 @ SV372 )
!= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
| ( SY2002
= ( c_HOL_Ozero__class_Ozero @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1757,plain,
! [SV373: $i] :
( ( ! [SY2004: $i,SY2005: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV373 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2004 @ SY2004 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SY2005 @ SY2005 @ SV373 ) @ SV373 )
!= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
| ( SY2005
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1758,plain,
! [SV374: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SY2006 @ SY2007 @ SV374 ) @ ( c_Polynomial_OpCons @ SY2008 @ SY2007 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
| ( SY2007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1759,plain,
! [SV375: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV375 )
| ( ( c_HOL_Ozero__class_Ozero @ SV375 )
!= ( c_HOL_Oone__class_Oone @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1760,plain,
! [SV376: $i] :
( ( ! [SY2009: $i,SY2010: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2009 @ SY2010 @ SV376 )
!= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SY2010
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SY2009
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1761,plain,
! [SV377: $i] :
( ( ! [SY2011: $i,SY2012: $i,SY2013: $i,SY2014: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2011 @ SY2012 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SY2013 @ SY2014 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2011 @ SY2014 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SY2013 @ SY2012 @ SV377 ) @ SV377 ) )
| ( SY2012 = SY2014 )
| ( SY2011 = SY2013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1762,plain,
! [SV378: $i] :
( ( ! [SY2015: $i,SY2016: $i] :
( ~ ( class_HOL_Ozero @ SV378 )
| ( ( c_Polynomial_OpCons @ SY2015 @ SY2016 @ SV378 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
| ( SY2016
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1763,plain,
! [SV379: $i] :
( ( ! [SY2017: $i,SY2018: $i,SY2019: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2017 @ SY2018 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SY2017 @ SY2019 @ SV379 ) )
| ( SY2018 = SY2019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1764,plain,
! [SV380: $i] :
( ( ! [SY2020: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV380 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2020 @ SV380 )
!= SY2020 )
| ( SY2020
= ( c_HOL_Ozero__class_Ozero @ SV380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1765,plain,
! [SV381: $i] :
( ( ! [SY2021: $i,SY2022: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV381 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2021 @ SY2021 @ SV381 )
!= ( c_HOL_Otimes__class_Otimes @ SY2022 @ SY2022 @ SV381 ) )
| ( SY2021
= ( c_HOL_Ouminus__class_Ouminus @ SY2022 @ SV381 ) )
| ( SY2021 = SY2022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1766,plain,
! [SV382: $i] :
( ( ! [SY2023: $i,SY2024: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV382 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2023 @ SY2023 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SY2024 @ SY2024 @ SV382 ) @ SV382 )
!= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
| ( SY2023
= ( c_HOL_Ozero__class_Ozero @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1767,plain,
! [SV383: $i] :
( ( ! [SY2025: $i,SY2026: $i,SY2027: $i,SY2028: $i,SY2029: $i] :
( ~ ( class_Divides_Oring__div @ SV383 )
| ( ( c_Divides_Odiv__class_Omod @ SY2025 @ SY2026 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2027 @ SY2026 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2028 @ SY2026 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2029 @ SY2026 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2028 @ SY2025 @ SV383 ) @ SY2026 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2029 @ SY2027 @ SV383 ) @ SY2026 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1768,plain,
! [SV384: $i] :
( ( ! [SY2030: $i,SY2031: $i,SY2032: $i,SY2033: $i] :
( ~ ( class_HOL_Ozero @ SV384 )
| ( ( c_Polynomial_OpCons @ SY2030 @ SY2031 @ SV384 )
!= ( c_Polynomial_OpCons @ SY2032 @ SY2033 @ SV384 ) )
| ( SY2030 = SY2032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1769,plain,
! [SV385: $i] :
( ( ! [SY2034: $i,SY2035: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV385 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2034 @ SY2035 @ SV385 )
!= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2034 @ SV385 )
= SY2035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1770,plain,
! [SV386: $i] :
( ( ! [SY2036: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV386 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2036 @ SV386 )
!= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
| ( SY2036
= ( c_HOL_Ozero__class_Ozero @ SV386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1771,plain,
! [SV387: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV387 )
| ( ( c_Polynomial_Osmult @ SY2037 @ SY2038 @ SV387 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SY2038
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SY2037
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1772,plain,
! [SV388: $i] :
( ( ! [SY2039: $i,SY2040: $i,SY2041: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV388 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2039 @ SY2040 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SY2041 @ SY2041 @ SV388 ) )
| ( SY2039 = SY2040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1773,plain,
! [SV389: $i] :
( ( ! [SY2042: $i,SY2043: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV389 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2042 @ SY2043 @ SV389 )
!= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
| ( SY2042 = SY2043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1774,plain,
! [SV390: $i] :
( ( ! [SY2044: $i,SY2045: $i,SY2046: $i,SY2047: $i,SY2048: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV390 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2044 @ SY2045 @ SV390 ) @ SY2046 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2047 @ SY2045 @ SV390 ) @ SY2048 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2044 @ SY2047 @ SV390 ) @ SY2045 @ SV390 ) @ SY2046 @ SV390 )
= SY2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1775,plain,
! [SV391: $i] :
( ( ! [SY2049: $i,SY2050: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV391 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2049 @ SY2050 @ SV391 )
!= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
| ( SY2049 = SY2050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1776,plain,
! [SV392: $i] :
( ( ! [SY2051: $i,SY2052: $i,SY2053: $i,SY2054: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2051 @ ( c_Polynomial_Osmult @ SY2052 @ SY2053 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SY2054 @ SY2053 @ SV392 ) )
| ( SY2054
= ( c_Polynomial_Opoly @ SY2051 @ SY2052 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1777,plain,
! [SV393: $i] :
( ( ! [SY2055: $i,SY2056: $i,SY2057: $i,SY2058: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV393 )
| ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2055 @ SY2056 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SY2057 @ SY2058 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2055 @ SY2058 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SY2057 @ SY2056 @ SV393 ) @ SV393 ) )
| ( SY2056 = SY2058 )
| ( SY2055 = SY2057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1778,plain,
! [SV394: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV394 )
| ( ( c_HOL_Oone__class_Oone @ SV394 )
!= ( c_HOL_Ozero__class_Ozero @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1779,plain,
! [SV395: $i] :
( ( ! [SY2059: $i,SY2060: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV395 )
| ( ( c_Polynomial_Opoly @ SY2059 @ SY2060 @ SV395 )
!= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SY2060 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SY2059 @ ( tc_Polynomial_Opoly @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1780,plain,
! [SV396: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV396 )
| ( ( c_Polynomial_Opoly__gcd @ SY2061 @ SY2062 @ SV396 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
| ( SY2061
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1781,plain,
! [SV397: $i] :
( ( ! [SY2063: $i,SY2064: $i,SY2065: $i] :
( ~ ( class_Divides_Oring__div @ SV397 )
| ( ( c_Divides_Odiv__class_Omod @ SY2063 @ SY2064 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SY2065 @ SY2064 @ SV397 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SY2063 @ SV397 ) @ SY2064 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SY2065 @ SV397 ) @ SY2064 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1782,plain,
! [SV398: $i] :
( ( ! [SY2066: $i,SY2067: $i,SY2068: $i,SY2069: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV398 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2066 @ ( c_HOL_Oplus__class_Oplus @ SY2067 @ SY2068 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SY2067 @ SY2069 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SY2066 @ SY2068 @ SV398 )
= SY2069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1783,plain,
! [SV399: $i] :
( ( ! [SY2070: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV399 )
| ( ( c_HOL_Oabs__class_Oabs @ SY2070 @ SV399 )
!= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
| ( SY2070
= ( c_HOL_Ozero__class_Ozero @ SV399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1784,plain,
! [SV400: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV400 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2071 @ ( c_HOL_Oplus__class_Oplus @ SY2072 @ SY2073 @ SV400 ) @ SV400 )
!= SY2072 )
| ( SY2071
= ( c_HOL_Ouminus__class_Ouminus @ SY2073 @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1785,plain,
! [SV401: $i] :
( ( ! [SY2074: $i,SY2075: $i,SY2076: $i,SY2077: $i,SY2078: $i] :
( ~ ( class_Divides_Osemiring__div @ SV401 )
| ( ( c_Divides_Odiv__class_Omod @ SY2074 @ SY2075 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2076 @ SY2075 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2077 @ SY2075 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2078 @ SY2075 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2077 @ SY2074 @ SV401 ) @ SY2075 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2078 @ SY2076 @ SV401 ) @ SY2075 @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1786,plain,
! [SV402: $i] :
( ( ! [SY2079: $i,SY2080: $i,SY2081: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV402 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2079 @ SY2079 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SY2080 @ SY2081 @ SV402 ) )
| ( SY2080 = SY2081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1787,plain,
! [SV403: $i] :
( ( ! [SY2082: $i,SY2083: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV403 )
| ~ ( class_Int_Onumber__ring @ SV403 )
| ( SY2082
!= ( c_HOL_Oplus__class_Oplus @ SY2082 @ SY2083 @ SV403 ) )
| ( SY2083
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1788,plain,
! [SV404: $i] :
( ( ! [SY2084: $i,SY2085: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV404 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2084 @ SV404 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2085 @ SV404 ) )
| ( SY2084 = SY2085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1789,plain,
! [SV405: $i] :
( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( class_HOL_Ozero @ SV405 )
| ( ( c_Polynomial_OpCons @ SY2086 @ SY2087 @ SV405 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
| ( SY2086
= ( c_HOL_Ozero__class_Ozero @ SV405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1790,plain,
! [SV406: $i] :
( ( ! [SY2088: $i,SY2089: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV406 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2088 @ SV406 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2089 @ SV406 ) )
| ( SY2088 = SY2089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1791,plain,
! [SV407: $i,SV1: $i] :
( ( ! [SY2090: $i,SY2091: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV1 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ SV407 @ SY2090 @ SV1 ) @ SY2091 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SY2091 @ ( c_Polynomial_Opoly @ SY2090 @ SY2091 @ SV1 ) @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1792,plain,
! [SV408: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV2 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV2 ) ) @ SV408 @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1793,plain,
! [SV409: $i,SV3: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV3 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV3 ) ) @ SV409 @ SV3 )
= ( c_HOL_Ozero__class_Ozero @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1794,plain,
! [SV410: $i,SV4: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV4 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ SV410 @ SY2092 @ SV4 ) @ SY2093 @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ SV410 @ ( c_Polynomial_Opoly @ SY2092 @ SY2093 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1795,plain,
! [SV411: $i,SV5: $i] :
( ( ! [SY2094: $i,SY2095: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV5 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SY2094 @ ( tc_Polynomial_Opoly @ SV5 ) ) @ SY2095 @ SV5 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ SV411 @ SY2095 @ SV5 ) @ ( c_Polynomial_Opoly @ SY2094 @ SY2095 @ SV5 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1796,plain,
! [SV412: $i,SV6: $i] :
( ( ! [SY2096: $i,SY2097: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV6 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ SV412 @ SY2096 @ ( tc_Polynomial_Opoly @ SV6 ) ) @ SY2097 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ SV412 @ SY2097 @ SV6 ) @ ( c_Polynomial_Opoly @ SY2096 @ SY2097 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1797,plain,
! [SV413: $i,SV7: $i] :
( ( ! [SY2098: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV7 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ SV413 @ ( tc_Polynomial_Opoly @ SV7 ) ) @ SY2098 @ SV7 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ SV413 @ SY2098 @ SV7 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1798,plain,
! [SV414: $i,SV8: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV8 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ SV414 @ SY2099 @ ( tc_Polynomial_Opoly @ SV8 ) ) @ SY2100 @ SV8 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ SV414 @ SY2100 @ SV8 ) @ ( c_Polynomial_Opoly @ SY2099 @ SY2100 @ SV8 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1799,plain,
! [SV415: $i,SV9: $i] :
( ( ! [SY2101: $i,SY2102: $i,SY2103: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV9 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SV415 @ SY2101 @ SV9 ) @ ( c_Polynomial_OpCons @ SY2102 @ SY2103 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SV415 @ SY2102 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SY2101 @ SY2103 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1800,plain,
! [SV416: $i,SV10: $i] :
( ( ! [SY2104: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV10 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ SV416 @ SY2104 @ SV10 ) @ ( tc_Polynomial_Opoly @ SV10 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV416 @ SV10 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2104 @ ( tc_Polynomial_Opoly @ SV10 ) ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1801,plain,
! [SV417: $i,SV11: $i] :
( ( ! [SY2105: $i,SY2106: $i,SY2107: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SV417 @ SY2105 @ SV11 ) @ ( c_Polynomial_OpCons @ SY2106 @ SY2107 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SV417 @ SY2106 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SY2105 @ SY2107 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1802,plain,
! [SV418: $i,SV12: $i] :
( ( ! [SY2108: $i,SY2109: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV12 )
| ( ( c_Polynomial_Osmult @ SV418 @ ( c_Polynomial_OpCons @ SY2108 @ SY2109 @ SV12 ) @ SV12 )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SY2108 @ SV12 ) @ ( c_Polynomial_Osmult @ SV418 @ SY2109 @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1803,plain,
! [SV13: $i] :
( ( ( ~ ( class_HOL_Ozero @ SV13 ) )
= $true )
| ( ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV13 ) ) @ SV13 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1804,plain,
! [SV419: $i,SV14: $i] :
( ( ! [SY2110: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV14 )
| ( ( c_Polynomial_Opoly @ SV419 @ SY2110 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SY2110 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SV419 @ ( tc_Polynomial_Opoly @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1805,plain,
! [SV420: $i,SV15: $i] :
( ( ! [SY2111: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV15 )
| ( ( c_Polynomial_Opoly @ SV420 @ ( c_HOL_Ouminus__class_Ouminus @ SY2111 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SY2111 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SV420 @ ( tc_Polynomial_Opoly @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1806,plain,
! [SV421: $i,SV16: $i] :
( ( ! [SY2112: $i] :
( ~ ( class_Divides_Osemiring__div @ SV16 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV421 @ SY2112 @ SV16 ) @ SV421 @ SV16 )
= SY2112 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1807,plain,
! [SV422: $i,SV17: $i] :
( ( ! [SY2113: $i] :
( ~ ( class_Divides_Osemiring__div @ SV17 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV422 @ SY2113 @ SV17 ) @ SY2113 @ SV17 )
= SV422 )
| ( SY2113
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1808,plain,
! [SV423: $i,SV18: $i] :
( ( ! [SY2114: $i,SY2115: $i,SY2116: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SY2114 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SY2115 @ SY2116 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SY2115 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SY2114 @ SY2116 @ SV18 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1809,plain,
! [SV424: $i,SV19: $i] :
( ( ! [SY2117: $i,SY2118: $i,SY2119: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV424 @ SY2117 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SY2118 @ SY2119 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SV424 @ ( c_HOL_Otimes__class_Otimes @ SY2117 @ ( c_HOL_Otimes__class_Otimes @ SY2118 @ SY2119 @ SV19 ) @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1810,plain,
! [SV425: $i,SV20: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SY2120 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SY2121 @ SY2122 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SY2121 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SY2120 @ SV20 ) @ SY2122 @ SV20 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1811,plain,
! [SV426: $i,SV21: $i] :
( ( ! [SY2123: $i,SY2124: $i,SY2125: $i,SY2126: $i,SY2127: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SV426 = SY2123 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2124 @ SY2125 @ SY2123 @ SY2126 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2124 @ SY2125 @ SV426 @ SY2127 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1812,plain,
! [SV427: $i,SV22: $i] :
( ( ! [SY2128: $i,SY2129: $i,SY2130: $i,SY2131: $i,SY2132: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SV427 = SY2128 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2129 @ SY2130 @ SY2131 @ SY2128 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2129 @ SY2130 @ SY2132 @ SV427 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1813,plain,
! [SV428: $i,SV23: $i] :
( ( ! [SY2133: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV428 @ SV23 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SY2133 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1814,plain,
! [SV429: $i,SV24: $i] :
( ( ! [SY2134: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV24 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ ( c_HOL_Otimes__class_Otimes @ SY2134 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1815,plain,
! [SV25: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV25 ) )
= $true )
| ( ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) @ SV25 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1816,plain,
! [SV430: $i,SV26: $i] :
( ( ! [SY2135: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV26 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SY2135 @ SV26 ) @ SV26 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV430 @ SV26 ) @ ( c_HOL_Oabs__class_Oabs @ SY2135 @ SV26 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1817,plain,
! [SV431: $i,SV27: $i] :
( ( ! [SY2136: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV27 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SY2136 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV431 @ SV27 ) @ SY2136 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1818,plain,
! [SV432: $i,SV28: $i] :
( ( ! [SY2137: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV28 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV432 @ SY2137 @ SV28 ) @ SV28 )
= ( c_HOL_Otimes__class_Otimes @ SV432 @ ( c_HOL_Ouminus__class_Ouminus @ SY2137 @ SV28 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1819,plain,
! [SV433: $i,SV29: $i] :
( ( ! [SY2138: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
| ( ( c_HOL_Otimes__class_Otimes @ SV433 @ ( c_HOL_Otimes__class_Otimes @ SV433 @ SY2138 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV433 @ SY2138 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1820,plain,
! [SV434: $i,SV30: $i] :
( ( ! [SY2139: $i,SY2140: $i,SY2141: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SY2139 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SY2140 @ SY2141 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SY2140 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SY2139 @ SY2141 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2141 @ SY2140 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2139 @ SV434 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1821,plain,
! [SV435: $i,SV31: $i] :
( ( ! [SY2142: $i,SY2143: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV31 )
| ( SV435 = SY2142 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2142 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SY2143 @ SV435 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1822,plain,
! [SV436: $i,SV32: $i] :
( ( ! [SY2144: $i] :
( ~ ( class_Divides_Osemiring__div @ SV32 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV436 @ SV32 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SY2144 @ SV32 ) @ SV32 )
= ( c_HOL_Ozero__class_Ozero @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1823,plain,
! [SV437: $i,SV33: $i] :
( ( ! [SY2145: $i] :
( ~ ( class_Divides_Osemiring__div @ SV33 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SY2145 @ SV33 ) @ SV437 @ SV33 )
= ( c_Divides_Odiv__class_Omod @ SY2145 @ SV437 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1824,plain,
! [SV438: $i,SV34: $i] :
( ( ! [SY2146: $i] :
( ~ ( class_Divides_Osemiring__div @ SV34 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV438 @ SY2146 @ SV34 ) @ SY2146 @ SV34 )
= ( c_Divides_Odiv__class_Omod @ SV438 @ SY2146 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1825,plain,
! [SV439: $i,SV35: $i] :
( ( ! [SY2147: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SV439 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV439 @ SV35 ) @ SY2147 @ SV35 ) @ SV35 )
= SY2147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1826,plain,
! [SV440: $i,SV36: $i] :
( ( ! [SY2148: $i,SY2149: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV36 )
| ( ( c_Divides_Odiv__class_Omod @ SV440 @ ( c_HOL_Otimes__class_Otimes @ SY2148 @ SY2149 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2148 @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ SV440 @ SY2148 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ SY2149 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( c_Divides_Odiv__class_Omod @ SV440 @ SY2148 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1827,plain,
! [SV441: $i,SV37: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV37 )
| ( ( c_HOL_Otimes__class_Otimes @ SV441 @ SV441 @ SV37 )
= SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1828,plain,
! [SV442: $i,SV38: $i] :
( ( ! [SY2150: $i,SY2151: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV38 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SY2150 @ SY2151 @ SV38 )
| ( SY2150
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1829,plain,
! [SV443: $i,SV39: $i] :
( ( ! [SY2152: $i,SY2153: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV39 )
| ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SY2152 @ SV443 @ SY2153 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1830,plain,
! [SV444: $i,SV40: $i] :
( ( ! [SY2154: $i,SY2155: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV40 )
| ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SY2154 @ SY2155 @ SV444 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1831,plain,
! [SV445: $i,SV41: $i] :
( ( ! [SY2156: $i,SY2157: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV41 )
| ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2156 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SY2157 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1832,plain,
! [SV446: $i,SV42: $i] :
( ( ! [SY2158: $i,SY2159: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SY2158 @ SV42 ) @ SY2159 @ SV42 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV446 @ SY2159 @ SV42 ) @ ( c_Power_Opower__class_Opower @ SY2158 @ SY2159 @ SV42 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1833,plain,
! [SV447: $i,SV43: $i] :
( ( ! [SY2160: $i,SY2161: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV43 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SY2160 @ SV43 ) @ SY2161 @ SV43 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV447 @ SY2161 @ SV43 ) @ ( c_Power_Opower__class_Opower @ SY2160 @ SY2161 @ SV43 ) @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1834,plain,
! [SV448: $i,SV44: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ~ ( class_Divides_Osemiring__div @ SV44 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ ( c_Divides_Odiv__class_Omod @ SY2162 @ SY2163 @ SV44 ) @ SV44 ) @ SY2163 @ SV44 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SY2162 @ SV44 ) @ SY2163 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1835,plain,
! [SV449: $i,SV45: $i] :
( ( ! [SY2164: $i,SY2165: $i] :
( ~ ( class_Divides_Osemiring__div @ SV45 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV449 @ SY2164 @ SV45 ) @ SY2165 @ SV45 ) @ SY2164 @ SV45 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV449 @ SY2165 @ SV45 ) @ SY2164 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1836,plain,
! [SV450: $i,SV46: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i,SY2169: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV46 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2166 @ ( c_HOL_Otimes__class_Otimes @ SY2167 @ SY2168 @ SV46 ) @ SV46 ) @ SY2169 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SY2166 @ SY2169 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SY2168 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1837,plain,
! [SV451: $i,SV47: $i] :
( ( ! [SY2170: $i,SY2171: $i,SY2172: $i,SY2173: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV47 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SY2170 @ SY2171 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2170 @ ( c_HOL_Otimes__class_Otimes @ SY2172 @ SY2173 @ SV47 ) @ SV47 ) @ SY2171 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SY2173 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1838,plain,
! [SV452: $i,SV48: $i] :
( ( ! [SY2174: $i] :
( ~ ( class_Divides_Osemiring__div @ SV48 )
| ( SV452
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV452 @ SY2174 @ SV48 ) @ SY2174 @ SV48 ) @ ( c_Divides_Odiv__class_Omod @ SV452 @ SY2174 @ SV48 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1839,plain,
! [SV453: $i,SV49: $i] :
( ( ! [SY2175: $i] :
( ~ ( class_Divides_Osemiring__div @ SV49 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV453 @ SY2175 @ SV49 ) @ SY2175 @ SV49 ) @ ( c_Divides_Odiv__class_Omod @ SV453 @ SY2175 @ SV49 ) @ SV49 )
= SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1840,plain,
! [SV454: $i,SV50: $i] :
( ( ! [SY2176: $i] :
( ~ ( class_Divides_Osemiring__div @ SV50 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_Divides_Odiv__class_Odiv @ SY2176 @ SV454 @ SV50 ) @ SV50 ) @ ( c_Divides_Odiv__class_Omod @ SY2176 @ SV454 @ SV50 ) @ SV50 )
= SY2176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1841,plain,
! [SV455: $i,SV51: $i] :
( ( ~ ( class_Int_Onumber__ring @ SV51 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV455 @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV51 ) @ SV455 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1842,plain,
! [SV456: $i,SV52: $i] :
( ( ! [SY2177: $i] :
( ~ ( class_Divides_Oring__div @ SV52 )
| ( ( c_Divides_Odiv__class_Odiv @ SV456 @ ( c_HOL_Ouminus__class_Ouminus @ SY2177 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV456 @ SY2177 @ SV52 ) @ SV52 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2177 @ SV456 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1843,plain,
! [SV457: $i,SV53: $i] :
( ( ! [SY2178: $i] :
( ~ ( class_Divides_Oring__div @ SV53 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV457 @ SV53 ) @ SY2178 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV457 @ SY2178 @ SV53 ) @ SV53 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2178 @ SV457 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1844,plain,
! [SV458: $i,SV54: $i] :
( ( ! [SY2179: $i,SY2180: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY2179 @ SV54 ) @ SY2180 @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV458 @ ( c_HOL_Otimes__class_Otimes @ SY2179 @ SY2180 @ SV54 ) @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1845,plain,
! [SV459: $i,SV55: $i] :
( ( ! [SY2181: $i,SY2182: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SY2181 @ SV55 ) @ SY2182 @ SV55 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SY2182 @ SV55 ) @ SY2181 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1846,plain,
! [SV460: $i,SV56: $i] :
( ( ! [SY2183: $i,SY2184: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV460 @ SY2183 @ SV56 ) @ SY2184 @ SV56 )
= ( c_HOL_Otimes__class_Otimes @ SV460 @ ( c_HOL_Otimes__class_Otimes @ SY2183 @ SY2184 @ SV56 ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1847,plain,
! [SV461: $i,SV57: $i] :
( ( ! [SY2185: $i,SY2186: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SY2185 @ SY2186 @ SV57 ) @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV461 @ SY2185 @ SV57 ) @ SY2186 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1848,plain,
! [SV462: $i,SV58: $i] :
( ( ! [SY2187: $i,SY2188: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV58 )
| ( ( c_HOL_Otimes__class_Otimes @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SY2187 @ SY2188 @ SV58 ) @ SV58 )
= ( c_HOL_Otimes__class_Otimes @ SY2187 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SY2188 @ SV58 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1849,plain,
! [SV463: $i,SV59: $i] :
( ( ! [SY2189: $i,SY2190: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( c_HOL_Otimes__class_Otimes @ SV463 @ ( c_HOL_Otimes__class_Otimes @ SY2189 @ SY2190 @ SV59 ) @ SV59 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV463 @ SY2189 @ SV59 ) @ SY2190 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1850,plain,
! [SV464: $i,SV60: $i] :
( ( ! [SY2191: $i,SY2192: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV464 @ SY2191 @ SV60 ) @ SY2192 @ SV60 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV464 @ SY2192 @ SV60 ) @ ( c_HOL_Otimes__class_Otimes @ SY2191 @ SY2192 @ SV60 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1851,plain,
! [SV465: $i,SV61: $i] :
( ( ! [SY2193: $i,SY2194: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV61 )
| ( ( c_HOL_Otimes__class_Otimes @ SV465 @ ( c_HOL_Oplus__class_Oplus @ SY2193 @ SY2194 @ SV61 ) @ SV61 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SY2193 @ SV61 ) @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SY2194 @ SV61 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1852,plain,
! [SV466: $i,SV62: $i] :
( ( ! [SY2195: $i,SY2196: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV62 )
| ( ( c_HOL_Otimes__class_Otimes @ SV466 @ ( c_HOL_Oplus__class_Oplus @ SY2195 @ SY2196 @ SV62 ) @ SV62 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SY2195 @ SV62 ) @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SY2196 @ SV62 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1853,plain,
! [SV467: $i,SV63: $i] :
( ( ! [SY2197: $i,SY2198: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV63 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV467 @ SY2197 @ SV63 ) @ SY2198 @ SV63 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV467 @ SY2198 @ SV63 ) @ ( c_HOL_Otimes__class_Otimes @ SY2197 @ SY2198 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1854,plain,
! [SV468: $i,SV64: $i] :
( ( ! [SY2199: $i,SY2200: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV64 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SY2199 @ SV64 ) @ SY2200 @ SV64 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SY2200 @ SV64 ) @ ( c_HOL_Otimes__class_Otimes @ SY2199 @ SY2200 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1855,plain,
! [SV469: $i,SV65: $i] :
( ( ! [SY2201: $i,SY2202: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV65 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV469 @ SY2201 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ SY2202 @ ( tc_Polynomial_Opoly @ SV65 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV469 @ SY2202 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY2201 @ SY2202 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( tc_Polynomial_Opoly @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1856,plain,
! [SV470: $i,SV66: $i] :
( ( ! [SY2203: $i,SY2204: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ SV470 @ ( c_HOL_Oplus__class_Oplus @ SY2203 @ SY2204 @ SV66 ) @ SV66 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SY2203 @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SY2204 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1857,plain,
! [SV471: $i,SV67: $i] :
( ( ! [SY2205: $i,SY2206: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV471 @ SY2205 @ SV67 ) @ SY2206 @ SV67 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV471 @ SY2206 @ SV67 ) @ ( c_HOL_Otimes__class_Otimes @ SY2205 @ SY2206 @ SV67 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1858,plain,
! [SV472: $i,SV68: $i] :
( ( ! [SY2207: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV68 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV472 @ SY2207 @ SV68 ) @ SV68 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY2207 @ SV472 @ SV68 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1859,plain,
! [SV473: $i,SV69: $i] :
( ( ! [SY2208: $i] :
( ~ ( class_Divides_Osemiring__div @ SV69 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SY2208 @ SV69 ) @ SV473 @ SV69 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SY2208 @ SV473 @ SV69 ) @ ( c_HOL_Oone__class_Oone @ SV69 ) @ SV69 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1860,plain,
! [SV474: $i,SV70: $i] :
( ( ! [SY2209: $i] :
( ~ ( class_Divides_Osemiring__div @ SV70 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SY2209 @ SV70 ) @ SY2209 @ SV70 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV474 @ SY2209 @ SV70 ) @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV70 ) )
| ( SY2209
= ( c_HOL_Ozero__class_Ozero @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1861,plain,
! [SV71: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV71 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ SV71 ) @ SV71 )
= ( c_HOL_Oone__class_Oone @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1862,plain,
! [SV475: $i,SV72: $i] :
( ( ! [SY2210: $i,SY2211: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SY2210 @ SV72 ) @ ( c_HOL_Otimes__class_Otimes @ SY2211 @ SY2210 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV475 @ SY2211 @ SV72 ) @ SY2210 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1863,plain,
! [SV476: $i,SV73: $i] :
( ( ! [SY2212: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV73 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV476 @ SV73 ) @ SY2212 @ SV73 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SY2212 @ SV73 ) @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1864,plain,
! [SV477: $i,SV74: $i] :
( ( ! [SY2213: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV74 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV477 @ SV74 ) @ SY2213 @ SV74 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV477 @ SY2213 @ SV74 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1865,plain,
! [SV478: $i,SV75: $i] :
( ( ! [SY2214: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV75 )
| ( ( c_HOL_Otimes__class_Otimes @ SV478 @ ( c_HOL_Ouminus__class_Ouminus @ SY2214 @ SV75 ) @ SV75 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV478 @ SY2214 @ SV75 ) @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1866,plain,
! [SV479: $i,SV76: $i] :
( ( ! [SY2215: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV76 )
| ( ( c_HOL_Otimes__class_Otimes @ SV479 @ ( c_HOL_Ouminus__class_Ouminus @ SY2215 @ SV76 ) @ SV76 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SY2215 @ SV76 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1867,plain,
! [SV480: $i,SV77: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV77 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV77 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV77 ) @ SV77 )
= ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1868,plain,
! [SV481: $i,SV78: $i] :
( ( ! [SY2216: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV78 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV78 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2216 @ SV78 ) @ SV78 )
= ( c_HOL_Otimes__class_Otimes @ SV481 @ SY2216 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1869,plain,
! [SV482: $i,SV79: $i] :
( ( ! [SY2217: $i,SY2218: $i] :
( ~ ( class_Divides_Osemiring__div @ SV79 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SY2217 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SY2218 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SY2217 @ SY2218 @ SV79 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1870,plain,
! [SV483: $i,SV80: $i] :
( ( ! [SY2219: $i,SY2220: $i] :
( ~ ( class_Divides_Osemiring__div @ SV80 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV483 @ SY2219 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SY2220 @ SY2219 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SV483 @ SY2220 @ SV80 ) )
| ( SY2219
= ( c_HOL_Ozero__class_Ozero @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1871,plain,
! [SV484: $i,SV81: $i] :
( ( ! [SY2221: $i] :
( ~ ( class_Divides_Oring__div @ SV81 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV484 @ SV81 ) @ SY2221 @ SV81 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV484 @ SY2221 @ SV81 ) @ SV81 ) @ SY2221 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1872,plain,
! [SV485: $i,SV82: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV82 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV485 @ SV82 )
= ( c_HOL_Ouminus__class_Ouminus @ SV485 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1873,plain,
! [SV486: $i,SV83: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV83 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV83 ) ) @ SV486 @ ( tc_Polynomial_Opoly @ SV83 ) )
= ( c_HOL_Ouminus__class_Ouminus @ SV486 @ ( tc_Polynomial_Opoly @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1874,plain,
! [SV487: $i,SV84: $i] :
( ( ! [SY2222: $i,SY2223: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ SV487 @ SY2222 @ SV84 ) @ SY2223 @ ( tc_Polynomial_Opoly @ SV84 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV487 @ SY2223 @ SV84 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( c_HOL_Otimes__class_Otimes @ SY2222 @ SY2223 @ ( tc_Polynomial_Opoly @ SV84 ) ) @ SV84 ) @ ( tc_Polynomial_Opoly @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1875,plain,
! [SV488: $i,SV85: $i] :
( ( ! [SY2224: $i,SY2225: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV85 )
| ( ( c_HOL_Otimes__class_Otimes @ SV488 @ ( c_Polynomial_OpCons @ SY2224 @ SY2225 @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SY2224 @ SV488 @ SV85 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_HOL_Otimes__class_Otimes @ SV488 @ SY2225 @ ( tc_Polynomial_Opoly @ SV85 ) ) @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1876,plain,
! [SV489: $i,SV86: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV86 )
| ( ( c_Divides_Odiv__class_Odiv @ SV489 @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1877,plain,
! [SV490: $i,SV87: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV87 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV490 @ SV87 )
= ( c_HOL_Ozero__class_Ozero @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1878,plain,
! [SV491: $i,SV88: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV88 )
| ( ( c_HOL_Ominus__class_Ominus @ SV491 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV88 ) ) @ ( tc_Polynomial_Opoly @ SV88 ) )
= SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1879,plain,
! [SV492: $i,SV89: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV89 )
| ( ( c_HOL_Ominus__class_Ominus @ SV492 @ SV492 @ SV89 )
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1880,plain,
! [SV493: $i,SV90: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV90 )
| ( ( c_HOL_Ominus__class_Ominus @ SV493 @ SV493 @ SV90 )
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1881,plain,
! [SV494: $i,SV91: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV91 )
| ( ( c_HOL_Ominus__class_Ominus @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1882,plain,
! [SV495: $i,SV92: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV92 )
| ( ( c_HOL_Ominus__class_Ominus @ SV495 @ SV495 @ SV92 )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1883,plain,
! [SV496: $i,SV93: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV93 )
| ~ ( class_Int_Onumber__ring @ SV93 )
| ( ( c_HOL_Ominus__class_Ominus @ SV496 @ SV496 @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1884,plain,
! [SV497: $i,SV94: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV94 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV94 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SV497 @ SV94 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1885,plain,
! [SV498: $i,SV95: $i] :
( ( ! [SY2226: $i,SY2227: $i,SY2228: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2226 @ SY2227 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SY2228 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SY2227 @ SY2226 @ SY2228 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1886,plain,
! [SV499: $i,SV96: $i] :
( ( ! [SY2229: $i,SY2230: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV96 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ SV499 @ SY2229 @ SV96 ) @ SY2230 @ SV96 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV499 @ SY2230 @ SV96 ) @ ( c_Polynomial_Osmult @ SY2229 @ SY2230 @ SV96 ) @ ( tc_Polynomial_Opoly @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1887,plain,
! [SV500: $i,SV97: $i] :
( ( ! [SY2231: $i,SY2232: $i,SY2233: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV97 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SY2231 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2232 @ SV500 @ SV97 ) @ SY2231 @ SV97 ) @ SY2233 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2232 @ SY2231 @ SV97 ) @ SY2233 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1888,plain,
! [SV501: $i,SV98: $i] :
( ( ! [SY2234: $i,SY2235: $i] :
( ~ ( class_Divides_Osemiring__div @ SV98 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SY2234 @ SV98 ) @ SY2235 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SY2235 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SY2234 @ SY2235 @ SV98 ) @ SV98 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2235 @ SY2234 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2235 @ SV501 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1889,plain,
! [SV502: $i,SV99: $i] :
( ( ! [SY2236: $i,SY2237: $i] :
( ~ ( class_Divides_Osemiring__div @ SV99 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV502 @ SY2236 @ SV99 ) @ SY2237 @ SV99 ) @ SY2236 @ SV99 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SY2237 @ SV99 ) @ SY2236 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1890,plain,
! [SV503: $i,SV100: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ SV503 @ ( c_HOL_Oone__class_Oone @ SV100 ) @ SV100 )
= SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1891,plain,
! [SV504: $i,SV101: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV504 @ SV101 )
= SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1892,plain,
! [SV505: $i,SV102: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV102 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV505 @ SV102 )
= SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1893,plain,
! [SV506: $i,SV103: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV506 @ SV103 )
= SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1894,plain,
! [SV507: $i,SV104: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV104 )
| ( ( c_HOL_Otimes__class_Otimes @ SV507 @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV104 )
= SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1895,plain,
! [SV508: $i,SV105: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV105 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV508 @ SV105 )
= SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1896,plain,
! [SV509: $i,SV106: $i] :
( ( ! [SY2238: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV106 )
| ( c_Polynomial_Opdivmod__rel @ SV509 @ SY2238 @ ( c_Divides_Odiv__class_Odiv @ SV509 @ SY2238 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ ( c_Divides_Odiv__class_Omod @ SV509 @ SY2238 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1897,plain,
! [SV510: $i,SV107: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV107 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV510 @ SV107 )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1898,plain,
! [SV511: $i,SV108: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV108 )
| ~ ( class_Int_Onumber__ring @ SV108 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SY2239 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SY2240 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SY2240 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SY2239 @ SV108 ) @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1899,plain,
! [SV512: $i,SV109: $i] :
( ( ! [SY2241: $i,SY2242: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV109 )
| ~ ( class_Int_Onumber__ring @ SV109 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SY2241 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SY2242 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SY2242 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SY2241 @ SV109 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1900,plain,
! [SV513: $i,SV110: $i] :
( ( ! [SY2243: $i,SY2244: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV110 )
| ( ( c_Polynomial_Opoly__gcd @ SV513 @ ( c_Polynomial_Opoly__gcd @ SY2243 @ SY2244 @ SV110 ) @ SV110 )
= ( c_Polynomial_Opoly__gcd @ SY2243 @ ( c_Polynomial_Opoly__gcd @ SV513 @ SY2244 @ SV110 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1901,plain,
! [SV514: $i,SV111: $i] :
( ( ! [SY2245: $i,SY2246: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV111 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ SV514 @ SY2245 @ SV111 ) @ SY2246 @ SV111 )
= ( c_Polynomial_Opoly__gcd @ SV514 @ ( c_Polynomial_Opoly__gcd @ SY2245 @ SY2246 @ SV111 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1902,plain,
! [SV515: $i,SV112: $i] :
( ( ! [SY2247: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV112 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SY2247 @ SV112 ) @ SY2247 @ SV112 )
= SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1903,plain,
! [SV516: $i,SV113: $i] :
( ( ! [SY2248: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV113 )
| ( ( c_Polynomial_Opoly__gcd @ SV516 @ ( c_HOL_Ouminus__class_Ouminus @ SY2248 @ ( tc_Polynomial_Opoly @ SV113 ) ) @ SV113 )
= ( c_Polynomial_Opoly__gcd @ SV516 @ SY2248 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1904,plain,
! [SV517: $i,SV114: $i] :
( ( ! [SY2249: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV114 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ SV517 @ ( tc_Polynomial_Opoly @ SV114 ) ) @ SY2249 @ SV114 )
= ( c_Polynomial_Opoly__gcd @ SV517 @ SY2249 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1905,plain,
! [SV518: $i,SV115: $i] :
( ( ! [SY2250: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( c_HOL_Otimes__class_Otimes @ SV518 @ SY2250 @ SV115 )
= ( c_HOL_Otimes__class_Otimes @ SY2250 @ SV518 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1906,plain,
! [SV116: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV116 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1907,plain,
! [SV519: $i,SV117: $i] :
( ( ! [SY2251: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( c_HOL_Otimes__class_Otimes @ SV519 @ SY2251 @ SV117 )
= ( c_HOL_Otimes__class_Otimes @ SY2251 @ SV519 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1908,plain,
! [SV520: $i,SV118: $i] :
( ( ! [SY2252: $i,SY2253: $i] :
( ~ ( class_Divides_Osemiring__div @ SV118 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV520 @ SY2252 @ SV118 ) @ SY2253 @ SV118 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV520 @ SY2253 @ SV118 ) @ ( c_Divides_Odiv__class_Omod @ SY2252 @ SY2253 @ SV118 ) @ SV118 ) @ SY2253 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1909,plain,
! [SV119: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV119 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
= ( c_HOL_Ozero__class_Ozero @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1910,plain,
! [SV521: $i,SV120: $i] :
( ( ! [SY2254: $i,SY2255: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV120 )
| ( ( c_HOL_Oplus__class_Oplus @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SY2254 @ SY2255 @ SV120 ) @ SV120 )
= ( c_HOL_Oplus__class_Oplus @ SY2254 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SY2255 @ SV120 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1911,plain,
! [SV522: $i,SV121: $i] :
( ( ! [SY2256: $i,SY2257: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV121 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV522 @ SY2256 @ SV121 ) @ SY2257 @ SV121 )
= ( c_HOL_Oplus__class_Oplus @ SV522 @ ( c_HOL_Oplus__class_Oplus @ SY2256 @ SY2257 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1912,plain,
! [SV523: $i,SV122: $i] :
( ( ! [SY2258: $i,SY2259: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Oplus__class_Oplus @ SV523 @ ( c_HOL_Oplus__class_Oplus @ SY2258 @ SY2259 @ SV122 ) @ SV122 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV523 @ SY2258 @ SV122 ) @ SY2259 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1913,plain,
! [SV524: $i,SV123: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV123 )
| ( ( c_HOL_Oplus__class_Oplus @ SV524 @ ( c_HOL_Oplus__class_Oplus @ SY2260 @ SY2261 @ SV123 ) @ SV123 )
= ( c_HOL_Oplus__class_Oplus @ SY2260 @ ( c_HOL_Oplus__class_Oplus @ SV524 @ SY2261 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1914,plain,
! [SV525: $i,SV124: $i] :
( ( ! [SY2262: $i,SY2263: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SY2262 @ SV124 ) @ SY2263 @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ SV525 @ ( c_HOL_Oplus__class_Oplus @ SY2262 @ SY2263 @ SV124 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1915,plain,
! [SV526: $i,SV125: $i] :
( ( ! [SY2264: $i,SY2265: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ SV526 @ ( c_HOL_Oplus__class_Oplus @ SY2264 @ SY2265 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SY2264 @ SV125 ) @ SY2265 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1916,plain,
! [SV527: $i,SV126: $i] :
( ( ! [SY2266: $i,SY2267: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SY2266 @ SV126 ) @ SY2267 @ SV126 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SY2267 @ SV126 ) @ SY2266 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1917,plain,
! [SV528: $i,SV127: $i] :
( ( ! [SY2268: $i,SY2269: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Oplus__class_Oplus @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SY2268 @ SY2269 @ SV127 ) @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ SY2268 @ ( c_HOL_Oplus__class_Oplus @ SV528 @ SY2269 @ SV127 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1918,plain,
! [SV529: $i,SV128: $i] :
( ( ! [SY2270: $i,SY2271: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV529 @ SY2270 @ SV128 ) @ SY2271 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ SV529 @ ( c_HOL_Oplus__class_Oplus @ SY2270 @ SY2271 @ SV128 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1919,plain,
! [SV530: $i,SV129: $i] :
( ( ! [SY2272: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV129 )
| ( ( c_Divides_Odiv__class_Odiv @ SV530 @ ( c_HOL_Ouminus__class_Ouminus @ SY2272 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV530 @ SY2272 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1920,plain,
! [SV531: $i,SV130: $i] :
( ( ! [SY2273: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV130 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV531 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ SY2273 @ ( tc_Polynomial_Opoly @ SV130 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV531 @ SY2273 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ ( tc_Polynomial_Opoly @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1921,plain,
! [SV532: $i,SV131: $i] :
( ( ! [SY2274: $i,SY2275: $i] :
( ~ ( class_Divides_Osemiring__div @ SV131 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SY2274 @ SV131 ) @ SY2275 @ SV131 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ ( c_Divides_Odiv__class_Omod @ SY2274 @ SY2275 @ SV131 ) @ SV131 ) @ SY2275 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1922,plain,
! [SV533: $i,SV132: $i] :
( ( ! [SY2276: $i,SY2277: $i] :
( ~ ( class_Divides_Osemiring__div @ SV132 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SY2276 @ SV132 ) @ SY2277 @ SV132 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV533 @ SY2277 @ SV132 ) @ SY2276 @ SV132 ) @ SY2277 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1923,plain,
! [SV534: $i,SV133: $i] :
( ( ! [SY2278: $i,SY2279: $i,SY2280: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( ( c_Divides_Odiv__class_Omod @ SV534 @ SY2278 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SY2279 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SY2278 @ SY2280 @ SY2279 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1924,plain,
! [SV535: $i,SV134: $i] :
( ( ! [SY2281: $i,SY2282: $i,SY2283: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV134 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV535 @ SY2281 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SY2282 @ SY2283 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SY2282 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SY2281 @ SY2283 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SY2282 @ SV134 ) @ SY2283 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SY2282 @ ( c_HOL_Ominus__class_Ominus @ SY2281 @ SY2283 @ SV134 ) @ SV134 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1925,plain,
! [SV536: $i,SV135: $i] :
( ( ! [SY2284: $i,SY2285: $i,SY2286: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV536 @ SY2284 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2285 @ SY2284 @ SV135 ) @ SY2286 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV536 @ SY2285 @ SV135 ) @ SY2284 @ SV135 ) @ SY2286 @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1926,plain,
! [SV537: $i,SV136: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV136 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV537 @ SV136 ) @ SV537 @ SV136 )
= ( c_HOL_Ozero__class_Ozero @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1927,plain,
! [SV538: $i,SV137: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV538 @ SV137 ) @ SV538 @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1928,plain,
! [SV539: $i,SV138: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Ouminus__class_Ouminus @ SV539 @ SV138 ) @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1929,plain,
! [SV540: $i,SV139: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV139 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV540 @ SV139 ) @ SV540 @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1930,plain,
! [SV541: $i,SV140: $i] :
( ( ! [SY2287: $i,SY2288: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV140 )
| ( ( c_HOL_Otimes__class_Otimes @ SV541 @ ( c_HOL_Ominus__class_Ominus @ SY2287 @ SY2288 @ SV140 ) @ SV140 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SY2287 @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SY2288 @ SV140 ) @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1931,plain,
! [SV542: $i,SV141: $i] :
( ( ! [SY2289: $i,SY2290: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV141 )
| ( ( c_HOL_Otimes__class_Otimes @ SV542 @ ( c_HOL_Ominus__class_Ominus @ SY2289 @ SY2290 @ SV141 ) @ SV141 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SY2289 @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SY2290 @ SV141 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1932,plain,
! [SV543: $i,SV142: $i] :
( ( ! [SY2291: $i,SY2292: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV543 @ SY2291 @ SV142 ) @ SY2292 @ SV142 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV543 @ SY2292 @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY2291 @ SY2292 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1933,plain,
! [SV544: $i,SV143: $i] :
( ( ! [SY2293: $i,SY2294: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV143 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV544 @ SY2293 @ SV143 ) @ SY2294 @ SV143 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV544 @ SY2294 @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SY2293 @ SY2294 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1934,plain,
! [SV545: $i,SV144: $i] :
( ( ! [SY2295: $i,SY2296: $i,SY2297: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV144 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SY2295 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SY2296 @ SY2297 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV545 @ SY2296 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SY2295 @ SY2297 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1935,plain,
! [SV546: $i,SV145: $i] :
( ( ! [SY2298: $i,SY2299: $i] :
( ~ ( class_Divides_Osemiring__div @ SV145 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SY2298 @ SV145 ) @ SY2299 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SY2299 @ SV145 ) @ SY2298 @ SV145 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2298 @ SV546 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1936,plain,
! [SV547: $i,SV146: $i] :
( ( ! [SY2300: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV547 @ SY2300 @ SV146 ) @ SV146 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV547 @ SV146 ) @ SY2300 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1937,plain,
! [SV548: $i,SV147: $i] :
( ( ! [SY2301: $i,SY2302: $i] :
( ~ ( class_Divides_Osemiring__div @ SV147 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ SY2301 @ SV147 ) @ SY2302 @ SV147 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ ( c_Divides_Odiv__class_Omod @ SY2301 @ SY2302 @ SV147 ) @ SV147 ) @ SY2302 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1938,plain,
! [SV549: $i,SV148: $i] :
( ( ! [SY2303: $i,SY2304: $i] :
( ~ ( class_Divides_Osemiring__div @ SV148 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV549 @ SY2303 @ SV148 ) @ SY2304 @ SV148 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV549 @ SY2304 @ SV148 ) @ SY2303 @ SV148 ) @ SY2304 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1939,plain,
! [SV550: $i,SV149: $i] :
( ( ! [SY2305: $i,SY2306: $i,SY2307: $i,SY2308: $i,SY2309: $i,SY2310: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SY2305 @ SY2306 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2307 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2305 @ SY2308 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2309 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2310 @ SY2306 @ SY2307 @ SY2308 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SY2305 @ SY2310 @ SY2309 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1940,plain,
! [SV551: $i,SV150: $i] :
( ( ! [SY2311: $i] :
( ~ ( class_Divides_Osemiring__div @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ SV551 @ ( c_Divides_Odiv__class_Odiv @ SY2311 @ SV551 @ SV150 ) @ SV150 )
= SY2311 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV551 @ SY2311 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1941,plain,
! [SV552: $i,SV151: $i] :
( ( ! [SY2312: $i] :
( ~ ( class_Divides_Osemiring__div @ SV151 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV552 @ SY2312 @ SV151 ) @ SY2312 @ SV151 )
= SV552 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2312 @ SV552 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1942,plain,
! [SV553: $i,SV152: $i] :
( ( ! [SY2313: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV152 )
| ( ( c_HOL_Ominus__class_Ominus @ SV553 @ ( c_HOL_Ouminus__class_Ouminus @ SY2313 @ SV152 ) @ SV152 )
= ( c_HOL_Oplus__class_Oplus @ SV553 @ SY2313 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1943,plain,
! [SV554: $i,SV153: $i] :
( ( ! [SY2314: $i,SY2315: $i] :
( ~ ( class_Divides_Osemiring__div @ SV153 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV554 @ ( c_HOL_Otimes__class_Otimes @ SY2314 @ SY2315 @ SV153 ) @ SV153 ) @ SY2314 @ SV153 )
= ( c_Divides_Odiv__class_Omod @ SV554 @ SY2314 @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1944,plain,
! [SV555: $i,SV154: $i] :
( ( ! [SY2316: $i,SY2317: $i] :
( ~ ( class_Divides_Osemiring__div @ SV154 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SY2316 @ SY2317 @ SV154 ) @ SV154 ) @ SY2317 @ SV154 )
= ( c_Divides_Odiv__class_Omod @ SV555 @ SY2317 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1945,plain,
! [SV556: $i,SV155: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV155 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SY2318 @ SV155 )
| ( SY2319
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SY2319 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SY2318 @ SY2319 @ SV155 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1946,plain,
! [SV557: $i,SV156: $i] :
( ( ! [SY2320: $i,SY2321: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV156 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SY2320 @ SV156 )
| ( SY2321
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2321 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SY2321 @ SY2320 @ SV156 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1947,plain,
! [SV558: $i,SV157: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV157 ) ) @ SV558 @ ( tc_Polynomial_Opoly @ SV157 ) )
= SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1948,plain,
! [SV559: $i,SV158: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV158 )
| ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV158 ) ) @ ( tc_Polynomial_Opoly @ SV158 ) )
= SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1949,plain,
! [SV560: $i,SV159: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV159 )
| ( ( c_HOL_Oplus__class_Oplus @ SV560 @ ( c_HOL_Ozero__class_Ozero @ SV159 ) @ SV159 )
= SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1950,plain,
! [SV561: $i,SV160: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV160 ) @ SV561 @ SV160 )
= SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1951,plain,
! [SV562: $i,SV161: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV161 )
| ( ( c_HOL_Oplus__class_Oplus @ SV562 @ ( c_HOL_Ozero__class_Ozero @ SV161 ) @ SV161 )
= SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1952,plain,
! [SV563: $i,SV162: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV162 )
| ~ ( class_Int_Onumber__ring @ SV162 )
| ( SV563
= ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1953,plain,
! [SV564: $i,SV163: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV163 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV163 ) @ SV564 @ SV163 )
= SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1954,plain,
! [SV565: $i,SV164: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV164 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV565 @ SV164 )
= SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1955,plain,
! [SV566: $i,SV165: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV165 )
| ( ( c_HOL_Oplus__class_Oplus @ SV566 @ ( c_HOL_Ozero__class_Ozero @ SV165 ) @ SV165 )
= SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1956,plain,
! [SV567: $i,SV166: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV166 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV166 ) @ SV567 @ SV166 )
= SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1957,plain,
! [SV568: $i,SV167: $i] :
( ( ! [SY2322: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV167 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV568 @ SY2322 @ SV167 ) @ SY2322 @ SV167 )
= SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1958,plain,
! [SV569: $i,SV168: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV168 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV569 @ SV168 ) @ SV168 )
= SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1959,plain,
! [SV570: $i,SV169: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV169 )
| ( SV570
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV570 @ SV169 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1960,plain,
! [SV571: $i,SV170: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV170 )
| ( SV571
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV571 @ SV170 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1961,plain,
! [SV572: $i,SV171: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV171 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV572 @ SV171 ) @ SV171 )
= SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1962,plain,
! [SV573: $i,SV172: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV172 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV573 @ SV172 ) @ SV172 )
= SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1963,plain,
! [SV574: $i,SV173: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV173 )
| ( ( c_Divides_Odiv__class_Odiv @ SV574 @ ( c_HOL_Oone__class_Oone @ SV173 ) @ SV173 )
= SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1964,plain,
! [SV575: $i,SV174: $i] :
( ( ! [SY2323: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV174 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV575 @ SY2323 @ SV174 ) @ SV174 )
= ( c_HOL_Ominus__class_Ominus @ SY2323 @ SV575 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1965,plain,
! [SV576: $i,SV175: $i] :
( ( ! [SY2324: $i,SY2325: $i,SY2326: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SY2324 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY2325 @ SY2326 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SY2325 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY2324 @ SY2326 @ SV175 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1966,plain,
! [SV577: $i,SV176: $i] :
( ( ! [SY2327: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV176 )
| ( ( c_HOL_Ominus__class_Ominus @ SV577 @ SY2327 @ SV176 )
= ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Ouminus__class_Ouminus @ SY2327 @ SV176 ) @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1967,plain,
! [SV578: $i,SV177: $i] :
( ( ! [SY2328: $i] :
( ~ ( class_Int_Onumber__ring @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ SV578 @ SY2328 @ SV177 )
= ( c_HOL_Oplus__class_Oplus @ SV578 @ ( c_HOL_Ouminus__class_Ouminus @ SY2328 @ SV177 ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1968,plain,
! [SV579: $i,SV178: $i] :
( ( ! [SY2329: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV178 )
| ( ( c_HOL_Ominus__class_Ominus @ SV579 @ SY2329 @ SV178 )
= ( c_HOL_Oplus__class_Oplus @ SV579 @ ( c_HOL_Ouminus__class_Ouminus @ SY2329 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1969,plain,
! [SV580: $i,SV179: $i] :
( ( ! [SY2330: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV179 )
| ( ( c_HOL_Ominus__class_Ominus @ SV580 @ SY2330 @ SV179 )
= ( c_HOL_Oplus__class_Oplus @ SV580 @ ( c_HOL_Ouminus__class_Ouminus @ SY2330 @ SV179 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1970,plain,
! [SV581: $i,SV180: $i] :
( ( ! [SY2331: $i,SY2332: $i] :
( ~ ( class_Divides_Oring__div @ SV180 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV581 @ SY2331 @ SV180 ) @ SY2332 @ SV180 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV581 @ SY2332 @ SV180 ) @ ( c_Divides_Odiv__class_Omod @ SY2331 @ SY2332 @ SV180 ) @ SV180 ) @ SY2332 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1971,plain,
! [SV582: $i,SV181: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV181 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ SV582 @ SV181 ) @ SV181 )
= ( c_HOL_Oabs__class_Oabs @ SV582 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1972,plain,
! [SV583: $i,SV182: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV182 )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV583 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1973,plain,
! [SV584: $i,SV183: $i] :
( ( ! [SY2333: $i] :
( ~ ( class_Divides_Osemiring__div @ SV183 )
| ( ( c_Divides_Odiv__class_Omod @ SV584 @ SY2333 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2333 @ SV584 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1974,plain,
! [SV585: $i,SV184: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV184 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV184 ) @ SV585 @ SV184 )
= ( c_HOL_Oone__class_Oone @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1975,plain,
! [SV586: $i,SV185: $i] :
( ( ! [SY2334: $i,SY2335: $i] :
( ~ ( class_Divides_Oring__div @ SV185 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV586 @ SY2334 @ SV185 ) @ SY2335 @ SV185 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV586 @ SY2335 @ SV185 ) @ SY2334 @ SV185 ) @ SY2335 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1976,plain,
! [SV587: $i,SV186: $i] :
( ( ! [SY2336: $i,SY2337: $i] :
( ~ ( class_Divides_Oring__div @ SV186 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SY2336 @ SV186 ) @ SY2337 @ SV186 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ ( c_Divides_Odiv__class_Omod @ SY2336 @ SY2337 @ SV186 ) @ SV186 ) @ SY2337 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1977,plain,
! [SV588: $i,SV187: $i] :
( ( ! [SY2338: $i,SY2339: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV187 )
| ( ( c_Divides_Odiv__class_Omod @ SV588 @ ( c_Polynomial_Osmult @ SY2338 @ SY2339 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SV588 @ SY2339 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
| ( SY2338
= ( c_HOL_Ozero__class_Ozero @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1978,plain,
! [SV589: $i,SV188: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV188 )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV589 @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV589 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1979,plain,
! [SV590: $i,SV189: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV189 )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SV590 @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SV590 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1980,plain,
! [SV591: $i,SV190: $i] :
( ( ! [SY2340: $i] :
( ~ ( class_Divides_Osemiring__div @ SV190 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV591 @ SY2340 @ SV190 ) @ SY2340 @ SV190 )
= ( c_Divides_Odiv__class_Omod @ SV591 @ SY2340 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1981,plain,
! [SV592: $i,SV191: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV191 )
| ( ( c_Divides_Odiv__class_Odiv @ SV592 @ SV592 @ SV191 )
= ( c_HOL_Oone__class_Oone @ SV191 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1982,plain,
! [SV593: $i,SV192: $i] :
( ( ! [SY2341: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV192 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ SV593 @ SV192 ) @ SY2341 @ SV192 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV593 @ SY2341 @ SV192 ) @ ( tc_Polynomial_Opoly @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1983,plain,
! [SV594: $i,SV193: $i] :
( ( ! [SY2342: $i,SY2343: $i,SY2344: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV193 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV594 @ SY2342 @ SV193 ) @ SY2343 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2344 @ SY2342 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV594 @ SY2344 @ SV193 ) @ SY2342 @ SV193 ) @ SY2343 @ SV193 ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1984,plain,
! [SV595: $i,SV194: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV194 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV595 @ SV194 ) @ SV194 )
= ( c_HOL_Oabs__class_Oabs @ SV595 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1985,plain,
! [SV596: $i,SV195: $i] :
( ( ! [SY2345: $i,SY2346: $i] :
( ~ ( class_Divides_Osemiring__div @ SV195 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV596 @ SY2345 @ SV195 ) @ SY2345 @ SV195 ) @ ( c_Divides_Odiv__class_Omod @ SV596 @ SY2345 @ SV195 ) @ SV195 ) @ SY2346 @ SV195 )
= ( c_HOL_Oplus__class_Oplus @ SV596 @ SY2346 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1986,plain,
! [SV597: $i,SV196: $i] :
( ( ! [SY2347: $i,SY2348: $i] :
( ~ ( class_Divides_Osemiring__div @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV597 @ ( c_Divides_Odiv__class_Odiv @ SY2347 @ SV597 @ SV196 ) @ SV196 ) @ ( c_Divides_Odiv__class_Omod @ SY2347 @ SV597 @ SV196 ) @ SV196 ) @ SY2348 @ SV196 )
= ( c_HOL_Oplus__class_Oplus @ SY2347 @ SY2348 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1987,plain,
! [SV598: $i,SV197: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV197 )
| ( c_Polynomial_Opdivmod__rel @ SV598 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ SV598 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1988,plain,
! [SV599: $i,SV198: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV198 )
| ( ( c_Divides_Odiv__class_Omod @ SV599 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= SV599 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1989,plain,
! [SV600: $i,SV199: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV199 )
| ( ( c_Divides_Odiv__class_Omod @ SV600 @ SV600 @ SV199 )
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1990,plain,
! [SV601: $i,SV200: $i] :
( ( ! [SY2349: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV200 )
| ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SY2349 @ SV200 )
= ( c_HOL_Oplus__class_Oplus @ SY2349 @ SV601 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1991,plain,
! [SV602: $i,SV201: $i] :
( ( ! [SY2350: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ SV602 @ SY2350 @ SV201 )
= ( c_HOL_Oplus__class_Oplus @ SY2350 @ SV602 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1992,plain,
! [SV603: $i,SV202: $i] :
( ( ! [SY2351: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV202 )
| ( ( c_HOL_Oplus__class_Oplus @ SV603 @ SY2351 @ SV202 )
= ( c_HOL_Oplus__class_Oplus @ SY2351 @ SV603 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1993,plain,
! [SV604: $i,SV203: $i] :
( ( ! [SY2352: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV203 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV604 @ SV203 ) @ SY2352 @ SV203 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV203 ) @ SV203 ) @ SY2352 @ SV203 ) @ ( c_Power_Opower__class_Opower @ SV604 @ SY2352 @ SV203 ) @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1994,plain,
! [SV605: $i,SV204: $i] :
( ( ! [SY2353: $i] :
( ~ ( class_Divides_Osemiring__div @ SV204 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ SV605 @ SY2353 @ SV204 ) @ SY2353 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1995,plain,
! [SV606: $i,SV205: $i] :
( ( ! [SY2354: $i,SY2355: $i] :
( ~ ( class_Divides_Osemiring__div @ SV205 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV606 @ SY2354 @ SV205 ) @ SY2355 @ SV205 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV606 @ SY2355 @ SV205 ) @ ( c_Divides_Odiv__class_Omod @ SY2354 @ SY2355 @ SV205 ) @ SV205 ) @ SY2355 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1996,plain,
! [SV607: $i,SV206: $i] :
( ( ! [SY2356: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV206 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV607 @ SY2356 @ SV206 ) @ SV607 @ SV206 )
= ( c_HOL_Otimes__class_Otimes @ SV607 @ ( c_Power_Opower__class_Opower @ SV607 @ SY2356 @ SV206 ) @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1997,plain,
! [SV608: $i,SV207: $i] :
( ( ! [SY2357: $i,SY2358: $i] :
( ~ ( class_Divides_Osemiring__div @ SV207 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV608 @ ( c_HOL_Otimes__class_Otimes @ SY2357 @ SY2358 @ SV207 ) @ SV207 ) @ SY2358 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SY2357 @ ( c_Divides_Odiv__class_Odiv @ SV608 @ SY2358 @ SV207 ) @ SV207 ) )
| ( SY2358
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1998,plain,
! [SV609: $i,SV208: $i] :
( ( ! [SY2359: $i,SY2360: $i] :
( ~ ( class_Divides_Osemiring__div @ SV208 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV609 @ ( c_HOL_Otimes__class_Otimes @ SY2359 @ SY2360 @ SV208 ) @ SV208 ) @ SY2359 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SY2360 @ ( c_Divides_Odiv__class_Odiv @ SV609 @ SY2359 @ SV208 ) @ SV208 ) )
| ( SY2359
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1999,plain,
! [SV610: $i,SV209: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV209 )
| ( ( c_HOL_Oplus__class_Oplus @ SV610 @ SV610 @ SV209 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV209 ) @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV209 ) @ SV610 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2000,plain,
! [SV611: $i,SV210: $i] :
( ( ! [SY2361: $i,SY2362: $i,SY2363: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV210 )
| ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SY2361 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SY2362 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SY2361 @ SY2362 @ SY2363 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2001,plain,
! [SV612: $i,SV211: $i] :
( ( ! [SY2364: $i,SY2365: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV211 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ SV612 @ SY2364 @ SV211 ) @ SY2365 @ SV211 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV612 @ SY2365 @ SV211 ) @ ( c_Polynomial_Osmult @ SY2364 @ SY2365 @ SV211 ) @ ( tc_Polynomial_Opoly @ SV211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2002,plain,
! [SV613: $i,SV212: $i] :
( ( ! [SY2366: $i,SY2367: $i] :
( ~ ( class_Divides_Osemiring__div @ SV212 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SY2366 @ SV212 ) @ SY2367 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SY2367 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SY2366 @ SY2367 @ SV212 ) @ SV212 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2366 @ SV613 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2003,plain,
! [SV614: $i,SV213: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV213 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV614 @ SV213 ) @ ( c_HOL_Oabs__class_Oabs @ SV614 @ SV213 ) @ SV213 )
= ( c_HOL_Otimes__class_Otimes @ SV614 @ SV614 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2004,plain,
! [SV615: $i,SV214: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV214 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV615 @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2005,plain,
! [SV616: $i,SV215: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV215 )
| ( ( c_HOL_Otimes__class_Otimes @ SV616 @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2006,plain,
! [SV617: $i,SV216: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV617 @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2007,plain,
! [SV618: $i,SV217: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV217 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV618 @ SV217 )
= ( c_HOL_Ozero__class_Ozero @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2008,plain,
! [SV619: $i,SV218: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV218 )
| ( ( c_HOL_Otimes__class_Otimes @ SV619 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2009,plain,
! [SV620: $i,SV219: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV219 )
| ( ( c_HOL_Otimes__class_Otimes @ SV620 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2010,plain,
! [SV621: $i,SV220: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV220 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) @ SV621 @ ( tc_Polynomial_Opoly @ SV220 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2011,plain,
! [SV622: $i,SV221: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV221 )
| ( ( c_HOL_Otimes__class_Otimes @ SV622 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) @ ( tc_Polynomial_Opoly @ SV221 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2012,plain,
! [SV623: $i,SV222: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV222 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV623 @ SV222 )
= ( c_HOL_Ozero__class_Ozero @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2013,plain,
! [SV624: $i,SV223: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV223 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SV624 @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2014,plain,
! [SV625: $i,SV224: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV224 )
| ( ( c_HOL_Otimes__class_Otimes @ SV625 @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2015,plain,
! [SV626: $i,SV225: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV225 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SV626 @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2016,plain,
! [SV627: $i,SV226: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV226 )
| ( ( c_HOL_Otimes__class_Otimes @ SV627 @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 )
= ( c_HOL_Ozero__class_Ozero @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2017,plain,
! [SV628: $i,SV227: $i] :
( ( ! [SY2368: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV227 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV628 @ SV227 ) @ SY2368 @ SV227 ) @ SV227 )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV628 @ SY2368 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2018,plain,
! [SV629: $i,SV228: $i] :
( ( ! [SY2369: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV629 @ SY2369 @ SV228 ) @ SY2369 @ SV228 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV629 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 ) @ SY2369 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2019,plain,
! [SV630: $i,SV229: $i] :
( ( ! [SY2370: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV229 )
| ( ( c_HOL_Oplus__class_Oplus @ SV630 @ ( c_HOL_Otimes__class_Otimes @ SY2370 @ SV630 @ SV229 ) @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2370 @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV229 ) @ SV630 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2020,plain,
! [SV631: $i,SV230: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV230 )
| ( ( c_Divides_Odiv__class_Omod @ SV631 @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 )
= ( c_HOL_Ozero__class_Ozero @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2021,plain,
! [SV632: $i,SV231: $i] :
( ( ! [SY2371: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV632 @ SV231 ) @ ( c_HOL_Oplus__class_Oplus @ SY2371 @ SV632 @ SV231 ) @ SV231 )
= SY2371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2022,plain,
! [SV633: $i,SV232: $i] :
( ( ! [SY2372: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV633 @ SV232 ) @ ( c_HOL_Oplus__class_Oplus @ SV633 @ SY2372 @ SV232 ) @ SV232 )
= SY2372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2023,plain,
! [SV634: $i,SV233: $i] :
( ( ! [SY2373: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV233 )
| ( ( c_Divides_Odiv__class_Omod @ SV634 @ ( c_HOL_Ouminus__class_Ouminus @ SY2373 @ ( tc_Polynomial_Opoly @ SV233 ) ) @ ( tc_Polynomial_Opoly @ SV233 ) )
= ( c_Divides_Odiv__class_Omod @ SV634 @ SY2373 @ ( tc_Polynomial_Opoly @ SV233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2024,plain,
! [SV234: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV234 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV234 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(2025,plain,
! [SV635: $i,SV235: $i] :
( ( ! [SY2374: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV235 )
| ( ( c_Polynomial_Opoly__gcd @ SV635 @ SY2374 @ SV235 )
= ( c_Polynomial_Opoly__gcd @ SY2374 @ SV635 @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2026,plain,
! [SV636: $i,SV236: $i] :
( ( ! [SY2375: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV236 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV636 @ SV236 ) @ SY2375 @ SV236 )
= ( c_HOL_Otimes__class_Otimes @ SV636 @ ( c_HOL_Ouminus__class_Ouminus @ SY2375 @ SV236 ) @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2027,plain,
! [SV237: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV237 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 )
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(2028,plain,
! [SV238: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV238 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV238 ) @ SV238 )
= ( c_HOL_Ozero__class_Ozero @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(2029,plain,
! [SV239: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV239 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV239 ) ) @ ( tc_Polynomial_Opoly @ SV239 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(2030,plain,
! [SV637: $i,SV240: $i] :
( ( ! [SY2376: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV240 )
| ( ( c_Polynomial_Opoly__gcd @ SV637 @ SY2376 @ SV240 )
= ( c_Polynomial_Opoly__gcd @ SY2376 @ ( c_Divides_Odiv__class_Omod @ SV637 @ SY2376 @ ( tc_Polynomial_Opoly @ SV240 ) ) @ SV240 ) )
| ( SY2376
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV240 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2031,plain,
! [SV638: $i,SV241: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV241 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV638 @ SV241 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2032,plain,
! [SV639: $i,SV242: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV242 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV639 @ SV242 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2033,plain,
! [SV640: $i,SV243: $i] :
( ( ! [SY2377: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ SV640 @ SV243 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2377 @ SV243 ) @ SV243 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SY2377 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2034,plain,
! [SV641: $i,SV244: $i] :
( ( ! [SY2378: $i,SY2379: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV244 )
| ( ( c_Divides_Odiv__class_Odiv @ SV641 @ ( c_HOL_Otimes__class_Otimes @ SY2378 @ SY2379 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ ( tc_Polynomial_Opoly @ SV244 ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ SV641 @ SY2378 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ SY2379 @ ( tc_Polynomial_Opoly @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2035,plain,
! [SV642: $i,SV245: $i] :
( ( ! [SY2380: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV245 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SY2380 @ SV245 ) @ SV245 ) @ SV245 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SY2380 @ SV245 ) @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2036,plain,
! [SV643: $i,SV246: $i] :
( ( ! [SY2381: $i] :
( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV643 @ SY2381 @ SV246 ) @ SV643 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2037,plain,
! [SV644: $i,SV247: $i] :
( ( ! [SY2382: $i] :
( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV644 @ SY2382 @ SV247 ) @ SY2382 @ SV247 )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2038,plain,
! [SV645: $i,SV248: $i] :
( ( ! [SY2383: $i] :
( ~ ( class_Divides_Osemiring__div @ SV248 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV645 @ SY2383 @ SV248 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV645 @ SY2383 @ SV248 ) @ SY2383 @ SV248 ) @ SV248 )
= SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2039,plain,
! [SV249: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV249 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV249 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV249 ) @ SV249 )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(2040,plain,
! [SV646: $i,SV250: $i] :
( ( ! [SY2384: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV250 )
| ( SV646
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2384 @ SV646 @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV646 @ SY2384 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2041,plain,
! [SV647: $i,SV251: $i] :
( ( ! [SY2385: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV251 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV647 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ SY2385 @ ( tc_Polynomial_Opoly @ SV251 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV647 @ SY2385 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ ( tc_Polynomial_Opoly @ SV251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2042,plain,
! [SV648: $i,SV252: $i] :
( ( ! [SY2386: $i,SY2387: $i] :
( ~ ( class_Divides_Osemiring__div @ SV252 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SY2386 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SY2387 @ SV252 ) @ SV252 )
= ( c_HOL_Otimes__class_Otimes @ SV648 @ ( c_Divides_Odiv__class_Omod @ SY2386 @ SY2387 @ SV252 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2043,plain,
! [SV649: $i,SV253: $i] :
( ( ! [SY2388: $i,SY2389: $i] :
( ~ ( class_Divides_Osemiring__div @ SV253 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV649 @ SY2388 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SY2389 @ SY2388 @ SV253 ) @ SV253 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV649 @ SY2389 @ SV253 ) @ SY2388 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2044,plain,
! [SV650: $i,SV254: $i] :
( ( ! [SY2390: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV254 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV650 @ SY2390 @ SV254 ) @ SV254 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SY2390 @ SV254 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV650 @ SV254 ) @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2045,plain,
! [SV651: $i,SV255: $i] :
( ( ! [SY2391: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV255 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SY2391 @ SV255 ) @ SV255 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV651 @ SV255 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2391 @ SV255 ) @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2046,plain,
! [SV652: $i,SV256: $i] :
( ( ! [SY2392: $i,SY2393: $i,SY2394: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SY2392 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SY2393 @ SY2394 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2392 @ SY2394 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SY2393 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2047,plain,
! [SV653: $i,SV257: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV257 )
| ( ( c_Polynomial_Osmult @ SV653 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) @ SV257 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2048,plain,
! [SV654: $i,SV258: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV258 )
| ( ( c_Polynomial_Osmult @ SV654 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) @ SV258 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2049,plain,
! [SV655: $i,SV259: $i] :
( ( ! [SY2395: $i,SY2396: $i] :
( ~ ( class_Divides_Osemiring__div @ SV259 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SY2395 @ SV259 ) @ SY2396 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SY2396 @ SV259 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2396 @ SY2395 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2050,plain,
! [SV656: $i,SV260: $i] :
( ( ! [SY2397: $i,SY2398: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV260 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SY2397 @ SY2398 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SY2398 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SY2397 @ ( tc_Polynomial_Opoly @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2051,plain,
! [SV657: $i,SV261: $i] :
( ( ! [SY2399: $i,SY2400: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV261 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SY2399 @ SY2400 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SY2400 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SY2399 @ ( tc_Polynomial_Opoly @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2052,plain,
! [SV658: $i,SV262: $i] :
( ( ! [SY2401: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV262 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV658 @ SY2401 @ SV262 ) @ SV658 @ ( tc_Polynomial_Opoly @ SV262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2053,plain,
! [SV659: $i,SV263: $i] :
( ( ! [SY2402: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV263 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV659 @ SY2402 @ SV263 ) @ SY2402 @ ( tc_Polynomial_Opoly @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2054,plain,
! [SV660: $i,SV264: $i] :
( ( ! [SY2403: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV264 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV660 @ SV264 ) @ SY2403 @ ( tc_Polynomial_Opoly @ SV264 ) )
| ( SY2403
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2055,plain,
! [SV661: $i,SV265: $i] :
( ( ! [SY2404: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV265 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ ( c_HOL_Oabs__class_Oabs @ SY2404 @ SV265 ) @ SV265 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ SY2404 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2056,plain,
! [SV662: $i,SV266: $i] :
( ( ! [SY2405: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV266 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ SY2405 @ SV266 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ ( c_HOL_Oabs__class_Oabs @ SY2405 @ SV266 ) @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2057,plain,
! [SV663: $i,SV267: $i] :
( ( ! [SY2406: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV267 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV663 @ SV267 ) @ SY2406 @ SV267 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV663 @ SY2406 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2058,plain,
! [SV664: $i,SV268: $i] :
( ( ! [SY2407: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV268 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV664 @ SY2407 @ SV268 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV664 @ SV268 ) @ SY2407 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2059,plain,
! [SV665: $i,SV269: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV665 @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2060,plain,
! [SV666: $i,SV270: $i] :
( ( ! [SY2408: $i,SY2409: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV270 )
| ( ( c_Polynomial_Osmult @ SV666 @ ( c_HOL_Ominus__class_Ominus @ SY2408 @ SY2409 @ ( tc_Polynomial_Opoly @ SV270 ) ) @ SV270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV666 @ SY2408 @ SV270 ) @ ( c_Polynomial_Osmult @ SV666 @ SY2409 @ SV270 ) @ ( tc_Polynomial_Opoly @ SV270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2061,plain,
! [SV667: $i,SV271: $i] :
( ( ! [SY2410: $i,SY2411: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV271 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SY2410 @ ( tc_Polynomial_Opoly @ SV271 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SY2411 @ SY2410 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2062,plain,
! [SV668: $i,SV272: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV272 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SY2412 @ ( tc_Polynomial_Opoly @ SV272 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SY2412 @ SY2413 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2063,plain,
! [SV669: $i,SV273: $i] :
( ( ! [SY2414: $i,SY2415: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV273 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SY2414 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SY2415 @ SY2414 @ SV273 ) @ SV273 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SY2415 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2064,plain,
! [SV670: $i,SV274: $i] :
( ( ! [SY2416: $i,SY2417: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV274 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SY2416 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SY2417 @ SV274 ) @ SV274 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2416 @ SY2417 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2065,plain,
! [SV671: $i,SV275: $i] :
( ( ! [SY2418: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV275 )
| ( ( c_Polynomial_Osmult @ SV671 @ ( c_HOL_Ouminus__class_Ouminus @ SY2418 @ ( tc_Polynomial_Opoly @ SV275 ) ) @ SV275 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV671 @ SY2418 @ SV275 ) @ ( tc_Polynomial_Opoly @ SV275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2066,plain,
! [SV672: $i,SV276: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
| ( SV672
= ( c_HOL_Ozero__class_Ozero @ SV276 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV672 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2067,plain,
! [SV673: $i,SV277: $i] :
( ( ! [SY2419: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV673 @ SV277 ) @ SY2419 @ SV277 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV673 @ SY2419 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2068,plain,
! [SV674: $i,SV278: $i] :
( ( ! [SY2420: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV674 @ SY2420 @ SV278 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV674 @ SV278 ) @ SY2420 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2069,plain,
! [SV675: $i,SV279: $i] :
( ( ! [SY2421: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ ( c_HOL_Ouminus__class_Ouminus @ SY2421 @ SV279 ) @ SV279 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ SY2421 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2070,plain,
! [SV676: $i,SV280: $i] :
( ( ! [SY2422: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ SY2422 @ SV280 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ ( c_HOL_Ouminus__class_Ouminus @ SY2422 @ SV280 ) @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2071,plain,
! [SV677: $i,SV281: $i] :
( ( ! [SY2423: $i,SY2424: $i] :
( ~ ( class_Divides_Osemiring__div @ SV281 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SY2423 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SY2424 @ SY2423 @ SV281 ) @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SY2424 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2423 @ SY2424 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2423 @ SV677 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2072,plain,
! [SV678: $i,SV282: $i] :
( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( class_Divides_Osemiring__div @ SV282 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SY2425 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SY2426 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SY2425 @ SY2426 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2426 @ SY2425 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2426 @ SV678 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2073,plain,
! [SV679: $i,SV283: $i] :
( ( ! [SY2427: $i,SY2428: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SY2427 @ SY2428 @ SV283 ) @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SY2428 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SY2427 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2074,plain,
! [SV680: $i,SV284: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV284 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV680 @ SV284 )
= SV680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2075,plain,
! [SV681: $i,SV285: $i] :
( ( ! [SY2429: $i,SY2430: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV285 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ SV681 @ SY2429 @ SV285 ) @ SY2430 @ ( tc_Polynomial_Opoly @ SV285 ) )
= ( c_Polynomial_Osmult @ SV681 @ ( c_Divides_Odiv__class_Omod @ SY2429 @ SY2430 @ ( tc_Polynomial_Opoly @ SV285 ) ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2076,plain,
! [SV682: $i,SV286: $i] :
( ( ! [SY2431: $i,SY2432: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV286 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SY2431 @ ( tc_Polynomial_Opoly @ SV286 ) )
| ( SY2432
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SY2432 @ SY2431 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2077,plain,
! [SV683: $i,SV287: $i] :
( ( ! [SY2433: $i,SY2434: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV287 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SY2433 @ SV287 ) @ SY2434 @ ( tc_Polynomial_Opoly @ SV287 ) )
| ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2433 @ SY2434 @ ( tc_Polynomial_Opoly @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2078,plain,
! [SV684: $i,SV288: $i] :
( ( ! [SY2435: $i,SY2436: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV288 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SY2435 @ ( tc_Polynomial_Opoly @ SV288 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SY2436 @ SY2435 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SY2436
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2079,plain,
! [SV685: $i,SV289: $i] :
( ( ! [SY2437: $i,SY2438: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV289 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SY2437 @ SY2438 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SY2438 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SY2437
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2080,plain,
! [SV686: $i,SV290: $i] :
( ( ! [SY2439: $i,SY2440: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV290 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SY2439 @ ( tc_Polynomial_Opoly @ SV290 ) )
| ( SY2440
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY2440 @ SV686 @ SV290 ) @ SY2439 @ ( tc_Polynomial_Opoly @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2081,plain,
! [SV687: $i,SV291: $i] :
( ( ! [SY2441: $i,SY2442: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV291 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SY2441 @ SV291 ) @ SY2442 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2441 @ SY2442 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2082,plain,
! [SV688: $i,SV292: $i] :
( ( ! [SY2443: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV292 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV688 @ SY2443 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2443 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2083,plain,
! [SV689: $i,SV293: $i] :
( ( ! [SY2444: $i,SY2445: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SY2444 @ SV293 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2445 @ SV689 @ SV293 ) @ SY2444 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2084,plain,
! [SV690: $i,SV294: $i] :
( ( ! [SY2446: $i,SY2447: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SY2446 @ SV294 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SY2447 @ SV294 ) @ SY2446 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2085,plain,
! [SV691: $i,SV295: $i] :
( ( ! [SY2448: $i,SY2449: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SY2448 @ SY2449 @ SV295 ) @ SV295 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SY2448 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2086,plain,
! [SV692: $i,SV296: $i] :
( ( ! [SY2450: $i,SY2451: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SY2450 @ SY2451 @ SV296 ) @ SV296 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SY2451 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2087,plain,
! [SV693: $i,SV297: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV297 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV693 @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2088,plain,
! [SV694: $i,SV298: $i] :
( ( ! [SY2452: $i,SY2453: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SY2452 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2453 @ SY2452 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SY2453 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2089,plain,
! [SV695: $i,SV299: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV299 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV695 @ SV695 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2090,plain,
! [SV696: $i,SV300: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV300 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV696 @ SV300 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV300 ) ) @ ( tc_Polynomial_Opoly @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2091,plain,
! [SV697: $i,SV301: $i] :
( ( ! [SY2454: $i,SY2455: $i,SY2456: $i,SY2457: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV301 )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SY2454 @ SV301 ) @ SY2455 @ ( c_Polynomial_Osmult @ SV697 @ SY2456 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SY2457 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2454 @ SY2455 @ SY2456 @ SY2457 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2092,plain,
! [SV698: $i,SV302: $i] :
( ( ! [SY2458: $i,SY2459: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SY2458 @ SY2459 @ SV302 ) @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SY2459 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SY2458 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2093,plain,
! [SV699: $i,SV303: $i] :
( ( ! [SY2460: $i,SY2461: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV303 )
| ( ( c_Polynomial_Osmult @ SV699 @ ( c_HOL_Oplus__class_Oplus @ SY2460 @ SY2461 @ ( tc_Polynomial_Opoly @ SV303 ) ) @ SV303 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV699 @ SY2460 @ SV303 ) @ ( c_Polynomial_Osmult @ SV699 @ SY2461 @ SV303 ) @ ( tc_Polynomial_Opoly @ SV303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2094,plain,
! [SV700: $i,SV304: $i] :
( ( ! [SY2462: $i,SY2463: $i] :
( ~ ( class_Divides_Osemiring__div @ SV304 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SY2462 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SY2463 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SY2462 @ SY2463 @ SV304 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2095,plain,
! [SV701: $i,SV305: $i] :
( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( class_Divides_Osemiring__div @ SV305 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SY2464 @ SY2465 @ SV305 ) @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SY2464 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SY2465 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2096,plain,
! [SV702: $i,SV306: $i] :
( ( ! [SY2466: $i,SY2467: $i] :
( ~ ( class_Divides_Osemiring__div @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SY2466 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SY2466 @ SY2467 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SY2467 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2097,plain,
! [SV703: $i,SV307: $i] :
( ( ! [SY2468: $i,SY2469: $i] :
( ~ ( class_Divides_Osemiring__div @ SV307 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SY2468 @ SY2469 @ SV307 ) @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SY2469 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SY2468 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2098,plain,
! [SV704: $i,SV308: $i] :
( ( ! [SY2470: $i,SY2471: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV308 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ SV704 @ SY2470 @ SV308 ) @ SY2471 @ ( tc_Polynomial_Opoly @ SV308 ) )
= ( c_Polynomial_Osmult @ SV704 @ ( c_Divides_Odiv__class_Odiv @ SY2470 @ SY2471 @ ( tc_Polynomial_Opoly @ SV308 ) ) @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2099,plain,
! [SV705: $i,SV309: $i] :
( ( ! [SY2472: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV309 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV705 @ ( c_HOL_Otimes__class_Otimes @ SY2472 @ SV705 @ SV309 ) @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2100,plain,
! [SV706: $i,SV310: $i] :
( ( ! [SY2473: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV310 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV706 @ ( c_HOL_Otimes__class_Otimes @ SV706 @ SY2473 @ SV310 ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2101,plain,
! [SV707: $i,SV311: $i] :
( ( ! [SY2474: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV311 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV707 @ ( c_HOL_Otimes__class_Otimes @ SV707 @ SY2474 @ SV311 ) @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2102,plain,
! [SV708: $i,SV312: $i] :
( ( ! [SY2475: $i,SY2476: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SY2475 @ ( tc_Polynomial_Opoly @ SV312 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY2476 @ SV708 @ SV312 ) @ SY2475 @ ( tc_Polynomial_Opoly @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2103,plain,
! [SV709: $i,SV313: $i] :
( ( ! [SY2477: $i,SY2478: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SY2477 @ SY2478 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SY2478 @ ( tc_Polynomial_Opoly @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2104,plain,
! [SV710: $i,SV314: $i] :
( ( ! [SY2479: $i,SY2480: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SY2479 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SY2480 @ SY2479 @ SV314 ) @ SV314 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SY2480 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2105,plain,
! [SV711: $i,SV315: $i] :
( ( ! [SY2481: $i,SY2482: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV315 )
| ( ( c_HOL_Otimes__class_Otimes @ SV711 @ ( c_Polynomial_Osmult @ SY2481 @ SY2482 @ SV315 ) @ ( tc_Polynomial_Opoly @ SV315 ) )
= ( c_Polynomial_Osmult @ SY2481 @ ( c_HOL_Otimes__class_Otimes @ SV711 @ SY2482 @ ( tc_Polynomial_Opoly @ SV315 ) ) @ SV315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2106,plain,
! [SV712: $i,SV316: $i] :
( ( ! [SY2483: $i,SY2484: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV316 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ SV712 @ SY2483 @ SV316 ) @ SY2484 @ ( tc_Polynomial_Opoly @ SV316 ) )
= ( c_Polynomial_Osmult @ SV712 @ ( c_HOL_Otimes__class_Otimes @ SY2483 @ SY2484 @ ( tc_Polynomial_Opoly @ SV316 ) ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2107,plain,
! [SV713: $i,SV317: $i] :
( ( ! [SY2485: $i,SY2486: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV317 )
| ( ( c_Polynomial_Osmult @ SV713 @ ( c_Polynomial_Osmult @ SY2485 @ SY2486 @ SV317 ) @ SV317 )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ SV713 @ SY2485 @ SV317 ) @ SY2486 @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2108,plain,
! [SV318: $i] :
( ( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ SV318 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(2109,plain,
! [SV319: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ SV319 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oidom @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(2110,plain,
! [SV320: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ SV320 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(2111,plain,
! [SV321: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ SV321 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oidom @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(2112,plain,
! [SV322: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ SV322 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(2113,plain,
! [SV323: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ SV323 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(2114,plain,
! [SV324: $i] :
( ( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ SV324 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(2115,plain,
! [SV325: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ SV325 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(2116,plain,
! [SV326: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ SV326 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oidom @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(2117,plain,
! [SV327: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ SV327 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(2118,plain,
! [SV328: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ SV328 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(2119,plain,
! [SV329: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ SV329 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(2120,plain,
! [SV330: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ SV330 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(2121,plain,
! [SV331: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ SV331 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(2122,plain,
! [SV332: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ SV332 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(2123,plain,
! [SV333: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ SV333 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(2124,plain,
! [SV334: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ SV334 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(2125,plain,
! [SV335: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ SV335 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(2126,plain,
! [SV336: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ SV336 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(2127,plain,
! [SV337: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ SV337 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(2128,plain,
! [SV338: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ SV338 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(2129,plain,
! [SV339: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ SV339 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(2130,plain,
! [SV340: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ SV340 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(2131,plain,
! [SV341: $i] :
( ( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ SV341 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(2132,plain,
! [SV342: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ SV342 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(2133,plain,
! [SV343: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ SV343 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(2134,plain,
! [SV344: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ SV344 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV344 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(2135,plain,
! [SV345: $i] :
( ( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ SV345 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ofield @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(2136,plain,
! [SV346: $i] :
( ( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ SV346 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(2137,plain,
! [SV347: $i] :
( ( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ SV347 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Oidom @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(2138,plain,
! [SV348: $i] :
( ( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ SV348 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(2139,plain,
! [SV349: $i] :
( ( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ SV349 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ofield @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(2140,plain,
! [SV350: $i] :
( ( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ SV350 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(2141,plain,
! [SV351: $i] :
( ( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ SV351 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(2142,plain,
! [SV352: $i] :
( ( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ SV352 ) )
= $true )
| ( ( ~ ( class_HOL_Ozero @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(2143,plain,
! [SV714: $i,SV353: $i] :
( ( ! [SY2487: $i,SY2488: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV353 )
| ~ ( class_Int_Onumber__ring @ SV353 )
| ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SY2487 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SY2488 @ SV353 ) )
| ( SY2487 = SY2488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2144,plain,
! [SV715: $i,SV354: $i] :
( ( ! [SY2489: $i,SY2490: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
| ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SY2489 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SV715 @ SY2490 @ SV354 ) )
| ( SY2489 = SY2490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2145,plain,
! [SV716: $i,SV355: $i] :
( ( ! [SY2491: $i] :
( ~ ( class_Divides_Osemiring__div @ SV355 )
| ( ( c_Divides_Odiv__class_Omod @ SV716 @ SY2491 @ SV355 )
!= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2491 @ SV716 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2146,plain,
! [SV717: $i,SV356: $i] :
( ( ! [SY2492: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
| ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SY2492 @ SV356 )
!= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SY2492
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2147,plain,
! [SV718: $i,SV357: $i] :
( ( ! [SY2493: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
| ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SY2493 @ SV357 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SY2493
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2148,plain,
! [SV719: $i,SV358: $i] :
( ( ! [SY2494: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV358 )
| ( ( c_HOL_Oplus__class_Oplus @ SV719 @ SY2494 @ SV358 )
!= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
| ( SV719
= ( c_HOL_Ouminus__class_Ouminus @ SY2494 @ SV358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2149,plain,
! [SV720: $i,SV359: $i] :
( ( ! [SY2495: $i,SY2496: $i,SY2497: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV359 )
| ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SY2495 @ SY2496 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SY2495 @ SY2497 @ SV359 ) @ SV359 ) )
| ( SY2496 = SY2497 )
| ( SY2495
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2150,plain,
! [SV721: $i,SV360: $i] :
( ( ! [SY2498: $i,SY2499: $i,SY2500: $i] :
( ~ ( class_HOL_Ozero @ SV360 )
| ( ( c_Polynomial_OpCons @ SV721 @ SY2498 @ SV360 )
!= ( c_Polynomial_OpCons @ SY2499 @ SY2500 @ SV360 ) )
| ( SY2498 = SY2500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2151,plain,
! [SV722: $i,SV361: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV361 )
| ( ( c_HOL_Oplus__class_Oplus @ SV722 @ SV722 @ SV361 )
!= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
| ( SV722
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2152,plain,
! [SV723: $i,SV362: $i] :
( ( ! [SY2501: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV362 )
| ( ( c_HOL_Oabs__class_Oabs @ SV723 @ SV362 )
!= ( c_HOL_Oabs__class_Oabs @ SY2501 @ SV362 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV723 @ SY2501 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2153,plain,
! [SV724: $i,SV363: $i] :
( ( ! [SY2502: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV363 )
| ( ( c_Polynomial_Opoly @ SV724 @ ( c_HOL_Ouminus__class_Ouminus @ SY2502 @ SV363 ) @ SV363 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SY2502 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SV724 @ ( tc_Polynomial_Opoly @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2154,plain,
! [SV725: $i,SV364: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV364 )
| ( ( c_HOL_Ozero__class_Ozero @ SV364 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV725 @ SV364 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= SV725 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2155,plain,
! [SV726: $i,SV365: $i] :
( ( ! [SY2503: $i,SY2504: $i,SY2505: $i,SY2506: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV365 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SY2503 @ SV365 ) @ SY2504 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2505 @ SY2503 @ SV365 ) @ SY2506 @ SV365 ) )
| ( SY2504
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2505 @ SV726 @ SV365 ) @ SY2503 @ SV365 ) @ SY2506 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2156,plain,
! [SV727: $i,SV366: $i] :
( ( ! [SY2507: $i,SY2508: $i,SY2509: $i,SY2510: $i] :
( ~ ( class_Divides_Osemiring__div @ SV366 )
| ( ( c_Divides_Odiv__class_Omod @ SV727 @ SY2507 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY2508 @ SY2507 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2509 @ SY2507 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY2510 @ SY2507 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2509 @ SV727 @ SV366 ) @ SY2507 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2510 @ SY2508 @ SV366 ) @ SY2507 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2157,plain,
! [SV728: $i,SV367: $i] :
( ( ! [SY2511: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SY2511 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2158,plain,
! [SV729: $i,SV368: $i] :
( ( ! [SY2512: $i,SY2513: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
| ( ( c_Polynomial_Osmult @ SV729 @ SY2512 @ SV368 )
!= ( c_Polynomial_OpCons @ SY2513 @ SY2512 @ SV368 ) )
| ( SY2512
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2159,plain,
! [SV730: $i,SV369: $i] :
( ( ! [SY2514: $i,SY2515: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
| ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SY2514 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SY2515 @ SY2514 @ SV369 ) )
| ( SV730 = SY2515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2160,plain,
! [SV731: $i,SV370: $i] :
( ( ! [SY2516: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV370 )
| ( ( c_Polynomial_Opoly__gcd @ SV731 @ SY2516 @ SV370 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
| ( SY2516
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2161,plain,
! [SV732: $i,SV371: $i] :
( ( ! [SY2517: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV371 )
| ~ ( class_Int_Onumber__ring @ SV371 )
| ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SY2517 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SV732 = SY2517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2162,plain,
! [SV733: $i,SV372: $i] :
( ( ! [SY2518: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 )
| ( ( c_Power_Opower__class_Opower @ SV733 @ SY2518 @ SV372 )
!= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
| ( SV733
= ( c_HOL_Ozero__class_Ozero @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2163,plain,
! [SV734: $i,SV373: $i] :
( ( ! [SY2519: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV373 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV734 @ SV734 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SY2519 @ SY2519 @ SV373 ) @ SV373 )
!= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
| ( SY2519
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2164,plain,
! [SV735: $i,SV374: $i] :
( ( ! [SY2520: $i,SY2521: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SY2520 @ SV374 ) @ ( c_Polynomial_OpCons @ SY2521 @ SY2520 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
| ( SY2520
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2165,plain,
! [SV375: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV375 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV375 )
!= ( c_HOL_Oone__class_Oone @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(2166,plain,
! [SV736: $i,SV376: $i] :
( ( ! [SY2522: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
| ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SY2522 @ SV376 )
!= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SY2522
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2167,plain,
! [SV737: $i,SV377: $i] :
( ( ! [SY2523: $i,SY2524: $i,SY2525: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SY2523 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SY2524 @ SY2525 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SY2525 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SY2524 @ SY2523 @ SV377 ) @ SV377 ) )
| ( SY2523 = SY2525 )
| ( SV737 = SY2524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2168,plain,
! [SV738: $i,SV378: $i] :
( ( ! [SY2526: $i] :
( ~ ( class_HOL_Ozero @ SV378 )
| ( ( c_Polynomial_OpCons @ SV738 @ SY2526 @ SV378 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
| ( SY2526
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2169,plain,
! [SV739: $i,SV379: $i] :
( ( ! [SY2527: $i,SY2528: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SY2527 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SV739 @ SY2528 @ SV379 ) )
| ( SY2527 = SY2528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2170,plain,
! [SV740: $i,SV380: $i] :
( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV380 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV740 @ SV380 )
!= SV740 )
| ( SV740
= ( c_HOL_Ozero__class_Ozero @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2171,plain,
! [SV741: $i,SV381: $i] :
( ( ! [SY2529: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV381 )
| ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
!= ( c_HOL_Otimes__class_Otimes @ SY2529 @ SY2529 @ SV381 ) )
| ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SY2529 @ SV381 ) )
| ( SV741 = SY2529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2172,plain,
! [SV742: $i,SV382: $i] :
( ( ! [SY2530: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV382 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV742 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SY2530 @ SY2530 @ SV382 ) @ SV382 )
!= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
| ( SV742
= ( c_HOL_Ozero__class_Ozero @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2173,plain,
! [SV743: $i,SV383: $i] :
( ( ! [SY2531: $i,SY2532: $i,SY2533: $i,SY2534: $i] :
( ~ ( class_Divides_Oring__div @ SV383 )
| ( ( c_Divides_Odiv__class_Omod @ SV743 @ SY2531 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2532 @ SY2531 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2533 @ SY2531 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2534 @ SY2531 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2533 @ SV743 @ SV383 ) @ SY2531 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2534 @ SY2532 @ SV383 ) @ SY2531 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2174,plain,
! [SV744: $i,SV384: $i] :
( ( ! [SY2535: $i,SY2536: $i,SY2537: $i] :
( ~ ( class_HOL_Ozero @ SV384 )
| ( ( c_Polynomial_OpCons @ SV744 @ SY2535 @ SV384 )
!= ( c_Polynomial_OpCons @ SY2536 @ SY2537 @ SV384 ) )
| ( SV744 = SY2536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2175,plain,
! [SV745: $i,SV385: $i] :
( ( ! [SY2538: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV385 )
| ( ( c_HOL_Oplus__class_Oplus @ SV745 @ SY2538 @ SV385 )
!= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV745 @ SV385 )
= SY2538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2176,plain,
! [SV746: $i,SV386: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV386 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV746 @ SV386 )
!= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
| ( SV746
= ( c_HOL_Ozero__class_Ozero @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2177,plain,
! [SV747: $i,SV387: $i] :
( ( ! [SY2539: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV387 )
| ( ( c_Polynomial_Osmult @ SV747 @ SY2539 @ SV387 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SY2539
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2178,plain,
! [SV748: $i,SV388: $i] :
( ( ! [SY2540: $i,SY2541: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV388 )
| ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SY2540 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SY2541 @ SY2541 @ SV388 ) )
| ( SV748 = SY2540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2179,plain,
! [SV749: $i,SV389: $i] :
( ( ! [SY2542: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV389 )
| ( ( c_HOL_Ominus__class_Ominus @ SV749 @ SY2542 @ SV389 )
!= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
| ( SV749 = SY2542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2180,plain,
! [SV750: $i,SV390: $i] :
( ( ! [SY2543: $i,SY2544: $i,SY2545: $i,SY2546: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV390 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SY2543 @ SV390 ) @ SY2544 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2545 @ SY2543 @ SV390 ) @ SY2546 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SY2545 @ SV390 ) @ SY2543 @ SV390 ) @ SY2544 @ SV390 )
= SY2546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2181,plain,
! [SV751: $i,SV391: $i] :
( ( ! [SY2547: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV391 )
| ( ( c_HOL_Ominus__class_Ominus @ SV751 @ SY2547 @ SV391 )
!= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
| ( SV751 = SY2547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2182,plain,
! [SV752: $i,SV392: $i] :
( ( ! [SY2548: $i,SY2549: $i,SY2550: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
| ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SY2548 @ SY2549 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SY2550 @ SY2549 @ SV392 ) )
| ( SY2550
= ( c_Polynomial_Opoly @ SV752 @ SY2548 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2183,plain,
! [SV753: $i,SV393: $i] :
( ( ! [SY2551: $i,SY2552: $i,SY2553: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV393 )
| ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SY2551 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SY2552 @ SY2553 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SY2553 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SY2552 @ SY2551 @ SV393 ) @ SV393 ) )
| ( SY2551 = SY2553 )
| ( SV753 = SY2552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2184,plain,
! [SV394: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV394 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV394 )
!= ( c_HOL_Ozero__class_Ozero @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(2185,plain,
! [SV754: $i,SV395: $i] :
( ( ! [SY2554: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV395 )
| ( ( c_Polynomial_Opoly @ SV754 @ SY2554 @ SV395 )
!= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SY2554 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SV754 @ ( tc_Polynomial_Opoly @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2186,plain,
! [SV755: $i,SV396: $i] :
( ( ! [SY2555: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV396 )
| ( ( c_Polynomial_Opoly__gcd @ SV755 @ SY2555 @ SV396 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
| ( SV755
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2187,plain,
! [SV756: $i,SV397: $i] :
( ( ! [SY2556: $i,SY2557: $i] :
( ~ ( class_Divides_Oring__div @ SV397 )
| ( ( c_Divides_Odiv__class_Omod @ SV756 @ SY2556 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SY2557 @ SY2556 @ SV397 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SY2556 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SY2557 @ SV397 ) @ SY2556 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2188,plain,
! [SV757: $i,SV398: $i] :
( ( ! [SY2558: $i,SY2559: $i,SY2560: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV398 )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SY2558 @ SY2559 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SY2558 @ SY2560 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SY2559 @ SV398 )
= SY2560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2189,plain,
! [SV758: $i,SV399: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV399 )
| ( ( c_HOL_Oabs__class_Oabs @ SV758 @ SV399 )
!= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
| ( SV758
= ( c_HOL_Ozero__class_Ozero @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2190,plain,
! [SV759: $i,SV400: $i] :
( ( ! [SY2561: $i,SY2562: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV400 )
| ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SY2561 @ SY2562 @ SV400 ) @ SV400 )
!= SY2561 )
| ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SY2562 @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2191,plain,
! [SV760: $i,SV401: $i] :
( ( ! [SY2563: $i,SY2564: $i,SY2565: $i,SY2566: $i] :
( ~ ( class_Divides_Osemiring__div @ SV401 )
| ( ( c_Divides_Odiv__class_Omod @ SV760 @ SY2563 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2564 @ SY2563 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2565 @ SY2563 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2566 @ SY2563 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2565 @ SV760 @ SV401 ) @ SY2563 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2566 @ SY2564 @ SV401 ) @ SY2563 @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2192,plain,
! [SV761: $i,SV402: $i] :
( ( ! [SY2567: $i,SY2568: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV402 )
| ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SY2567 @ SY2568 @ SV402 ) )
| ( SY2567 = SY2568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2193,plain,
! [SV762: $i,SV403: $i] :
( ( ! [SY2569: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV403 )
| ~ ( class_Int_Onumber__ring @ SV403 )
| ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SY2569 @ SV403 ) )
| ( SY2569
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2194,plain,
! [SV763: $i,SV404: $i] :
( ( ! [SY2570: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV404 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV763 @ SV404 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2570 @ SV404 ) )
| ( SV763 = SY2570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2195,plain,
! [SV764: $i,SV405: $i] :
( ( ! [SY2571: $i] :
( ~ ( class_HOL_Ozero @ SV405 )
| ( ( c_Polynomial_OpCons @ SV764 @ SY2571 @ SV405 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
| ( SV764
= ( c_HOL_Ozero__class_Ozero @ SV405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2196,plain,
! [SV765: $i,SV406: $i] :
( ( ! [SY2572: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV406 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV765 @ SV406 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2572 @ SV406 ) )
| ( SV765 = SY2572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2197,plain,
! [SV766: $i,SV407: $i,SV1: $i] :
( ( ! [SY2573: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV1 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ SV407 @ SV766 @ SV1 ) @ SY2573 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SY2573 @ ( c_Polynomial_Opoly @ SV766 @ SY2573 @ SV1 ) @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2198,plain,
! [SV408: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV2 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV2 ) ) @ SV408 @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(2199,plain,
! [SV409: $i,SV3: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV3 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV3 ) ) @ SV409 @ SV3 )
= ( c_HOL_Ozero__class_Ozero @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(2200,plain,
! [SV767: $i,SV410: $i,SV4: $i] :
( ( ! [SY2574: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV4 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ SV410 @ SV767 @ SV4 ) @ SY2574 @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ SV410 @ ( c_Polynomial_Opoly @ SV767 @ SY2574 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2201,plain,
! [SV768: $i,SV411: $i,SV5: $i] :
( ( ! [SY2575: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV5 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV768 @ ( tc_Polynomial_Opoly @ SV5 ) ) @ SY2575 @ SV5 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ SV411 @ SY2575 @ SV5 ) @ ( c_Polynomial_Opoly @ SV768 @ SY2575 @ SV5 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2202,plain,
! [SV769: $i,SV412: $i,SV6: $i] :
( ( ! [SY2576: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV6 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ SV412 @ SV769 @ ( tc_Polynomial_Opoly @ SV6 ) ) @ SY2576 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ SV412 @ SY2576 @ SV6 ) @ ( c_Polynomial_Opoly @ SV769 @ SY2576 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2203,plain,
! [SV770: $i,SV413: $i,SV7: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV7 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ SV413 @ ( tc_Polynomial_Opoly @ SV7 ) ) @ SV770 @ SV7 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ SV413 @ SV770 @ SV7 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2204,plain,
! [SV771: $i,SV414: $i,SV8: $i] :
( ( ! [SY2577: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV8 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ SV414 @ SV771 @ ( tc_Polynomial_Opoly @ SV8 ) ) @ SY2577 @ SV8 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ SV414 @ SY2577 @ SV8 ) @ ( c_Polynomial_Opoly @ SV771 @ SY2577 @ SV8 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2205,plain,
! [SV772: $i,SV415: $i,SV9: $i] :
( ( ! [SY2578: $i,SY2579: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV9 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SV415 @ SV772 @ SV9 ) @ ( c_Polynomial_OpCons @ SY2578 @ SY2579 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SV415 @ SY2578 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SV772 @ SY2579 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2206,plain,
! [SV773: $i,SV416: $i,SV10: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV10 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ SV416 @ SV773 @ SV10 ) @ ( tc_Polynomial_Opoly @ SV10 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV416 @ SV10 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV773 @ ( tc_Polynomial_Opoly @ SV10 ) ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2207,plain,
! [SV774: $i,SV417: $i,SV11: $i] :
( ( ! [SY2580: $i,SY2581: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SV417 @ SV774 @ SV11 ) @ ( c_Polynomial_OpCons @ SY2580 @ SY2581 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SV417 @ SY2580 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SV774 @ SY2581 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2208,plain,
! [SV775: $i,SV418: $i,SV12: $i] :
( ( ! [SY2582: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV12 )
| ( ( c_Polynomial_Osmult @ SV418 @ ( c_Polynomial_OpCons @ SV775 @ SY2582 @ SV12 ) @ SV12 )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV775 @ SV12 ) @ ( c_Polynomial_Osmult @ SV418 @ SY2582 @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2209,plain,
! [SV13: $i] :
( ( ( class_HOL_Ozero @ SV13 )
= $false )
| ( ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV13 ) ) @ SV13 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(2210,plain,
! [SV776: $i,SV419: $i,SV14: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV14 )
| ( ( c_Polynomial_Opoly @ SV419 @ SV776 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV776 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SV419 @ ( tc_Polynomial_Opoly @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2211,plain,
! [SV777: $i,SV420: $i,SV15: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV15 )
| ( ( c_Polynomial_Opoly @ SV420 @ ( c_HOL_Ouminus__class_Ouminus @ SV777 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV777 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SV420 @ ( tc_Polynomial_Opoly @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2212,plain,
! [SV778: $i,SV421: $i,SV16: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV16 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV421 @ SV778 @ SV16 ) @ SV421 @ SV16 )
= SV778 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2213,plain,
! [SV779: $i,SV422: $i,SV17: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV17 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV422 @ SV779 @ SV17 ) @ SV779 @ SV17 )
= SV422 )
| ( SV779
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2214,plain,
! [SV780: $i,SV423: $i,SV18: $i] :
( ( ! [SY2583: $i,SY2584: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV780 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SY2583 @ SY2584 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SY2583 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV780 @ SY2584 @ SV18 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2215,plain,
! [SV781: $i,SV424: $i,SV19: $i] :
( ( ! [SY2585: $i,SY2586: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV424 @ SV781 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SY2585 @ SY2586 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SV424 @ ( c_HOL_Otimes__class_Otimes @ SV781 @ ( c_HOL_Otimes__class_Otimes @ SY2585 @ SY2586 @ SV19 ) @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2216,plain,
! [SV782: $i,SV425: $i,SV20: $i] :
( ( ! [SY2587: $i,SY2588: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SY2587 @ SY2588 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SY2587 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ SY2588 @ SV20 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2217,plain,
! [SV783: $i,SV426: $i,SV21: $i] :
( ( ! [SY2589: $i,SY2590: $i,SY2591: $i,SY2592: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2589 @ SY2590 @ SV783 @ SY2591 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2589 @ SY2590 @ SV426 @ SY2592 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2218,plain,
! [SV784: $i,SV427: $i,SV22: $i] :
( ( ! [SY2593: $i,SY2594: $i,SY2595: $i,SY2596: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2593 @ SY2594 @ SY2595 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2593 @ SY2594 @ SY2596 @ SV427 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2219,plain,
! [SV785: $i,SV428: $i,SV23: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV428 @ SV23 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV785 @ SV23 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2220,plain,
! [SV786: $i,SV429: $i,SV24: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV24 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ ( c_HOL_Otimes__class_Otimes @ SV786 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2221,plain,
! [SV25: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV25 )
= $false )
| ( ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) @ SV25 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(2222,plain,
! [SV787: $i,SV430: $i,SV26: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV26 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV787 @ SV26 ) @ SV26 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV430 @ SV26 ) @ ( c_HOL_Oabs__class_Oabs @ SV787 @ SV26 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2223,plain,
! [SV788: $i,SV431: $i,SV27: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV27 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV788 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV431 @ SV27 ) @ SV788 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2224,plain,
! [SV789: $i,SV432: $i,SV28: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV28 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV432 @ SV789 @ SV28 ) @ SV28 )
= ( c_HOL_Otimes__class_Otimes @ SV432 @ ( c_HOL_Ouminus__class_Ouminus @ SV789 @ SV28 ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2225,plain,
! [SV790: $i,SV433: $i,SV29: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
| ( ( c_HOL_Otimes__class_Otimes @ SV433 @ ( c_HOL_Otimes__class_Otimes @ SV433 @ SV790 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV433 @ SV790 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2226,plain,
! [SV791: $i,SV434: $i,SV30: $i] :
( ( ! [SY2597: $i,SY2598: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SY2597 @ SY2598 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SY2597 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SY2598 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2598 @ SY2597 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2227,plain,
! [SV792: $i,SV435: $i,SV31: $i] :
( ( ! [SY2599: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV31 )
| ( SV435 = SV792 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV792 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SY2599 @ SV435 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2228,plain,
! [SV793: $i,SV436: $i,SV32: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV32 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV436 @ SV32 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV793 @ SV32 ) @ SV32 )
= ( c_HOL_Ozero__class_Ozero @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2229,plain,
! [SV794: $i,SV437: $i,SV33: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV33 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV794 @ SV33 ) @ SV437 @ SV33 )
= ( c_Divides_Odiv__class_Omod @ SV794 @ SV437 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2230,plain,
! [SV795: $i,SV438: $i,SV34: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV34 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV438 @ SV795 @ SV34 ) @ SV795 @ SV34 )
= ( c_Divides_Odiv__class_Omod @ SV438 @ SV795 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2231,plain,
! [SV796: $i,SV439: $i,SV35: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SV439 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV439 @ SV35 ) @ SV796 @ SV35 ) @ SV35 )
= SV796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2232,plain,
! [SV797: $i,SV440: $i,SV36: $i] :
( ( ! [SY2600: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV36 )
| ( ( c_Divides_Odiv__class_Omod @ SV440 @ ( c_HOL_Otimes__class_Otimes @ SV797 @ SY2600 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV797 @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ SY2600 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( c_Divides_Odiv__class_Omod @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2233,plain,
! [SV441: $i,SV37: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV37 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV441 @ SV441 @ SV37 )
= SV441 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2234,plain,
! [SV798: $i,SV442: $i,SV38: $i] :
( ( ! [SY2601: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV38 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SV798 @ SY2601 @ SV38 )
| ( SV798
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2235,plain,
! [SV799: $i,SV443: $i,SV39: $i] :
( ( ! [SY2602: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV39 )
| ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SV799 @ SV443 @ SY2602 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2236,plain,
! [SV800: $i,SV444: $i,SV40: $i] :
( ( ! [SY2603: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV40 )
| ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SV800 @ SY2603 @ SV444 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2237,plain,
! [SV801: $i,SV445: $i,SV41: $i] :
( ( ! [SY2604: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV41 )
| ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV801 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SY2604 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2238,plain,
! [SV802: $i,SV446: $i,SV42: $i] :
( ( ! [SY2605: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV802 @ SV42 ) @ SY2605 @ SV42 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV446 @ SY2605 @ SV42 ) @ ( c_Power_Opower__class_Opower @ SV802 @ SY2605 @ SV42 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2239,plain,
! [SV803: $i,SV447: $i,SV43: $i] :
( ( ! [SY2606: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV43 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV803 @ SV43 ) @ SY2606 @ SV43 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV447 @ SY2606 @ SV43 ) @ ( c_Power_Opower__class_Opower @ SV803 @ SY2606 @ SV43 ) @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2240,plain,
! [SV804: $i,SV448: $i,SV44: $i] :
( ( ! [SY2607: $i] :
( ~ ( class_Divides_Osemiring__div @ SV44 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ ( c_Divides_Odiv__class_Omod @ SV804 @ SY2607 @ SV44 ) @ SV44 ) @ SY2607 @ SV44 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV804 @ SV44 ) @ SY2607 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2241,plain,
! [SV805: $i,SV449: $i,SV45: $i] :
( ( ! [SY2608: $i] :
( ~ ( class_Divides_Osemiring__div @ SV45 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV449 @ SV805 @ SV45 ) @ SY2608 @ SV45 ) @ SV805 @ SV45 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV449 @ SY2608 @ SV45 ) @ SV805 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2242,plain,
! [SV806: $i,SV450: $i,SV46: $i] :
( ( ! [SY2609: $i,SY2610: $i,SY2611: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV46 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SY2609 @ SY2610 @ SV46 ) @ SV46 ) @ SY2611 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SY2611 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SY2610 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2243,plain,
! [SV807: $i,SV451: $i,SV47: $i] :
( ( ! [SY2612: $i,SY2613: $i,SY2614: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV47 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SY2612 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SY2613 @ SY2614 @ SV47 ) @ SV47 ) @ SY2612 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SY2614 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2244,plain,
! [SV808: $i,SV452: $i,SV48: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV48 )
| ( SV452
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV452 @ SV808 @ SV48 ) @ SV808 @ SV48 ) @ ( c_Divides_Odiv__class_Omod @ SV452 @ SV808 @ SV48 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2245,plain,
! [SV809: $i,SV453: $i,SV49: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV49 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV453 @ SV809 @ SV49 ) @ SV809 @ SV49 ) @ ( c_Divides_Odiv__class_Omod @ SV453 @ SV809 @ SV49 ) @ SV49 )
= SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2246,plain,
! [SV810: $i,SV454: $i,SV50: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV50 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_Divides_Odiv__class_Odiv @ SV810 @ SV454 @ SV50 ) @ SV50 ) @ ( c_Divides_Odiv__class_Omod @ SV810 @ SV454 @ SV50 ) @ SV50 )
= SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2247,plain,
! [SV455: $i,SV51: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV51 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ SV455 @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV51 ) @ SV455 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2248,plain,
! [SV811: $i,SV456: $i,SV52: $i] :
( ( ~ ( class_Divides_Oring__div @ SV52 )
| ( ( c_Divides_Odiv__class_Odiv @ SV456 @ ( c_HOL_Ouminus__class_Ouminus @ SV811 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV456 @ SV811 @ SV52 ) @ SV52 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV811 @ SV456 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2249,plain,
! [SV812: $i,SV457: $i,SV53: $i] :
( ( ~ ( class_Divides_Oring__div @ SV53 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV457 @ SV53 ) @ SV812 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV457 @ SV812 @ SV53 ) @ SV53 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV812 @ SV457 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2250,plain,
! [SV813: $i,SV458: $i,SV54: $i] :
( ( ! [SY2615: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV813 @ SV54 ) @ SY2615 @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV458 @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SY2615 @ SV54 ) @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2251,plain,
! [SV814: $i,SV459: $i,SV55: $i] :
( ( ! [SY2616: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV814 @ SV55 ) @ SY2616 @ SV55 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SY2616 @ SV55 ) @ SV814 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2252,plain,
! [SV815: $i,SV460: $i,SV56: $i] :
( ( ! [SY2617: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV460 @ SV815 @ SV56 ) @ SY2617 @ SV56 )
= ( c_HOL_Otimes__class_Otimes @ SV460 @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SY2617 @ SV56 ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2253,plain,
! [SV816: $i,SV461: $i,SV57: $i] :
( ( ! [SY2618: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SY2618 @ SV57 ) @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV461 @ SV816 @ SV57 ) @ SY2618 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2254,plain,
! [SV817: $i,SV462: $i,SV58: $i] :
( ( ! [SY2619: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV58 )
| ( ( c_HOL_Otimes__class_Otimes @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV817 @ SY2619 @ SV58 ) @ SV58 )
= ( c_HOL_Otimes__class_Otimes @ SV817 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SY2619 @ SV58 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2255,plain,
! [SV818: $i,SV463: $i,SV59: $i] :
( ( ! [SY2620: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( c_HOL_Otimes__class_Otimes @ SV463 @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SY2620 @ SV59 ) @ SV59 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV463 @ SV818 @ SV59 ) @ SY2620 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2256,plain,
! [SV819: $i,SV464: $i,SV60: $i] :
( ( ! [SY2621: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV464 @ SV819 @ SV60 ) @ SY2621 @ SV60 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV464 @ SY2621 @ SV60 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SY2621 @ SV60 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2257,plain,
! [SV820: $i,SV465: $i,SV61: $i] :
( ( ! [SY2622: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV61 )
| ( ( c_HOL_Otimes__class_Otimes @ SV465 @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SY2622 @ SV61 ) @ SV61 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV820 @ SV61 ) @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SY2622 @ SV61 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2258,plain,
! [SV821: $i,SV466: $i,SV62: $i] :
( ( ! [SY2623: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV62 )
| ( ( c_HOL_Otimes__class_Otimes @ SV466 @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SY2623 @ SV62 ) @ SV62 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV821 @ SV62 ) @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SY2623 @ SV62 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2259,plain,
! [SV822: $i,SV467: $i,SV63: $i] :
( ( ! [SY2624: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV63 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV467 @ SV822 @ SV63 ) @ SY2624 @ SV63 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV467 @ SY2624 @ SV63 ) @ ( c_HOL_Otimes__class_Otimes @ SV822 @ SY2624 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2260,plain,
! [SV823: $i,SV468: $i,SV64: $i] :
( ( ! [SY2625: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV64 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SV823 @ SV64 ) @ SY2625 @ SV64 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SY2625 @ SV64 ) @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SY2625 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2261,plain,
! [SV824: $i,SV469: $i,SV65: $i] :
( ( ! [SY2626: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV65 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV469 @ SV824 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ SY2626 @ ( tc_Polynomial_Opoly @ SV65 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV469 @ SY2626 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SY2626 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( tc_Polynomial_Opoly @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2262,plain,
! [SV825: $i,SV470: $i,SV66: $i] :
( ( ! [SY2627: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ SV470 @ ( c_HOL_Oplus__class_Oplus @ SV825 @ SY2627 @ SV66 ) @ SV66 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV825 @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SY2627 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2263,plain,
! [SV826: $i,SV471: $i,SV67: $i] :
( ( ! [SY2628: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV471 @ SV826 @ SV67 ) @ SY2628 @ SV67 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV471 @ SY2628 @ SV67 ) @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SY2628 @ SV67 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2264,plain,
! [SV827: $i,SV472: $i,SV68: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV68 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV472 @ SV827 @ SV68 ) @ SV68 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV827 @ SV472 @ SV68 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2265,plain,
! [SV828: $i,SV473: $i,SV69: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV69 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV828 @ SV69 ) @ SV473 @ SV69 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV828 @ SV473 @ SV69 ) @ ( c_HOL_Oone__class_Oone @ SV69 ) @ SV69 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2266,plain,
! [SV829: $i,SV474: $i,SV70: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV70 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV829 @ SV70 ) @ SV829 @ SV70 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV474 @ SV829 @ SV70 ) @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV70 ) )
| ( SV829
= ( c_HOL_Ozero__class_Ozero @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2267,plain,
! [SV71: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV71 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ SV71 ) @ SV71 )
= ( c_HOL_Oone__class_Oone @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2268,plain,
! [SV830: $i,SV475: $i,SV72: $i] :
( ( ! [SY2629: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV830 @ SV72 ) @ ( c_HOL_Otimes__class_Otimes @ SY2629 @ SV830 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV475 @ SY2629 @ SV72 ) @ SV830 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2269,plain,
! [SV831: $i,SV476: $i,SV73: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV73 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV476 @ SV73 ) @ SV831 @ SV73 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV831 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2270,plain,
! [SV832: $i,SV477: $i,SV74: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV74 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV477 @ SV74 ) @ SV832 @ SV74 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV477 @ SV832 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2271,plain,
! [SV833: $i,SV478: $i,SV75: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV75 )
| ( ( c_HOL_Otimes__class_Otimes @ SV478 @ ( c_HOL_Ouminus__class_Ouminus @ SV833 @ SV75 ) @ SV75 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV478 @ SV833 @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2272,plain,
! [SV834: $i,SV479: $i,SV76: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV76 )
| ( ( c_HOL_Otimes__class_Otimes @ SV479 @ ( c_HOL_Ouminus__class_Ouminus @ SV834 @ SV76 ) @ SV76 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV834 @ SV76 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2273,plain,
! [SV480: $i,SV77: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV77 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV77 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV77 ) @ SV77 )
= ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2274,plain,
! [SV835: $i,SV481: $i,SV78: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV78 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV78 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV78 ) @ SV78 )
= ( c_HOL_Otimes__class_Otimes @ SV481 @ SV835 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2275,plain,
! [SV836: $i,SV482: $i,SV79: $i] :
( ( ! [SY2630: $i] :
( ~ ( class_Divides_Osemiring__div @ SV79 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV836 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SY2630 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SV836 @ SY2630 @ SV79 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2276,plain,
! [SV837: $i,SV483: $i,SV80: $i] :
( ( ! [SY2631: $i] :
( ~ ( class_Divides_Osemiring__div @ SV80 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV483 @ SV837 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SY2631 @ SV837 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SV483 @ SY2631 @ SV80 ) )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2277,plain,
! [SV838: $i,SV484: $i,SV81: $i] :
( ( ~ ( class_Divides_Oring__div @ SV81 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV484 @ SV81 ) @ SV838 @ SV81 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV484 @ SV838 @ SV81 ) @ SV81 ) @ SV838 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2278,plain,
! [SV485: $i,SV82: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV82 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV485 @ SV82 )
= ( c_HOL_Ouminus__class_Ouminus @ SV485 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2279,plain,
! [SV486: $i,SV83: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV83 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV83 ) ) @ SV486 @ ( tc_Polynomial_Opoly @ SV83 ) )
= ( c_HOL_Ouminus__class_Ouminus @ SV486 @ ( tc_Polynomial_Opoly @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2280,plain,
! [SV839: $i,SV487: $i,SV84: $i] :
( ( ! [SY2632: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ SV487 @ SV839 @ SV84 ) @ SY2632 @ ( tc_Polynomial_Opoly @ SV84 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV487 @ SY2632 @ SV84 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( c_HOL_Otimes__class_Otimes @ SV839 @ SY2632 @ ( tc_Polynomial_Opoly @ SV84 ) ) @ SV84 ) @ ( tc_Polynomial_Opoly @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2281,plain,
! [SV840: $i,SV488: $i,SV85: $i] :
( ( ! [SY2633: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV85 )
| ( ( c_HOL_Otimes__class_Otimes @ SV488 @ ( c_Polynomial_OpCons @ SV840 @ SY2633 @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV840 @ SV488 @ SV85 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_HOL_Otimes__class_Otimes @ SV488 @ SY2633 @ ( tc_Polynomial_Opoly @ SV85 ) ) @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2282,plain,
! [SV489: $i,SV86: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV86 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV489 @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2283,plain,
! [SV490: $i,SV87: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV87 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV490 @ SV87 )
= ( c_HOL_Ozero__class_Ozero @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2284,plain,
! [SV491: $i,SV88: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV88 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV491 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV88 ) ) @ ( tc_Polynomial_Opoly @ SV88 ) )
= SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2285,plain,
! [SV492: $i,SV89: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV89 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV492 @ SV492 @ SV89 )
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2286,plain,
! [SV493: $i,SV90: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV90 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV493 @ SV493 @ SV90 )
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2287,plain,
! [SV494: $i,SV91: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV91 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2288,plain,
! [SV495: $i,SV92: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV92 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV495 @ SV495 @ SV92 )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2289,plain,
! [SV496: $i,SV93: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV93 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV93 )
| ( ( c_HOL_Ominus__class_Ominus @ SV496 @ SV496 @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2290,plain,
! [SV497: $i,SV94: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV94 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV94 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SV497 @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2291,plain,
! [SV841: $i,SV498: $i,SV95: $i] :
( ( ! [SY2634: $i,SY2635: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SY2634 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SY2635 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SY2634 @ SV841 @ SY2635 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2292,plain,
! [SV842: $i,SV499: $i,SV96: $i] :
( ( ! [SY2636: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV96 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ SV499 @ SV842 @ SV96 ) @ SY2636 @ SV96 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV499 @ SY2636 @ SV96 ) @ ( c_Polynomial_Osmult @ SV842 @ SY2636 @ SV96 ) @ ( tc_Polynomial_Opoly @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2293,plain,
! [SV843: $i,SV500: $i,SV97: $i] :
( ( ! [SY2637: $i,SY2638: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV97 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV843 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2637 @ SV500 @ SV97 ) @ SV843 @ SV97 ) @ SY2638 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2637 @ SV843 @ SV97 ) @ SY2638 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2294,plain,
! [SV844: $i,SV501: $i,SV98: $i] :
( ( ! [SY2639: $i] :
( ~ ( class_Divides_Osemiring__div @ SV98 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SY2639 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SY2639 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SY2639 @ SV98 ) @ SV98 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2639 @ SV844 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2639 @ SV501 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2295,plain,
! [SV845: $i,SV502: $i,SV99: $i] :
( ( ! [SY2640: $i] :
( ~ ( class_Divides_Osemiring__div @ SV99 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV502 @ SV845 @ SV99 ) @ SY2640 @ SV99 ) @ SV845 @ SV99 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SY2640 @ SV99 ) @ SV845 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2296,plain,
! [SV503: $i,SV100: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV100 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV503 @ ( c_HOL_Oone__class_Oone @ SV100 ) @ SV100 )
= SV503 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2297,plain,
! [SV504: $i,SV101: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV101 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV504 @ SV101 )
= SV504 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2298,plain,
! [SV505: $i,SV102: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV102 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV505 @ SV102 )
= SV505 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2299,plain,
! [SV506: $i,SV103: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV506 @ SV103 )
= SV506 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2300,plain,
! [SV507: $i,SV104: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV104 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV507 @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV104 )
= SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2301,plain,
! [SV508: $i,SV105: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV105 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV508 @ SV105 )
= SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2302,plain,
! [SV846: $i,SV509: $i,SV106: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV106 )
| ( c_Polynomial_Opdivmod__rel @ SV509 @ SV846 @ ( c_Divides_Odiv__class_Odiv @ SV509 @ SV846 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ ( c_Divides_Odiv__class_Omod @ SV509 @ SV846 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2303,plain,
! [SV510: $i,SV107: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV107 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV510 @ SV107 )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2304,plain,
! [SV847: $i,SV511: $i,SV108: $i] :
( ( ! [SY2641: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV108 )
| ~ ( class_Int_Onumber__ring @ SV108 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SY2641 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SY2641 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2305,plain,
! [SV848: $i,SV512: $i,SV109: $i] :
( ( ! [SY2642: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV109 )
| ~ ( class_Int_Onumber__ring @ SV109 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SY2642 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SY2642 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2306,plain,
! [SV849: $i,SV513: $i,SV110: $i] :
( ( ! [SY2643: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV110 )
| ( ( c_Polynomial_Opoly__gcd @ SV513 @ ( c_Polynomial_Opoly__gcd @ SV849 @ SY2643 @ SV110 ) @ SV110 )
= ( c_Polynomial_Opoly__gcd @ SV849 @ ( c_Polynomial_Opoly__gcd @ SV513 @ SY2643 @ SV110 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2307,plain,
! [SV850: $i,SV514: $i,SV111: $i] :
( ( ! [SY2644: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV111 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ SV514 @ SV850 @ SV111 ) @ SY2644 @ SV111 )
= ( c_Polynomial_Opoly__gcd @ SV514 @ ( c_Polynomial_Opoly__gcd @ SV850 @ SY2644 @ SV111 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2308,plain,
! [SV851: $i,SV515: $i,SV112: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV112 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV851 @ SV112 ) @ SV851 @ SV112 )
= SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2309,plain,
! [SV852: $i,SV516: $i,SV113: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV113 )
| ( ( c_Polynomial_Opoly__gcd @ SV516 @ ( c_HOL_Ouminus__class_Ouminus @ SV852 @ ( tc_Polynomial_Opoly @ SV113 ) ) @ SV113 )
= ( c_Polynomial_Opoly__gcd @ SV516 @ SV852 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2310,plain,
! [SV853: $i,SV517: $i,SV114: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV114 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ SV517 @ ( tc_Polynomial_Opoly @ SV114 ) ) @ SV853 @ SV114 )
= ( c_Polynomial_Opoly__gcd @ SV517 @ SV853 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2311,plain,
! [SV854: $i,SV518: $i,SV115: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( c_HOL_Otimes__class_Otimes @ SV518 @ SV854 @ SV115 )
= ( c_HOL_Otimes__class_Otimes @ SV854 @ SV518 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2312,plain,
! [SV116: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(2313,plain,
! [SV855: $i,SV519: $i,SV117: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
| ( ( c_HOL_Otimes__class_Otimes @ SV519 @ SV855 @ SV117 )
= ( c_HOL_Otimes__class_Otimes @ SV855 @ SV519 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2314,plain,
! [SV856: $i,SV520: $i,SV118: $i] :
( ( ! [SY2645: $i] :
( ~ ( class_Divides_Osemiring__div @ SV118 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV520 @ SV856 @ SV118 ) @ SY2645 @ SV118 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV520 @ SY2645 @ SV118 ) @ ( c_Divides_Odiv__class_Omod @ SV856 @ SY2645 @ SV118 ) @ SV118 ) @ SY2645 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2315,plain,
! [SV119: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV119 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
= ( c_HOL_Ozero__class_Ozero @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2316,plain,
! [SV857: $i,SV521: $i,SV120: $i] :
( ( ! [SY2646: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV120 )
| ( ( c_HOL_Oplus__class_Oplus @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SV857 @ SY2646 @ SV120 ) @ SV120 )
= ( c_HOL_Oplus__class_Oplus @ SV857 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SY2646 @ SV120 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2317,plain,
! [SV858: $i,SV522: $i,SV121: $i] :
( ( ! [SY2647: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV121 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV522 @ SV858 @ SV121 ) @ SY2647 @ SV121 )
= ( c_HOL_Oplus__class_Oplus @ SV522 @ ( c_HOL_Oplus__class_Oplus @ SV858 @ SY2647 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2318,plain,
! [SV859: $i,SV523: $i,SV122: $i] :
( ( ! [SY2648: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Oplus__class_Oplus @ SV523 @ ( c_HOL_Oplus__class_Oplus @ SV859 @ SY2648 @ SV122 ) @ SV122 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV523 @ SV859 @ SV122 ) @ SY2648 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2319,plain,
! [SV860: $i,SV524: $i,SV123: $i] :
( ( ! [SY2649: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV123 )
| ( ( c_HOL_Oplus__class_Oplus @ SV524 @ ( c_HOL_Oplus__class_Oplus @ SV860 @ SY2649 @ SV123 ) @ SV123 )
= ( c_HOL_Oplus__class_Oplus @ SV860 @ ( c_HOL_Oplus__class_Oplus @ SV524 @ SY2649 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2320,plain,
! [SV861: $i,SV525: $i,SV124: $i] :
( ( ! [SY2650: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV861 @ SV124 ) @ SY2650 @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ SV525 @ ( c_HOL_Oplus__class_Oplus @ SV861 @ SY2650 @ SV124 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2321,plain,
! [SV862: $i,SV526: $i,SV125: $i] :
( ( ! [SY2651: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ SV526 @ ( c_HOL_Oplus__class_Oplus @ SV862 @ SY2651 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV862 @ SV125 ) @ SY2651 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2322,plain,
! [SV863: $i,SV527: $i,SV126: $i] :
( ( ! [SY2652: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV863 @ SV126 ) @ SY2652 @ SV126 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SY2652 @ SV126 ) @ SV863 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2323,plain,
! [SV864: $i,SV528: $i,SV127: $i] :
( ( ! [SY2653: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Oplus__class_Oplus @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SY2653 @ SV127 ) @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ SV864 @ ( c_HOL_Oplus__class_Oplus @ SV528 @ SY2653 @ SV127 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2324,plain,
! [SV865: $i,SV529: $i,SV128: $i] :
( ( ! [SY2654: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV529 @ SV865 @ SV128 ) @ SY2654 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ SV529 @ ( c_HOL_Oplus__class_Oplus @ SV865 @ SY2654 @ SV128 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2325,plain,
! [SV866: $i,SV530: $i,SV129: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV129 )
| ( ( c_Divides_Odiv__class_Odiv @ SV530 @ ( c_HOL_Ouminus__class_Ouminus @ SV866 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV530 @ SV866 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2326,plain,
! [SV867: $i,SV531: $i,SV130: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV130 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV531 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ SV867 @ ( tc_Polynomial_Opoly @ SV130 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV531 @ SV867 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ ( tc_Polynomial_Opoly @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2327,plain,
! [SV868: $i,SV532: $i,SV131: $i] :
( ( ! [SY2655: $i] :
( ~ ( class_Divides_Osemiring__div @ SV131 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV868 @ SV131 ) @ SY2655 @ SV131 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ ( c_Divides_Odiv__class_Omod @ SV868 @ SY2655 @ SV131 ) @ SV131 ) @ SY2655 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2328,plain,
! [SV869: $i,SV533: $i,SV132: $i] :
( ( ! [SY2656: $i] :
( ~ ( class_Divides_Osemiring__div @ SV132 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV869 @ SV132 ) @ SY2656 @ SV132 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV533 @ SY2656 @ SV132 ) @ SV869 @ SV132 ) @ SY2656 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2329,plain,
! [SV870: $i,SV534: $i,SV133: $i] :
( ( ! [SY2657: $i,SY2658: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SY2657 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SY2658 @ SY2657 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2330,plain,
! [SV871: $i,SV535: $i,SV134: $i] :
( ( ! [SY2659: $i,SY2660: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV134 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV535 @ SV871 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SY2659 @ SY2660 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SY2659 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SY2660 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SY2659 @ SV134 ) @ SY2660 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SY2659 @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SY2660 @ SV134 ) @ SV134 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2331,plain,
! [SV872: $i,SV536: $i,SV135: $i] :
( ( ! [SY2661: $i,SY2662: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV536 @ SV872 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2661 @ SV872 @ SV135 ) @ SY2662 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV536 @ SY2661 @ SV135 ) @ SV872 @ SV135 ) @ SY2662 @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2332,plain,
! [SV537: $i,SV136: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV136 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV537 @ SV136 ) @ SV537 @ SV136 )
= ( c_HOL_Ozero__class_Ozero @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2333,plain,
! [SV538: $i,SV137: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV137 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV538 @ SV137 ) @ SV538 @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2334,plain,
! [SV539: $i,SV138: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV138 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Ouminus__class_Ouminus @ SV539 @ SV138 ) @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2335,plain,
! [SV540: $i,SV139: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV139 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV540 @ SV139 ) @ SV540 @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2336,plain,
! [SV873: $i,SV541: $i,SV140: $i] :
( ( ! [SY2663: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV140 )
| ( ( c_HOL_Otimes__class_Otimes @ SV541 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SY2663 @ SV140 ) @ SV140 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV873 @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SY2663 @ SV140 ) @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2337,plain,
! [SV874: $i,SV542: $i,SV141: $i] :
( ( ! [SY2664: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV141 )
| ( ( c_HOL_Otimes__class_Otimes @ SV542 @ ( c_HOL_Ominus__class_Ominus @ SV874 @ SY2664 @ SV141 ) @ SV141 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV874 @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SY2664 @ SV141 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2338,plain,
! [SV875: $i,SV543: $i,SV142: $i] :
( ( ! [SY2665: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV543 @ SV875 @ SV142 ) @ SY2665 @ SV142 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV543 @ SY2665 @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV875 @ SY2665 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2339,plain,
! [SV876: $i,SV544: $i,SV143: $i] :
( ( ! [SY2666: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV143 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV544 @ SV876 @ SV143 ) @ SY2666 @ SV143 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV544 @ SY2666 @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV876 @ SY2666 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2340,plain,
! [SV877: $i,SV545: $i,SV144: $i] :
( ( ! [SY2667: $i,SY2668: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV144 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV877 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SY2667 @ SY2668 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV545 @ SY2667 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SV877 @ SY2668 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2341,plain,
! [SV878: $i,SV546: $i,SV145: $i] :
( ( ! [SY2669: $i] :
( ~ ( class_Divides_Osemiring__div @ SV145 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SV878 @ SV145 ) @ SY2669 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SY2669 @ SV145 ) @ SV878 @ SV145 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV878 @ SV546 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2342,plain,
! [SV879: $i,SV547: $i,SV146: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV547 @ SV879 @ SV146 ) @ SV146 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV547 @ SV146 ) @ SV879 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2343,plain,
! [SV880: $i,SV548: $i,SV147: $i] :
( ( ! [SY2670: $i] :
( ~ ( class_Divides_Osemiring__div @ SV147 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ SV880 @ SV147 ) @ SY2670 @ SV147 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ ( c_Divides_Odiv__class_Omod @ SV880 @ SY2670 @ SV147 ) @ SV147 ) @ SY2670 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2344,plain,
! [SV881: $i,SV549: $i,SV148: $i] :
( ( ! [SY2671: $i] :
( ~ ( class_Divides_Osemiring__div @ SV148 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV549 @ SV881 @ SV148 ) @ SY2671 @ SV148 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV549 @ SY2671 @ SV148 ) @ SV881 @ SV148 ) @ SY2671 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2345,plain,
! [SV882: $i,SV550: $i,SV149: $i] :
( ( ! [SY2672: $i,SY2673: $i,SY2674: $i,SY2675: $i,SY2676: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SY2672 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2673 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SY2674 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2675 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2676 @ SY2672 @ SY2673 @ SY2674 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SY2676 @ SY2675 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2346,plain,
! [SV883: $i,SV551: $i,SV150: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ SV551 @ ( c_Divides_Odiv__class_Odiv @ SV883 @ SV551 @ SV150 ) @ SV150 )
= SV883 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV551 @ SV883 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2347,plain,
! [SV884: $i,SV552: $i,SV151: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV151 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV552 @ SV884 @ SV151 ) @ SV884 @ SV151 )
= SV552 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV884 @ SV552 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2348,plain,
! [SV885: $i,SV553: $i,SV152: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV152 )
| ( ( c_HOL_Ominus__class_Ominus @ SV553 @ ( c_HOL_Ouminus__class_Ouminus @ SV885 @ SV152 ) @ SV152 )
= ( c_HOL_Oplus__class_Oplus @ SV553 @ SV885 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2349,plain,
! [SV886: $i,SV554: $i,SV153: $i] :
( ( ! [SY2677: $i] :
( ~ ( class_Divides_Osemiring__div @ SV153 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV554 @ ( c_HOL_Otimes__class_Otimes @ SV886 @ SY2677 @ SV153 ) @ SV153 ) @ SV886 @ SV153 )
= ( c_Divides_Odiv__class_Omod @ SV554 @ SV886 @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2350,plain,
! [SV887: $i,SV555: $i,SV154: $i] :
( ( ! [SY2678: $i] :
( ~ ( class_Divides_Osemiring__div @ SV154 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV887 @ SY2678 @ SV154 ) @ SV154 ) @ SY2678 @ SV154 )
= ( c_Divides_Odiv__class_Omod @ SV555 @ SY2678 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2351,plain,
! [SV888: $i,SV556: $i,SV155: $i] :
( ( ! [SY2679: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV155 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
| ( SY2679
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SY2679 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SY2679 @ SV155 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2352,plain,
! [SV889: $i,SV557: $i,SV156: $i] :
( ( ! [SY2680: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV156 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
| ( SY2680
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2680 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SY2680 @ SV889 @ SV156 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2353,plain,
! [SV558: $i,SV157: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV157 ) ) @ SV558 @ ( tc_Polynomial_Opoly @ SV157 ) )
= SV558 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2354,plain,
! [SV559: $i,SV158: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV158 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV158 ) ) @ ( tc_Polynomial_Opoly @ SV158 ) )
= SV559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2355,plain,
! [SV560: $i,SV159: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV159 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV560 @ ( c_HOL_Ozero__class_Ozero @ SV159 ) @ SV159 )
= SV560 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2356,plain,
! [SV561: $i,SV160: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV160 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV160 ) @ SV561 @ SV160 )
= SV561 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2357,plain,
! [SV562: $i,SV161: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV161 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV562 @ ( c_HOL_Ozero__class_Ozero @ SV161 ) @ SV161 )
= SV562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2358,plain,
! [SV563: $i,SV162: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV162 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV162 )
| ( SV563
= ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2359,plain,
! [SV564: $i,SV163: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV163 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV163 ) @ SV564 @ SV163 )
= SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2360,plain,
! [SV565: $i,SV164: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV164 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV565 @ SV164 )
= SV565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2361,plain,
! [SV566: $i,SV165: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV165 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV566 @ ( c_HOL_Ozero__class_Ozero @ SV165 ) @ SV165 )
= SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2362,plain,
! [SV567: $i,SV166: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV166 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV166 ) @ SV567 @ SV166 )
= SV567 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2363,plain,
! [SV890: $i,SV568: $i,SV167: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV167 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV568 @ SV890 @ SV167 ) @ SV890 @ SV167 )
= SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2364,plain,
! [SV569: $i,SV168: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV168 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV569 @ SV168 ) @ SV168 )
= SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2365,plain,
! [SV570: $i,SV169: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV169 ) )
= $true )
| ( ( SV570
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV570 @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2366,plain,
! [SV571: $i,SV170: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV170 ) )
= $true )
| ( ( SV571
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV571 @ SV170 ) @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2367,plain,
! [SV572: $i,SV171: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV171 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV572 @ SV171 ) @ SV171 )
= SV572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2368,plain,
! [SV573: $i,SV172: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV172 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV573 @ SV172 ) @ SV172 )
= SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2369,plain,
! [SV574: $i,SV173: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV173 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV574 @ ( c_HOL_Oone__class_Oone @ SV173 ) @ SV173 )
= SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2370,plain,
! [SV891: $i,SV575: $i,SV174: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV174 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV575 @ SV891 @ SV174 ) @ SV174 )
= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV575 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2371,plain,
! [SV892: $i,SV576: $i,SV175: $i] :
( ( ! [SY2681: $i,SY2682: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV892 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY2681 @ SY2682 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SY2681 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV892 @ SY2682 @ SV175 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2372,plain,
! [SV893: $i,SV577: $i,SV176: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV176 )
| ( ( c_HOL_Ominus__class_Ominus @ SV577 @ SV893 @ SV176 )
= ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Ouminus__class_Ouminus @ SV893 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2373,plain,
! [SV894: $i,SV578: $i,SV177: $i] :
( ( ~ ( class_Int_Onumber__ring @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ SV578 @ SV894 @ SV177 )
= ( c_HOL_Oplus__class_Oplus @ SV578 @ ( c_HOL_Ouminus__class_Ouminus @ SV894 @ SV177 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2374,plain,
! [SV895: $i,SV579: $i,SV178: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV178 )
| ( ( c_HOL_Ominus__class_Ominus @ SV579 @ SV895 @ SV178 )
= ( c_HOL_Oplus__class_Oplus @ SV579 @ ( c_HOL_Ouminus__class_Ouminus @ SV895 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2375,plain,
! [SV896: $i,SV580: $i,SV179: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV179 )
| ( ( c_HOL_Ominus__class_Ominus @ SV580 @ SV896 @ SV179 )
= ( c_HOL_Oplus__class_Oplus @ SV580 @ ( c_HOL_Ouminus__class_Ouminus @ SV896 @ SV179 ) @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2376,plain,
! [SV897: $i,SV581: $i,SV180: $i] :
( ( ! [SY2683: $i] :
( ~ ( class_Divides_Oring__div @ SV180 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV581 @ SV897 @ SV180 ) @ SY2683 @ SV180 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV581 @ SY2683 @ SV180 ) @ ( c_Divides_Odiv__class_Omod @ SV897 @ SY2683 @ SV180 ) @ SV180 ) @ SY2683 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2377,plain,
! [SV582: $i,SV181: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV181 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ SV582 @ SV181 ) @ SV181 )
= ( c_HOL_Oabs__class_Oabs @ SV582 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2378,plain,
! [SV583: $i,SV182: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV182 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV583 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2379,plain,
! [SV898: $i,SV584: $i,SV183: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV183 )
| ( ( c_Divides_Odiv__class_Omod @ SV584 @ SV898 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV898 @ SV584 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2380,plain,
! [SV585: $i,SV184: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV184 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV184 ) @ SV585 @ SV184 )
= ( c_HOL_Oone__class_Oone @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(2381,plain,
! [SV899: $i,SV586: $i,SV185: $i] :
( ( ! [SY2684: $i] :
( ~ ( class_Divides_Oring__div @ SV185 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV586 @ SV899 @ SV185 ) @ SY2684 @ SV185 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV586 @ SY2684 @ SV185 ) @ SV899 @ SV185 ) @ SY2684 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2382,plain,
! [SV900: $i,SV587: $i,SV186: $i] :
( ( ! [SY2685: $i] :
( ~ ( class_Divides_Oring__div @ SV186 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SV900 @ SV186 ) @ SY2685 @ SV186 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ ( c_Divides_Odiv__class_Omod @ SV900 @ SY2685 @ SV186 ) @ SV186 ) @ SY2685 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2383,plain,
! [SV901: $i,SV588: $i,SV187: $i] :
( ( ! [SY2686: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV187 )
| ( ( c_Divides_Odiv__class_Omod @ SV588 @ ( c_Polynomial_Osmult @ SV901 @ SY2686 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SV588 @ SY2686 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
| ( SV901
= ( c_HOL_Ozero__class_Ozero @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2384,plain,
! [SV589: $i,SV188: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV188 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV589 @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV589 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2385,plain,
! [SV590: $i,SV189: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV189 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SV590 @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SV590 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2386,plain,
! [SV902: $i,SV591: $i,SV190: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV190 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV591 @ SV902 @ SV190 ) @ SV902 @ SV190 )
= ( c_Divides_Odiv__class_Omod @ SV591 @ SV902 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2387,plain,
! [SV592: $i,SV191: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV191 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV592 @ SV592 @ SV191 )
= ( c_HOL_Oone__class_Oone @ SV191 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2388,plain,
! [SV903: $i,SV593: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV192 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ SV593 @ SV192 ) @ SV903 @ SV192 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV593 @ SV903 @ SV192 ) @ ( tc_Polynomial_Opoly @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2389,plain,
! [SV904: $i,SV594: $i,SV193: $i] :
( ( ! [SY2687: $i,SY2688: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV193 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV594 @ SV904 @ SV193 ) @ SY2687 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2688 @ SV904 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV594 @ SY2688 @ SV193 ) @ SV904 @ SV193 ) @ SY2687 @ SV193 ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2390,plain,
! [SV595: $i,SV194: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV194 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV595 @ SV194 ) @ SV194 )
= ( c_HOL_Oabs__class_Oabs @ SV595 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2391,plain,
! [SV905: $i,SV596: $i,SV195: $i] :
( ( ! [SY2689: $i] :
( ~ ( class_Divides_Osemiring__div @ SV195 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV596 @ SV905 @ SV195 ) @ SV905 @ SV195 ) @ ( c_Divides_Odiv__class_Omod @ SV596 @ SV905 @ SV195 ) @ SV195 ) @ SY2689 @ SV195 )
= ( c_HOL_Oplus__class_Oplus @ SV596 @ SY2689 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2392,plain,
! [SV906: $i,SV597: $i,SV196: $i] :
( ( ! [SY2690: $i] :
( ~ ( class_Divides_Osemiring__div @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV597 @ ( c_Divides_Odiv__class_Odiv @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ ( c_Divides_Odiv__class_Omod @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ SY2690 @ SV196 )
= ( c_HOL_Oplus__class_Oplus @ SV906 @ SY2690 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2393,plain,
! [SV598: $i,SV197: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV197 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ SV598 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ SV598 @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2394,plain,
! [SV599: $i,SV198: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV198 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV599 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= SV599 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2395,plain,
! [SV600: $i,SV199: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV199 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV600 @ SV600 @ SV199 )
= ( c_HOL_Ozero__class_Ozero @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2396,plain,
! [SV907: $i,SV601: $i,SV200: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV200 )
| ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV907 @ SV200 )
= ( c_HOL_Oplus__class_Oplus @ SV907 @ SV601 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2397,plain,
! [SV908: $i,SV602: $i,SV201: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ SV602 @ SV908 @ SV201 )
= ( c_HOL_Oplus__class_Oplus @ SV908 @ SV602 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2398,plain,
! [SV909: $i,SV603: $i,SV202: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV202 )
| ( ( c_HOL_Oplus__class_Oplus @ SV603 @ SV909 @ SV202 )
= ( c_HOL_Oplus__class_Oplus @ SV909 @ SV603 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2399,plain,
! [SV910: $i,SV604: $i,SV203: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV203 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV604 @ SV203 ) @ SV910 @ SV203 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV203 ) @ SV203 ) @ SV910 @ SV203 ) @ ( c_Power_Opower__class_Opower @ SV604 @ SV910 @ SV203 ) @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2400,plain,
! [SV911: $i,SV605: $i,SV204: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV204 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ SV605 @ SV911 @ SV204 ) @ SV911 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2401,plain,
! [SV912: $i,SV606: $i,SV205: $i] :
( ( ! [SY2691: $i] :
( ~ ( class_Divides_Osemiring__div @ SV205 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV606 @ SV912 @ SV205 ) @ SY2691 @ SV205 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV606 @ SY2691 @ SV205 ) @ ( c_Divides_Odiv__class_Omod @ SV912 @ SY2691 @ SV205 ) @ SV205 ) @ SY2691 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2402,plain,
! [SV913: $i,SV607: $i,SV206: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV206 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV607 @ SV913 @ SV206 ) @ SV607 @ SV206 )
= ( c_HOL_Otimes__class_Otimes @ SV607 @ ( c_Power_Opower__class_Opower @ SV607 @ SV913 @ SV206 ) @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2403,plain,
! [SV914: $i,SV608: $i,SV207: $i] :
( ( ! [SY2692: $i] :
( ~ ( class_Divides_Osemiring__div @ SV207 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV608 @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SY2692 @ SV207 ) @ SV207 ) @ SY2692 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SV914 @ ( c_Divides_Odiv__class_Odiv @ SV608 @ SY2692 @ SV207 ) @ SV207 ) )
| ( SY2692
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2404,plain,
! [SV915: $i,SV609: $i,SV208: $i] :
( ( ! [SY2693: $i] :
( ~ ( class_Divides_Osemiring__div @ SV208 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV609 @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SY2693 @ SV208 ) @ SV208 ) @ SV915 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SY2693 @ ( c_Divides_Odiv__class_Odiv @ SV609 @ SV915 @ SV208 ) @ SV208 ) )
| ( SV915
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2405,plain,
! [SV610: $i,SV209: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV209 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV610 @ SV610 @ SV209 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV209 ) @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV209 ) @ SV610 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2406,plain,
! [SV916: $i,SV611: $i,SV210: $i] :
( ( ! [SY2694: $i,SY2695: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV210 )
| ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SY2694 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SY2694 @ SY2695 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2407,plain,
! [SV917: $i,SV612: $i,SV211: $i] :
( ( ! [SY2696: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV211 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ SV612 @ SV917 @ SV211 ) @ SY2696 @ SV211 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV612 @ SY2696 @ SV211 ) @ ( c_Polynomial_Osmult @ SV917 @ SY2696 @ SV211 ) @ ( tc_Polynomial_Opoly @ SV211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2408,plain,
! [SV918: $i,SV613: $i,SV212: $i] :
( ( ! [SY2697: $i] :
( ~ ( class_Divides_Osemiring__div @ SV212 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SV918 @ SV212 ) @ SY2697 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SY2697 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV918 @ SY2697 @ SV212 ) @ SV212 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV918 @ SV613 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2409,plain,
! [SV614: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV213 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV614 @ SV213 ) @ ( c_HOL_Oabs__class_Oabs @ SV614 @ SV213 ) @ SV213 )
= ( c_HOL_Otimes__class_Otimes @ SV614 @ SV614 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2410,plain,
! [SV615: $i,SV214: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV214 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV615 @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2411,plain,
! [SV616: $i,SV215: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV215 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV616 @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2412,plain,
! [SV617: $i,SV216: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV617 @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2413,plain,
! [SV618: $i,SV217: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV217 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV618 @ SV217 )
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2414,plain,
! [SV619: $i,SV218: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV218 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV619 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2415,plain,
! [SV620: $i,SV219: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV219 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV620 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2416,plain,
! [SV621: $i,SV220: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV220 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) @ SV621 @ ( tc_Polynomial_Opoly @ SV220 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2417,plain,
! [SV622: $i,SV221: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV221 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV622 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) @ ( tc_Polynomial_Opoly @ SV221 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2418,plain,
! [SV623: $i,SV222: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV222 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV623 @ SV222 )
= ( c_HOL_Ozero__class_Ozero @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2419,plain,
! [SV624: $i,SV223: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV223 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SV624 @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2420,plain,
! [SV625: $i,SV224: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV224 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV625 @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2421,plain,
! [SV626: $i,SV225: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV225 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SV626 @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2422,plain,
! [SV627: $i,SV226: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV226 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV627 @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 )
= ( c_HOL_Ozero__class_Ozero @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2423,plain,
! [SV919: $i,SV628: $i,SV227: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV227 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV628 @ SV227 ) @ SV919 @ SV227 ) @ SV227 )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV628 @ SV919 @ SV227 ) @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2424,plain,
! [SV920: $i,SV629: $i,SV228: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV629 @ SV920 @ SV228 ) @ SV920 @ SV228 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV629 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 ) @ SV920 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2425,plain,
! [SV921: $i,SV630: $i,SV229: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV229 )
| ( ( c_HOL_Oplus__class_Oplus @ SV630 @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV630 @ SV229 ) @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV921 @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV229 ) @ SV630 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2426,plain,
! [SV631: $i,SV230: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV230 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV631 @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 )
= ( c_HOL_Ozero__class_Ozero @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2427,plain,
! [SV922: $i,SV632: $i,SV231: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV632 @ SV231 ) @ ( c_HOL_Oplus__class_Oplus @ SV922 @ SV632 @ SV231 ) @ SV231 )
= SV922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2428,plain,
! [SV923: $i,SV633: $i,SV232: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV633 @ SV232 ) @ ( c_HOL_Oplus__class_Oplus @ SV633 @ SV923 @ SV232 ) @ SV232 )
= SV923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2429,plain,
! [SV924: $i,SV634: $i,SV233: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV233 )
| ( ( c_Divides_Odiv__class_Omod @ SV634 @ ( c_HOL_Ouminus__class_Ouminus @ SV924 @ ( tc_Polynomial_Opoly @ SV233 ) ) @ ( tc_Polynomial_Opoly @ SV233 ) )
= ( c_Divides_Odiv__class_Omod @ SV634 @ SV924 @ ( tc_Polynomial_Opoly @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2430,plain,
! [SV234: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV234 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV234 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2431,plain,
! [SV925: $i,SV635: $i,SV235: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV235 )
| ( ( c_Polynomial_Opoly__gcd @ SV635 @ SV925 @ SV235 )
= ( c_Polynomial_Opoly__gcd @ SV925 @ SV635 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2432,plain,
! [SV926: $i,SV636: $i,SV236: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV236 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV636 @ SV236 ) @ SV926 @ SV236 )
= ( c_HOL_Otimes__class_Otimes @ SV636 @ ( c_HOL_Ouminus__class_Ouminus @ SV926 @ SV236 ) @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2433,plain,
! [SV237: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV237 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 )
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2434,plain,
! [SV238: $i] :
( ( ( class_OrderedGroup_Oordered__ab__group__add @ SV238 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ SV238 ) @ SV238 )
= ( c_HOL_Ozero__class_Ozero @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2435,plain,
! [SV239: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV239 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV239 ) ) @ ( tc_Polynomial_Opoly @ SV239 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2436,plain,
! [SV927: $i,SV637: $i,SV240: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV240 )
| ( ( c_Polynomial_Opoly__gcd @ SV637 @ SV927 @ SV240 )
= ( c_Polynomial_Opoly__gcd @ SV927 @ ( c_Divides_Odiv__class_Omod @ SV637 @ SV927 @ ( tc_Polynomial_Opoly @ SV240 ) ) @ SV240 ) )
| ( SV927
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2437,plain,
! [SV638: $i,SV241: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV241 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV638 @ SV241 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2438,plain,
! [SV639: $i,SV242: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV242 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV639 @ SV242 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2439,plain,
! [SV928: $i,SV640: $i,SV243: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ SV640 @ SV243 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV928 @ SV243 ) @ SV243 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SV928 @ SV243 ) @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2440,plain,
! [SV929: $i,SV641: $i,SV244: $i] :
( ( ! [SY2698: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV244 )
| ( ( c_Divides_Odiv__class_Odiv @ SV641 @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SY2698 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ ( tc_Polynomial_Opoly @ SV244 ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ SV641 @ SV929 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ SY2698 @ ( tc_Polynomial_Opoly @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2441,plain,
! [SV930: $i,SV642: $i,SV245: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV245 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SV930 @ SV245 ) @ SV245 ) @ SV245 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SV930 @ SV245 ) @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2442,plain,
! [SV931: $i,SV643: $i,SV246: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV643 @ SV931 @ SV246 ) @ SV643 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2443,plain,
! [SV932: $i,SV644: $i,SV247: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV644 @ SV932 @ SV247 ) @ SV932 @ SV247 )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2444,plain,
! [SV933: $i,SV645: $i,SV248: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV248 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV645 @ SV933 @ SV248 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV645 @ SV933 @ SV248 ) @ SV933 @ SV248 ) @ SV248 )
= SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2445,plain,
! [SV249: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV249 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV249 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV249 ) @ SV249 )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2446,plain,
! [SV934: $i,SV646: $i,SV250: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV250 )
| ( SV646
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV646 @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV646 @ SV934 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2447,plain,
! [SV935: $i,SV647: $i,SV251: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV251 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV647 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ SV935 @ ( tc_Polynomial_Opoly @ SV251 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV647 @ SV935 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ ( tc_Polynomial_Opoly @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2448,plain,
! [SV936: $i,SV648: $i,SV252: $i] :
( ( ! [SY2699: $i] :
( ~ ( class_Divides_Osemiring__div @ SV252 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV936 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SY2699 @ SV252 ) @ SV252 )
= ( c_HOL_Otimes__class_Otimes @ SV648 @ ( c_Divides_Odiv__class_Omod @ SV936 @ SY2699 @ SV252 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2449,plain,
! [SV937: $i,SV649: $i,SV253: $i] :
( ( ! [SY2700: $i] :
( ~ ( class_Divides_Osemiring__div @ SV253 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV649 @ SV937 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SY2700 @ SV937 @ SV253 ) @ SV253 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV649 @ SY2700 @ SV253 ) @ SV937 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2450,plain,
! [SV938: $i,SV650: $i,SV254: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV254 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV650 @ SV938 @ SV254 ) @ SV254 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV938 @ SV254 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV650 @ SV254 ) @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2451,plain,
! [SV939: $i,SV651: $i,SV255: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV255 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV939 @ SV255 ) @ SV255 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV651 @ SV255 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV939 @ SV255 ) @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2452,plain,
! [SV940: $i,SV652: $i,SV256: $i] :
( ( ! [SY2701: $i,SY2702: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SY2701 @ SY2702 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SY2702 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SY2701 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2453,plain,
! [SV653: $i,SV257: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV257 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV653 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) @ SV257 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2454,plain,
! [SV654: $i,SV258: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV258 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV654 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) @ SV258 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2455,plain,
! [SV941: $i,SV655: $i,SV259: $i] :
( ( ! [SY2703: $i] :
( ~ ( class_Divides_Osemiring__div @ SV259 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SV941 @ SV259 ) @ SY2703 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SY2703 @ SV259 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2703 @ SV941 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2456,plain,
! [SV942: $i,SV656: $i,SV260: $i] :
( ( ! [SY2704: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV260 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SY2704 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SY2704 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2457,plain,
! [SV943: $i,SV657: $i,SV261: $i] :
( ( ! [SY2705: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV261 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SY2705 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SY2705 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2458,plain,
! [SV944: $i,SV658: $i,SV262: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV262 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV658 @ SV944 @ SV262 ) @ SV658 @ ( tc_Polynomial_Opoly @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2459,plain,
! [SV945: $i,SV659: $i,SV263: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV263 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV659 @ SV945 @ SV263 ) @ SV945 @ ( tc_Polynomial_Opoly @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2460,plain,
! [SV946: $i,SV660: $i,SV264: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV264 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV660 @ SV264 ) @ SV946 @ ( tc_Polynomial_Opoly @ SV264 ) )
| ( SV946
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2461,plain,
! [SV947: $i,SV661: $i,SV265: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV265 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ ( c_HOL_Oabs__class_Oabs @ SV947 @ SV265 ) @ SV265 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ SV947 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2462,plain,
! [SV948: $i,SV662: $i,SV266: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV266 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ SV948 @ SV266 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ ( c_HOL_Oabs__class_Oabs @ SV948 @ SV266 ) @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2463,plain,
! [SV949: $i,SV663: $i,SV267: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV267 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV663 @ SV267 ) @ SV949 @ SV267 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV663 @ SV949 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2464,plain,
! [SV950: $i,SV664: $i,SV268: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV268 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV664 @ SV950 @ SV268 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV664 @ SV268 ) @ SV950 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2465,plain,
! [SV665: $i,SV269: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV665 @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2466,plain,
! [SV951: $i,SV666: $i,SV270: $i] :
( ( ! [SY2706: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ SV270 )
| ( ( c_Polynomial_Osmult @ SV666 @ ( c_HOL_Ominus__class_Ominus @ SV951 @ SY2706 @ ( tc_Polynomial_Opoly @ SV270 ) ) @ SV270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV666 @ SV951 @ SV270 ) @ ( c_Polynomial_Osmult @ SV666 @ SY2706 @ SV270 ) @ ( tc_Polynomial_Opoly @ SV270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2467,plain,
! [SV952: $i,SV667: $i,SV271: $i] :
( ( ! [SY2707: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV271 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SV952 @ ( tc_Polynomial_Opoly @ SV271 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SY2707 @ SV952 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2468,plain,
! [SV953: $i,SV668: $i,SV272: $i] :
( ( ! [SY2708: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV272 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SV953 @ ( tc_Polynomial_Opoly @ SV272 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SV953 @ SY2708 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2469,plain,
! [SV954: $i,SV669: $i,SV273: $i] :
( ( ! [SY2709: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV273 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV954 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SY2709 @ SV954 @ SV273 ) @ SV273 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SY2709 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2470,plain,
! [SV955: $i,SV670: $i,SV274: $i] :
( ( ! [SY2710: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV274 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV955 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SY2710 @ SV274 ) @ SV274 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV955 @ SY2710 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2471,plain,
! [SV956: $i,SV671: $i,SV275: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV275 )
| ( ( c_Polynomial_Osmult @ SV671 @ ( c_HOL_Ouminus__class_Ouminus @ SV956 @ ( tc_Polynomial_Opoly @ SV275 ) ) @ SV275 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV671 @ SV956 @ SV275 ) @ ( tc_Polynomial_Opoly @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2472,plain,
! [SV672: $i,SV276: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 ) )
= $true )
| ( ( ( SV672
= ( c_HOL_Ozero__class_Ozero @ SV276 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV672 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2473,plain,
! [SV957: $i,SV673: $i,SV277: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV673 @ SV277 ) @ SV957 @ SV277 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV673 @ SV957 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2474,plain,
! [SV958: $i,SV674: $i,SV278: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV674 @ SV958 @ SV278 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV674 @ SV278 ) @ SV958 @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2475,plain,
! [SV959: $i,SV675: $i,SV279: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ ( c_HOL_Ouminus__class_Ouminus @ SV959 @ SV279 ) @ SV279 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ SV959 @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2476,plain,
! [SV960: $i,SV676: $i,SV280: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ SV960 @ SV280 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ ( c_HOL_Ouminus__class_Ouminus @ SV960 @ SV280 ) @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2477,plain,
! [SV961: $i,SV677: $i,SV281: $i] :
( ( ! [SY2711: $i] :
( ~ ( class_Divides_Osemiring__div @ SV281 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SY2711 @ SV961 @ SV281 ) @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SY2711 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SY2711 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2478,plain,
! [SV962: $i,SV678: $i,SV282: $i] :
( ( ! [SY2712: $i] :
( ~ ( class_Divides_Osemiring__div @ SV282 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SY2712 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SY2712 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2712 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2712 @ SV678 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2479,plain,
! [SV963: $i,SV679: $i,SV283: $i] :
( ( ! [SY2713: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SY2713 @ SV283 ) @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SY2713 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2480,plain,
! [SV680: $i,SV284: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV284 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV680 @ SV284 )
= SV680 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2481,plain,
! [SV964: $i,SV681: $i,SV285: $i] :
( ( ! [SY2714: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV285 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ SV681 @ SV964 @ SV285 ) @ SY2714 @ ( tc_Polynomial_Opoly @ SV285 ) )
= ( c_Polynomial_Osmult @ SV681 @ ( c_Divides_Odiv__class_Omod @ SV964 @ SY2714 @ ( tc_Polynomial_Opoly @ SV285 ) ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2482,plain,
! [SV965: $i,SV682: $i,SV286: $i] :
( ( ! [SY2715: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV286 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
| ( SY2715
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SY2715 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2483,plain,
! [SV966: $i,SV683: $i,SV287: $i] :
( ( ! [SY2716: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV287 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SY2716 @ ( tc_Polynomial_Opoly @ SV287 ) )
| ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SY2716 @ ( tc_Polynomial_Opoly @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2484,plain,
! [SV967: $i,SV684: $i,SV288: $i] :
( ( ! [SY2717: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV288 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SY2717 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SY2717
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2485,plain,
! [SV968: $i,SV685: $i,SV289: $i] :
( ( ! [SY2718: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV289 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SY2718 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SY2718 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2486,plain,
! [SV969: $i,SV686: $i,SV290: $i] :
( ( ! [SY2719: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV290 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
| ( SY2719
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY2719 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2487,plain,
! [SV970: $i,SV687: $i,SV291: $i] :
( ( ! [SY2720: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV291 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SY2720 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SY2720 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2488,plain,
! [SV971: $i,SV688: $i,SV292: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV292 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV688 @ SV971 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV971 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2489,plain,
! [SV972: $i,SV689: $i,SV293: $i] :
( ( ! [SY2721: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SV972 @ SV293 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2721 @ SV689 @ SV293 ) @ SV972 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2490,plain,
! [SV973: $i,SV690: $i,SV294: $i] :
( ( ! [SY2722: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SV973 @ SV294 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SY2722 @ SV294 ) @ SV973 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2491,plain,
! [SV974: $i,SV691: $i,SV295: $i] :
( ( ! [SY2723: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV974 @ SY2723 @ SV295 ) @ SV295 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SV974 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2492,plain,
! [SV975: $i,SV692: $i,SV296: $i] :
( ( ! [SY2724: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SV975 @ SY2724 @ SV296 ) @ SV296 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SY2724 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2493,plain,
! [SV693: $i,SV297: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV297 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV693 @ SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2494,plain,
! [SV976: $i,SV694: $i,SV298: $i] :
( ( ! [SY2725: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2725 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SY2725 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2495,plain,
! [SV695: $i,SV299: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV299 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV695 @ SV695 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2496,plain,
! [SV696: $i,SV300: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV300 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV696 @ SV300 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV300 ) ) @ ( tc_Polynomial_Opoly @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2497,plain,
! [SV977: $i,SV697: $i,SV301: $i] :
( ( ! [SY2726: $i,SY2727: $i,SY2728: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV301 )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SY2726 @ ( c_Polynomial_Osmult @ SV697 @ SY2727 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SY2728 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SY2726 @ SY2727 @ SY2728 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2498,plain,
! [SV978: $i,SV698: $i,SV302: $i] :
( ( ! [SY2729: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SY2729 @ SV302 ) @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SY2729 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2499,plain,
! [SV979: $i,SV699: $i,SV303: $i] :
( ( ! [SY2730: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV303 )
| ( ( c_Polynomial_Osmult @ SV699 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SY2730 @ ( tc_Polynomial_Opoly @ SV303 ) ) @ SV303 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV699 @ SV979 @ SV303 ) @ ( c_Polynomial_Osmult @ SV699 @ SY2730 @ SV303 ) @ ( tc_Polynomial_Opoly @ SV303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2500,plain,
! [SV980: $i,SV700: $i,SV304: $i] :
( ( ! [SY2731: $i] :
( ~ ( class_Divides_Osemiring__div @ SV304 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SY2731 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SY2731 @ SV304 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2501,plain,
! [SV981: $i,SV701: $i,SV305: $i] :
( ( ! [SY2732: $i] :
( ~ ( class_Divides_Osemiring__div @ SV305 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SY2732 @ SV305 ) @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SY2732 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2502,plain,
! [SV982: $i,SV702: $i,SV306: $i] :
( ( ! [SY2733: $i] :
( ~ ( class_Divides_Osemiring__div @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SY2733 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SY2733 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2503,plain,
! [SV983: $i,SV703: $i,SV307: $i] :
( ( ! [SY2734: $i] :
( ~ ( class_Divides_Osemiring__div @ SV307 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SY2734 @ SV307 ) @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SY2734 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2504,plain,
! [SV984: $i,SV704: $i,SV308: $i] :
( ( ! [SY2735: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV308 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ SV704 @ SV984 @ SV308 ) @ SY2735 @ ( tc_Polynomial_Opoly @ SV308 ) )
= ( c_Polynomial_Osmult @ SV704 @ ( c_Divides_Odiv__class_Odiv @ SV984 @ SY2735 @ ( tc_Polynomial_Opoly @ SV308 ) ) @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2505,plain,
! [SV985: $i,SV705: $i,SV309: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV309 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV705 @ ( c_HOL_Otimes__class_Otimes @ SV985 @ SV705 @ SV309 ) @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2506,plain,
! [SV986: $i,SV706: $i,SV310: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV310 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV706 @ ( c_HOL_Otimes__class_Otimes @ SV706 @ SV986 @ SV310 ) @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2507,plain,
! [SV987: $i,SV707: $i,SV311: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV311 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV707 @ ( c_HOL_Otimes__class_Otimes @ SV707 @ SV987 @ SV311 ) @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2508,plain,
! [SV988: $i,SV708: $i,SV312: $i] :
( ( ! [SY2736: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SY2736 @ SV708 @ SV312 ) @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2509,plain,
! [SV989: $i,SV709: $i,SV313: $i] :
( ( ! [SY2737: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SV989 @ SY2737 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SY2737 @ ( tc_Polynomial_Opoly @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2510,plain,
! [SV990: $i,SV710: $i,SV314: $i] :
( ( ! [SY2738: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SV990 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SY2738 @ SV990 @ SV314 ) @ SV314 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SY2738 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2511,plain,
! [SV991: $i,SV711: $i,SV315: $i] :
( ( ! [SY2739: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV315 )
| ( ( c_HOL_Otimes__class_Otimes @ SV711 @ ( c_Polynomial_Osmult @ SV991 @ SY2739 @ SV315 ) @ ( tc_Polynomial_Opoly @ SV315 ) )
= ( c_Polynomial_Osmult @ SV991 @ ( c_HOL_Otimes__class_Otimes @ SV711 @ SY2739 @ ( tc_Polynomial_Opoly @ SV315 ) ) @ SV315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2512,plain,
! [SV992: $i,SV712: $i,SV316: $i] :
( ( ! [SY2740: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV316 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ SV712 @ SV992 @ SV316 ) @ SY2740 @ ( tc_Polynomial_Opoly @ SV316 ) )
= ( c_Polynomial_Osmult @ SV712 @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SY2740 @ ( tc_Polynomial_Opoly @ SV316 ) ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2513,plain,
! [SV993: $i,SV713: $i,SV317: $i] :
( ( ! [SY2741: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV317 )
| ( ( c_Polynomial_Osmult @ SV713 @ ( c_Polynomial_Osmult @ SV993 @ SY2741 @ SV317 ) @ SV317 )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ SV713 @ SV993 @ SV317 ) @ SY2741 @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2514,plain,
! [SV318: $i] :
( ( ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV318 )
= $false )
| ( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2515,plain,
! [SV319: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV319 )
= $false )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2516,plain,
! [SV320: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV320 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2517,plain,
! [SV321: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV321 )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2518,plain,
! [SV322: $i] :
( ( ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV322 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2519,plain,
! [SV323: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV323 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2520,plain,
! [SV324: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV324 )
= $false )
| ( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2521,plain,
! [SV325: $i] :
( ( ( class_OrderedGroup_Ocancel__comm__monoid__add @ SV325 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2522,plain,
! [SV326: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV326 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2523,plain,
! [SV327: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2524,plain,
! [SV328: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV328 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2525,plain,
! [SV329: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV329 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2526,plain,
! [SV330: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV330 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2527,plain,
! [SV331: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV331 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2528,plain,
! [SV332: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2529,plain,
! [SV333: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV333 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2530,plain,
! [SV334: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2531,plain,
! [SV335: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV335 )
= $false )
| ( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2532,plain,
! [SV336: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV336 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2533,plain,
! [SV337: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV337 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2534,plain,
! [SV338: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV338 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2535,plain,
! [SV339: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV339 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2536,plain,
! [SV340: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV340 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2537,plain,
! [SV341: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV341 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2538,plain,
! [SV342: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV342 )
= $false )
| ( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2539,plain,
! [SV343: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false )
| ( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2540,plain,
! [SV344: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV344 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2541,plain,
! [SV345: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV345 )
= $false )
| ( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2542,plain,
! [SV346: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV346 )
= $false )
| ( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2543,plain,
! [SV347: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV347 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2544,plain,
! [SV348: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV348 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2545,plain,
! [SV349: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV349 )
= $false )
| ( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2546,plain,
! [SV350: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV350 )
= $false )
| ( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2547,plain,
! [SV351: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV351 )
= $false )
| ( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2548,plain,
! [SV352: $i] :
( ( ( class_HOL_Ozero @ SV352 )
= $false )
| ( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2549,plain,
! [SV994: $i,SV714: $i,SV353: $i] :
( ( ! [SY2742: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV353 )
| ~ ( class_Int_Onumber__ring @ SV353 )
| ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SY2742 @ SV353 ) )
| ( SV994 = SY2742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2550,plain,
! [SV995: $i,SV715: $i,SV354: $i] :
( ( ! [SY2743: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
| ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SV995 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SV715 @ SY2743 @ SV354 ) )
| ( SV995 = SY2743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2551,plain,
! [SV996: $i,SV716: $i,SV355: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV355 )
| ( ( c_Divides_Odiv__class_Omod @ SV716 @ SV996 @ SV355 )
!= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV996 @ SV716 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2552,plain,
! [SV997: $i,SV717: $i,SV356: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
| ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SV997 @ SV356 )
!= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV997
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2553,plain,
! [SV998: $i,SV718: $i,SV357: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
| ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SV998 @ SV357 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV998
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2554,plain,
! [SV999: $i,SV719: $i,SV358: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV358 )
| ( ( c_HOL_Oplus__class_Oplus @ SV719 @ SV999 @ SV358 )
!= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
| ( SV719
= ( c_HOL_Ouminus__class_Ouminus @ SV999 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2555,plain,
! [SV1000: $i,SV720: $i,SV359: $i] :
( ( ! [SY2744: $i,SY2745: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV359 )
| ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SY2744 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SY2745 @ SV359 ) @ SV359 ) )
| ( SY2744 = SY2745 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2556,plain,
! [SV1001: $i,SV721: $i,SV360: $i] :
( ( ! [SY2746: $i,SY2747: $i] :
( ~ ( class_HOL_Ozero @ SV360 )
| ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
!= ( c_Polynomial_OpCons @ SY2746 @ SY2747 @ SV360 ) )
| ( SV1001 = SY2747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2557,plain,
! [SV722: $i,SV361: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV361 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV722 @ SV722 @ SV361 )
!= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
| ( SV722
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2558,plain,
! [SV1002: $i,SV723: $i,SV362: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV362 )
| ( ( c_HOL_Oabs__class_Oabs @ SV723 @ SV362 )
!= ( c_HOL_Oabs__class_Oabs @ SV1002 @ SV362 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV723 @ SV1002 @ SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2559,plain,
! [SV1003: $i,SV724: $i,SV363: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV363 )
| ( ( c_Polynomial_Opoly @ SV724 @ ( c_HOL_Ouminus__class_Ouminus @ SV1003 @ SV363 ) @ SV363 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV1003 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SV724 @ ( tc_Polynomial_Opoly @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2560,plain,
! [SV725: $i,SV364: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV364 ) )
= $true )
| ( ( ( ( c_HOL_Ozero__class_Ozero @ SV364 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV725 @ SV364 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= SV725 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2561,plain,
! [SV1004: $i,SV726: $i,SV365: $i] :
( ( ! [SY2748: $i,SY2749: $i,SY2750: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV365 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SY2748 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2749 @ SV1004 @ SV365 ) @ SY2750 @ SV365 ) )
| ( SY2748
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2749 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SY2750 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2562,plain,
! [SV1005: $i,SV727: $i,SV366: $i] :
( ( ! [SY2751: $i,SY2752: $i,SY2753: $i] :
( ~ ( class_Divides_Osemiring__div @ SV366 )
| ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY2751 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2752 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY2753 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2752 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2753 @ SY2751 @ SV366 ) @ SV1005 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2563,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2564,plain,
! [SV1007: $i,SV729: $i,SV368: $i] :
( ( ! [SY2754: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
| ( ( c_Polynomial_Osmult @ SV729 @ SV1007 @ SV368 )
!= ( c_Polynomial_OpCons @ SY2754 @ SV1007 @ SV368 ) )
| ( SV1007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2565,plain,
! [SV1008: $i,SV730: $i,SV369: $i] :
( ( ! [SY2755: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
| ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SV1008 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SY2755 @ SV1008 @ SV369 ) )
| ( SV730 = SY2755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2566,plain,
! [SV1009: $i,SV731: $i,SV370: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV370 )
| ( ( c_Polynomial_Opoly__gcd @ SV731 @ SV1009 @ SV370 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
| ( SV1009
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2567,plain,
! [SV1010: $i,SV732: $i,SV371: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV371 )
| ~ ( class_Int_Onumber__ring @ SV371 )
| ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SV732 = SV1010 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2568,plain,
! [SV1011: $i,SV733: $i,SV372: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 )
| ( ( c_Power_Opower__class_Opower @ SV733 @ SV1011 @ SV372 )
!= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
| ( SV733
= ( c_HOL_Ozero__class_Ozero @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2569,plain,
! [SV1012: $i,SV734: $i,SV373: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV373 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV734 @ SV734 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1012 @ SV373 ) @ SV373 )
!= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
| ( SV1012
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2570,plain,
! [SV1013: $i,SV735: $i,SV374: $i] :
( ( ! [SY2756: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SV1013 @ SV374 ) @ ( c_Polynomial_OpCons @ SY2756 @ SV1013 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
| ( SV1013
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2571,plain,
! [SV375: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV375 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV375 )
!= ( c_HOL_Oone__class_Oone @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2572,plain,
! [SV1014: $i,SV736: $i,SV376: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
| ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SV1014 @ SV376 )
!= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV1014
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2573,plain,
! [SV1015: $i,SV737: $i,SV377: $i] :
( ( ! [SY2757: $i,SY2758: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SY2757 @ SY2758 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SY2758 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SY2757 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SY2758 )
| ( SV737 = SY2757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2574,plain,
! [SV1016: $i,SV738: $i,SV378: $i] :
( ( ~ ( class_HOL_Ozero @ SV378 )
| ( ( c_Polynomial_OpCons @ SV738 @ SV1016 @ SV378 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
| ( SV1016
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2575,plain,
! [SV1017: $i,SV739: $i,SV379: $i] :
( ( ! [SY2759: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1017 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SV739 @ SY2759 @ SV379 ) )
| ( SV1017 = SY2759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2576,plain,
! [SV740: $i,SV380: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV380 ) )
= $true )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV740 @ SV380 )
!= SV740 )
| ( SV740
= ( c_HOL_Ozero__class_Ozero @ SV380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2577,plain,
! [SV1018: $i,SV741: $i,SV381: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV381 )
| ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
!= ( c_HOL_Otimes__class_Otimes @ SV1018 @ SV1018 @ SV381 ) )
| ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SV1018 @ SV381 ) )
| ( SV741 = SV1018 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2578,plain,
! [SV1019: $i,SV742: $i,SV382: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV382 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV742 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SV1019 @ SV1019 @ SV382 ) @ SV382 )
!= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
| ( SV742
= ( c_HOL_Ozero__class_Ozero @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2579,plain,
! [SV1020: $i,SV743: $i,SV383: $i] :
( ( ! [SY2760: $i,SY2761: $i,SY2762: $i] :
( ~ ( class_Divides_Oring__div @ SV383 )
| ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2760 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2761 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2762 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2761 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2762 @ SY2760 @ SV383 ) @ SV1020 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2580,plain,
! [SV1021: $i,SV744: $i,SV384: $i] :
( ( ! [SY2763: $i,SY2764: $i] :
( ~ ( class_HOL_Ozero @ SV384 )
| ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
!= ( c_Polynomial_OpCons @ SY2763 @ SY2764 @ SV384 ) )
| ( SV744 = SY2763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2581,plain,
! [SV1022: $i,SV745: $i,SV385: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV385 )
| ( ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1022 @ SV385 )
!= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV745 @ SV385 )
= SV1022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2582,plain,
! [SV746: $i,SV386: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV386 ) )
= $true )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV746 @ SV386 )
!= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
| ( SV746
= ( c_HOL_Ozero__class_Ozero @ SV386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2583,plain,
! [SV1023: $i,SV747: $i,SV387: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV387 )
| ( ( c_Polynomial_Osmult @ SV747 @ SV1023 @ SV387 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV1023
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2584,plain,
! [SV1024: $i,SV748: $i,SV388: $i] :
( ( ! [SY2765: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV388 )
| ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SV1024 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SY2765 @ SY2765 @ SV388 ) )
| ( SV748 = SV1024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2585,plain,
! [SV1025: $i,SV749: $i,SV389: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV389 )
| ( ( c_HOL_Ominus__class_Ominus @ SV749 @ SV1025 @ SV389 )
!= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
| ( SV749 = SV1025 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2586,plain,
! [SV1026: $i,SV750: $i,SV390: $i] :
( ( ! [SY2766: $i,SY2767: $i,SY2768: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV390 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SY2766 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2767 @ SV1026 @ SV390 ) @ SY2768 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SY2767 @ SV390 ) @ SV1026 @ SV390 ) @ SY2766 @ SV390 )
= SY2768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2587,plain,
! [SV1027: $i,SV751: $i,SV391: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV391 )
| ( ( c_HOL_Ominus__class_Ominus @ SV751 @ SV1027 @ SV391 )
!= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
| ( SV751 = SV1027 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2588,plain,
! [SV1028: $i,SV752: $i,SV392: $i] :
( ( ! [SY2769: $i,SY2770: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
| ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SY2769 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SY2770 @ SY2769 @ SV392 ) )
| ( SY2770
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2589,plain,
! [SV1029: $i,SV753: $i,SV393: $i] :
( ( ! [SY2771: $i,SY2772: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV393 )
| ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SY2771 @ SY2772 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SY2772 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SY2771 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SY2772 )
| ( SV753 = SY2771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2590,plain,
! [SV394: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV394 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV394 )
!= ( c_HOL_Ozero__class_Ozero @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2591,plain,
! [SV1030: $i,SV754: $i,SV395: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV395 )
| ( ( c_Polynomial_Opoly @ SV754 @ SV1030 @ SV395 )
!= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV1030 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SV754 @ ( tc_Polynomial_Opoly @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2592,plain,
! [SV1031: $i,SV755: $i,SV396: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV396 )
| ( ( c_Polynomial_Opoly__gcd @ SV755 @ SV1031 @ SV396 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
| ( SV755
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2593,plain,
! [SV1032: $i,SV756: $i,SV397: $i] :
( ( ! [SY2773: $i] :
( ~ ( class_Divides_Oring__div @ SV397 )
| ( ( c_Divides_Odiv__class_Omod @ SV756 @ SV1032 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SY2773 @ SV1032 @ SV397 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SY2773 @ SV397 ) @ SV1032 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2594,plain,
! [SV1033: $i,SV757: $i,SV398: $i] :
( ( ! [SY2774: $i,SY2775: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV398 )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SY2774 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SY2775 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SY2774 @ SV398 )
= SY2775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2595,plain,
! [SV758: $i,SV399: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV399 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV758 @ SV399 )
!= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
| ( SV758
= ( c_HOL_Ozero__class_Ozero @ SV399 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2596,plain,
! [SV1034: $i,SV759: $i,SV400: $i] :
( ( ! [SY2776: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV400 )
| ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SV1034 @ SY2776 @ SV400 ) @ SV400 )
!= SV1034 )
| ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SY2776 @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2597,plain,
! [SV1035: $i,SV760: $i,SV401: $i] :
( ( ! [SY2777: $i,SY2778: $i,SY2779: $i] :
( ~ ( class_Divides_Osemiring__div @ SV401 )
| ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2777 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2778 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2779 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2778 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2779 @ SY2777 @ SV401 ) @ SV1035 @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2598,plain,
! [SV1036: $i,SV761: $i,SV402: $i] :
( ( ! [SY2780: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV402 )
| ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SV1036 @ SY2780 @ SV402 ) )
| ( SV1036 = SY2780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2599,plain,
! [SV1037: $i,SV762: $i,SV403: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV403 )
| ~ ( class_Int_Onumber__ring @ SV403 )
| ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
| ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2600,plain,
! [SV1038: $i,SV763: $i,SV404: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV404 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV763 @ SV404 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1038 @ SV404 ) )
| ( SV763 = SV1038 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2601,plain,
! [SV1039: $i,SV764: $i,SV405: $i] :
( ( ~ ( class_HOL_Ozero @ SV405 )
| ( ( c_Polynomial_OpCons @ SV764 @ SV1039 @ SV405 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
| ( SV764
= ( c_HOL_Ozero__class_Ozero @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2602,plain,
! [SV1040: $i,SV765: $i,SV406: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV406 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV765 @ SV406 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1040 @ SV406 ) )
| ( SV765 = SV1040 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2603,plain,
! [SV1041: $i,SV766: $i,SV407: $i,SV1: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV1 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ SV407 @ SV766 @ SV1 ) @ SV1041 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV1041 @ ( c_Polynomial_Opoly @ SV766 @ SV1041 @ SV1 ) @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2604,plain,
! [SV408: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV2 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV2 ) ) @ SV408 @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2605,plain,
! [SV409: $i,SV3: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV3 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV3 ) ) @ SV409 @ SV3 )
= ( c_HOL_Ozero__class_Ozero @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2606,plain,
! [SV1042: $i,SV767: $i,SV410: $i,SV4: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV4 )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ SV410 @ SV767 @ SV4 ) @ SV1042 @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ SV410 @ ( c_Polynomial_Opoly @ SV767 @ SV1042 @ SV4 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2607,plain,
! [SV1043: $i,SV768: $i,SV411: $i,SV5: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV5 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV768 @ ( tc_Polynomial_Opoly @ SV5 ) ) @ SV1043 @ SV5 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ SV411 @ SV1043 @ SV5 ) @ ( c_Polynomial_Opoly @ SV768 @ SV1043 @ SV5 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2608,plain,
! [SV1044: $i,SV769: $i,SV412: $i,SV6: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV6 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ SV412 @ SV769 @ ( tc_Polynomial_Opoly @ SV6 ) ) @ SV1044 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ SV412 @ SV1044 @ SV6 ) @ ( c_Polynomial_Opoly @ SV769 @ SV1044 @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2609,plain,
! [SV770: $i,SV413: $i,SV7: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV7 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ SV413 @ ( tc_Polynomial_Opoly @ SV7 ) ) @ SV770 @ SV7 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ SV413 @ SV770 @ SV7 ) @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2610,plain,
! [SV1045: $i,SV771: $i,SV414: $i,SV8: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV8 )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ SV414 @ SV771 @ ( tc_Polynomial_Opoly @ SV8 ) ) @ SV1045 @ SV8 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ SV414 @ SV1045 @ SV8 ) @ ( c_Polynomial_Opoly @ SV771 @ SV1045 @ SV8 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2611,plain,
! [SV1046: $i,SV772: $i,SV415: $i,SV9: $i] :
( ( ! [SY2781: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV9 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SV415 @ SV772 @ SV9 ) @ ( c_Polynomial_OpCons @ SV1046 @ SY2781 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SV415 @ SV1046 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SV772 @ SY2781 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2612,plain,
! [SV773: $i,SV416: $i,SV10: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV10 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ SV416 @ SV773 @ SV10 ) @ ( tc_Polynomial_Opoly @ SV10 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV416 @ SV10 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV773 @ ( tc_Polynomial_Opoly @ SV10 ) ) @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2613,plain,
! [SV1047: $i,SV774: $i,SV417: $i,SV11: $i] :
( ( ! [SY2782: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SV417 @ SV774 @ SV11 ) @ ( c_Polynomial_OpCons @ SV1047 @ SY2782 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SV417 @ SV1047 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SV774 @ SY2782 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2614,plain,
! [SV1048: $i,SV775: $i,SV418: $i,SV12: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV12 )
| ( ( c_Polynomial_Osmult @ SV418 @ ( c_Polynomial_OpCons @ SV775 @ SV1048 @ SV12 ) @ SV12 )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV775 @ SV12 ) @ ( c_Polynomial_Osmult @ SV418 @ SV1048 @ SV12 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2615,plain,
! [SV776: $i,SV419: $i,SV14: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV14 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly @ SV419 @ SV776 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV776 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SV419 @ ( tc_Polynomial_Opoly @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2616,plain,
! [SV777: $i,SV420: $i,SV15: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV15 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly @ SV420 @ ( c_HOL_Ouminus__class_Ouminus @ SV777 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV777 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SV420 @ ( tc_Polynomial_Opoly @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2617,plain,
! [SV778: $i,SV421: $i,SV16: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV16 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV421 @ SV778 @ SV16 ) @ SV421 @ SV16 )
= SV778 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2618,plain,
! [SV779: $i,SV422: $i,SV17: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV17 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV422 @ SV779 @ SV17 ) @ SV779 @ SV17 )
= SV422 )
| ( SV779
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2619,plain,
! [SV1049: $i,SV780: $i,SV423: $i,SV18: $i] :
( ( ! [SY2783: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV780 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV1049 @ SY2783 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV1049 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV780 @ SY2783 @ SV18 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2620,plain,
! [SV1050: $i,SV781: $i,SV424: $i,SV19: $i] :
( ( ! [SY2784: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV424 @ SV781 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SY2784 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SV424 @ ( c_HOL_Otimes__class_Otimes @ SV781 @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SY2784 @ SV19 ) @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2621,plain,
! [SV1051: $i,SV782: $i,SV425: $i,SV20: $i] :
( ( ! [SY2785: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SY2785 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SV1051 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ SY2785 @ SV20 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2622,plain,
! [SV1052: $i,SV783: $i,SV426: $i,SV21: $i] :
( ( ! [SY2786: $i,SY2787: $i,SY2788: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SY2786 @ SV783 @ SY2787 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SY2786 @ SV426 @ SY2788 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2623,plain,
! [SV1053: $i,SV784: $i,SV427: $i,SV22: $i] :
( ( ! [SY2789: $i,SY2790: $i,SY2791: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SY2789 @ SY2790 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SY2789 @ SY2791 @ SV427 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2624,plain,
! [SV785: $i,SV428: $i,SV23: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV23 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV428 @ SV23 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV785 @ SV23 ) @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2625,plain,
! [SV786: $i,SV429: $i,SV24: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV24 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ ( c_HOL_Otimes__class_Otimes @ SV786 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2626,plain,
! [SV787: $i,SV430: $i,SV26: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV26 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV787 @ SV26 ) @ SV26 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV430 @ SV26 ) @ ( c_HOL_Oabs__class_Oabs @ SV787 @ SV26 ) @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2627,plain,
! [SV788: $i,SV431: $i,SV27: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV27 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV788 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV431 @ SV27 ) @ SV788 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2628,plain,
! [SV789: $i,SV432: $i,SV28: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV28 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV432 @ SV789 @ SV28 ) @ SV28 )
= ( c_HOL_Otimes__class_Otimes @ SV432 @ ( c_HOL_Ouminus__class_Ouminus @ SV789 @ SV28 ) @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2629,plain,
! [SV790: $i,SV433: $i,SV29: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV433 @ ( c_HOL_Otimes__class_Otimes @ SV433 @ SV790 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV433 @ SV790 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2630,plain,
! [SV1054: $i,SV791: $i,SV434: $i,SV30: $i] :
( ( ! [SY2792: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SY2792 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SY2792 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2792 @ SV1054 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2631,plain,
! [SV1055: $i,SV792: $i,SV435: $i,SV31: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV31 )
| ( SV435 = SV792 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV792 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SV1055 @ SV435 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2632,plain,
! [SV793: $i,SV436: $i,SV32: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV32 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV436 @ SV32 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV793 @ SV32 ) @ SV32 )
= ( c_HOL_Ozero__class_Ozero @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2633,plain,
! [SV794: $i,SV437: $i,SV33: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV33 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV794 @ SV33 ) @ SV437 @ SV33 )
= ( c_Divides_Odiv__class_Omod @ SV794 @ SV437 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2634,plain,
! [SV795: $i,SV438: $i,SV34: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV34 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV438 @ SV795 @ SV34 ) @ SV795 @ SV34 )
= ( c_Divides_Odiv__class_Omod @ SV438 @ SV795 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2635,plain,
! [SV796: $i,SV439: $i,SV35: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV35 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV439 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV439 @ SV35 ) @ SV796 @ SV35 ) @ SV35 )
= SV796 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2636,plain,
! [SV1056: $i,SV797: $i,SV440: $i,SV36: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV36 )
| ( ( c_Divides_Odiv__class_Omod @ SV440 @ ( c_HOL_Otimes__class_Otimes @ SV797 @ SV1056 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV797 @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ SV1056 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( c_Divides_Odiv__class_Omod @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2637,plain,
! [SV441: $i,SV37: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV37 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV441 @ SV441 @ SV37 )
= SV441 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2638,plain,
! [SV1057: $i,SV798: $i,SV442: $i,SV38: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV38 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SV798 @ SV1057 @ SV38 )
| ( SV798
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2639,plain,
! [SV1058: $i,SV799: $i,SV443: $i,SV39: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV39 )
| ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SV799 @ SV443 @ SV1058 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2640,plain,
! [SV1059: $i,SV800: $i,SV444: $i,SV40: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV40 )
| ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SV800 @ SV1059 @ SV444 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2641,plain,
! [SV1060: $i,SV801: $i,SV445: $i,SV41: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV41 )
| ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV801 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SV1060 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2642,plain,
! [SV1061: $i,SV802: $i,SV446: $i,SV42: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV802 @ SV42 ) @ SV1061 @ SV42 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV446 @ SV1061 @ SV42 ) @ ( c_Power_Opower__class_Opower @ SV802 @ SV1061 @ SV42 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2643,plain,
! [SV1062: $i,SV803: $i,SV447: $i,SV43: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV43 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV803 @ SV43 ) @ SV1062 @ SV43 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV447 @ SV1062 @ SV43 ) @ ( c_Power_Opower__class_Opower @ SV803 @ SV1062 @ SV43 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2644,plain,
! [SV1063: $i,SV804: $i,SV448: $i,SV44: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV44 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ ( c_Divides_Odiv__class_Omod @ SV804 @ SV1063 @ SV44 ) @ SV44 ) @ SV1063 @ SV44 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV804 @ SV44 ) @ SV1063 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2645,plain,
! [SV1064: $i,SV805: $i,SV449: $i,SV45: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV45 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV449 @ SV805 @ SV45 ) @ SV1064 @ SV45 ) @ SV805 @ SV45 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV449 @ SV1064 @ SV45 ) @ SV805 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2646,plain,
! [SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ! [SY2793: $i,SY2794: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV46 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SY2793 @ SV46 ) @ SV46 ) @ SY2794 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SY2794 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SY2793 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2647,plain,
! [SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ! [SY2795: $i,SY2796: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV47 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SY2795 @ SY2796 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SY2796 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2648,plain,
! [SV808: $i,SV452: $i,SV48: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV48 ) )
= $true )
| ( ( SV452
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV452 @ SV808 @ SV48 ) @ SV808 @ SV48 ) @ ( c_Divides_Odiv__class_Omod @ SV452 @ SV808 @ SV48 ) @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2649,plain,
! [SV809: $i,SV453: $i,SV49: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV49 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV453 @ SV809 @ SV49 ) @ SV809 @ SV49 ) @ ( c_Divides_Odiv__class_Omod @ SV453 @ SV809 @ SV49 ) @ SV49 )
= SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2650,plain,
! [SV810: $i,SV454: $i,SV50: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV50 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_Divides_Odiv__class_Odiv @ SV810 @ SV454 @ SV50 ) @ SV50 ) @ ( c_Divides_Odiv__class_Omod @ SV810 @ SV454 @ SV50 ) @ SV50 )
= SV810 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2651,plain,
! [SV455: $i,SV51: $i] :
( ( ( class_Int_Onumber__ring @ SV51 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ SV455 @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV51 ) @ SV455 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2652,plain,
! [SV811: $i,SV456: $i,SV52: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV52 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV456 @ ( c_HOL_Ouminus__class_Ouminus @ SV811 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV456 @ SV811 @ SV52 ) @ SV52 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV811 @ SV456 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2653,plain,
! [SV812: $i,SV457: $i,SV53: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV53 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV457 @ SV53 ) @ SV812 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV457 @ SV812 @ SV53 ) @ SV53 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV812 @ SV457 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2654,plain,
! [SV1067: $i,SV813: $i,SV458: $i,SV54: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV813 @ SV54 ) @ SV1067 @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV458 @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1067 @ SV54 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2655,plain,
! [SV1068: $i,SV814: $i,SV459: $i,SV55: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV814 @ SV55 ) @ SV1068 @ SV55 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV1068 @ SV55 ) @ SV814 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2656,plain,
! [SV1069: $i,SV815: $i,SV460: $i,SV56: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV460 @ SV815 @ SV56 ) @ SV1069 @ SV56 )
= ( c_HOL_Otimes__class_Otimes @ SV460 @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1069 @ SV56 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2657,plain,
! [SV1070: $i,SV816: $i,SV461: $i,SV57: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1070 @ SV57 ) @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV461 @ SV816 @ SV57 ) @ SV1070 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2658,plain,
! [SV1071: $i,SV817: $i,SV462: $i,SV58: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV58 )
| ( ( c_HOL_Otimes__class_Otimes @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV817 @ SV1071 @ SV58 ) @ SV58 )
= ( c_HOL_Otimes__class_Otimes @ SV817 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1071 @ SV58 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2659,plain,
! [SV1072: $i,SV818: $i,SV463: $i,SV59: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( c_HOL_Otimes__class_Otimes @ SV463 @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV1072 @ SV59 ) @ SV59 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV463 @ SV818 @ SV59 ) @ SV1072 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2660,plain,
! [SV1073: $i,SV819: $i,SV464: $i,SV60: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV464 @ SV819 @ SV60 ) @ SV1073 @ SV60 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV464 @ SV1073 @ SV60 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV1073 @ SV60 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2661,plain,
! [SV1074: $i,SV820: $i,SV465: $i,SV61: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV61 )
| ( ( c_HOL_Otimes__class_Otimes @ SV465 @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV1074 @ SV61 ) @ SV61 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV820 @ SV61 ) @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV1074 @ SV61 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2662,plain,
! [SV1075: $i,SV821: $i,SV466: $i,SV62: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV62 )
| ( ( c_HOL_Otimes__class_Otimes @ SV466 @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV1075 @ SV62 ) @ SV62 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV821 @ SV62 ) @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV1075 @ SV62 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2663,plain,
! [SV1076: $i,SV822: $i,SV467: $i,SV63: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV63 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV467 @ SV822 @ SV63 ) @ SV1076 @ SV63 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV467 @ SV1076 @ SV63 ) @ ( c_HOL_Otimes__class_Otimes @ SV822 @ SV1076 @ SV63 ) @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2664,plain,
! [SV1077: $i,SV823: $i,SV468: $i,SV64: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV64 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SV823 @ SV64 ) @ SV1077 @ SV64 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV1077 @ SV64 ) @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1077 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2665,plain,
! [SV1078: $i,SV824: $i,SV469: $i,SV65: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV65 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV469 @ SV824 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV469 @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( tc_Polynomial_Opoly @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2666,plain,
! [SV1079: $i,SV825: $i,SV470: $i,SV66: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ SV470 @ ( c_HOL_Oplus__class_Oplus @ SV825 @ SV1079 @ SV66 ) @ SV66 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV825 @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV1079 @ SV66 ) @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2667,plain,
! [SV1080: $i,SV826: $i,SV471: $i,SV67: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV471 @ SV826 @ SV67 ) @ SV1080 @ SV67 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV471 @ SV1080 @ SV67 ) @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1080 @ SV67 ) @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2668,plain,
! [SV827: $i,SV472: $i,SV68: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV68 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV472 @ SV827 @ SV68 ) @ SV68 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV827 @ SV472 @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2669,plain,
! [SV828: $i,SV473: $i,SV69: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV69 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV828 @ SV69 ) @ SV473 @ SV69 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV828 @ SV473 @ SV69 ) @ ( c_HOL_Oone__class_Oone @ SV69 ) @ SV69 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2670,plain,
! [SV829: $i,SV474: $i,SV70: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV70 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV829 @ SV70 ) @ SV829 @ SV70 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV474 @ SV829 @ SV70 ) @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV70 ) )
| ( SV829
= ( c_HOL_Ozero__class_Ozero @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2671,plain,
! [SV1081: $i,SV830: $i,SV475: $i,SV72: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV830 @ SV72 ) @ ( c_HOL_Otimes__class_Otimes @ SV1081 @ SV830 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV475 @ SV1081 @ SV72 ) @ SV830 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2672,plain,
! [SV831: $i,SV476: $i,SV73: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV73 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV476 @ SV73 ) @ SV831 @ SV73 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV831 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2673,plain,
! [SV832: $i,SV477: $i,SV74: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV74 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV477 @ SV74 ) @ SV832 @ SV74 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV477 @ SV832 @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2674,plain,
! [SV833: $i,SV478: $i,SV75: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV75 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV478 @ ( c_HOL_Ouminus__class_Ouminus @ SV833 @ SV75 ) @ SV75 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV478 @ SV833 @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2675,plain,
! [SV834: $i,SV479: $i,SV76: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV76 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV479 @ ( c_HOL_Ouminus__class_Ouminus @ SV834 @ SV76 ) @ SV76 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV834 @ SV76 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2676,plain,
! [SV480: $i,SV77: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV77 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV77 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV77 ) @ SV77 )
= ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2677,plain,
! [SV835: $i,SV481: $i,SV78: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV78 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV78 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV78 ) @ SV78 )
= ( c_HOL_Otimes__class_Otimes @ SV481 @ SV835 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2678,plain,
! [SV1082: $i,SV836: $i,SV482: $i,SV79: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV79 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV836 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV1082 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SV836 @ SV1082 @ SV79 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2679,plain,
! [SV1083: $i,SV837: $i,SV483: $i,SV80: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV80 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV483 @ SV837 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1083 @ SV837 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SV483 @ SV1083 @ SV80 ) )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2680,plain,
! [SV838: $i,SV484: $i,SV81: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV81 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV484 @ SV81 ) @ SV838 @ SV81 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV484 @ SV838 @ SV81 ) @ SV81 ) @ SV838 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2681,plain,
! [SV485: $i,SV82: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV82 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV485 @ SV82 )
= ( c_HOL_Ouminus__class_Ouminus @ SV485 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2682,plain,
! [SV486: $i,SV83: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV83 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV83 ) ) @ SV486 @ ( tc_Polynomial_Opoly @ SV83 ) )
= ( c_HOL_Ouminus__class_Ouminus @ SV486 @ ( tc_Polynomial_Opoly @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2683,plain,
! [SV1084: $i,SV839: $i,SV487: $i,SV84: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ SV487 @ SV839 @ SV84 ) @ SV1084 @ ( tc_Polynomial_Opoly @ SV84 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV487 @ SV1084 @ SV84 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( c_HOL_Otimes__class_Otimes @ SV839 @ SV1084 @ ( tc_Polynomial_Opoly @ SV84 ) ) @ SV84 ) @ ( tc_Polynomial_Opoly @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2684,plain,
! [SV1085: $i,SV840: $i,SV488: $i,SV85: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV85 )
| ( ( c_HOL_Otimes__class_Otimes @ SV488 @ ( c_Polynomial_OpCons @ SV840 @ SV1085 @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV840 @ SV488 @ SV85 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_HOL_Otimes__class_Otimes @ SV488 @ SV1085 @ ( tc_Polynomial_Opoly @ SV85 ) ) @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2685,plain,
! [SV489: $i,SV86: $i] :
( ( ( class_Divides_Osemiring__div @ SV86 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV489 @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2686,plain,
! [SV490: $i,SV87: $i] :
( ( ( class_Divides_Osemiring__div @ SV87 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV490 @ SV87 )
= ( c_HOL_Ozero__class_Ozero @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2687,plain,
! [SV491: $i,SV88: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV88 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV491 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV88 ) ) @ ( tc_Polynomial_Opoly @ SV88 ) )
= SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2688,plain,
! [SV492: $i,SV89: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV89 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV492 @ SV492 @ SV89 )
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2689,plain,
! [SV493: $i,SV90: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV90 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV493 @ SV493 @ SV90 )
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2690,plain,
! [SV494: $i,SV91: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV91 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2691,plain,
! [SV495: $i,SV92: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV92 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV495 @ SV495 @ SV92 )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2692,plain,
! [SV496: $i,SV93: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV93 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV93 )
| ( ( c_HOL_Ominus__class_Ominus @ SV496 @ SV496 @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2693,plain,
! [SV497: $i,SV94: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV94 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV94 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SV497 @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2694,plain,
! [SV1086: $i,SV841: $i,SV498: $i,SV95: $i] :
( ( ! [SY2797: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SV1086 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SY2797 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SV1086 @ SV841 @ SY2797 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2695,plain,
! [SV1087: $i,SV842: $i,SV499: $i,SV96: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV96 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ SV499 @ SV842 @ SV96 ) @ SV1087 @ SV96 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV499 @ SV1087 @ SV96 ) @ ( c_Polynomial_Osmult @ SV842 @ SV1087 @ SV96 ) @ ( tc_Polynomial_Opoly @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2696,plain,
! [SV1088: $i,SV843: $i,SV500: $i,SV97: $i] :
( ( ! [SY2798: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV97 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV843 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV500 @ SV97 ) @ SV843 @ SV97 ) @ SY2798 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1088 @ SV843 @ SV97 ) @ SY2798 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2697,plain,
! [SV1089: $i,SV844: $i,SV501: $i,SV98: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV98 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2698,plain,
! [SV1090: $i,SV845: $i,SV502: $i,SV99: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV99 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV502 @ SV845 @ SV99 ) @ SV1090 @ SV99 ) @ SV845 @ SV99 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV1090 @ SV99 ) @ SV845 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2699,plain,
! [SV503: $i,SV100: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV100 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV503 @ ( c_HOL_Oone__class_Oone @ SV100 ) @ SV100 )
= SV503 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2700,plain,
! [SV504: $i,SV101: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV101 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV504 @ SV101 )
= SV504 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2701,plain,
! [SV505: $i,SV102: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV102 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV505 @ SV102 )
= SV505 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2702,plain,
! [SV506: $i,SV103: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV506 @ SV103 )
= SV506 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2703,plain,
! [SV507: $i,SV104: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV104 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV507 @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV104 )
= SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2704,plain,
! [SV508: $i,SV105: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV105 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV508 @ SV105 )
= SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2705,plain,
! [SV846: $i,SV509: $i,SV106: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV106 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ SV509 @ SV846 @ ( c_Divides_Odiv__class_Odiv @ SV509 @ SV846 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ ( c_Divides_Odiv__class_Omod @ SV509 @ SV846 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2706,plain,
! [SV510: $i,SV107: $i] :
( ( ( class_Divides_Osemiring__div @ SV107 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV510 @ SV107 )
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2707,plain,
! [SV1091: $i,SV847: $i,SV511: $i,SV108: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV108 )
| ~ ( class_Int_Onumber__ring @ SV108 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2708,plain,
! [SV1092: $i,SV848: $i,SV512: $i,SV109: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV109 )
| ~ ( class_Int_Onumber__ring @ SV109 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2709,plain,
! [SV1093: $i,SV849: $i,SV513: $i,SV110: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV110 )
| ( ( c_Polynomial_Opoly__gcd @ SV513 @ ( c_Polynomial_Opoly__gcd @ SV849 @ SV1093 @ SV110 ) @ SV110 )
= ( c_Polynomial_Opoly__gcd @ SV849 @ ( c_Polynomial_Opoly__gcd @ SV513 @ SV1093 @ SV110 ) @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2710,plain,
! [SV1094: $i,SV850: $i,SV514: $i,SV111: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV111 )
| ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ SV514 @ SV850 @ SV111 ) @ SV1094 @ SV111 )
= ( c_Polynomial_Opoly__gcd @ SV514 @ ( c_Polynomial_Opoly__gcd @ SV850 @ SV1094 @ SV111 ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2711,plain,
! [SV851: $i,SV515: $i,SV112: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV112 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV851 @ SV112 ) @ SV851 @ SV112 )
= SV515 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2712,plain,
! [SV852: $i,SV516: $i,SV113: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV113 ) )
= $true )
| ( ( ( c_Polynomial_Opoly__gcd @ SV516 @ ( c_HOL_Ouminus__class_Ouminus @ SV852 @ ( tc_Polynomial_Opoly @ SV113 ) ) @ SV113 )
= ( c_Polynomial_Opoly__gcd @ SV516 @ SV852 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2713,plain,
! [SV853: $i,SV517: $i,SV114: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV114 ) )
= $true )
| ( ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ SV517 @ ( tc_Polynomial_Opoly @ SV114 ) ) @ SV853 @ SV114 )
= ( c_Polynomial_Opoly__gcd @ SV517 @ SV853 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2714,plain,
! [SV854: $i,SV518: $i,SV115: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV518 @ SV854 @ SV115 )
= ( c_HOL_Otimes__class_Otimes @ SV854 @ SV518 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2715,plain,
! [SV855: $i,SV519: $i,SV117: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV519 @ SV855 @ SV117 )
= ( c_HOL_Otimes__class_Otimes @ SV855 @ SV519 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2716,plain,
! [SV1095: $i,SV856: $i,SV520: $i,SV118: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV118 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV520 @ SV856 @ SV118 ) @ SV1095 @ SV118 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV520 @ SV1095 @ SV118 ) @ ( c_Divides_Odiv__class_Omod @ SV856 @ SV1095 @ SV118 ) @ SV118 ) @ SV1095 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2717,plain,
! [SV1096: $i,SV857: $i,SV521: $i,SV120: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV120 )
| ( ( c_HOL_Oplus__class_Oplus @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SV857 @ SV1096 @ SV120 ) @ SV120 )
= ( c_HOL_Oplus__class_Oplus @ SV857 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SV1096 @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2718,plain,
! [SV1097: $i,SV858: $i,SV522: $i,SV121: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV121 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV522 @ SV858 @ SV121 ) @ SV1097 @ SV121 )
= ( c_HOL_Oplus__class_Oplus @ SV522 @ ( c_HOL_Oplus__class_Oplus @ SV858 @ SV1097 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2719,plain,
! [SV1098: $i,SV859: $i,SV523: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Oplus__class_Oplus @ SV523 @ ( c_HOL_Oplus__class_Oplus @ SV859 @ SV1098 @ SV122 ) @ SV122 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV523 @ SV859 @ SV122 ) @ SV1098 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2720,plain,
! [SV1099: $i,SV860: $i,SV524: $i,SV123: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV123 )
| ( ( c_HOL_Oplus__class_Oplus @ SV524 @ ( c_HOL_Oplus__class_Oplus @ SV860 @ SV1099 @ SV123 ) @ SV123 )
= ( c_HOL_Oplus__class_Oplus @ SV860 @ ( c_HOL_Oplus__class_Oplus @ SV524 @ SV1099 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2721,plain,
! [SV1100: $i,SV861: $i,SV525: $i,SV124: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV861 @ SV124 ) @ SV1100 @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ SV525 @ ( c_HOL_Oplus__class_Oplus @ SV861 @ SV1100 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2722,plain,
! [SV1101: $i,SV862: $i,SV526: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ SV526 @ ( c_HOL_Oplus__class_Oplus @ SV862 @ SV1101 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV862 @ SV125 ) @ SV1101 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2723,plain,
! [SV1102: $i,SV863: $i,SV527: $i,SV126: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV863 @ SV126 ) @ SV1102 @ SV126 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV1102 @ SV126 ) @ SV863 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2724,plain,
! [SV1103: $i,SV864: $i,SV528: $i,SV127: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Oplus__class_Oplus @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SV1103 @ SV127 ) @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ SV864 @ ( c_HOL_Oplus__class_Oplus @ SV528 @ SV1103 @ SV127 ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2725,plain,
! [SV1104: $i,SV865: $i,SV529: $i,SV128: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV529 @ SV865 @ SV128 ) @ SV1104 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ SV529 @ ( c_HOL_Oplus__class_Oplus @ SV865 @ SV1104 @ SV128 ) @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2726,plain,
! [SV866: $i,SV530: $i,SV129: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV129 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV530 @ ( c_HOL_Ouminus__class_Ouminus @ SV866 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV530 @ SV866 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2727,plain,
! [SV867: $i,SV531: $i,SV130: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV130 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV531 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ SV867 @ ( tc_Polynomial_Opoly @ SV130 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV531 @ SV867 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ ( tc_Polynomial_Opoly @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2728,plain,
! [SV1105: $i,SV868: $i,SV532: $i,SV131: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV131 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV868 @ SV131 ) @ SV1105 @ SV131 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ ( c_Divides_Odiv__class_Omod @ SV868 @ SV1105 @ SV131 ) @ SV131 ) @ SV1105 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2729,plain,
! [SV1106: $i,SV869: $i,SV533: $i,SV132: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV132 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV869 @ SV132 ) @ SV1106 @ SV132 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV533 @ SV1106 @ SV132 ) @ SV869 @ SV132 ) @ SV1106 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2730,plain,
! [SV1107: $i,SV870: $i,SV534: $i,SV133: $i] :
( ( ! [SY2799: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SV1107 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SY2799 @ SV1107 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2731,plain,
! [SV1108: $i,SV871: $i,SV535: $i,SV134: $i] :
( ( ! [SY2800: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV134 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV535 @ SV871 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ SY2800 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SY2800 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ SY2800 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SY2800 @ SV134 ) @ SV134 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2732,plain,
! [SV1109: $i,SV872: $i,SV536: $i,SV135: $i] :
( ( ! [SY2801: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV536 @ SV872 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1109 @ SV872 @ SV135 ) @ SY2801 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV536 @ SV1109 @ SV135 ) @ SV872 @ SV135 ) @ SY2801 @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2733,plain,
! [SV537: $i,SV136: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV136 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV537 @ SV136 ) @ SV537 @ SV136 )
= ( c_HOL_Ozero__class_Ozero @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2734,plain,
! [SV538: $i,SV137: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV137 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV538 @ SV137 ) @ SV538 @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2735,plain,
! [SV539: $i,SV138: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV138 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Ouminus__class_Ouminus @ SV539 @ SV138 ) @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2736,plain,
! [SV540: $i,SV139: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV139 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV540 @ SV139 ) @ SV540 @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2737,plain,
! [SV1110: $i,SV873: $i,SV541: $i,SV140: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV140 )
| ( ( c_HOL_Otimes__class_Otimes @ SV541 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SV1110 @ SV140 ) @ SV140 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV873 @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1110 @ SV140 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2738,plain,
! [SV1111: $i,SV874: $i,SV542: $i,SV141: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV141 )
| ( ( c_HOL_Otimes__class_Otimes @ SV542 @ ( c_HOL_Ominus__class_Ominus @ SV874 @ SV1111 @ SV141 ) @ SV141 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV874 @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV1111 @ SV141 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2739,plain,
! [SV1112: $i,SV875: $i,SV543: $i,SV142: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV543 @ SV875 @ SV142 ) @ SV1112 @ SV142 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV543 @ SV1112 @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV875 @ SV1112 @ SV142 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2740,plain,
! [SV1113: $i,SV876: $i,SV544: $i,SV143: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV143 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV544 @ SV876 @ SV143 ) @ SV1113 @ SV143 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV544 @ SV1113 @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV876 @ SV1113 @ SV143 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2741,plain,
! [SV1114: $i,SV877: $i,SV545: $i,SV144: $i] :
( ( ! [SY2802: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV144 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV877 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SV1114 @ SY2802 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV545 @ SV1114 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SV877 @ SY2802 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2742,plain,
! [SV1115: $i,SV878: $i,SV546: $i,SV145: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV145 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SV878 @ SV145 ) @ SV1115 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SV1115 @ SV145 ) @ SV878 @ SV145 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV878 @ SV546 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2743,plain,
! [SV879: $i,SV547: $i,SV146: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV146 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV547 @ SV879 @ SV146 ) @ SV146 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV547 @ SV146 ) @ SV879 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2744,plain,
! [SV1116: $i,SV880: $i,SV548: $i,SV147: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV147 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ SV880 @ SV147 ) @ SV1116 @ SV147 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ ( c_Divides_Odiv__class_Omod @ SV880 @ SV1116 @ SV147 ) @ SV147 ) @ SV1116 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2745,plain,
! [SV1117: $i,SV881: $i,SV549: $i,SV148: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV148 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV549 @ SV881 @ SV148 ) @ SV1117 @ SV148 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV549 @ SV1117 @ SV148 ) @ SV881 @ SV148 ) @ SV1117 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2746,plain,
! [SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ! [SY2803: $i,SY2804: $i,SY2805: $i,SY2806: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2803 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SY2804 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2805 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2806 @ SV1118 @ SY2803 @ SY2804 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SY2806 @ SY2805 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2747,plain,
! [SV883: $i,SV551: $i,SV150: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV150 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV551 @ ( c_Divides_Odiv__class_Odiv @ SV883 @ SV551 @ SV150 ) @ SV150 )
= SV883 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV551 @ SV883 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2748,plain,
! [SV884: $i,SV552: $i,SV151: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV151 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV552 @ SV884 @ SV151 ) @ SV884 @ SV151 )
= SV552 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV884 @ SV552 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2749,plain,
! [SV885: $i,SV553: $i,SV152: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV152 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV553 @ ( c_HOL_Ouminus__class_Ouminus @ SV885 @ SV152 ) @ SV152 )
= ( c_HOL_Oplus__class_Oplus @ SV553 @ SV885 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2750,plain,
! [SV1119: $i,SV886: $i,SV554: $i,SV153: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV153 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV554 @ ( c_HOL_Otimes__class_Otimes @ SV886 @ SV1119 @ SV153 ) @ SV153 ) @ SV886 @ SV153 )
= ( c_Divides_Odiv__class_Omod @ SV554 @ SV886 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2751,plain,
! [SV1120: $i,SV887: $i,SV555: $i,SV154: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV154 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV887 @ SV1120 @ SV154 ) @ SV154 ) @ SV1120 @ SV154 )
= ( c_Divides_Odiv__class_Omod @ SV555 @ SV1120 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2752,plain,
! [SV1121: $i,SV888: $i,SV556: $i,SV155: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV155 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
| ( SV1121
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV1121 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SV1121 @ SV155 ) @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2753,plain,
! [SV1122: $i,SV889: $i,SV557: $i,SV156: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV156 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
| ( SV1122
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV889 @ SV156 ) @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2754,plain,
! [SV558: $i,SV157: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV157 ) ) @ SV558 @ ( tc_Polynomial_Opoly @ SV157 ) )
= SV558 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2755,plain,
! [SV559: $i,SV158: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV158 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV158 ) ) @ ( tc_Polynomial_Opoly @ SV158 ) )
= SV559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2756,plain,
! [SV560: $i,SV159: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV159 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV560 @ ( c_HOL_Ozero__class_Ozero @ SV159 ) @ SV159 )
= SV560 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2757,plain,
! [SV561: $i,SV160: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV160 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV160 ) @ SV561 @ SV160 )
= SV561 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2758,plain,
! [SV562: $i,SV161: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV161 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV562 @ ( c_HOL_Ozero__class_Ozero @ SV161 ) @ SV161 )
= SV562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2759,plain,
! [SV563: $i,SV162: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV162 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV162 )
| ( SV563
= ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2760,plain,
! [SV564: $i,SV163: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV163 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV163 ) @ SV564 @ SV163 )
= SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2761,plain,
! [SV565: $i,SV164: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV164 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV565 @ SV164 )
= SV565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2762,plain,
! [SV566: $i,SV165: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV165 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV566 @ ( c_HOL_Ozero__class_Ozero @ SV165 ) @ SV165 )
= SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2763,plain,
! [SV567: $i,SV166: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV166 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV166 ) @ SV567 @ SV166 )
= SV567 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2764,plain,
! [SV890: $i,SV568: $i,SV167: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV167 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV568 @ SV890 @ SV167 ) @ SV890 @ SV167 )
= SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2765,plain,
! [SV569: $i,SV168: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV168 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV569 @ SV168 ) @ SV168 )
= SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2766,plain,
! [SV570: $i,SV169: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV169 )
= $false )
| ( ( SV570
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV570 @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2767,plain,
! [SV571: $i,SV170: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV170 )
= $false )
| ( ( SV571
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV571 @ SV170 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2768,plain,
! [SV572: $i,SV171: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV171 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV572 @ SV171 ) @ SV171 )
= SV572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2769,plain,
! [SV573: $i,SV172: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV172 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV573 @ SV172 ) @ SV172 )
= SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2770,plain,
! [SV574: $i,SV173: $i] :
( ( ( class_Divides_Osemiring__div @ SV173 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV574 @ ( c_HOL_Oone__class_Oone @ SV173 ) @ SV173 )
= SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2771,plain,
! [SV891: $i,SV575: $i,SV174: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV174 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV575 @ SV891 @ SV174 ) @ SV174 )
= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV575 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2772,plain,
! [SV1123: $i,SV892: $i,SV576: $i,SV175: $i] :
( ( ! [SY2807: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV892 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1123 @ SY2807 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV1123 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV892 @ SY2807 @ SV175 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2773,plain,
! [SV893: $i,SV577: $i,SV176: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV176 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV577 @ SV893 @ SV176 )
= ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Ouminus__class_Ouminus @ SV893 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2774,plain,
! [SV894: $i,SV578: $i,SV177: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV177 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV578 @ SV894 @ SV177 )
= ( c_HOL_Oplus__class_Oplus @ SV578 @ ( c_HOL_Ouminus__class_Ouminus @ SV894 @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2775,plain,
! [SV895: $i,SV579: $i,SV178: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV178 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV579 @ SV895 @ SV178 )
= ( c_HOL_Oplus__class_Oplus @ SV579 @ ( c_HOL_Ouminus__class_Ouminus @ SV895 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2374]) ).
thf(2776,plain,
! [SV896: $i,SV580: $i,SV179: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV179 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV580 @ SV896 @ SV179 )
= ( c_HOL_Oplus__class_Oplus @ SV580 @ ( c_HOL_Ouminus__class_Ouminus @ SV896 @ SV179 ) @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2777,plain,
! [SV1124: $i,SV897: $i,SV581: $i,SV180: $i] :
( ( ~ ( class_Divides_Oring__div @ SV180 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV581 @ SV897 @ SV180 ) @ SV1124 @ SV180 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV581 @ SV1124 @ SV180 ) @ ( c_Divides_Odiv__class_Omod @ SV897 @ SV1124 @ SV180 ) @ SV180 ) @ SV1124 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2778,plain,
! [SV582: $i,SV181: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV181 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ SV582 @ SV181 ) @ SV181 )
= ( c_HOL_Oabs__class_Oabs @ SV582 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2779,plain,
! [SV583: $i,SV182: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV182 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV583 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV182 ) ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2780,plain,
! [SV898: $i,SV584: $i,SV183: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV183 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV584 @ SV898 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV898 @ SV584 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2781,plain,
! [SV585: $i,SV184: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV184 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV184 ) @ SV585 @ SV184 )
= ( c_HOL_Oone__class_Oone @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2782,plain,
! [SV1125: $i,SV899: $i,SV586: $i,SV185: $i] :
( ( ~ ( class_Divides_Oring__div @ SV185 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV586 @ SV899 @ SV185 ) @ SV1125 @ SV185 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV586 @ SV1125 @ SV185 ) @ SV899 @ SV185 ) @ SV1125 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2783,plain,
! [SV1126: $i,SV900: $i,SV587: $i,SV186: $i] :
( ( ~ ( class_Divides_Oring__div @ SV186 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SV900 @ SV186 ) @ SV1126 @ SV186 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ ( c_Divides_Odiv__class_Omod @ SV900 @ SV1126 @ SV186 ) @ SV186 ) @ SV1126 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2784,plain,
! [SV1127: $i,SV901: $i,SV588: $i,SV187: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV187 )
| ( ( c_Divides_Odiv__class_Omod @ SV588 @ ( c_Polynomial_Osmult @ SV901 @ SV1127 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SV588 @ SV1127 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
| ( SV901
= ( c_HOL_Ozero__class_Ozero @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2785,plain,
! [SV589: $i,SV188: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV188 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV589 @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV589 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV188 ) ) @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2786,plain,
! [SV590: $i,SV189: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV189 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SV590 @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV189 ) ) @ SV590 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2787,plain,
! [SV902: $i,SV591: $i,SV190: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV190 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV591 @ SV902 @ SV190 ) @ SV902 @ SV190 )
= ( c_Divides_Odiv__class_Omod @ SV591 @ SV902 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2788,plain,
! [SV592: $i,SV191: $i] :
( ( ( class_Divides_Osemiring__div @ SV191 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV592 @ SV592 @ SV191 )
= ( c_HOL_Oone__class_Oone @ SV191 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2789,plain,
! [SV903: $i,SV593: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV192 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ SV593 @ SV192 ) @ SV903 @ SV192 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV593 @ SV903 @ SV192 ) @ ( tc_Polynomial_Opoly @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2790,plain,
! [SV1128: $i,SV904: $i,SV594: $i,SV193: $i] :
( ( ! [SY2808: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV193 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV594 @ SV904 @ SV193 ) @ SV1128 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2808 @ SV904 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV594 @ SY2808 @ SV193 ) @ SV904 @ SV193 ) @ SV1128 @ SV193 ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2791,plain,
! [SV595: $i,SV194: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV194 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV595 @ SV194 ) @ SV194 )
= ( c_HOL_Oabs__class_Oabs @ SV595 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2792,plain,
! [SV1129: $i,SV905: $i,SV596: $i,SV195: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV195 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV596 @ SV905 @ SV195 ) @ SV905 @ SV195 ) @ ( c_Divides_Odiv__class_Omod @ SV596 @ SV905 @ SV195 ) @ SV195 ) @ SV1129 @ SV195 )
= ( c_HOL_Oplus__class_Oplus @ SV596 @ SV1129 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2793,plain,
! [SV1130: $i,SV906: $i,SV597: $i,SV196: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV597 @ ( c_Divides_Odiv__class_Odiv @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ ( c_Divides_Odiv__class_Omod @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ SV1130 @ SV196 )
= ( c_HOL_Oplus__class_Oplus @ SV906 @ SV1130 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2794,plain,
! [SV598: $i,SV197: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV197 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ SV598 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV197 ) ) @ SV598 @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2795,plain,
! [SV599: $i,SV198: $i] :
( ( ( class_Divides_Osemiring__div @ SV198 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV599 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= SV599 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2796,plain,
! [SV600: $i,SV199: $i] :
( ( ( class_Divides_Osemiring__div @ SV199 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV600 @ SV600 @ SV199 )
= ( c_HOL_Ozero__class_Ozero @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2797,plain,
! [SV907: $i,SV601: $i,SV200: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV200 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV907 @ SV200 )
= ( c_HOL_Oplus__class_Oplus @ SV907 @ SV601 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2798,plain,
! [SV908: $i,SV602: $i,SV201: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV602 @ SV908 @ SV201 )
= ( c_HOL_Oplus__class_Oplus @ SV908 @ SV602 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2799,plain,
! [SV909: $i,SV603: $i,SV202: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV202 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV603 @ SV909 @ SV202 )
= ( c_HOL_Oplus__class_Oplus @ SV909 @ SV603 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2800,plain,
! [SV910: $i,SV604: $i,SV203: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV203 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV604 @ SV203 ) @ SV910 @ SV203 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV203 ) @ SV203 ) @ SV910 @ SV203 ) @ ( c_Power_Opower__class_Opower @ SV604 @ SV910 @ SV203 ) @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2801,plain,
! [SV911: $i,SV605: $i,SV204: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV204 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ SV605 @ SV911 @ SV204 ) @ SV911 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2802,plain,
! [SV1131: $i,SV912: $i,SV606: $i,SV205: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV205 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV606 @ SV912 @ SV205 ) @ SV1131 @ SV205 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV606 @ SV1131 @ SV205 ) @ ( c_Divides_Odiv__class_Omod @ SV912 @ SV1131 @ SV205 ) @ SV205 ) @ SV1131 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2803,plain,
! [SV913: $i,SV607: $i,SV206: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV206 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV607 @ SV913 @ SV206 ) @ SV607 @ SV206 )
= ( c_HOL_Otimes__class_Otimes @ SV607 @ ( c_Power_Opower__class_Opower @ SV607 @ SV913 @ SV206 ) @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2804,plain,
! [SV1132: $i,SV914: $i,SV608: $i,SV207: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV207 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV608 @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV1132 @ SV207 ) @ SV207 ) @ SV1132 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SV914 @ ( c_Divides_Odiv__class_Odiv @ SV608 @ SV1132 @ SV207 ) @ SV207 ) )
| ( SV1132
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2805,plain,
! [SV1133: $i,SV915: $i,SV609: $i,SV208: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV208 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV609 @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1133 @ SV208 ) @ SV208 ) @ SV915 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SV1133 @ ( c_Divides_Odiv__class_Odiv @ SV609 @ SV915 @ SV208 ) @ SV208 ) )
| ( SV915
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2806,plain,
! [SV610: $i,SV209: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV209 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV610 @ SV610 @ SV209 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV209 ) @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV209 ) @ SV610 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2807,plain,
! [SV1134: $i,SV916: $i,SV611: $i,SV210: $i] :
( ( ! [SY2809: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV210 )
| ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SV1134 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SV1134 @ SY2809 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2808,plain,
! [SV1135: $i,SV917: $i,SV612: $i,SV211: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV211 )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ SV612 @ SV917 @ SV211 ) @ SV1135 @ SV211 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV612 @ SV1135 @ SV211 ) @ ( c_Polynomial_Osmult @ SV917 @ SV1135 @ SV211 ) @ ( tc_Polynomial_Opoly @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2809,plain,
! [SV1136: $i,SV918: $i,SV613: $i,SV212: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV212 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SV918 @ SV212 ) @ SV1136 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SV1136 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV918 @ SV1136 @ SV212 ) @ SV212 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV918 @ SV613 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2810,plain,
! [SV614: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV213 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV614 @ SV213 ) @ ( c_HOL_Oabs__class_Oabs @ SV614 @ SV213 ) @ SV213 )
= ( c_HOL_Otimes__class_Otimes @ SV614 @ SV614 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2811,plain,
! [SV615: $i,SV214: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV214 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV615 @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2812,plain,
! [SV616: $i,SV215: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV215 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV616 @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2813,plain,
! [SV617: $i,SV216: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV216 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV617 @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2814,plain,
! [SV618: $i,SV217: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV217 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV618 @ SV217 )
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2815,plain,
! [SV619: $i,SV218: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV218 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV619 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2816,plain,
! [SV620: $i,SV219: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV219 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV620 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2817,plain,
! [SV621: $i,SV220: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV220 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) @ SV621 @ ( tc_Polynomial_Opoly @ SV220 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2818,plain,
! [SV622: $i,SV221: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV221 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV622 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) @ ( tc_Polynomial_Opoly @ SV221 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2819,plain,
! [SV623: $i,SV222: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV222 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV623 @ SV222 )
= ( c_HOL_Ozero__class_Ozero @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2820,plain,
! [SV624: $i,SV223: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV223 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SV624 @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2821,plain,
! [SV625: $i,SV224: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV224 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV625 @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2822,plain,
! [SV626: $i,SV225: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV225 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SV626 @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2823,plain,
! [SV627: $i,SV226: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV226 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV627 @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 )
= ( c_HOL_Ozero__class_Ozero @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2824,plain,
! [SV919: $i,SV628: $i,SV227: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV227 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV628 @ SV227 ) @ SV919 @ SV227 ) @ SV227 )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV628 @ SV919 @ SV227 ) @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2825,plain,
! [SV920: $i,SV629: $i,SV228: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV228 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV629 @ SV920 @ SV228 ) @ SV920 @ SV228 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV629 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 ) @ SV920 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2826,plain,
! [SV921: $i,SV630: $i,SV229: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV229 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV630 @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV630 @ SV229 ) @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV921 @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV229 ) @ SV630 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2827,plain,
! [SV631: $i,SV230: $i] :
( ( ( class_Divides_Osemiring__div @ SV230 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV631 @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 )
= ( c_HOL_Ozero__class_Ozero @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2828,plain,
! [SV922: $i,SV632: $i,SV231: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV231 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV632 @ SV231 ) @ ( c_HOL_Oplus__class_Oplus @ SV922 @ SV632 @ SV231 ) @ SV231 )
= SV922 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2829,plain,
! [SV923: $i,SV633: $i,SV232: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV232 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV633 @ SV232 ) @ ( c_HOL_Oplus__class_Oplus @ SV633 @ SV923 @ SV232 ) @ SV232 )
= SV923 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2830,plain,
! [SV924: $i,SV634: $i,SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV233 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV634 @ ( c_HOL_Ouminus__class_Ouminus @ SV924 @ ( tc_Polynomial_Opoly @ SV233 ) ) @ ( tc_Polynomial_Opoly @ SV233 ) )
= ( c_Divides_Odiv__class_Omod @ SV634 @ SV924 @ ( tc_Polynomial_Opoly @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2831,plain,
! [SV925: $i,SV635: $i,SV235: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV235 ) )
= $true )
| ( ( ( c_Polynomial_Opoly__gcd @ SV635 @ SV925 @ SV235 )
= ( c_Polynomial_Opoly__gcd @ SV925 @ SV635 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2832,plain,
! [SV926: $i,SV636: $i,SV236: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV236 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV636 @ SV236 ) @ SV926 @ SV236 )
= ( c_HOL_Otimes__class_Otimes @ SV636 @ ( c_HOL_Ouminus__class_Ouminus @ SV926 @ SV236 ) @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2833,plain,
! [SV927: $i,SV637: $i,SV240: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV240 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly__gcd @ SV637 @ SV927 @ SV240 )
= ( c_Polynomial_Opoly__gcd @ SV927 @ ( c_Divides_Odiv__class_Omod @ SV637 @ SV927 @ ( tc_Polynomial_Opoly @ SV240 ) ) @ SV240 ) )
| ( SV927
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV240 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2834,plain,
! [SV638: $i,SV241: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV241 )
= $false )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV638 @ SV241 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2835,plain,
! [SV639: $i,SV242: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV242 )
= $false )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV639 @ SV242 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2836,plain,
! [SV928: $i,SV640: $i,SV243: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV243 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ SV640 @ SV243 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV928 @ SV243 ) @ SV243 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SV928 @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2837,plain,
! [SV1137: $i,SV929: $i,SV641: $i,SV244: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV244 )
| ( ( c_Divides_Odiv__class_Odiv @ SV641 @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SV1137 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ ( tc_Polynomial_Opoly @ SV244 ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ SV641 @ SV929 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ SV1137 @ ( tc_Polynomial_Opoly @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2838,plain,
! [SV930: $i,SV642: $i,SV245: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV245 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SV930 @ SV245 ) @ SV245 ) @ SV245 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SV930 @ SV245 ) @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2839,plain,
! [SV931: $i,SV643: $i,SV246: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV246 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV643 @ SV931 @ SV246 ) @ SV643 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2840,plain,
! [SV932: $i,SV644: $i,SV247: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV247 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV644 @ SV932 @ SV247 ) @ SV932 @ SV247 )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2841,plain,
! [SV933: $i,SV645: $i,SV248: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV248 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV645 @ SV933 @ SV248 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV645 @ SV933 @ SV248 ) @ SV933 @ SV248 ) @ SV248 )
= SV645 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2842,plain,
! [SV934: $i,SV646: $i,SV250: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV250 ) )
= $true )
| ( ( ( SV646
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV646 @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV646 @ SV934 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2843,plain,
! [SV935: $i,SV647: $i,SV251: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV251 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV647 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ SV935 @ ( tc_Polynomial_Opoly @ SV251 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV647 @ SV935 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ ( tc_Polynomial_Opoly @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2844,plain,
! [SV1138: $i,SV936: $i,SV648: $i,SV252: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV252 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV936 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV1138 @ SV252 ) @ SV252 )
= ( c_HOL_Otimes__class_Otimes @ SV648 @ ( c_Divides_Odiv__class_Omod @ SV936 @ SV1138 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2845,plain,
! [SV1139: $i,SV937: $i,SV649: $i,SV253: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV253 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV649 @ SV937 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV1139 @ SV937 @ SV253 ) @ SV253 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV649 @ SV1139 @ SV253 ) @ SV937 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2846,plain,
! [SV938: $i,SV650: $i,SV254: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV254 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV650 @ SV938 @ SV254 ) @ SV254 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV938 @ SV254 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV650 @ SV254 ) @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2847,plain,
! [SV939: $i,SV651: $i,SV255: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV255 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV939 @ SV255 ) @ SV255 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV651 @ SV255 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV939 @ SV255 ) @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2848,plain,
! [SV1140: $i,SV940: $i,SV652: $i,SV256: $i] :
( ( ! [SY2810: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SY2810 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SY2810 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2849,plain,
! [SV653: $i,SV257: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV257 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV653 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) @ SV257 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2850,plain,
! [SV654: $i,SV258: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV258 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV654 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) @ SV258 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2851,plain,
! [SV1141: $i,SV941: $i,SV655: $i,SV259: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV259 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SV941 @ SV259 ) @ SV1141 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SV1141 @ SV259 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1141 @ SV941 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2852,plain,
! [SV1142: $i,SV942: $i,SV656: $i,SV260: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV260 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2853,plain,
! [SV1143: $i,SV943: $i,SV657: $i,SV261: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV261 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2854,plain,
! [SV944: $i,SV658: $i,SV262: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV262 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV658 @ SV944 @ SV262 ) @ SV658 @ ( tc_Polynomial_Opoly @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2855,plain,
! [SV945: $i,SV659: $i,SV263: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV263 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV659 @ SV945 @ SV263 ) @ SV945 @ ( tc_Polynomial_Opoly @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2856,plain,
! [SV946: $i,SV660: $i,SV264: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV264 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV660 @ SV264 ) @ SV946 @ ( tc_Polynomial_Opoly @ SV264 ) )
| ( SV946
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2857,plain,
! [SV947: $i,SV661: $i,SV265: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV265 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ ( c_HOL_Oabs__class_Oabs @ SV947 @ SV265 ) @ SV265 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ SV947 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2858,plain,
! [SV948: $i,SV662: $i,SV266: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV266 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ SV948 @ SV266 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ ( c_HOL_Oabs__class_Oabs @ SV948 @ SV266 ) @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2859,plain,
! [SV949: $i,SV663: $i,SV267: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV267 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV663 @ SV267 ) @ SV949 @ SV267 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV663 @ SV949 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2860,plain,
! [SV950: $i,SV664: $i,SV268: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV268 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV664 @ SV950 @ SV268 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV664 @ SV268 ) @ SV950 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2861,plain,
! [SV665: $i,SV269: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV665 @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2862,plain,
! [SV1144: $i,SV951: $i,SV666: $i,SV270: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV270 )
| ( ( c_Polynomial_Osmult @ SV666 @ ( c_HOL_Ominus__class_Ominus @ SV951 @ SV1144 @ ( tc_Polynomial_Opoly @ SV270 ) ) @ SV270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV666 @ SV951 @ SV270 ) @ ( c_Polynomial_Osmult @ SV666 @ SV1144 @ SV270 ) @ ( tc_Polynomial_Opoly @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2863,plain,
! [SV1145: $i,SV952: $i,SV667: $i,SV271: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV271 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SV952 @ ( tc_Polynomial_Opoly @ SV271 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SV1145 @ SV952 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2864,plain,
! [SV1146: $i,SV953: $i,SV668: $i,SV272: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV272 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SV953 @ ( tc_Polynomial_Opoly @ SV272 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SV953 @ SV1146 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2865,plain,
! [SV1147: $i,SV954: $i,SV669: $i,SV273: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV273 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV954 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1147 @ SV954 @ SV273 ) @ SV273 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SV1147 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2866,plain,
! [SV1148: $i,SV955: $i,SV670: $i,SV274: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV274 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV955 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV1148 @ SV274 ) @ SV274 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV955 @ SV1148 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2867,plain,
! [SV956: $i,SV671: $i,SV275: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV275 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV671 @ ( c_HOL_Ouminus__class_Ouminus @ SV956 @ ( tc_Polynomial_Opoly @ SV275 ) ) @ SV275 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV671 @ SV956 @ SV275 ) @ ( tc_Polynomial_Opoly @ SV275 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2868,plain,
! [SV672: $i,SV276: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
= $false )
| ( ( ( SV672
= ( c_HOL_Ozero__class_Ozero @ SV276 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV672 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2869,plain,
! [SV957: $i,SV673: $i,SV277: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV673 @ SV277 ) @ SV957 @ SV277 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV673 @ SV957 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2870,plain,
! [SV958: $i,SV674: $i,SV278: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV674 @ SV958 @ SV278 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV674 @ SV278 ) @ SV958 @ SV278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2871,plain,
! [SV959: $i,SV675: $i,SV279: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ ( c_HOL_Ouminus__class_Ouminus @ SV959 @ SV279 ) @ SV279 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ SV959 @ SV279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2872,plain,
! [SV960: $i,SV676: $i,SV280: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ SV960 @ SV280 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ ( c_HOL_Ouminus__class_Ouminus @ SV960 @ SV280 ) @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2873,plain,
! [SV1149: $i,SV961: $i,SV677: $i,SV281: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV281 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2874,plain,
! [SV1150: $i,SV962: $i,SV678: $i,SV282: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV282 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2875,plain,
! [SV1151: $i,SV963: $i,SV679: $i,SV283: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2876,plain,
! [SV680: $i,SV284: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV284 )
= $false )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV680 @ SV284 )
= SV680 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2877,plain,
! [SV1152: $i,SV964: $i,SV681: $i,SV285: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV285 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ SV681 @ SV964 @ SV285 ) @ SV1152 @ ( tc_Polynomial_Opoly @ SV285 ) )
= ( c_Polynomial_Osmult @ SV681 @ ( c_Divides_Odiv__class_Omod @ SV964 @ SV1152 @ ( tc_Polynomial_Opoly @ SV285 ) ) @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2878,plain,
! [SV1153: $i,SV965: $i,SV682: $i,SV286: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV286 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SV1153 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2879,plain,
! [SV1154: $i,SV966: $i,SV683: $i,SV287: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV287 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
| ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(2880,plain,
! [SV1155: $i,SV967: $i,SV684: $i,SV288: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV288 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SV1155 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SV1155
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2881,plain,
! [SV1156: $i,SV968: $i,SV685: $i,SV289: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV289 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SV1156 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SV1156 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2882,plain,
! [SV1157: $i,SV969: $i,SV686: $i,SV290: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV290 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
| ( SV1157
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1157 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2883,plain,
! [SV1158: $i,SV970: $i,SV687: $i,SV291: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV291 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2884,plain,
! [SV971: $i,SV688: $i,SV292: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV292 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV688 @ SV971 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV971 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2885,plain,
! [SV1159: $i,SV972: $i,SV689: $i,SV293: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SV972 @ SV293 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1159 @ SV689 @ SV293 ) @ SV972 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2886,plain,
! [SV1160: $i,SV973: $i,SV690: $i,SV294: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SV973 @ SV294 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV1160 @ SV294 ) @ SV973 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2887,plain,
! [SV1161: $i,SV974: $i,SV691: $i,SV295: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV974 @ SV1161 @ SV295 ) @ SV295 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SV974 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2888,plain,
! [SV1162: $i,SV975: $i,SV692: $i,SV296: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SV975 @ SV1162 @ SV296 ) @ SV296 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SV1162 @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(2889,plain,
! [SV693: $i,SV297: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV297 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV693 @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2890,plain,
! [SV1163: $i,SV976: $i,SV694: $i,SV298: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2891,plain,
! [SV695: $i,SV299: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV299 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV695 @ SV695 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2892,plain,
! [SV696: $i,SV300: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV300 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV696 @ SV300 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV300 ) ) @ ( tc_Polynomial_Opoly @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2893,plain,
! [SV1164: $i,SV977: $i,SV697: $i,SV301: $i] :
( ( ! [SY2811: $i,SY2812: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV301 )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SY2811 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SY2812 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SY2811 @ SY2812 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2894,plain,
! [SV1165: $i,SV978: $i,SV698: $i,SV302: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2895,plain,
! [SV1166: $i,SV979: $i,SV699: $i,SV303: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV303 )
| ( ( c_Polynomial_Osmult @ SV699 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SV1166 @ ( tc_Polynomial_Opoly @ SV303 ) ) @ SV303 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV699 @ SV979 @ SV303 ) @ ( c_Polynomial_Osmult @ SV699 @ SV1166 @ SV303 ) @ ( tc_Polynomial_Opoly @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2896,plain,
! [SV1167: $i,SV980: $i,SV700: $i,SV304: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV304 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2897,plain,
! [SV1168: $i,SV981: $i,SV701: $i,SV305: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV305 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(2898,plain,
! [SV1169: $i,SV982: $i,SV702: $i,SV306: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2899,plain,
! [SV1170: $i,SV983: $i,SV703: $i,SV307: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV307 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(2900,plain,
! [SV1171: $i,SV984: $i,SV704: $i,SV308: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV308 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ SV704 @ SV984 @ SV308 ) @ SV1171 @ ( tc_Polynomial_Opoly @ SV308 ) )
= ( c_Polynomial_Osmult @ SV704 @ ( c_Divides_Odiv__class_Odiv @ SV984 @ SV1171 @ ( tc_Polynomial_Opoly @ SV308 ) ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2901,plain,
! [SV985: $i,SV705: $i,SV309: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV309 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV705 @ ( c_HOL_Otimes__class_Otimes @ SV985 @ SV705 @ SV309 ) @ SV309 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2902,plain,
! [SV986: $i,SV706: $i,SV310: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV310 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV706 @ ( c_HOL_Otimes__class_Otimes @ SV706 @ SV986 @ SV310 ) @ SV310 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2903,plain,
! [SV987: $i,SV707: $i,SV311: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV311 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV707 @ ( c_HOL_Otimes__class_Otimes @ SV707 @ SV987 @ SV311 ) @ SV311 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2904,plain,
! [SV1172: $i,SV988: $i,SV708: $i,SV312: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1172 @ SV708 @ SV312 ) @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2905,plain,
! [SV1173: $i,SV989: $i,SV709: $i,SV313: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SV989 @ SV1173 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SV1173 @ ( tc_Polynomial_Opoly @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2906,plain,
! [SV1174: $i,SV990: $i,SV710: $i,SV314: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SV990 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SV1174 @ SV990 @ SV314 ) @ SV314 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SV1174 @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2907,plain,
! [SV1175: $i,SV991: $i,SV711: $i,SV315: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV315 )
| ( ( c_HOL_Otimes__class_Otimes @ SV711 @ ( c_Polynomial_Osmult @ SV991 @ SV1175 @ SV315 ) @ ( tc_Polynomial_Opoly @ SV315 ) )
= ( c_Polynomial_Osmult @ SV991 @ ( c_HOL_Otimes__class_Otimes @ SV711 @ SV1175 @ ( tc_Polynomial_Opoly @ SV315 ) ) @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2908,plain,
! [SV1176: $i,SV992: $i,SV712: $i,SV316: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV316 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ SV712 @ SV992 @ SV316 ) @ SV1176 @ ( tc_Polynomial_Opoly @ SV316 ) )
= ( c_Polynomial_Osmult @ SV712 @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1176 @ ( tc_Polynomial_Opoly @ SV316 ) ) @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2909,plain,
! [SV1177: $i,SV993: $i,SV713: $i,SV317: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV317 )
| ( ( c_Polynomial_Osmult @ SV713 @ ( c_Polynomial_Osmult @ SV993 @ SV1177 @ SV317 ) @ SV317 )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ SV713 @ SV993 @ SV317 ) @ SV1177 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(2910,plain,
! [SV1178: $i,SV994: $i,SV714: $i,SV353: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV353 )
| ~ ( class_Int_Onumber__ring @ SV353 )
| ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
| ( SV994 = SV1178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2911,plain,
! [SV1179: $i,SV995: $i,SV715: $i,SV354: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
| ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SV995 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SV715 @ SV1179 @ SV354 ) )
| ( SV995 = SV1179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(2912,plain,
! [SV996: $i,SV716: $i,SV355: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV355 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV716 @ SV996 @ SV355 )
!= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV996 @ SV716 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2913,plain,
! [SV997: $i,SV717: $i,SV356: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV356 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SV997 @ SV356 )
!= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV997
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2914,plain,
! [SV998: $i,SV718: $i,SV357: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV357 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SV998 @ SV357 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV998
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2915,plain,
! [SV999: $i,SV719: $i,SV358: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV358 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV719 @ SV999 @ SV358 )
!= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
| ( SV719
= ( c_HOL_Ouminus__class_Ouminus @ SV999 @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2916,plain,
! [SV1180: $i,SV1000: $i,SV720: $i,SV359: $i] :
( ( ! [SY2813: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV359 )
| ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SY2813 @ SV359 ) @ SV359 ) )
| ( SV1180 = SY2813 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(2917,plain,
! [SV1181: $i,SV1001: $i,SV721: $i,SV360: $i] :
( ( ! [SY2814: $i] :
( ~ ( class_HOL_Ozero @ SV360 )
| ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
!= ( c_Polynomial_OpCons @ SV1181 @ SY2814 @ SV360 ) )
| ( SV1001 = SY2814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(2918,plain,
! [SV722: $i,SV361: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV361 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV722 @ SV722 @ SV361 )
!= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
| ( SV722
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2919,plain,
! [SV1002: $i,SV723: $i,SV362: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV362 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV723 @ SV362 )
!= ( c_HOL_Oabs__class_Oabs @ SV1002 @ SV362 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV723 @ SV1002 @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2920,plain,
! [SV1003: $i,SV724: $i,SV363: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV363 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly @ SV724 @ ( c_HOL_Ouminus__class_Ouminus @ SV1003 @ SV363 ) @ SV363 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV1003 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SV724 @ ( tc_Polynomial_Opoly @ SV363 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2921,plain,
! [SV725: $i,SV364: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV364 )
= $false )
| ( ( ( ( c_HOL_Ozero__class_Ozero @ SV364 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV725 @ SV364 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= SV725 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2922,plain,
! [SV1182: $i,SV1004: $i,SV726: $i,SV365: $i] :
( ( ! [SY2815: $i,SY2816: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV365 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2815 @ SV1004 @ SV365 ) @ SY2816 @ SV365 ) )
| ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2815 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SY2816 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(2923,plain,
! [SV1183: $i,SV1005: $i,SV727: $i,SV366: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ~ ( class_Divides_Osemiring__div @ SV366 )
| ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2817 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY2818 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2817 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2818 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(2924,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV367 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2925,plain,
! [SV1184: $i,SV1007: $i,SV729: $i,SV368: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
| ( ( c_Polynomial_Osmult @ SV729 @ SV1007 @ SV368 )
!= ( c_Polynomial_OpCons @ SV1184 @ SV1007 @ SV368 ) )
| ( SV1007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2926,plain,
! [SV1185: $i,SV1008: $i,SV730: $i,SV369: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
| ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SV1008 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SV1185 @ SV1008 @ SV369 ) )
| ( SV730 = SV1185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2927,plain,
! [SV1009: $i,SV731: $i,SV370: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV370 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly__gcd @ SV731 @ SV1009 @ SV370 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
| ( SV1009
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2928,plain,
! [SV1010: $i,SV732: $i,SV371: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV371 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV371 )
| ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SV732 = SV1010 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2929,plain,
! [SV1011: $i,SV733: $i,SV372: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV733 @ SV1011 @ SV372 )
!= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
| ( SV733
= ( c_HOL_Ozero__class_Ozero @ SV372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2930,plain,
! [SV1012: $i,SV734: $i,SV373: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV373 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV734 @ SV734 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1012 @ SV373 ) @ SV373 )
!= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
| ( SV1012
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2569]) ).
thf(2931,plain,
! [SV1186: $i,SV1013: $i,SV735: $i,SV374: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SV1013 @ SV374 ) @ ( c_Polynomial_OpCons @ SV1186 @ SV1013 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
| ( SV1013
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2932,plain,
! [SV375: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV375 )
= ( c_HOL_Oone__class_Oone @ SV375 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2933,plain,
! [SV1014: $i,SV736: $i,SV376: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SV1014 @ SV376 )
!= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV1014
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2572]) ).
thf(2934,plain,
! [SV1187: $i,SV1015: $i,SV737: $i,SV377: $i] :
( ( ! [SY2819: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SY2819 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SY2819 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SY2819 )
| ( SV737 = SV1187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2935,plain,
! [SV1016: $i,SV738: $i,SV378: $i] :
( ( ( ~ ( class_HOL_Ozero @ SV378 ) )
= $true )
| ( ( ( ( c_Polynomial_OpCons @ SV738 @ SV1016 @ SV378 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
| ( SV1016
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2936,plain,
! [SV1188: $i,SV1017: $i,SV739: $i,SV379: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1017 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1188 @ SV379 ) )
| ( SV1017 = SV1188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(2937,plain,
! [SV740: $i,SV380: $i] :
( ( ( class_OrderedGroup_Oordered__ab__group__add @ SV380 )
= $false )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV740 @ SV380 )
!= SV740 )
| ( SV740
= ( c_HOL_Ozero__class_Ozero @ SV380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2938,plain,
! [SV1018: $i,SV741: $i,SV381: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV381 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
!= ( c_HOL_Otimes__class_Otimes @ SV1018 @ SV1018 @ SV381 ) )
| ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SV1018 @ SV381 ) )
| ( SV741 = SV1018 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2939,plain,
! [SV1019: $i,SV742: $i,SV382: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV382 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV742 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SV1019 @ SV1019 @ SV382 ) @ SV382 )
!= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
| ( SV742
= ( c_HOL_Ozero__class_Ozero @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2940,plain,
! [SV1189: $i,SV1020: $i,SV743: $i,SV383: $i] :
( ( ! [SY2820: $i,SY2821: $i] :
( ~ ( class_Divides_Oring__div @ SV383 )
| ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2820 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2821 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2820 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2821 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2941,plain,
! [SV1190: $i,SV1021: $i,SV744: $i,SV384: $i] :
( ( ! [SY2822: $i] :
( ~ ( class_HOL_Ozero @ SV384 )
| ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
!= ( c_Polynomial_OpCons @ SV1190 @ SY2822 @ SV384 ) )
| ( SV744 = SV1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2942,plain,
! [SV1022: $i,SV745: $i,SV385: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV385 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1022 @ SV385 )
!= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV745 @ SV385 )
= SV1022 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2943,plain,
! [SV746: $i,SV386: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV386 )
= $false )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV746 @ SV386 )
!= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
| ( SV746
= ( c_HOL_Ozero__class_Ozero @ SV386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2944,plain,
! [SV1023: $i,SV747: $i,SV387: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV387 ) )
= $true )
| ( ( ( ( c_Polynomial_Osmult @ SV747 @ SV1023 @ SV387 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV1023
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2945,plain,
! [SV1191: $i,SV1024: $i,SV748: $i,SV388: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV388 )
| ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SV1024 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV388 ) )
| ( SV748 = SV1024 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2946,plain,
! [SV1025: $i,SV749: $i,SV389: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV389 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV749 @ SV1025 @ SV389 )
!= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
| ( SV749 = SV1025 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2947,plain,
! [SV1192: $i,SV1026: $i,SV750: $i,SV390: $i] :
( ( ! [SY2823: $i,SY2824: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV390 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2823 @ SV1026 @ SV390 ) @ SY2824 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SY2823 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SY2824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2948,plain,
! [SV1027: $i,SV751: $i,SV391: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV391 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV751 @ SV1027 @ SV391 )
!= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
| ( SV751 = SV1027 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2949,plain,
! [SV1193: $i,SV1028: $i,SV752: $i,SV392: $i] :
( ( ! [SY2825: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
| ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SV1193 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SY2825 @ SV1193 @ SV392 ) )
| ( SY2825
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2950,plain,
! [SV1194: $i,SV1029: $i,SV753: $i,SV393: $i] :
( ( ! [SY2826: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV393 )
| ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SY2826 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SY2826 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SY2826 )
| ( SV753 = SV1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(2951,plain,
! [SV394: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV394 )
= ( c_HOL_Ozero__class_Ozero @ SV394 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV394 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2952,plain,
! [SV1030: $i,SV754: $i,SV395: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV395 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly @ SV754 @ SV1030 @ SV395 )
!= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV1030 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SV754 @ ( tc_Polynomial_Opoly @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2591]) ).
thf(2953,plain,
! [SV1031: $i,SV755: $i,SV396: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV396 ) )
= $true )
| ( ( ( ( c_Polynomial_Opoly__gcd @ SV755 @ SV1031 @ SV396 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
| ( SV755
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2954,plain,
! [SV1195: $i,SV1032: $i,SV756: $i,SV397: $i] :
( ( ~ ( class_Divides_Oring__div @ SV397 )
| ( ( c_Divides_Odiv__class_Omod @ SV756 @ SV1032 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SV1195 @ SV1032 @ SV397 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ SV397 ) @ SV1032 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(2955,plain,
! [SV1196: $i,SV1033: $i,SV757: $i,SV398: $i] :
( ( ! [SY2827: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV398 )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1196 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SY2827 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SV1196 @ SV398 )
= SY2827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(2956,plain,
! [SV758: $i,SV399: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV399 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV758 @ SV399 )
!= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
| ( SV758
= ( c_HOL_Ozero__class_Ozero @ SV399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2957,plain,
! [SV1197: $i,SV1034: $i,SV759: $i,SV400: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV400 )
| ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SV1034 @ SV1197 @ SV400 ) @ SV400 )
!= SV1034 )
| ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SV1197 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2958,plain,
! [SV1198: $i,SV1035: $i,SV760: $i,SV401: $i] :
( ( ! [SY2828: $i,SY2829: $i] :
( ~ ( class_Divides_Osemiring__div @ SV401 )
| ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2828 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2829 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2828 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2829 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(2959,plain,
! [SV1199: $i,SV1036: $i,SV761: $i,SV402: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV402 )
| ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV1199 @ SV402 ) )
| ( SV1036 = SV1199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2960,plain,
! [SV1037: $i,SV762: $i,SV403: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV403 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV403 )
| ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
| ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2961,plain,
! [SV1038: $i,SV763: $i,SV404: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV404 ) )
= $true )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV763 @ SV404 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1038 @ SV404 ) )
| ( SV763 = SV1038 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2962,plain,
! [SV1039: $i,SV764: $i,SV405: $i] :
( ( ( ~ ( class_HOL_Ozero @ SV405 ) )
= $true )
| ( ( ( ( c_Polynomial_OpCons @ SV764 @ SV1039 @ SV405 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
| ( SV764
= ( c_HOL_Ozero__class_Ozero @ SV405 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2963,plain,
! [SV1040: $i,SV765: $i,SV406: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV406 ) )
= $true )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV765 @ SV406 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1040 @ SV406 ) )
| ( SV765 = SV1040 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2964,plain,
! [SV1041: $i,SV766: $i,SV407: $i,SV1: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV1 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ SV407 @ SV766 @ SV1 ) @ SV1041 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV1041 @ ( c_Polynomial_Opoly @ SV766 @ SV1041 @ SV1 ) @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2965,plain,
! [SV1042: $i,SV767: $i,SV410: $i,SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV4 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ SV410 @ SV767 @ SV4 ) @ SV1042 @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ SV410 @ ( c_Polynomial_Opoly @ SV767 @ SV1042 @ SV4 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2966,plain,
! [SV1043: $i,SV768: $i,SV411: $i,SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV5 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV768 @ ( tc_Polynomial_Opoly @ SV5 ) ) @ SV1043 @ SV5 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ SV411 @ SV1043 @ SV5 ) @ ( c_Polynomial_Opoly @ SV768 @ SV1043 @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2967,plain,
! [SV1044: $i,SV769: $i,SV412: $i,SV6: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV6 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ SV412 @ SV769 @ ( tc_Polynomial_Opoly @ SV6 ) ) @ SV1044 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ SV412 @ SV1044 @ SV6 ) @ ( c_Polynomial_Opoly @ SV769 @ SV1044 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2968,plain,
! [SV770: $i,SV413: $i,SV7: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV7 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ SV413 @ ( tc_Polynomial_Opoly @ SV7 ) ) @ SV770 @ SV7 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ SV413 @ SV770 @ SV7 ) @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2969,plain,
! [SV1045: $i,SV771: $i,SV414: $i,SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV8 ) )
= $true )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ SV414 @ SV771 @ ( tc_Polynomial_Opoly @ SV8 ) ) @ SV1045 @ SV8 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ SV414 @ SV1045 @ SV8 ) @ ( c_Polynomial_Opoly @ SV771 @ SV1045 @ SV8 ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2970,plain,
! [SV1200: $i,SV1046: $i,SV772: $i,SV415: $i,SV9: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV9 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SV415 @ SV772 @ SV9 ) @ ( c_Polynomial_OpCons @ SV1046 @ SV1200 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SV415 @ SV1046 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SV772 @ SV1200 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2971,plain,
! [SV773: $i,SV416: $i,SV10: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV10 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ SV416 @ SV773 @ SV10 ) @ ( tc_Polynomial_Opoly @ SV10 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV416 @ SV10 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV773 @ ( tc_Polynomial_Opoly @ SV10 ) ) @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2972,plain,
! [SV1201: $i,SV1047: $i,SV774: $i,SV417: $i,SV11: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SV417 @ SV774 @ SV11 ) @ ( c_Polynomial_OpCons @ SV1047 @ SV1201 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SV417 @ SV1047 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SV774 @ SV1201 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2973,plain,
! [SV1048: $i,SV775: $i,SV418: $i,SV12: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV12 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV418 @ ( c_Polynomial_OpCons @ SV775 @ SV1048 @ SV12 ) @ SV12 )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV775 @ SV12 ) @ ( c_Polynomial_Osmult @ SV418 @ SV1048 @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2974,plain,
! [SV776: $i,SV419: $i,SV14: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV14 )
= $false )
| ( ( ( ( c_Polynomial_Opoly @ SV419 @ SV776 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV776 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SV419 @ ( tc_Polynomial_Opoly @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2975,plain,
! [SV777: $i,SV420: $i,SV15: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV15 )
= $false )
| ( ( ( ( c_Polynomial_Opoly @ SV420 @ ( c_HOL_Ouminus__class_Ouminus @ SV777 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV777 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SV420 @ ( tc_Polynomial_Opoly @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2976,plain,
! [SV778: $i,SV421: $i,SV16: $i] :
( ( ( class_Divides_Osemiring__div @ SV16 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV421 @ SV778 @ SV16 ) @ SV421 @ SV16 )
= SV778 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2977,plain,
! [SV779: $i,SV422: $i,SV17: $i] :
( ( ( class_Divides_Osemiring__div @ SV17 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV422 @ SV779 @ SV17 ) @ SV779 @ SV17 )
= SV422 )
| ( SV779
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2978,plain,
! [SV1202: $i,SV1049: $i,SV780: $i,SV423: $i,SV18: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV780 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV1049 @ SV1202 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV1049 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV780 @ SV1202 @ SV18 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2979,plain,
! [SV1203: $i,SV1050: $i,SV781: $i,SV424: $i,SV19: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV424 @ SV781 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SV1203 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SV424 @ ( c_HOL_Otimes__class_Otimes @ SV781 @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SV1203 @ SV19 ) @ SV19 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2980,plain,
! [SV1204: $i,SV1051: $i,SV782: $i,SV425: $i,SV20: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1204 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SV1051 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ SV1204 @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(2981,plain,
! [SV1205: $i,SV1052: $i,SV783: $i,SV426: $i,SV21: $i] :
( ( ! [SY2830: $i,SY2831: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SY2830 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SY2831 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(2982,plain,
! [SV1206: $i,SV1053: $i,SV784: $i,SV427: $i,SV22: $i] :
( ( ! [SY2832: $i,SY2833: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SY2832 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SY2833 @ SV427 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(2983,plain,
! [SV785: $i,SV428: $i,SV23: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV23 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV428 @ SV23 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV785 @ SV23 ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2984,plain,
! [SV786: $i,SV429: $i,SV24: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV24 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ ( c_HOL_Otimes__class_Otimes @ SV786 @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2985,plain,
! [SV787: $i,SV430: $i,SV26: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV26 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV787 @ SV26 ) @ SV26 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV430 @ SV26 ) @ ( c_HOL_Oabs__class_Oabs @ SV787 @ SV26 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2986,plain,
! [SV788: $i,SV431: $i,SV27: $i] :
( ( ( class_Ring__and__Field_Oring @ SV27 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV788 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV431 @ SV27 ) @ SV788 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2987,plain,
! [SV789: $i,SV432: $i,SV28: $i] :
( ( ( class_Ring__and__Field_Oring @ SV28 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV432 @ SV789 @ SV28 ) @ SV28 )
= ( c_HOL_Otimes__class_Otimes @ SV432 @ ( c_HOL_Ouminus__class_Ouminus @ SV789 @ SV28 ) @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2988,plain,
! [SV790: $i,SV433: $i,SV29: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV433 @ ( c_HOL_Otimes__class_Otimes @ SV433 @ SV790 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV433 @ SV790 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2989,plain,
! [SV1207: $i,SV1054: $i,SV791: $i,SV434: $i,SV30: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(2990,plain,
! [SV1055: $i,SV792: $i,SV435: $i,SV31: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV31 ) )
= $true )
| ( ( ( SV435 = SV792 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV792 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SV1055 @ SV435 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2631]) ).
thf(2991,plain,
! [SV793: $i,SV436: $i,SV32: $i] :
( ( ( class_Divides_Osemiring__div @ SV32 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV436 @ SV32 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV793 @ SV32 ) @ SV32 )
= ( c_HOL_Ozero__class_Ozero @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2992,plain,
! [SV794: $i,SV437: $i,SV33: $i] :
( ( ( class_Divides_Osemiring__div @ SV33 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV794 @ SV33 ) @ SV437 @ SV33 )
= ( c_Divides_Odiv__class_Omod @ SV794 @ SV437 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2993,plain,
! [SV795: $i,SV438: $i,SV34: $i] :
( ( ( class_Divides_Osemiring__div @ SV34 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV438 @ SV795 @ SV34 ) @ SV795 @ SV34 )
= ( c_Divides_Odiv__class_Omod @ SV438 @ SV795 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2994,plain,
! [SV796: $i,SV439: $i,SV35: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV35 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV439 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV439 @ SV35 ) @ SV796 @ SV35 ) @ SV35 )
= SV796 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2995,plain,
! [SV1056: $i,SV797: $i,SV440: $i,SV36: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV36 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV440 @ ( c_HOL_Otimes__class_Otimes @ SV797 @ SV1056 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV797 @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ SV1056 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( c_Divides_Odiv__class_Omod @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2996,plain,
! [SV1057: $i,SV798: $i,SV442: $i,SV38: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV38 ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SV798 @ SV1057 @ SV38 )
| ( SV798
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(2997,plain,
! [SV1058: $i,SV799: $i,SV443: $i,SV39: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV39 ) )
= $true )
| ( ( ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SV799 @ SV443 @ SV1058 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2998,plain,
! [SV1059: $i,SV800: $i,SV444: $i,SV40: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV40 ) )
= $true )
| ( ( ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SV800 @ SV1059 @ SV444 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2999,plain,
! [SV1060: $i,SV801: $i,SV445: $i,SV41: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV41 ) )
= $true )
| ( ( ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV801 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SV1060 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(3000,plain,
! [SV1061: $i,SV802: $i,SV446: $i,SV42: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV802 @ SV42 ) @ SV1061 @ SV42 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV446 @ SV1061 @ SV42 ) @ ( c_Power_Opower__class_Opower @ SV802 @ SV1061 @ SV42 ) @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(3001,plain,
! [SV1062: $i,SV803: $i,SV447: $i,SV43: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV43 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV803 @ SV43 ) @ SV1062 @ SV43 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV447 @ SV1062 @ SV43 ) @ ( c_Power_Opower__class_Opower @ SV803 @ SV1062 @ SV43 ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(3002,plain,
! [SV1063: $i,SV804: $i,SV448: $i,SV44: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV44 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ ( c_Divides_Odiv__class_Omod @ SV804 @ SV1063 @ SV44 ) @ SV44 ) @ SV1063 @ SV44 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV804 @ SV44 ) @ SV1063 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(3003,plain,
! [SV1064: $i,SV805: $i,SV449: $i,SV45: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV45 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV449 @ SV805 @ SV45 ) @ SV1064 @ SV45 ) @ SV805 @ SV45 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV449 @ SV1064 @ SV45 ) @ SV805 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(3004,plain,
! [SV1208: $i,SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ! [SY2834: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV46 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SY2834 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SY2834 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3005,plain,
! [SV1209: $i,SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ! [SY2835: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV47 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SY2835 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SY2835 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3006,plain,
! [SV808: $i,SV452: $i,SV48: $i] :
( ( ( class_Divides_Osemiring__div @ SV48 )
= $false )
| ( ( SV452
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV452 @ SV808 @ SV48 ) @ SV808 @ SV48 ) @ ( c_Divides_Odiv__class_Omod @ SV452 @ SV808 @ SV48 ) @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(3007,plain,
! [SV809: $i,SV453: $i,SV49: $i] :
( ( ( class_Divides_Osemiring__div @ SV49 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV453 @ SV809 @ SV49 ) @ SV809 @ SV49 ) @ ( c_Divides_Odiv__class_Omod @ SV453 @ SV809 @ SV49 ) @ SV49 )
= SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(3008,plain,
! [SV810: $i,SV454: $i,SV50: $i] :
( ( ( class_Divides_Osemiring__div @ SV50 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_Divides_Odiv__class_Odiv @ SV810 @ SV454 @ SV50 ) @ SV50 ) @ ( c_Divides_Odiv__class_Omod @ SV810 @ SV454 @ SV50 ) @ SV50 )
= SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(3009,plain,
! [SV811: $i,SV456: $i,SV52: $i] :
( ( ( class_Divides_Oring__div @ SV52 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV456 @ ( c_HOL_Ouminus__class_Ouminus @ SV811 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV456 @ SV811 @ SV52 ) @ SV52 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV811 @ SV456 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(3010,plain,
! [SV812: $i,SV457: $i,SV53: $i] :
( ( ( class_Divides_Oring__div @ SV53 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV457 @ SV53 ) @ SV812 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV457 @ SV812 @ SV53 ) @ SV53 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV812 @ SV457 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(3011,plain,
! [SV1067: $i,SV813: $i,SV458: $i,SV54: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV54 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV813 @ SV54 ) @ SV1067 @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV458 @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1067 @ SV54 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(3012,plain,
! [SV1068: $i,SV814: $i,SV459: $i,SV55: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV814 @ SV55 ) @ SV1068 @ SV55 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV1068 @ SV55 ) @ SV814 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(3013,plain,
! [SV1069: $i,SV815: $i,SV460: $i,SV56: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV460 @ SV815 @ SV56 ) @ SV1069 @ SV56 )
= ( c_HOL_Otimes__class_Otimes @ SV460 @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1069 @ SV56 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(3014,plain,
! [SV1070: $i,SV816: $i,SV461: $i,SV57: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1070 @ SV57 ) @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV461 @ SV816 @ SV57 ) @ SV1070 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(3015,plain,
! [SV1071: $i,SV817: $i,SV462: $i,SV58: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV58 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV817 @ SV1071 @ SV58 ) @ SV58 )
= ( c_HOL_Otimes__class_Otimes @ SV817 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1071 @ SV58 ) @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(3016,plain,
! [SV1072: $i,SV818: $i,SV463: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV463 @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV1072 @ SV59 ) @ SV59 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV463 @ SV818 @ SV59 ) @ SV1072 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(3017,plain,
! [SV1073: $i,SV819: $i,SV464: $i,SV60: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV464 @ SV819 @ SV60 ) @ SV1073 @ SV60 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV464 @ SV1073 @ SV60 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV1073 @ SV60 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(3018,plain,
! [SV1074: $i,SV820: $i,SV465: $i,SV61: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV61 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV465 @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV1074 @ SV61 ) @ SV61 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV820 @ SV61 ) @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV1074 @ SV61 ) @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(3019,plain,
! [SV1075: $i,SV821: $i,SV466: $i,SV62: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV62 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV466 @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV1075 @ SV62 ) @ SV62 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV821 @ SV62 ) @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV1075 @ SV62 ) @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(3020,plain,
! [SV1076: $i,SV822: $i,SV467: $i,SV63: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV63 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV467 @ SV822 @ SV63 ) @ SV1076 @ SV63 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV467 @ SV1076 @ SV63 ) @ ( c_HOL_Otimes__class_Otimes @ SV822 @ SV1076 @ SV63 ) @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(3021,plain,
! [SV1077: $i,SV823: $i,SV468: $i,SV64: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV64 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SV823 @ SV64 ) @ SV1077 @ SV64 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV1077 @ SV64 ) @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1077 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(3022,plain,
! [SV1078: $i,SV824: $i,SV469: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV65 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV469 @ SV824 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV469 @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( tc_Polynomial_Opoly @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2665]) ).
thf(3023,plain,
! [SV1079: $i,SV825: $i,SV470: $i,SV66: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV470 @ ( c_HOL_Oplus__class_Oplus @ SV825 @ SV1079 @ SV66 ) @ SV66 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV825 @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV1079 @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(3024,plain,
! [SV1080: $i,SV826: $i,SV471: $i,SV67: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV67 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV471 @ SV826 @ SV67 ) @ SV1080 @ SV67 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV471 @ SV1080 @ SV67 ) @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1080 @ SV67 ) @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(3025,plain,
! [SV827: $i,SV472: $i,SV68: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV68 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV472 @ SV827 @ SV68 ) @ SV68 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV827 @ SV472 @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(3026,plain,
! [SV828: $i,SV473: $i,SV69: $i] :
( ( ( class_Divides_Osemiring__div @ SV69 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV828 @ SV69 ) @ SV473 @ SV69 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV828 @ SV473 @ SV69 ) @ ( c_HOL_Oone__class_Oone @ SV69 ) @ SV69 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(3027,plain,
! [SV829: $i,SV474: $i,SV70: $i] :
( ( ( class_Divides_Osemiring__div @ SV70 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV829 @ SV70 ) @ SV829 @ SV70 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV474 @ SV829 @ SV70 ) @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV70 ) )
| ( SV829
= ( c_HOL_Ozero__class_Ozero @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(3028,plain,
! [SV1081: $i,SV830: $i,SV475: $i,SV72: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV830 @ SV72 ) @ ( c_HOL_Otimes__class_Otimes @ SV1081 @ SV830 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV475 @ SV1081 @ SV72 ) @ SV830 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(3029,plain,
! [SV831: $i,SV476: $i,SV73: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV73 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV476 @ SV73 ) @ SV831 @ SV73 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV831 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(3030,plain,
! [SV832: $i,SV477: $i,SV74: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV74 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV477 @ SV74 ) @ SV832 @ SV74 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV477 @ SV832 @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(3031,plain,
! [SV833: $i,SV478: $i,SV75: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV75 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV478 @ ( c_HOL_Ouminus__class_Ouminus @ SV833 @ SV75 ) @ SV75 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV478 @ SV833 @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(3032,plain,
! [SV834: $i,SV479: $i,SV76: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV76 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV479 @ ( c_HOL_Ouminus__class_Ouminus @ SV834 @ SV76 ) @ SV76 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV834 @ SV76 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(3033,plain,
! [SV835: $i,SV481: $i,SV78: $i] :
( ( ( class_Ring__and__Field_Oring @ SV78 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV78 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV78 ) @ SV78 )
= ( c_HOL_Otimes__class_Otimes @ SV481 @ SV835 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(3034,plain,
! [SV1082: $i,SV836: $i,SV482: $i,SV79: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV79 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV836 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV1082 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SV836 @ SV1082 @ SV79 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(3035,plain,
! [SV1083: $i,SV837: $i,SV483: $i,SV80: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV80 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV483 @ SV837 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1083 @ SV837 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SV483 @ SV1083 @ SV80 ) )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(3036,plain,
! [SV838: $i,SV484: $i,SV81: $i] :
( ( ( class_Divides_Oring__div @ SV81 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV484 @ SV81 ) @ SV838 @ SV81 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV484 @ SV838 @ SV81 ) @ SV81 ) @ SV838 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(3037,plain,
! [SV1084: $i,SV839: $i,SV487: $i,SV84: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV84 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ SV487 @ SV839 @ SV84 ) @ SV1084 @ ( tc_Polynomial_Opoly @ SV84 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV487 @ SV1084 @ SV84 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( c_HOL_Otimes__class_Otimes @ SV839 @ SV1084 @ ( tc_Polynomial_Opoly @ SV84 ) ) @ SV84 ) @ ( tc_Polynomial_Opoly @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(3038,plain,
! [SV1085: $i,SV840: $i,SV488: $i,SV85: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV85 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV488 @ ( c_Polynomial_OpCons @ SV840 @ SV1085 @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV840 @ SV488 @ SV85 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_HOL_Otimes__class_Otimes @ SV488 @ SV1085 @ ( tc_Polynomial_Opoly @ SV85 ) ) @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(3039,plain,
! [SV496: $i,SV93: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV93 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV496 @ SV496 @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2692]) ).
thf(3040,plain,
! [SV1210: $i,SV1086: $i,SV841: $i,SV498: $i,SV95: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SV1086 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SV1210 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SV1086 @ SV841 @ SV1210 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3041,plain,
! [SV1087: $i,SV842: $i,SV499: $i,SV96: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV96 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ SV499 @ SV842 @ SV96 ) @ SV1087 @ SV96 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV499 @ SV1087 @ SV96 ) @ ( c_Polynomial_Osmult @ SV842 @ SV1087 @ SV96 ) @ ( tc_Polynomial_Opoly @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(3042,plain,
! [SV1211: $i,SV1088: $i,SV843: $i,SV500: $i,SV97: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV97 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV843 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV500 @ SV97 ) @ SV843 @ SV97 ) @ SV1211 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1088 @ SV843 @ SV97 ) @ SV1211 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3043,plain,
! [SV1089: $i,SV844: $i,SV501: $i,SV98: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV98 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2697]) ).
thf(3044,plain,
! [SV1090: $i,SV845: $i,SV502: $i,SV99: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV99 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV502 @ SV845 @ SV99 ) @ SV1090 @ SV99 ) @ SV845 @ SV99 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV1090 @ SV99 ) @ SV845 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2698]) ).
thf(3045,plain,
! [SV846: $i,SV509: $i,SV106: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV106 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ SV509 @ SV846 @ ( c_Divides_Odiv__class_Odiv @ SV509 @ SV846 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ ( c_Divides_Odiv__class_Omod @ SV509 @ SV846 @ ( tc_Polynomial_Opoly @ SV106 ) ) @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(3046,plain,
! [SV1091: $i,SV847: $i,SV511: $i,SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV108 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV108 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(3047,plain,
! [SV1092: $i,SV848: $i,SV512: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV109 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV109 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(3048,plain,
! [SV1093: $i,SV849: $i,SV513: $i,SV110: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV110 ) )
= $true )
| ( ( ( c_Polynomial_Opoly__gcd @ SV513 @ ( c_Polynomial_Opoly__gcd @ SV849 @ SV1093 @ SV110 ) @ SV110 )
= ( c_Polynomial_Opoly__gcd @ SV849 @ ( c_Polynomial_Opoly__gcd @ SV513 @ SV1093 @ SV110 ) @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(3049,plain,
! [SV1094: $i,SV850: $i,SV514: $i,SV111: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV111 ) )
= $true )
| ( ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ SV514 @ SV850 @ SV111 ) @ SV1094 @ SV111 )
= ( c_Polynomial_Opoly__gcd @ SV514 @ ( c_Polynomial_Opoly__gcd @ SV850 @ SV1094 @ SV111 ) @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(3050,plain,
! [SV851: $i,SV515: $i,SV112: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV112 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV851 @ SV112 ) @ SV851 @ SV112 )
= SV515 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(3051,plain,
! [SV852: $i,SV516: $i,SV113: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV113 )
= $false )
| ( ( ( c_Polynomial_Opoly__gcd @ SV516 @ ( c_HOL_Ouminus__class_Ouminus @ SV852 @ ( tc_Polynomial_Opoly @ SV113 ) ) @ SV113 )
= ( c_Polynomial_Opoly__gcd @ SV516 @ SV852 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(3052,plain,
! [SV853: $i,SV517: $i,SV114: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV114 )
= $false )
| ( ( ( c_Polynomial_Opoly__gcd @ ( c_HOL_Ouminus__class_Ouminus @ SV517 @ ( tc_Polynomial_Opoly @ SV114 ) ) @ SV853 @ SV114 )
= ( c_Polynomial_Opoly__gcd @ SV517 @ SV853 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(3053,plain,
! [SV854: $i,SV518: $i,SV115: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV518 @ SV854 @ SV115 )
= ( c_HOL_Otimes__class_Otimes @ SV854 @ SV518 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(3054,plain,
! [SV855: $i,SV519: $i,SV117: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV117 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV519 @ SV855 @ SV117 )
= ( c_HOL_Otimes__class_Otimes @ SV855 @ SV519 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(3055,plain,
! [SV1095: $i,SV856: $i,SV520: $i,SV118: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV118 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV520 @ SV856 @ SV118 ) @ SV1095 @ SV118 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV520 @ SV1095 @ SV118 ) @ ( c_Divides_Odiv__class_Omod @ SV856 @ SV1095 @ SV118 ) @ SV118 ) @ SV1095 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(3056,plain,
! [SV1096: $i,SV857: $i,SV521: $i,SV120: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV120 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SV857 @ SV1096 @ SV120 ) @ SV120 )
= ( c_HOL_Oplus__class_Oplus @ SV857 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SV1096 @ SV120 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(3057,plain,
! [SV1097: $i,SV858: $i,SV522: $i,SV121: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV121 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV522 @ SV858 @ SV121 ) @ SV1097 @ SV121 )
= ( c_HOL_Oplus__class_Oplus @ SV522 @ ( c_HOL_Oplus__class_Oplus @ SV858 @ SV1097 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(3058,plain,
! [SV1098: $i,SV859: $i,SV523: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV523 @ ( c_HOL_Oplus__class_Oplus @ SV859 @ SV1098 @ SV122 ) @ SV122 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV523 @ SV859 @ SV122 ) @ SV1098 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(3059,plain,
! [SV1099: $i,SV860: $i,SV524: $i,SV123: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV123 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV524 @ ( c_HOL_Oplus__class_Oplus @ SV860 @ SV1099 @ SV123 ) @ SV123 )
= ( c_HOL_Oplus__class_Oplus @ SV860 @ ( c_HOL_Oplus__class_Oplus @ SV524 @ SV1099 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(3060,plain,
! [SV1100: $i,SV861: $i,SV525: $i,SV124: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV124 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV861 @ SV124 ) @ SV1100 @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ SV525 @ ( c_HOL_Oplus__class_Oplus @ SV861 @ SV1100 @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(3061,plain,
! [SV1101: $i,SV862: $i,SV526: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV526 @ ( c_HOL_Oplus__class_Oplus @ SV862 @ SV1101 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV862 @ SV125 ) @ SV1101 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2722]) ).
thf(3062,plain,
! [SV1102: $i,SV863: $i,SV527: $i,SV126: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV863 @ SV126 ) @ SV1102 @ SV126 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV1102 @ SV126 ) @ SV863 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(3063,plain,
! [SV1103: $i,SV864: $i,SV528: $i,SV127: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SV1103 @ SV127 ) @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ SV864 @ ( c_HOL_Oplus__class_Oplus @ SV528 @ SV1103 @ SV127 ) @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(3064,plain,
! [SV1104: $i,SV865: $i,SV529: $i,SV128: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV529 @ SV865 @ SV128 ) @ SV1104 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ SV529 @ ( c_HOL_Oplus__class_Oplus @ SV865 @ SV1104 @ SV128 ) @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(3065,plain,
! [SV866: $i,SV530: $i,SV129: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV129 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV530 @ ( c_HOL_Ouminus__class_Ouminus @ SV866 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV530 @ SV866 @ ( tc_Polynomial_Opoly @ SV129 ) ) @ ( tc_Polynomial_Opoly @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(3066,plain,
! [SV867: $i,SV531: $i,SV130: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV130 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV531 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ SV867 @ ( tc_Polynomial_Opoly @ SV130 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV531 @ SV867 @ ( tc_Polynomial_Opoly @ SV130 ) ) @ ( tc_Polynomial_Opoly @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(3067,plain,
! [SV1105: $i,SV868: $i,SV532: $i,SV131: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV131 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV868 @ SV131 ) @ SV1105 @ SV131 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ ( c_Divides_Odiv__class_Omod @ SV868 @ SV1105 @ SV131 ) @ SV131 ) @ SV1105 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(3068,plain,
! [SV1106: $i,SV869: $i,SV533: $i,SV132: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV132 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV869 @ SV132 ) @ SV1106 @ SV132 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV533 @ SV1106 @ SV132 ) @ SV869 @ SV132 ) @ SV1106 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(3069,plain,
! [SV1212: $i,SV1107: $i,SV870: $i,SV534: $i,SV133: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SV1107 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SV1212 @ SV1107 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3070,plain,
! [SV1213: $i,SV1108: $i,SV871: $i,SV535: $i,SV134: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV134 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV535 @ SV871 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ SV1213 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SV1213 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ SV1213 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SV1213 @ SV134 ) @ SV134 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3071,plain,
! [SV1214: $i,SV1109: $i,SV872: $i,SV536: $i,SV135: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV536 @ SV872 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1109 @ SV872 @ SV135 ) @ SV1214 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV536 @ SV1109 @ SV135 ) @ SV872 @ SV135 ) @ SV1214 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3072,plain,
! [SV1110: $i,SV873: $i,SV541: $i,SV140: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV140 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV541 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SV1110 @ SV140 ) @ SV140 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV873 @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1110 @ SV140 ) @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(3073,plain,
! [SV1111: $i,SV874: $i,SV542: $i,SV141: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV141 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV542 @ ( c_HOL_Ominus__class_Ominus @ SV874 @ SV1111 @ SV141 ) @ SV141 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV874 @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV1111 @ SV141 ) @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(3074,plain,
! [SV1112: $i,SV875: $i,SV543: $i,SV142: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV142 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV543 @ SV875 @ SV142 ) @ SV1112 @ SV142 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV543 @ SV1112 @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV875 @ SV1112 @ SV142 ) @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(3075,plain,
! [SV1113: $i,SV876: $i,SV544: $i,SV143: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV143 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV544 @ SV876 @ SV143 ) @ SV1113 @ SV143 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV544 @ SV1113 @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV876 @ SV1113 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(3076,plain,
! [SV1215: $i,SV1114: $i,SV877: $i,SV545: $i,SV144: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV144 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV877 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SV1114 @ SV1215 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV545 @ SV1114 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SV877 @ SV1215 @ SV144 ) @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3077,plain,
! [SV1115: $i,SV878: $i,SV546: $i,SV145: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV145 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SV878 @ SV145 ) @ SV1115 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SV1115 @ SV145 ) @ SV878 @ SV145 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV878 @ SV546 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(3078,plain,
! [SV879: $i,SV547: $i,SV146: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV146 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV547 @ SV879 @ SV146 ) @ SV146 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV547 @ SV146 ) @ SV879 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(3079,plain,
! [SV1116: $i,SV880: $i,SV548: $i,SV147: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV147 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ SV880 @ SV147 ) @ SV1116 @ SV147 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ ( c_Divides_Odiv__class_Omod @ SV880 @ SV1116 @ SV147 ) @ SV147 ) @ SV1116 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(3080,plain,
! [SV1117: $i,SV881: $i,SV549: $i,SV148: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV148 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV549 @ SV881 @ SV148 ) @ SV1117 @ SV148 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV549 @ SV1117 @ SV148 ) @ SV881 @ SV148 ) @ SV1117 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(3081,plain,
! [SV1216: $i,SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ! [SY2836: $i,SY2837: $i,SY2838: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SY2836 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2837 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2838 @ SV1118 @ SV1216 @ SY2836 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SY2838 @ SY2837 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3082,plain,
! [SV883: $i,SV551: $i,SV150: $i] :
( ( ( class_Divides_Osemiring__div @ SV150 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV551 @ ( c_Divides_Odiv__class_Odiv @ SV883 @ SV551 @ SV150 ) @ SV150 )
= SV883 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV551 @ SV883 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(3083,plain,
! [SV884: $i,SV552: $i,SV151: $i] :
( ( ( class_Divides_Osemiring__div @ SV151 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV552 @ SV884 @ SV151 ) @ SV884 @ SV151 )
= SV552 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV884 @ SV552 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(3084,plain,
! [SV885: $i,SV553: $i,SV152: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV152 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV553 @ ( c_HOL_Ouminus__class_Ouminus @ SV885 @ SV152 ) @ SV152 )
= ( c_HOL_Oplus__class_Oplus @ SV553 @ SV885 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3085,plain,
! [SV1119: $i,SV886: $i,SV554: $i,SV153: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV153 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV554 @ ( c_HOL_Otimes__class_Otimes @ SV886 @ SV1119 @ SV153 ) @ SV153 ) @ SV886 @ SV153 )
= ( c_Divides_Odiv__class_Omod @ SV554 @ SV886 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(3086,plain,
! [SV1120: $i,SV887: $i,SV555: $i,SV154: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV154 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV887 @ SV1120 @ SV154 ) @ SV154 ) @ SV1120 @ SV154 )
= ( c_Divides_Odiv__class_Omod @ SV555 @ SV1120 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2751]) ).
thf(3087,plain,
! [SV1121: $i,SV888: $i,SV556: $i,SV155: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV155 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
| ( SV1121
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV1121 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SV1121 @ SV155 ) @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2752]) ).
thf(3088,plain,
! [SV1122: $i,SV889: $i,SV557: $i,SV156: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV156 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
| ( SV1122
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV889 @ SV156 ) @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(3089,plain,
! [SV563: $i,SV162: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV162 ) )
= $true )
| ( ( SV563
= ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(3090,plain,
! [SV890: $i,SV568: $i,SV167: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV167 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV568 @ SV890 @ SV167 ) @ SV890 @ SV167 )
= SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(3091,plain,
! [SV891: $i,SV575: $i,SV174: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV174 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV575 @ SV891 @ SV174 ) @ SV174 )
= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV575 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(3092,plain,
! [SV1217: $i,SV1123: $i,SV892: $i,SV576: $i,SV175: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV892 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1123 @ SV1217 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV1123 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV892 @ SV1217 @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3093,plain,
! [SV893: $i,SV577: $i,SV176: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV176 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV577 @ SV893 @ SV176 )
= ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Ouminus__class_Ouminus @ SV893 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(3094,plain,
! [SV894: $i,SV578: $i,SV177: $i] :
( ( ( class_Int_Onumber__ring @ SV177 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV578 @ SV894 @ SV177 )
= ( c_HOL_Oplus__class_Oplus @ SV578 @ ( c_HOL_Ouminus__class_Ouminus @ SV894 @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(3095,plain,
! [SV895: $i,SV579: $i,SV178: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV178 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV579 @ SV895 @ SV178 )
= ( c_HOL_Oplus__class_Oplus @ SV579 @ ( c_HOL_Ouminus__class_Ouminus @ SV895 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(3096,plain,
! [SV896: $i,SV580: $i,SV179: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV179 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV580 @ SV896 @ SV179 )
= ( c_HOL_Oplus__class_Oplus @ SV580 @ ( c_HOL_Ouminus__class_Ouminus @ SV896 @ SV179 ) @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(3097,plain,
! [SV1124: $i,SV897: $i,SV581: $i,SV180: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV180 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV581 @ SV897 @ SV180 ) @ SV1124 @ SV180 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV581 @ SV1124 @ SV180 ) @ ( c_Divides_Odiv__class_Omod @ SV897 @ SV1124 @ SV180 ) @ SV180 ) @ SV1124 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(3098,plain,
! [SV898: $i,SV584: $i,SV183: $i] :
( ( ( class_Divides_Osemiring__div @ SV183 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV584 @ SV898 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV898 @ SV584 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(3099,plain,
! [SV1125: $i,SV899: $i,SV586: $i,SV185: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV185 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV586 @ SV899 @ SV185 ) @ SV1125 @ SV185 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV586 @ SV1125 @ SV185 ) @ SV899 @ SV185 ) @ SV1125 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3100,plain,
! [SV1126: $i,SV900: $i,SV587: $i,SV186: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV186 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SV900 @ SV186 ) @ SV1126 @ SV186 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ ( c_Divides_Odiv__class_Omod @ SV900 @ SV1126 @ SV186 ) @ SV186 ) @ SV1126 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3101,plain,
! [SV1127: $i,SV901: $i,SV588: $i,SV187: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV187 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV588 @ ( c_Polynomial_Osmult @ SV901 @ SV1127 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SV588 @ SV1127 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
| ( SV901
= ( c_HOL_Ozero__class_Ozero @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(3102,plain,
! [SV902: $i,SV591: $i,SV190: $i] :
( ( ( class_Divides_Osemiring__div @ SV190 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV591 @ SV902 @ SV190 ) @ SV902 @ SV190 )
= ( c_Divides_Odiv__class_Omod @ SV591 @ SV902 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(3103,plain,
! [SV191: $i,SV592: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ SV592 @ SV592 @ SV191 )
= ( c_HOL_Oone__class_Oone @ SV191 ) )
= $true )
| ( ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(3104,plain,
! [SV903: $i,SV593: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV192 )
= $false )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ SV593 @ SV192 ) @ SV903 @ SV192 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV593 @ SV903 @ SV192 ) @ ( tc_Polynomial_Opoly @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3105,plain,
! [SV1218: $i,SV1128: $i,SV904: $i,SV594: $i,SV193: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV193 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV594 @ SV904 @ SV193 ) @ SV1128 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1218 @ SV904 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV594 @ SV1218 @ SV193 ) @ SV904 @ SV193 ) @ SV1128 @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3106,plain,
! [SV1129: $i,SV905: $i,SV596: $i,SV195: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV195 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV596 @ SV905 @ SV195 ) @ SV905 @ SV195 ) @ ( c_Divides_Odiv__class_Omod @ SV596 @ SV905 @ SV195 ) @ SV195 ) @ SV1129 @ SV195 )
= ( c_HOL_Oplus__class_Oplus @ SV596 @ SV1129 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(3107,plain,
! [SV1130: $i,SV906: $i,SV597: $i,SV196: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV196 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV597 @ ( c_Divides_Odiv__class_Odiv @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ ( c_Divides_Odiv__class_Omod @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ SV1130 @ SV196 )
= ( c_HOL_Oplus__class_Oplus @ SV906 @ SV1130 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(3108,plain,
! [SV907: $i,SV601: $i,SV200: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV200 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV907 @ SV200 )
= ( c_HOL_Oplus__class_Oplus @ SV907 @ SV601 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3109,plain,
! [SV908: $i,SV602: $i,SV201: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV602 @ SV908 @ SV201 )
= ( c_HOL_Oplus__class_Oplus @ SV908 @ SV602 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3110,plain,
! [SV909: $i,SV603: $i,SV202: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV202 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV603 @ SV909 @ SV202 )
= ( c_HOL_Oplus__class_Oplus @ SV909 @ SV603 @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(3111,plain,
! [SV910: $i,SV604: $i,SV203: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV203 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV604 @ SV203 ) @ SV910 @ SV203 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ SV203 ) @ SV203 ) @ SV910 @ SV203 ) @ ( c_Power_Opower__class_Opower @ SV604 @ SV910 @ SV203 ) @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(3112,plain,
! [SV911: $i,SV605: $i,SV204: $i] :
( ( ( class_Divides_Osemiring__div @ SV204 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ SV605 @ SV911 @ SV204 ) @ SV911 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(3113,plain,
! [SV1131: $i,SV912: $i,SV606: $i,SV205: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV205 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV606 @ SV912 @ SV205 ) @ SV1131 @ SV205 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV606 @ SV1131 @ SV205 ) @ ( c_Divides_Odiv__class_Omod @ SV912 @ SV1131 @ SV205 ) @ SV205 ) @ SV1131 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(3114,plain,
! [SV913: $i,SV607: $i,SV206: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV206 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV607 @ SV913 @ SV206 ) @ SV607 @ SV206 )
= ( c_HOL_Otimes__class_Otimes @ SV607 @ ( c_Power_Opower__class_Opower @ SV607 @ SV913 @ SV206 ) @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(3115,plain,
! [SV1132: $i,SV914: $i,SV608: $i,SV207: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV207 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV608 @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV1132 @ SV207 ) @ SV207 ) @ SV1132 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SV914 @ ( c_Divides_Odiv__class_Odiv @ SV608 @ SV1132 @ SV207 ) @ SV207 ) )
| ( SV1132
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(3116,plain,
! [SV1133: $i,SV915: $i,SV609: $i,SV208: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV208 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV609 @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1133 @ SV208 ) @ SV208 ) @ SV915 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SV1133 @ ( c_Divides_Odiv__class_Odiv @ SV609 @ SV915 @ SV208 ) @ SV208 ) )
| ( SV915
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3117,plain,
! [SV1219: $i,SV1134: $i,SV916: $i,SV611: $i,SV210: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV210 )
| ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SV1134 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SV1134 @ SV1219 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3118,plain,
! [SV1135: $i,SV917: $i,SV612: $i,SV211: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV211 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ SV612 @ SV917 @ SV211 ) @ SV1135 @ SV211 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV612 @ SV1135 @ SV211 ) @ ( c_Polynomial_Osmult @ SV917 @ SV1135 @ SV211 ) @ ( tc_Polynomial_Opoly @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(3119,plain,
! [SV1136: $i,SV918: $i,SV613: $i,SV212: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV212 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SV918 @ SV212 ) @ SV1136 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SV1136 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV918 @ SV1136 @ SV212 ) @ SV212 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV918 @ SV613 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(3120,plain,
! [SV919: $i,SV628: $i,SV227: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV227 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ SV628 @ SV227 ) @ SV919 @ SV227 ) @ SV227 )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV628 @ SV919 @ SV227 ) @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(3121,plain,
! [SV920: $i,SV629: $i,SV228: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV228 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV629 @ SV920 @ SV228 ) @ SV920 @ SV228 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV629 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 ) @ SV920 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3122,plain,
! [SV921: $i,SV630: $i,SV229: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV229 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV630 @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV630 @ SV229 ) @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV921 @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV229 ) @ SV630 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2826]) ).
thf(3123,plain,
! [SV922: $i,SV632: $i,SV231: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV231 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV632 @ SV231 ) @ ( c_HOL_Oplus__class_Oplus @ SV922 @ SV632 @ SV231 ) @ SV231 )
= SV922 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(3124,plain,
! [SV923: $i,SV633: $i,SV232: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV232 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV633 @ SV232 ) @ ( c_HOL_Oplus__class_Oplus @ SV633 @ SV923 @ SV232 ) @ SV232 )
= SV923 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(3125,plain,
! [SV924: $i,SV634: $i,SV233: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV233 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV634 @ ( c_HOL_Ouminus__class_Ouminus @ SV924 @ ( tc_Polynomial_Opoly @ SV233 ) ) @ ( tc_Polynomial_Opoly @ SV233 ) )
= ( c_Divides_Odiv__class_Omod @ SV634 @ SV924 @ ( tc_Polynomial_Opoly @ SV233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(3126,plain,
! [SV925: $i,SV635: $i,SV235: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV235 )
= $false )
| ( ( ( c_Polynomial_Opoly__gcd @ SV635 @ SV925 @ SV235 )
= ( c_Polynomial_Opoly__gcd @ SV925 @ SV635 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3127,plain,
! [SV926: $i,SV636: $i,SV236: $i] :
( ( ( class_Ring__and__Field_Oring @ SV236 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ SV636 @ SV236 ) @ SV926 @ SV236 )
= ( c_HOL_Otimes__class_Otimes @ SV636 @ ( c_HOL_Ouminus__class_Ouminus @ SV926 @ SV236 ) @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(3128,plain,
! [SV927: $i,SV637: $i,SV240: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV240 )
= $false )
| ( ( ( ( c_Polynomial_Opoly__gcd @ SV637 @ SV927 @ SV240 )
= ( c_Polynomial_Opoly__gcd @ SV927 @ ( c_Divides_Odiv__class_Omod @ SV637 @ SV927 @ ( tc_Polynomial_Opoly @ SV240 ) ) @ SV240 ) )
| ( SV927
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3129,plain,
! [SV928: $i,SV640: $i,SV243: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV243 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ SV640 @ SV243 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV928 @ SV243 ) @ SV243 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SV928 @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(3130,plain,
! [SV1137: $i,SV929: $i,SV641: $i,SV244: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV244 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV641 @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SV1137 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ ( tc_Polynomial_Opoly @ SV244 ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ SV641 @ SV929 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ SV1137 @ ( tc_Polynomial_Opoly @ SV244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(3131,plain,
! [SV930: $i,SV642: $i,SV245: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV245 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SV930 @ SV245 ) @ SV245 ) @ SV245 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV642 @ SV245 ) @ ( c_HOL_Oabs__class_Oabs @ SV930 @ SV245 ) @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(3132,plain,
! [SV931: $i,SV643: $i,SV246: $i] :
( ( ( class_Divides_Osemiring__div @ SV246 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV643 @ SV931 @ SV246 ) @ SV643 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(3133,plain,
! [SV932: $i,SV644: $i,SV247: $i] :
( ( ( class_Divides_Osemiring__div @ SV247 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV644 @ SV932 @ SV247 ) @ SV932 @ SV247 )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(3134,plain,
! [SV933: $i,SV645: $i,SV248: $i] :
( ( ( class_Divides_Osemiring__div @ SV248 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV645 @ SV933 @ SV248 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV645 @ SV933 @ SV248 ) @ SV933 @ SV248 ) @ SV248 )
= SV645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(3135,plain,
! [SV934: $i,SV646: $i,SV250: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV250 )
= $false )
| ( ( ( SV646
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) )
| ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV646 @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV646 @ SV934 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(3136,plain,
! [SV935: $i,SV647: $i,SV251: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV251 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV647 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ SV935 @ ( tc_Polynomial_Opoly @ SV251 ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ SV647 @ SV935 @ ( tc_Polynomial_Opoly @ SV251 ) ) @ ( tc_Polynomial_Opoly @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3137,plain,
! [SV1138: $i,SV936: $i,SV648: $i,SV252: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV252 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV936 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV1138 @ SV252 ) @ SV252 )
= ( c_HOL_Otimes__class_Otimes @ SV648 @ ( c_Divides_Odiv__class_Omod @ SV936 @ SV1138 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3138,plain,
! [SV1139: $i,SV937: $i,SV649: $i,SV253: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV253 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV649 @ SV937 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV1139 @ SV937 @ SV253 ) @ SV253 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV649 @ SV1139 @ SV253 ) @ SV937 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3139,plain,
! [SV938: $i,SV650: $i,SV254: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV254 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV650 @ SV938 @ SV254 ) @ SV254 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV938 @ SV254 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV650 @ SV254 ) @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(3140,plain,
! [SV939: $i,SV651: $i,SV255: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV255 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV939 @ SV255 ) @ SV255 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ SV651 @ SV255 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV939 @ SV255 ) @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(3141,plain,
! [SV1220: $i,SV1140: $i,SV940: $i,SV652: $i,SV256: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3142,plain,
! [SV1141: $i,SV941: $i,SV655: $i,SV259: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV259 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SV941 @ SV259 ) @ SV1141 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SV1141 @ SV259 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1141 @ SV941 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(3143,plain,
! [SV1142: $i,SV942: $i,SV656: $i,SV260: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV260 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(3144,plain,
! [SV1143: $i,SV943: $i,SV657: $i,SV261: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV261 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3145,plain,
! [SV944: $i,SV658: $i,SV262: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV262 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV658 @ SV944 @ SV262 ) @ SV658 @ ( tc_Polynomial_Opoly @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3146,plain,
! [SV945: $i,SV659: $i,SV263: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV263 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Opoly__gcd @ SV659 @ SV945 @ SV263 ) @ SV945 @ ( tc_Polynomial_Opoly @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(3147,plain,
! [SV946: $i,SV660: $i,SV264: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV264 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV660 @ SV264 ) @ SV946 @ ( tc_Polynomial_Opoly @ SV264 ) )
| ( SV946
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3148,plain,
! [SV947: $i,SV661: $i,SV265: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV265 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ ( c_HOL_Oabs__class_Oabs @ SV947 @ SV265 ) @ SV265 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ SV947 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3149,plain,
! [SV948: $i,SV662: $i,SV266: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV266 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ SV948 @ SV266 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ ( c_HOL_Oabs__class_Oabs @ SV948 @ SV266 ) @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(3150,plain,
! [SV949: $i,SV663: $i,SV267: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV267 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV663 @ SV267 ) @ SV949 @ SV267 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV663 @ SV949 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(3151,plain,
! [SV950: $i,SV664: $i,SV268: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV268 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV664 @ SV950 @ SV268 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV664 @ SV268 ) @ SV950 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3152,plain,
! [SV1144: $i,SV951: $i,SV666: $i,SV270: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV270 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV666 @ ( c_HOL_Ominus__class_Ominus @ SV951 @ SV1144 @ ( tc_Polynomial_Opoly @ SV270 ) ) @ SV270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV666 @ SV951 @ SV270 ) @ ( c_Polynomial_Osmult @ SV666 @ SV1144 @ SV270 ) @ ( tc_Polynomial_Opoly @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(3153,plain,
! [SV1145: $i,SV952: $i,SV667: $i,SV271: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV271 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SV952 @ ( tc_Polynomial_Opoly @ SV271 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SV1145 @ SV952 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(3154,plain,
! [SV1146: $i,SV953: $i,SV668: $i,SV272: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV272 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SV953 @ ( tc_Polynomial_Opoly @ SV272 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SV953 @ SV1146 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(3155,plain,
! [SV1147: $i,SV954: $i,SV669: $i,SV273: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV273 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV954 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1147 @ SV954 @ SV273 ) @ SV273 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SV1147 @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(3156,plain,
! [SV1148: $i,SV955: $i,SV670: $i,SV274: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV274 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV955 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV1148 @ SV274 ) @ SV274 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV955 @ SV1148 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(3157,plain,
! [SV956: $i,SV671: $i,SV275: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV275 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV671 @ ( c_HOL_Ouminus__class_Ouminus @ SV956 @ ( tc_Polynomial_Opoly @ SV275 ) ) @ SV275 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ SV671 @ SV956 @ SV275 ) @ ( tc_Polynomial_Opoly @ SV275 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(3158,plain,
! [SV276: $i,SV672: $i] :
( ( ( SV672
= ( c_HOL_Ozero__class_Ozero @ SV276 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV672 @ SV276 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3159,plain,
! [SV957: $i,SV673: $i,SV277: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV673 @ SV277 ) @ SV957 @ SV277 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV673 @ SV957 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(3160,plain,
! [SV958: $i,SV674: $i,SV278: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV674 @ SV958 @ SV278 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV674 @ SV278 ) @ SV958 @ SV278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3161,plain,
! [SV959: $i,SV675: $i,SV279: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ ( c_HOL_Ouminus__class_Ouminus @ SV959 @ SV279 ) @ SV279 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ SV959 @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(3162,plain,
! [SV960: $i,SV676: $i,SV280: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ SV960 @ SV280 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ ( c_HOL_Ouminus__class_Ouminus @ SV960 @ SV280 ) @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(3163,plain,
! [SV1149: $i,SV961: $i,SV677: $i,SV281: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV281 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3164,plain,
! [SV1150: $i,SV962: $i,SV678: $i,SV282: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV282 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3165,plain,
! [SV1151: $i,SV963: $i,SV679: $i,SV283: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3166,plain,
! [SV1152: $i,SV964: $i,SV681: $i,SV285: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV285 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ SV681 @ SV964 @ SV285 ) @ SV1152 @ ( tc_Polynomial_Opoly @ SV285 ) )
= ( c_Polynomial_Osmult @ SV681 @ ( c_Divides_Odiv__class_Omod @ SV964 @ SV1152 @ ( tc_Polynomial_Opoly @ SV285 ) ) @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(3167,plain,
! [SV1153: $i,SV965: $i,SV682: $i,SV286: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV286 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SV1153 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3168,plain,
! [SV1154: $i,SV966: $i,SV683: $i,SV287: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV287 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
| ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(3169,plain,
! [SV1155: $i,SV967: $i,SV684: $i,SV288: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV288 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SV1155 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SV1155
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3170,plain,
! [SV1156: $i,SV968: $i,SV685: $i,SV289: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV289 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SV1156 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SV1156 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(3171,plain,
! [SV1157: $i,SV969: $i,SV686: $i,SV290: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV290 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
| ( SV1157
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1157 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3172,plain,
! [SV1158: $i,SV970: $i,SV687: $i,SV291: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV291 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3173,plain,
! [SV971: $i,SV688: $i,SV292: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV292 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV688 @ SV971 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV971 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(3174,plain,
! [SV1159: $i,SV972: $i,SV689: $i,SV293: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SV972 @ SV293 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1159 @ SV689 @ SV293 ) @ SV972 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(3175,plain,
! [SV1160: $i,SV973: $i,SV690: $i,SV294: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SV973 @ SV294 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV1160 @ SV294 ) @ SV973 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3176,plain,
! [SV1161: $i,SV974: $i,SV691: $i,SV295: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV974 @ SV1161 @ SV295 ) @ SV295 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SV974 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3177,plain,
! [SV1162: $i,SV975: $i,SV692: $i,SV296: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SV975 @ SV1162 @ SV296 ) @ SV296 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SV1162 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(3178,plain,
! [SV1163: $i,SV976: $i,SV694: $i,SV298: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(3179,plain,
! [SV1221: $i,SV1164: $i,SV977: $i,SV697: $i,SV301: $i] :
( ( ! [SY2839: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV301 )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SV1221 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SY2839 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SV1221 @ SY2839 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3180,plain,
! [SV1165: $i,SV978: $i,SV698: $i,SV302: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3181,plain,
! [SV1166: $i,SV979: $i,SV699: $i,SV303: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV303 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV699 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SV1166 @ ( tc_Polynomial_Opoly @ SV303 ) ) @ SV303 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV699 @ SV979 @ SV303 ) @ ( c_Polynomial_Osmult @ SV699 @ SV1166 @ SV303 ) @ ( tc_Polynomial_Opoly @ SV303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3182,plain,
! [SV1167: $i,SV980: $i,SV700: $i,SV304: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV304 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3183,plain,
! [SV1168: $i,SV981: $i,SV701: $i,SV305: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV305 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3184,plain,
! [SV1169: $i,SV982: $i,SV702: $i,SV306: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV306 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2898]) ).
thf(3185,plain,
! [SV1170: $i,SV983: $i,SV703: $i,SV307: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV307 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(3186,plain,
! [SV1171: $i,SV984: $i,SV704: $i,SV308: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV308 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ SV704 @ SV984 @ SV308 ) @ SV1171 @ ( tc_Polynomial_Opoly @ SV308 ) )
= ( c_Polynomial_Osmult @ SV704 @ ( c_Divides_Odiv__class_Odiv @ SV984 @ SV1171 @ ( tc_Polynomial_Opoly @ SV308 ) ) @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(3187,plain,
! [SV985: $i,SV705: $i,SV309: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV309 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV705 @ ( c_HOL_Otimes__class_Otimes @ SV985 @ SV705 @ SV309 ) @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3188,plain,
! [SV986: $i,SV706: $i,SV310: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV310 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV706 @ ( c_HOL_Otimes__class_Otimes @ SV706 @ SV986 @ SV310 ) @ SV310 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3189,plain,
! [SV987: $i,SV707: $i,SV311: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV311 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV707 @ ( c_HOL_Otimes__class_Otimes @ SV707 @ SV987 @ SV311 ) @ SV311 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(3190,plain,
! [SV1172: $i,SV988: $i,SV708: $i,SV312: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1172 @ SV708 @ SV312 ) @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(3191,plain,
! [SV1173: $i,SV989: $i,SV709: $i,SV313: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SV989 @ SV1173 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SV1173 @ ( tc_Polynomial_Opoly @ SV313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(3192,plain,
! [SV1174: $i,SV990: $i,SV710: $i,SV314: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SV990 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SV1174 @ SV990 @ SV314 ) @ SV314 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SV1174 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2906]) ).
thf(3193,plain,
! [SV1175: $i,SV991: $i,SV711: $i,SV315: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV315 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV711 @ ( c_Polynomial_Osmult @ SV991 @ SV1175 @ SV315 ) @ ( tc_Polynomial_Opoly @ SV315 ) )
= ( c_Polynomial_Osmult @ SV991 @ ( c_HOL_Otimes__class_Otimes @ SV711 @ SV1175 @ ( tc_Polynomial_Opoly @ SV315 ) ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(3194,plain,
! [SV1176: $i,SV992: $i,SV712: $i,SV316: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV316 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ SV712 @ SV992 @ SV316 ) @ SV1176 @ ( tc_Polynomial_Opoly @ SV316 ) )
= ( c_Polynomial_Osmult @ SV712 @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1176 @ ( tc_Polynomial_Opoly @ SV316 ) ) @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2908]) ).
thf(3195,plain,
! [SV1177: $i,SV993: $i,SV713: $i,SV317: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV317 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV713 @ ( c_Polynomial_Osmult @ SV993 @ SV1177 @ SV317 ) @ SV317 )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ SV713 @ SV993 @ SV317 ) @ SV1177 @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3196,plain,
! [SV1178: $i,SV994: $i,SV714: $i,SV353: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV353 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV353 )
| ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
| ( SV994 = SV1178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3197,plain,
! [SV1179: $i,SV995: $i,SV715: $i,SV354: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SV995 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SV715 @ SV1179 @ SV354 ) )
| ( SV995 = SV1179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(3198,plain,
! [SV996: $i,SV716: $i,SV355: $i] :
( ( ( class_Divides_Osemiring__div @ SV355 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV716 @ SV996 @ SV355 )
!= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV996 @ SV716 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3199,plain,
! [SV997: $i,SV717: $i,SV356: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SV997 @ SV356 )
!= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV997
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(3200,plain,
! [SV998: $i,SV718: $i,SV357: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SV998 @ SV357 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV998
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(3201,plain,
! [SV999: $i,SV719: $i,SV358: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV358 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV719 @ SV999 @ SV358 )
!= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
| ( SV719
= ( c_HOL_Ouminus__class_Ouminus @ SV999 @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(3202,plain,
! [SV1222: $i,SV1180: $i,SV1000: $i,SV720: $i,SV359: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV359 )
| ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
| ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3203,plain,
! [SV1223: $i,SV1181: $i,SV1001: $i,SV721: $i,SV360: $i] :
( ( ~ ( class_HOL_Ozero @ SV360 )
| ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
!= ( c_Polynomial_OpCons @ SV1181 @ SV1223 @ SV360 ) )
| ( SV1001 = SV1223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3204,plain,
! [SV361: $i,SV722: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV722 @ SV722 @ SV361 )
!= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
= $true )
| ( ( SV722
= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(3205,plain,
! [SV1002: $i,SV723: $i,SV362: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV362 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV723 @ SV362 )
!= ( c_HOL_Oabs__class_Oabs @ SV1002 @ SV362 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV723 @ SV1002 @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3206,plain,
! [SV1003: $i,SV724: $i,SV363: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV363 )
= $false )
| ( ( ( ( c_Polynomial_Opoly @ SV724 @ ( c_HOL_Ouminus__class_Ouminus @ SV1003 @ SV363 ) @ SV363 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV1003 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SV724 @ ( tc_Polynomial_Opoly @ SV363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3207,plain,
! [SV725: $i,SV364: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV364 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV725 @ SV364 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= SV725 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3208,plain,
! [SV1224: $i,SV1182: $i,SV1004: $i,SV726: $i,SV365: $i] :
( ( ! [SY2840: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV365 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1224 @ SV1004 @ SV365 ) @ SY2840 @ SV365 ) )
| ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1224 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SY2840 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3209,plain,
! [SV1225: $i,SV1183: $i,SV1005: $i,SV727: $i,SV366: $i] :
( ( ! [SY2841: $i] :
( ~ ( class_Divides_Osemiring__div @ SV366 )
| ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SY2841 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2841 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3210,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3211,plain,
! [SV1184: $i,SV1007: $i,SV729: $i,SV368: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 ) )
= $true )
| ( ( ( ( c_Polynomial_Osmult @ SV729 @ SV1007 @ SV368 )
!= ( c_Polynomial_OpCons @ SV1184 @ SV1007 @ SV368 ) )
| ( SV1007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3212,plain,
! [SV1185: $i,SV1008: $i,SV730: $i,SV369: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SV1008 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SV1185 @ SV1008 @ SV369 ) )
| ( SV730 = SV1185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3213,plain,
! [SV1009: $i,SV731: $i,SV370: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV370 )
= $false )
| ( ( ( ( c_Polynomial_Opoly__gcd @ SV731 @ SV1009 @ SV370 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
| ( SV1009
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3214,plain,
! [SV1010: $i,SV732: $i,SV371: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV371 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV371 )
| ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SV732 = SV1010 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3215,plain,
! [SV1011: $i,SV733: $i,SV372: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV733 @ SV1011 @ SV372 )
!= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
| ( SV733
= ( c_HOL_Ozero__class_Ozero @ SV372 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3216,plain,
! [SV1012: $i,SV734: $i,SV373: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV373 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV734 @ SV734 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1012 @ SV373 ) @ SV373 )
!= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
| ( SV1012
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3217,plain,
! [SV1186: $i,SV1013: $i,SV735: $i,SV374: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SV1013 @ SV374 ) @ ( c_Polynomial_OpCons @ SV1186 @ SV1013 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
| ( SV1013
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(3218,plain,
! [SV1014: $i,SV736: $i,SV376: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SV1014 @ SV376 )
!= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV1014
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(3219,plain,
! [SV1226: $i,SV1187: $i,SV1015: $i,SV737: $i,SV377: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3220,plain,
! [SV1016: $i,SV738: $i,SV378: $i] :
( ( ( class_HOL_Ozero @ SV378 )
= $false )
| ( ( ( ( c_Polynomial_OpCons @ SV738 @ SV1016 @ SV378 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
| ( SV1016
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(3221,plain,
! [SV1188: $i,SV1017: $i,SV739: $i,SV379: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1017 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1188 @ SV379 ) )
| ( SV1017 = SV1188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(3222,plain,
! [SV380: $i,SV740: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV740 @ SV380 )
!= SV740 )
= $true )
| ( ( SV740
= ( c_HOL_Ozero__class_Ozero @ SV380 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__ab__group__add @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3223,plain,
! [SV1018: $i,SV741: $i,SV381: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV381 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
!= ( c_HOL_Otimes__class_Otimes @ SV1018 @ SV1018 @ SV381 ) )
| ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SV1018 @ SV381 ) )
| ( SV741 = SV1018 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3224,plain,
! [SV1019: $i,SV742: $i,SV382: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV382 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV742 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SV1019 @ SV1019 @ SV382 ) @ SV382 )
!= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
| ( SV742
= ( c_HOL_Ozero__class_Ozero @ SV382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3225,plain,
! [SV1227: $i,SV1189: $i,SV1020: $i,SV743: $i,SV383: $i] :
( ( ! [SY2842: $i] :
( ~ ( class_Divides_Oring__div @ SV383 )
| ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SY2842 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2842 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3226,plain,
! [SV1228: $i,SV1190: $i,SV1021: $i,SV744: $i,SV384: $i] :
( ( ~ ( class_HOL_Ozero @ SV384 )
| ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
!= ( c_Polynomial_OpCons @ SV1190 @ SV1228 @ SV384 ) )
| ( SV744 = SV1190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3227,plain,
! [SV1022: $i,SV745: $i,SV385: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV385 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1022 @ SV385 )
!= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV745 @ SV385 )
= SV1022 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3228,plain,
! [SV386: $i,SV746: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV746 @ SV386 )
!= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
= $true )
| ( ( SV746
= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2943]) ).
thf(3229,plain,
! [SV1023: $i,SV747: $i,SV387: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV387 )
= $false )
| ( ( ( ( c_Polynomial_Osmult @ SV747 @ SV1023 @ SV387 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV1023
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3230,plain,
! [SV1191: $i,SV1024: $i,SV748: $i,SV388: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV388 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SV1024 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV388 ) )
| ( SV748 = SV1024 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2945]) ).
thf(3231,plain,
! [SV1025: $i,SV749: $i,SV389: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV749 @ SV1025 @ SV389 )
!= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
| ( SV749 = SV1025 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3232,plain,
! [SV1229: $i,SV1192: $i,SV1026: $i,SV750: $i,SV390: $i] :
( ( ! [SY2843: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV390 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1229 @ SV1026 @ SV390 ) @ SY2843 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SV1229 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SY2843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3233,plain,
! [SV1027: $i,SV751: $i,SV391: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV391 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV751 @ SV1027 @ SV391 )
!= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
| ( SV751 = SV1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3234,plain,
! [SV1230: $i,SV1193: $i,SV1028: $i,SV752: $i,SV392: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
| ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SV1193 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SV1230 @ SV1193 @ SV392 ) )
| ( SV1230
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3235,plain,
! [SV1231: $i,SV1194: $i,SV1029: $i,SV753: $i,SV393: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV393 )
| ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3236,plain,
! [SV1030: $i,SV754: $i,SV395: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV395 )
= $false )
| ( ( ( ( c_Polynomial_Opoly @ SV754 @ SV1030 @ SV395 )
!= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV1030 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SV754 @ ( tc_Polynomial_Opoly @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(3237,plain,
! [SV1031: $i,SV755: $i,SV396: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV396 )
= $false )
| ( ( ( ( c_Polynomial_Opoly__gcd @ SV755 @ SV1031 @ SV396 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
| ( SV755
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3238,plain,
! [SV1195: $i,SV1032: $i,SV756: $i,SV397: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV397 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV756 @ SV1032 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SV1195 @ SV1032 @ SV397 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ SV397 ) @ SV1032 @ SV397 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(3239,plain,
! [SV1232: $i,SV1196: $i,SV1033: $i,SV757: $i,SV398: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV398 )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1196 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1232 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SV1196 @ SV398 )
= SV1232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3240,plain,
! [SV399: $i,SV758: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV758 @ SV399 )
!= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
= $true )
| ( ( SV758
= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV399 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3241,plain,
! [SV1197: $i,SV1034: $i,SV759: $i,SV400: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV400 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SV1034 @ SV1197 @ SV400 ) @ SV400 )
!= SV1034 )
| ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SV1197 @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3242,plain,
! [SV1233: $i,SV1198: $i,SV1035: $i,SV760: $i,SV401: $i] :
( ( ! [SY2844: $i] :
( ~ ( class_Divides_Osemiring__div @ SV401 )
| ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SY2844 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2844 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3243,plain,
! [SV1199: $i,SV1036: $i,SV761: $i,SV402: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV402 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV1199 @ SV402 ) )
| ( SV1036 = SV1199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3244,plain,
! [SV1037: $i,SV762: $i,SV403: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV403 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV403 )
| ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
| ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3245,plain,
! [SV1038: $i,SV763: $i,SV404: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV404 )
= $false )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV763 @ SV404 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1038 @ SV404 ) )
| ( SV763 = SV1038 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3246,plain,
! [SV1039: $i,SV764: $i,SV405: $i] :
( ( ( class_HOL_Ozero @ SV405 )
= $false )
| ( ( ( ( c_Polynomial_OpCons @ SV764 @ SV1039 @ SV405 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
| ( SV764
= ( c_HOL_Ozero__class_Ozero @ SV405 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3247,plain,
! [SV1040: $i,SV765: $i,SV406: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV406 )
= $false )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV765 @ SV406 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1040 @ SV406 ) )
| ( SV765 = SV1040 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3248,plain,
! [SV1041: $i,SV766: $i,SV407: $i,SV1: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV1 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ SV407 @ SV766 @ SV1 ) @ SV1041 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV1041 @ ( c_Polynomial_Opoly @ SV766 @ SV1041 @ SV1 ) @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3249,plain,
! [SV1042: $i,SV767: $i,SV410: $i,SV4: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV4 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ SV410 @ SV767 @ SV4 ) @ SV1042 @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ SV410 @ ( c_Polynomial_Opoly @ SV767 @ SV1042 @ SV4 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3250,plain,
! [SV1043: $i,SV768: $i,SV411: $i,SV5: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV5 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV768 @ ( tc_Polynomial_Opoly @ SV5 ) ) @ SV1043 @ SV5 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ SV411 @ SV1043 @ SV5 ) @ ( c_Polynomial_Opoly @ SV768 @ SV1043 @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3251,plain,
! [SV1044: $i,SV769: $i,SV412: $i,SV6: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV6 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Oplus__class_Oplus @ SV412 @ SV769 @ ( tc_Polynomial_Opoly @ SV6 ) ) @ SV1044 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Opoly @ SV412 @ SV1044 @ SV6 ) @ ( c_Polynomial_Opoly @ SV769 @ SV1044 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3252,plain,
! [SV1045: $i,SV771: $i,SV414: $i,SV8: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV8 )
= $false )
| ( ( ( c_Polynomial_Opoly @ ( c_HOL_Ominus__class_Ominus @ SV414 @ SV771 @ ( tc_Polynomial_Opoly @ SV8 ) ) @ SV1045 @ SV8 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Opoly @ SV414 @ SV1045 @ SV8 ) @ ( c_Polynomial_Opoly @ SV771 @ SV1045 @ SV8 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3253,plain,
! [SV1200: $i,SV1046: $i,SV772: $i,SV415: $i,SV9: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV9 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SV415 @ SV772 @ SV9 ) @ ( c_Polynomial_OpCons @ SV1046 @ SV1200 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SV415 @ SV1046 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SV772 @ SV1200 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(3254,plain,
! [SV1201: $i,SV1047: $i,SV774: $i,SV417: $i,SV11: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SV417 @ SV774 @ SV11 ) @ ( c_Polynomial_OpCons @ SV1047 @ SV1201 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SV417 @ SV1047 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SV774 @ SV1201 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3255,plain,
! [SV1048: $i,SV775: $i,SV418: $i,SV12: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV12 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV418 @ ( c_Polynomial_OpCons @ SV775 @ SV1048 @ SV12 ) @ SV12 )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV775 @ SV12 ) @ ( c_Polynomial_Osmult @ SV418 @ SV1048 @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3256,plain,
! [SV14: $i,SV776: $i,SV419: $i] :
( ( ( ( c_Polynomial_Opoly @ SV419 @ SV776 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV776 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SV419 @ ( tc_Polynomial_Opoly @ SV14 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3257,plain,
! [SV15: $i,SV777: $i,SV420: $i] :
( ( ( ( c_Polynomial_Opoly @ SV420 @ ( c_HOL_Ouminus__class_Ouminus @ SV777 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV777 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SV420 @ ( tc_Polynomial_Opoly @ SV15 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3258,plain,
! [SV16: $i,SV778: $i,SV421: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV421 @ SV778 @ SV16 ) @ SV421 @ SV16 )
= SV778 )
= $true )
| ( ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV16 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3259,plain,
! [SV17: $i,SV779: $i,SV422: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV422 @ SV779 @ SV17 ) @ SV779 @ SV17 )
= SV422 )
= $true )
| ( ( SV779
= ( c_HOL_Ozero__class_Ozero @ SV17 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3260,plain,
! [SV1202: $i,SV1049: $i,SV780: $i,SV423: $i,SV18: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV780 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV1049 @ SV1202 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV1049 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV780 @ SV1202 @ SV18 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3261,plain,
! [SV1203: $i,SV1050: $i,SV781: $i,SV424: $i,SV19: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV424 @ SV781 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SV1203 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SV424 @ ( c_HOL_Otimes__class_Otimes @ SV781 @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SV1203 @ SV19 ) @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3262,plain,
! [SV1204: $i,SV1051: $i,SV782: $i,SV425: $i,SV20: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1204 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SV1051 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ SV1204 @ SV20 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3263,plain,
! [SV1234: $i,SV1205: $i,SV1052: $i,SV783: $i,SV426: $i,SV21: $i] :
( ( ! [SY2845: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SY2845 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3264,plain,
! [SV1235: $i,SV1206: $i,SV1053: $i,SV784: $i,SV427: $i,SV22: $i] :
( ( ! [SY2846: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SY2846 @ SV427 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3265,plain,
! [SV1207: $i,SV1054: $i,SV791: $i,SV434: $i,SV30: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV30 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3266,plain,
! [SV1055: $i,SV792: $i,SV435: $i,SV31: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV31 )
= $false )
| ( ( ( SV435 = SV792 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV792 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SV1055 @ SV435 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3267,plain,
! [SV1056: $i,SV797: $i,SV440: $i,SV36: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV36 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV440 @ ( c_HOL_Otimes__class_Otimes @ SV797 @ SV1056 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV797 @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ SV1056 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( c_Divides_Odiv__class_Omod @ SV440 @ SV797 @ ( tc_Polynomial_Opoly @ SV36 ) ) @ ( tc_Polynomial_Opoly @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3268,plain,
! [SV1057: $i,SV798: $i,SV442: $i,SV38: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV38 )
= $false )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SV798 @ SV1057 @ SV38 )
| ( SV798
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3269,plain,
! [SV1058: $i,SV799: $i,SV443: $i,SV39: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV39 )
= $false )
| ( ( ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SV799 @ SV443 @ SV1058 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2997]) ).
thf(3270,plain,
! [SV1059: $i,SV800: $i,SV444: $i,SV40: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV40 )
= $false )
| ( ( ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SV800 @ SV1059 @ SV444 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3271,plain,
! [SV1060: $i,SV801: $i,SV445: $i,SV41: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV41 )
= $false )
| ( ( ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV801 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SV1060 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3272,plain,
! [SV1061: $i,SV802: $i,SV446: $i,SV42: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV42 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV802 @ SV42 ) @ SV1061 @ SV42 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV446 @ SV1061 @ SV42 ) @ ( c_Power_Opower__class_Opower @ SV802 @ SV1061 @ SV42 ) @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3273,plain,
! [SV1062: $i,SV803: $i,SV447: $i,SV43: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV43 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV803 @ SV43 ) @ SV1062 @ SV43 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV447 @ SV1062 @ SV43 ) @ ( c_Power_Opower__class_Opower @ SV803 @ SV1062 @ SV43 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3274,plain,
! [SV1063: $i,SV804: $i,SV448: $i,SV44: $i] :
( ( ( class_Divides_Osemiring__div @ SV44 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ ( c_Divides_Odiv__class_Omod @ SV804 @ SV1063 @ SV44 ) @ SV44 ) @ SV1063 @ SV44 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV804 @ SV44 ) @ SV1063 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3275,plain,
! [SV1064: $i,SV805: $i,SV449: $i,SV45: $i] :
( ( ( class_Divides_Osemiring__div @ SV45 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV449 @ SV805 @ SV45 ) @ SV1064 @ SV45 ) @ SV805 @ SV45 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV449 @ SV1064 @ SV45 ) @ SV805 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3276,plain,
! [SV1236: $i,SV1208: $i,SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV46 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3277,plain,
! [SV1237: $i,SV1209: $i,SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV47 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3278,plain,
! [SV52: $i,SV811: $i,SV456: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ SV456 @ ( c_HOL_Ouminus__class_Ouminus @ SV811 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV456 @ SV811 @ SV52 ) @ SV52 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV811 @ SV456 @ SV52 ) )
= $true )
| ( ( class_Divides_Oring__div @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3279,plain,
! [SV812: $i,SV53: $i,SV457: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV457 @ SV53 ) @ SV812 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV457 @ SV812 @ SV53 ) @ SV53 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV812 @ SV457 @ SV53 ) )
= $true )
| ( ( class_Divides_Oring__div @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3280,plain,
! [SV1067: $i,SV813: $i,SV458: $i,SV54: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV54 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV813 @ SV54 ) @ SV1067 @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV458 @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1067 @ SV54 ) @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3281,plain,
! [SV1068: $i,SV814: $i,SV459: $i,SV55: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV814 @ SV55 ) @ SV1068 @ SV55 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV459 @ SV1068 @ SV55 ) @ SV814 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3282,plain,
! [SV1069: $i,SV815: $i,SV460: $i,SV56: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV460 @ SV815 @ SV56 ) @ SV1069 @ SV56 )
= ( c_HOL_Otimes__class_Otimes @ SV460 @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1069 @ SV56 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3283,plain,
! [SV1070: $i,SV816: $i,SV461: $i,SV57: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1070 @ SV57 ) @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV461 @ SV816 @ SV57 ) @ SV1070 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3284,plain,
! [SV1071: $i,SV817: $i,SV462: $i,SV58: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV58 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV817 @ SV1071 @ SV58 ) @ SV58 )
= ( c_HOL_Otimes__class_Otimes @ SV817 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1071 @ SV58 ) @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3285,plain,
! [SV1072: $i,SV818: $i,SV463: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV463 @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV1072 @ SV59 ) @ SV59 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV463 @ SV818 @ SV59 ) @ SV1072 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3286,plain,
! [SV1073: $i,SV819: $i,SV464: $i,SV60: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV464 @ SV819 @ SV60 ) @ SV1073 @ SV60 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV464 @ SV1073 @ SV60 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV1073 @ SV60 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3287,plain,
! [SV1074: $i,SV820: $i,SV465: $i,SV61: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV61 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV465 @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV1074 @ SV61 ) @ SV61 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV820 @ SV61 ) @ ( c_HOL_Otimes__class_Otimes @ SV465 @ SV1074 @ SV61 ) @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3288,plain,
! [SV1075: $i,SV821: $i,SV466: $i,SV62: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV62 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV466 @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV1075 @ SV62 ) @ SV62 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV821 @ SV62 ) @ ( c_HOL_Otimes__class_Otimes @ SV466 @ SV1075 @ SV62 ) @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3289,plain,
! [SV1076: $i,SV822: $i,SV467: $i,SV63: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV63 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV467 @ SV822 @ SV63 ) @ SV1076 @ SV63 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV467 @ SV1076 @ SV63 ) @ ( c_HOL_Otimes__class_Otimes @ SV822 @ SV1076 @ SV63 ) @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3290,plain,
! [SV1077: $i,SV823: $i,SV468: $i,SV64: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV64 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SV823 @ SV64 ) @ SV1077 @ SV64 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV1077 @ SV64 ) @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1077 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3291,plain,
! [SV1078: $i,SV824: $i,SV469: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV65 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV469 @ SV824 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV469 @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1078 @ ( tc_Polynomial_Opoly @ SV65 ) ) @ ( tc_Polynomial_Opoly @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3292,plain,
! [SV1079: $i,SV825: $i,SV470: $i,SV66: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV470 @ ( c_HOL_Oplus__class_Oplus @ SV825 @ SV1079 @ SV66 ) @ SV66 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV825 @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV470 @ SV1079 @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3293,plain,
! [SV1080: $i,SV826: $i,SV471: $i,SV67: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV67 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV471 @ SV826 @ SV67 ) @ SV1080 @ SV67 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV471 @ SV1080 @ SV67 ) @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1080 @ SV67 ) @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3294,plain,
! [SV69: $i,SV828: $i,SV473: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV828 @ SV69 ) @ SV473 @ SV69 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV828 @ SV473 @ SV69 ) @ ( c_HOL_Oone__class_Oone @ SV69 ) @ SV69 ) )
= $true )
| ( ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV69 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3295,plain,
! [SV70: $i,SV829: $i,SV474: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV829 @ SV70 ) @ SV829 @ SV70 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV474 @ SV829 @ SV70 ) @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV70 ) )
= $true )
| ( ( SV829
= ( c_HOL_Ozero__class_Ozero @ SV70 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3296,plain,
! [SV1081: $i,SV830: $i,SV475: $i,SV72: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV830 @ SV72 ) @ ( c_HOL_Otimes__class_Otimes @ SV1081 @ SV830 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV475 @ SV1081 @ SV72 ) @ SV830 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3297,plain,
! [SV1082: $i,SV836: $i,SV482: $i,SV79: $i] :
( ( ( class_Divides_Osemiring__div @ SV79 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV836 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV1082 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SV836 @ SV1082 @ SV79 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3298,plain,
! [SV1083: $i,SV837: $i,SV483: $i,SV80: $i] :
( ( ( class_Divides_Osemiring__div @ SV80 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV483 @ SV837 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1083 @ SV837 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SV483 @ SV1083 @ SV80 ) )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3299,plain,
! [SV1084: $i,SV839: $i,SV487: $i,SV84: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV84 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_OpCons @ SV487 @ SV839 @ SV84 ) @ SV1084 @ ( tc_Polynomial_Opoly @ SV84 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV487 @ SV1084 @ SV84 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( c_HOL_Otimes__class_Otimes @ SV839 @ SV1084 @ ( tc_Polynomial_Opoly @ SV84 ) ) @ SV84 ) @ ( tc_Polynomial_Opoly @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3300,plain,
! [SV1085: $i,SV840: $i,SV488: $i,SV85: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV85 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV488 @ ( c_Polynomial_OpCons @ SV840 @ SV1085 @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV840 @ SV488 @ SV85 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_HOL_Otimes__class_Otimes @ SV488 @ SV1085 @ ( tc_Polynomial_Opoly @ SV85 ) ) @ SV85 ) @ ( tc_Polynomial_Opoly @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3301,plain,
! [SV496: $i,SV93: $i] :
( ( ( class_Int_Onumber__ring @ SV93 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV496 @ SV496 @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3302,plain,
! [SV1210: $i,SV1086: $i,SV841: $i,SV498: $i,SV95: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV95 ) )
= $true )
| ( ( ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SV1086 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SV1210 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SV1086 @ SV841 @ SV1210 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3303,plain,
! [SV1087: $i,SV842: $i,SV499: $i,SV96: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV96 )
= $false )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Oplus__class_Oplus @ SV499 @ SV842 @ SV96 ) @ SV1087 @ SV96 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV499 @ SV1087 @ SV96 ) @ ( c_Polynomial_Osmult @ SV842 @ SV1087 @ SV96 ) @ ( tc_Polynomial_Opoly @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3304,plain,
! [SV1211: $i,SV1088: $i,SV843: $i,SV500: $i,SV97: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV97 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV843 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV500 @ SV97 ) @ SV843 @ SV97 ) @ SV1211 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1088 @ SV843 @ SV97 ) @ SV1211 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3305,plain,
! [SV1089: $i,SV844: $i,SV501: $i,SV98: $i] :
( ( ( class_Divides_Osemiring__div @ SV98 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3306,plain,
! [SV1090: $i,SV845: $i,SV502: $i,SV99: $i] :
( ( ( class_Divides_Osemiring__div @ SV99 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV502 @ SV845 @ SV99 ) @ SV1090 @ SV99 ) @ SV845 @ SV99 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV1090 @ SV99 ) @ SV845 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3307,plain,
! [SV1091: $i,SV847: $i,SV511: $i,SV108: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV108 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV108 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ SV108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3308,plain,
! [SV1092: $i,SV848: $i,SV512: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV109 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV109 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3309,plain,
! [SV1093: $i,SV849: $i,SV513: $i,SV110: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV110 )
= $false )
| ( ( ( c_Polynomial_Opoly__gcd @ SV513 @ ( c_Polynomial_Opoly__gcd @ SV849 @ SV1093 @ SV110 ) @ SV110 )
= ( c_Polynomial_Opoly__gcd @ SV849 @ ( c_Polynomial_Opoly__gcd @ SV513 @ SV1093 @ SV110 ) @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3310,plain,
! [SV1094: $i,SV850: $i,SV514: $i,SV111: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV111 )
= $false )
| ( ( ( c_Polynomial_Opoly__gcd @ ( c_Polynomial_Opoly__gcd @ SV514 @ SV850 @ SV111 ) @ SV1094 @ SV111 )
= ( c_Polynomial_Opoly__gcd @ SV514 @ ( c_Polynomial_Opoly__gcd @ SV850 @ SV1094 @ SV111 ) @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3311,plain,
! [SV1095: $i,SV856: $i,SV520: $i,SV118: $i] :
( ( ( class_Divides_Osemiring__div @ SV118 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV520 @ SV856 @ SV118 ) @ SV1095 @ SV118 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV520 @ SV1095 @ SV118 ) @ ( c_Divides_Odiv__class_Omod @ SV856 @ SV1095 @ SV118 ) @ SV118 ) @ SV1095 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3312,plain,
! [SV1096: $i,SV857: $i,SV521: $i,SV120: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV120 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SV857 @ SV1096 @ SV120 ) @ SV120 )
= ( c_HOL_Oplus__class_Oplus @ SV857 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SV1096 @ SV120 ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3313,plain,
! [SV1097: $i,SV858: $i,SV522: $i,SV121: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV121 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV522 @ SV858 @ SV121 ) @ SV1097 @ SV121 )
= ( c_HOL_Oplus__class_Oplus @ SV522 @ ( c_HOL_Oplus__class_Oplus @ SV858 @ SV1097 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3314,plain,
! [SV1098: $i,SV859: $i,SV523: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV523 @ ( c_HOL_Oplus__class_Oplus @ SV859 @ SV1098 @ SV122 ) @ SV122 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV523 @ SV859 @ SV122 ) @ SV1098 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3315,plain,
! [SV1099: $i,SV860: $i,SV524: $i,SV123: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV123 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV524 @ ( c_HOL_Oplus__class_Oplus @ SV860 @ SV1099 @ SV123 ) @ SV123 )
= ( c_HOL_Oplus__class_Oplus @ SV860 @ ( c_HOL_Oplus__class_Oplus @ SV524 @ SV1099 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3316,plain,
! [SV1100: $i,SV861: $i,SV525: $i,SV124: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV124 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV861 @ SV124 ) @ SV1100 @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ SV525 @ ( c_HOL_Oplus__class_Oplus @ SV861 @ SV1100 @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3317,plain,
! [SV1101: $i,SV862: $i,SV526: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV526 @ ( c_HOL_Oplus__class_Oplus @ SV862 @ SV1101 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV862 @ SV125 ) @ SV1101 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3318,plain,
! [SV1102: $i,SV863: $i,SV527: $i,SV126: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV863 @ SV126 ) @ SV1102 @ SV126 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV527 @ SV1102 @ SV126 ) @ SV863 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3319,plain,
! [SV1103: $i,SV864: $i,SV528: $i,SV127: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SV1103 @ SV127 ) @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ SV864 @ ( c_HOL_Oplus__class_Oplus @ SV528 @ SV1103 @ SV127 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3320,plain,
! [SV1104: $i,SV865: $i,SV529: $i,SV128: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV529 @ SV865 @ SV128 ) @ SV1104 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ SV529 @ ( c_HOL_Oplus__class_Oplus @ SV865 @ SV1104 @ SV128 ) @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3321,plain,
! [SV1105: $i,SV868: $i,SV532: $i,SV131: $i] :
( ( ( class_Divides_Osemiring__div @ SV131 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV868 @ SV131 ) @ SV1105 @ SV131 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV532 @ ( c_Divides_Odiv__class_Omod @ SV868 @ SV1105 @ SV131 ) @ SV131 ) @ SV1105 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3322,plain,
! [SV1106: $i,SV869: $i,SV533: $i,SV132: $i] :
( ( ( class_Divides_Osemiring__div @ SV132 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV869 @ SV132 ) @ SV1106 @ SV132 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV533 @ SV1106 @ SV132 ) @ SV869 @ SV132 ) @ SV1106 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3323,plain,
! [SV1212: $i,SV1107: $i,SV870: $i,SV534: $i,SV133: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV133 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SV1107 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SV1212 @ SV1107 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3324,plain,
! [SV1213: $i,SV1108: $i,SV871: $i,SV535: $i,SV134: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV134 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV535 @ SV871 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ SV1213 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SV1213 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ SV1213 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SV1213 @ SV134 ) @ SV134 ) @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3325,plain,
! [SV1214: $i,SV1109: $i,SV872: $i,SV536: $i,SV135: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV135 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV536 @ SV872 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1109 @ SV872 @ SV135 ) @ SV1214 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV536 @ SV1109 @ SV135 ) @ SV872 @ SV135 ) @ SV1214 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3326,plain,
! [SV1110: $i,SV873: $i,SV541: $i,SV140: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV140 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV541 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SV1110 @ SV140 ) @ SV140 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV873 @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1110 @ SV140 ) @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3327,plain,
! [SV1111: $i,SV874: $i,SV542: $i,SV141: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV141 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV542 @ ( c_HOL_Ominus__class_Ominus @ SV874 @ SV1111 @ SV141 ) @ SV141 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV874 @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV542 @ SV1111 @ SV141 ) @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3328,plain,
! [SV1112: $i,SV875: $i,SV543: $i,SV142: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV142 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV543 @ SV875 @ SV142 ) @ SV1112 @ SV142 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV543 @ SV1112 @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV875 @ SV1112 @ SV142 ) @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3074]) ).
thf(3329,plain,
! [SV1113: $i,SV876: $i,SV544: $i,SV143: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV143 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV544 @ SV876 @ SV143 ) @ SV1113 @ SV143 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV544 @ SV1113 @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV876 @ SV1113 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3330,plain,
! [SV1215: $i,SV1114: $i,SV877: $i,SV545: $i,SV144: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV144 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV877 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SV1114 @ SV1215 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV545 @ SV1114 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SV877 @ SV1215 @ SV144 ) @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3331,plain,
! [SV1115: $i,SV878: $i,SV546: $i,SV145: $i] :
( ( ( class_Divides_Osemiring__div @ SV145 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SV878 @ SV145 ) @ SV1115 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SV1115 @ SV145 ) @ SV878 @ SV145 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV878 @ SV546 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3332,plain,
! [SV1116: $i,SV880: $i,SV548: $i,SV147: $i] :
( ( ( class_Divides_Osemiring__div @ SV147 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ SV880 @ SV147 ) @ SV1116 @ SV147 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV548 @ ( c_Divides_Odiv__class_Omod @ SV880 @ SV1116 @ SV147 ) @ SV147 ) @ SV1116 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3333,plain,
! [SV1117: $i,SV881: $i,SV549: $i,SV148: $i] :
( ( ( class_Divides_Osemiring__div @ SV148 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV549 @ SV881 @ SV148 ) @ SV1117 @ SV148 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV549 @ SV1117 @ SV148 ) @ SV881 @ SV148 ) @ SV1117 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3080]) ).
thf(3334,plain,
! [SV1238: $i,SV1216: $i,SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ! [SY2847: $i,SY2848: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SY2847 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2848 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SY2848 @ SY2847 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3335,plain,
! [SV150: $i,SV883: $i,SV551: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV551 @ ( c_Divides_Odiv__class_Odiv @ SV883 @ SV551 @ SV150 ) @ SV150 )
= SV883 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV551 @ SV883 @ SV150 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3336,plain,
! [SV151: $i,SV884: $i,SV552: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV552 @ SV884 @ SV151 ) @ SV884 @ SV151 )
= SV552 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV884 @ SV552 @ SV151 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3337,plain,
! [SV1119: $i,SV886: $i,SV554: $i,SV153: $i] :
( ( ( class_Divides_Osemiring__div @ SV153 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV554 @ ( c_HOL_Otimes__class_Otimes @ SV886 @ SV1119 @ SV153 ) @ SV153 ) @ SV886 @ SV153 )
= ( c_Divides_Odiv__class_Omod @ SV554 @ SV886 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3338,plain,
! [SV1120: $i,SV887: $i,SV555: $i,SV154: $i] :
( ( ( class_Divides_Osemiring__div @ SV154 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV887 @ SV1120 @ SV154 ) @ SV154 ) @ SV1120 @ SV154 )
= ( c_Divides_Odiv__class_Omod @ SV555 @ SV1120 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3339,plain,
! [SV1121: $i,SV888: $i,SV556: $i,SV155: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV155 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
| ( SV1121
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV1121 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SV1121 @ SV155 ) @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3087]) ).
thf(3340,plain,
! [SV1122: $i,SV889: $i,SV557: $i,SV156: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV156 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
| ( SV1122
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV889 @ SV156 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3088]) ).
thf(3341,plain,
! [SV563: $i,SV162: $i] :
( ( ( class_Int_Onumber__ring @ SV162 )
= $false )
| ( ( SV563
= ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3342,plain,
! [SV1217: $i,SV1123: $i,SV892: $i,SV576: $i,SV175: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV892 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1123 @ SV1217 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV1123 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV892 @ SV1217 @ SV175 ) @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3343,plain,
! [SV1124: $i,SV897: $i,SV581: $i,SV180: $i] :
( ( ( class_Divides_Oring__div @ SV180 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV581 @ SV897 @ SV180 ) @ SV1124 @ SV180 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV581 @ SV1124 @ SV180 ) @ ( c_Divides_Odiv__class_Omod @ SV897 @ SV1124 @ SV180 ) @ SV180 ) @ SV1124 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3344,plain,
! [SV183: $i,SV898: $i,SV584: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV584 @ SV898 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV898 @ SV584 @ SV183 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3345,plain,
! [SV1125: $i,SV899: $i,SV586: $i,SV185: $i] :
( ( ( class_Divides_Oring__div @ SV185 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV586 @ SV899 @ SV185 ) @ SV1125 @ SV185 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV586 @ SV1125 @ SV185 ) @ SV899 @ SV185 ) @ SV1125 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3346,plain,
! [SV1126: $i,SV900: $i,SV587: $i,SV186: $i] :
( ( ( class_Divides_Oring__div @ SV186 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SV900 @ SV186 ) @ SV1126 @ SV186 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV587 @ ( c_Divides_Odiv__class_Omod @ SV900 @ SV1126 @ SV186 ) @ SV186 ) @ SV1126 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3347,plain,
! [SV1127: $i,SV901: $i,SV588: $i,SV187: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV187 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV588 @ ( c_Polynomial_Osmult @ SV901 @ SV1127 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SV588 @ SV1127 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
| ( SV901
= ( c_HOL_Ozero__class_Ozero @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3348,plain,
! [SV1218: $i,SV1128: $i,SV904: $i,SV594: $i,SV193: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV193 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV594 @ SV904 @ SV193 ) @ SV1128 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1218 @ SV904 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV594 @ SV1218 @ SV193 ) @ SV904 @ SV193 ) @ SV1128 @ SV193 ) @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3349,plain,
! [SV1129: $i,SV905: $i,SV596: $i,SV195: $i] :
( ( ( class_Divides_Osemiring__div @ SV195 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV596 @ SV905 @ SV195 ) @ SV905 @ SV195 ) @ ( c_Divides_Odiv__class_Omod @ SV596 @ SV905 @ SV195 ) @ SV195 ) @ SV1129 @ SV195 )
= ( c_HOL_Oplus__class_Oplus @ SV596 @ SV1129 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3350,plain,
! [SV1130: $i,SV906: $i,SV597: $i,SV196: $i] :
( ( ( class_Divides_Osemiring__div @ SV196 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV597 @ ( c_Divides_Odiv__class_Odiv @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ ( c_Divides_Odiv__class_Omod @ SV906 @ SV597 @ SV196 ) @ SV196 ) @ SV1130 @ SV196 )
= ( c_HOL_Oplus__class_Oplus @ SV906 @ SV1130 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3351,plain,
! [SV1131: $i,SV912: $i,SV606: $i,SV205: $i] :
( ( ( class_Divides_Osemiring__div @ SV205 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV606 @ SV912 @ SV205 ) @ SV1131 @ SV205 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV606 @ SV1131 @ SV205 ) @ ( c_Divides_Odiv__class_Omod @ SV912 @ SV1131 @ SV205 ) @ SV205 ) @ SV1131 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3352,plain,
! [SV1132: $i,SV914: $i,SV608: $i,SV207: $i] :
( ( ( class_Divides_Osemiring__div @ SV207 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV608 @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV1132 @ SV207 ) @ SV207 ) @ SV1132 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SV914 @ ( c_Divides_Odiv__class_Odiv @ SV608 @ SV1132 @ SV207 ) @ SV207 ) )
| ( SV1132
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3353,plain,
! [SV1133: $i,SV915: $i,SV609: $i,SV208: $i] :
( ( ( class_Divides_Osemiring__div @ SV208 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV609 @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1133 @ SV208 ) @ SV208 ) @ SV915 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SV1133 @ ( c_Divides_Odiv__class_Odiv @ SV609 @ SV915 @ SV208 ) @ SV208 ) )
| ( SV915
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3354,plain,
! [SV1219: $i,SV1134: $i,SV916: $i,SV611: $i,SV210: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV210 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SV1134 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SV1134 @ SV1219 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3117]) ).
thf(3355,plain,
! [SV1135: $i,SV917: $i,SV612: $i,SV211: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV211 )
= $false )
| ( ( ( c_Polynomial_Osmult @ ( c_HOL_Ominus__class_Ominus @ SV612 @ SV917 @ SV211 ) @ SV1135 @ SV211 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV612 @ SV1135 @ SV211 ) @ ( c_Polynomial_Osmult @ SV917 @ SV1135 @ SV211 ) @ ( tc_Polynomial_Opoly @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3356,plain,
! [SV1136: $i,SV918: $i,SV613: $i,SV212: $i] :
( ( ( class_Divides_Osemiring__div @ SV212 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SV918 @ SV212 ) @ SV1136 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SV1136 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV918 @ SV1136 @ SV212 ) @ SV212 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV918 @ SV613 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3357,plain,
! [SV240: $i,SV927: $i,SV637: $i] :
( ( ( ( c_Polynomial_Opoly__gcd @ SV637 @ SV927 @ SV240 )
= ( c_Polynomial_Opoly__gcd @ SV927 @ ( c_Divides_Odiv__class_Omod @ SV637 @ SV927 @ ( tc_Polynomial_Opoly @ SV240 ) ) @ SV240 ) )
= $true )
| ( ( SV927
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV240 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3358,plain,
! [SV1137: $i,SV929: $i,SV641: $i,SV244: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV244 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV641 @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SV1137 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ ( tc_Polynomial_Opoly @ SV244 ) )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ SV641 @ SV929 @ ( tc_Polynomial_Opoly @ SV244 ) ) @ SV1137 @ ( tc_Polynomial_Opoly @ SV244 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3359,plain,
! [SV934: $i,SV250: $i,SV646: $i] :
( ( ( SV646
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV646 @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV646 @ SV934 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV250 ) ) @ SV250 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3360,plain,
! [SV1138: $i,SV936: $i,SV648: $i,SV252: $i] :
( ( ( class_Divides_Osemiring__div @ SV252 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV936 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV1138 @ SV252 ) @ SV252 )
= ( c_HOL_Otimes__class_Otimes @ SV648 @ ( c_Divides_Odiv__class_Omod @ SV936 @ SV1138 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3361,plain,
! [SV1139: $i,SV937: $i,SV649: $i,SV253: $i] :
( ( ( class_Divides_Osemiring__div @ SV253 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV649 @ SV937 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV1139 @ SV937 @ SV253 ) @ SV253 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV649 @ SV1139 @ SV253 ) @ SV937 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3362,plain,
! [SV1220: $i,SV1140: $i,SV940: $i,SV652: $i,SV256: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3141]) ).
thf(3363,plain,
! [SV1141: $i,SV941: $i,SV655: $i,SV259: $i] :
( ( ( class_Divides_Osemiring__div @ SV259 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SV941 @ SV259 ) @ SV1141 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SV1141 @ SV259 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1141 @ SV941 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3364,plain,
! [SV1142: $i,SV942: $i,SV656: $i,SV260: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV260 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3365,plain,
! [SV1143: $i,SV943: $i,SV657: $i,SV261: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV261 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3366,plain,
! [SV946: $i,SV660: $i,SV264: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV660 @ SV264 ) @ SV946 @ ( tc_Polynomial_Opoly @ SV264 ) ) )
= $true )
| ( ( SV946
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3367,plain,
! [SV265: $i,SV947: $i,SV661: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ ( c_HOL_Oabs__class_Oabs @ SV947 @ SV265 ) @ SV265 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ SV947 @ SV265 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3368,plain,
! [SV266: $i,SV948: $i,SV662: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ SV948 @ SV266 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ ( c_HOL_Oabs__class_Oabs @ SV948 @ SV266 ) @ SV266 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3369,plain,
! [SV949: $i,SV267: $i,SV663: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV663 @ SV267 ) @ SV949 @ SV267 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV663 @ SV949 @ SV267 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3370,plain,
! [SV268: $i,SV950: $i,SV664: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV664 @ SV950 @ SV268 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV664 @ SV268 ) @ SV950 @ SV268 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3371,plain,
! [SV1144: $i,SV951: $i,SV666: $i,SV270: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV270 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV666 @ ( c_HOL_Ominus__class_Ominus @ SV951 @ SV1144 @ ( tc_Polynomial_Opoly @ SV270 ) ) @ SV270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_Osmult @ SV666 @ SV951 @ SV270 ) @ ( c_Polynomial_Osmult @ SV666 @ SV1144 @ SV270 ) @ ( tc_Polynomial_Opoly @ SV270 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3372,plain,
! [SV1145: $i,SV952: $i,SV667: $i,SV271: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV271 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SV952 @ ( tc_Polynomial_Opoly @ SV271 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SV1145 @ SV952 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3373,plain,
! [SV1146: $i,SV953: $i,SV668: $i,SV272: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV272 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SV953 @ ( tc_Polynomial_Opoly @ SV272 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SV953 @ SV1146 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3154]) ).
thf(3374,plain,
! [SV1147: $i,SV954: $i,SV669: $i,SV273: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV273 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV954 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1147 @ SV954 @ SV273 ) @ SV273 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SV1147 @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3375,plain,
! [SV1148: $i,SV955: $i,SV670: $i,SV274: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV274 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV955 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV1148 @ SV274 ) @ SV274 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV955 @ SV1148 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3376,plain,
! [SV672: $i,SV276: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV672 @ SV276 )
= $false )
| ( ( SV672
= ( c_HOL_Ozero__class_Ozero @ SV276 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3377,plain,
! [SV957: $i,SV277: $i,SV673: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV673 @ SV277 ) @ SV957 @ SV277 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV673 @ SV957 @ SV277 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3378,plain,
! [SV278: $i,SV958: $i,SV674: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV674 @ SV958 @ SV278 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV674 @ SV278 ) @ SV958 @ SV278 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3379,plain,
! [SV279: $i,SV959: $i,SV675: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ ( c_HOL_Ouminus__class_Ouminus @ SV959 @ SV279 ) @ SV279 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ SV959 @ SV279 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3380,plain,
! [SV280: $i,SV960: $i,SV676: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ SV960 @ SV280 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ ( c_HOL_Ouminus__class_Ouminus @ SV960 @ SV280 ) @ SV280 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3381,plain,
! [SV1149: $i,SV961: $i,SV677: $i,SV281: $i] :
( ( ( class_Divides_Osemiring__div @ SV281 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3382,plain,
! [SV1150: $i,SV962: $i,SV678: $i,SV282: $i] :
( ( ( class_Divides_Osemiring__div @ SV282 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3383,plain,
! [SV1151: $i,SV963: $i,SV679: $i,SV283: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3384,plain,
! [SV1152: $i,SV964: $i,SV681: $i,SV285: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV285 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Polynomial_Osmult @ SV681 @ SV964 @ SV285 ) @ SV1152 @ ( tc_Polynomial_Opoly @ SV285 ) )
= ( c_Polynomial_Osmult @ SV681 @ ( c_Divides_Odiv__class_Omod @ SV964 @ SV1152 @ ( tc_Polynomial_Opoly @ SV285 ) ) @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3385,plain,
! [SV1153: $i,SV965: $i,SV682: $i,SV286: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV286 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SV1153 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3386,plain,
! [SV1154: $i,SV966: $i,SV683: $i,SV287: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV287 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
| ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3168]) ).
thf(3387,plain,
! [SV1155: $i,SV967: $i,SV684: $i,SV288: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV288 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SV1155 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SV1155
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3169]) ).
thf(3388,plain,
! [SV1156: $i,SV968: $i,SV685: $i,SV289: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV289 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SV1156 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SV1156 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3389,plain,
! [SV1157: $i,SV969: $i,SV686: $i,SV290: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV290 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
| ( SV1157
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1157 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3390,plain,
! [SV1158: $i,SV970: $i,SV687: $i,SV291: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV291 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3391,plain,
! [SV292: $i,SV971: $i,SV688: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV688 @ SV971 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV971 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3392,plain,
! [SV1159: $i,SV972: $i,SV689: $i,SV293: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SV972 @ SV293 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1159 @ SV689 @ SV293 ) @ SV972 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3393,plain,
! [SV1160: $i,SV973: $i,SV690: $i,SV294: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SV973 @ SV294 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV1160 @ SV294 ) @ SV973 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3394,plain,
! [SV1161: $i,SV974: $i,SV691: $i,SV295: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV974 @ SV1161 @ SV295 ) @ SV295 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SV974 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3395,plain,
! [SV1162: $i,SV975: $i,SV692: $i,SV296: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SV975 @ SV1162 @ SV296 ) @ SV296 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SV1162 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3396,plain,
! [SV1163: $i,SV976: $i,SV694: $i,SV298: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3397,plain,
! [SV1239: $i,SV1221: $i,SV1164: $i,SV977: $i,SV697: $i,SV301: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV301 )
| ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SV1221 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SV1239 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SV1221 @ SV1239 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3398,plain,
! [SV1165: $i,SV978: $i,SV698: $i,SV302: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3399,plain,
! [SV1166: $i,SV979: $i,SV699: $i,SV303: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV303 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV699 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SV1166 @ ( tc_Polynomial_Opoly @ SV303 ) ) @ SV303 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV699 @ SV979 @ SV303 ) @ ( c_Polynomial_Osmult @ SV699 @ SV1166 @ SV303 ) @ ( tc_Polynomial_Opoly @ SV303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3400,plain,
! [SV1167: $i,SV980: $i,SV700: $i,SV304: $i] :
( ( ( class_Divides_Osemiring__div @ SV304 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3401,plain,
! [SV1168: $i,SV981: $i,SV701: $i,SV305: $i] :
( ( ( class_Divides_Osemiring__div @ SV305 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3402,plain,
! [SV1169: $i,SV982: $i,SV702: $i,SV306: $i] :
( ( ( class_Divides_Osemiring__div @ SV306 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3403,plain,
! [SV1170: $i,SV983: $i,SV703: $i,SV307: $i] :
( ( ( class_Divides_Osemiring__div @ SV307 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3404,plain,
! [SV1171: $i,SV984: $i,SV704: $i,SV308: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV308 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_Polynomial_Osmult @ SV704 @ SV984 @ SV308 ) @ SV1171 @ ( tc_Polynomial_Opoly @ SV308 ) )
= ( c_Polynomial_Osmult @ SV704 @ ( c_Divides_Odiv__class_Odiv @ SV984 @ SV1171 @ ( tc_Polynomial_Opoly @ SV308 ) ) @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3405,plain,
! [SV1172: $i,SV988: $i,SV708: $i,SV312: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1172 @ SV708 @ SV312 ) @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3406,plain,
! [SV1173: $i,SV989: $i,SV709: $i,SV313: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SV989 @ SV1173 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SV1173 @ ( tc_Polynomial_Opoly @ SV313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3407,plain,
! [SV1174: $i,SV990: $i,SV710: $i,SV314: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SV990 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SV1174 @ SV990 @ SV314 ) @ SV314 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SV1174 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3408,plain,
! [SV1175: $i,SV991: $i,SV711: $i,SV315: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV315 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV711 @ ( c_Polynomial_Osmult @ SV991 @ SV1175 @ SV315 ) @ ( tc_Polynomial_Opoly @ SV315 ) )
= ( c_Polynomial_Osmult @ SV991 @ ( c_HOL_Otimes__class_Otimes @ SV711 @ SV1175 @ ( tc_Polynomial_Opoly @ SV315 ) ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3409,plain,
! [SV1176: $i,SV992: $i,SV712: $i,SV316: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV316 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ SV712 @ SV992 @ SV316 ) @ SV1176 @ ( tc_Polynomial_Opoly @ SV316 ) )
= ( c_Polynomial_Osmult @ SV712 @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1176 @ ( tc_Polynomial_Opoly @ SV316 ) ) @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3410,plain,
! [SV1177: $i,SV993: $i,SV713: $i,SV317: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV317 )
= $false )
| ( ( ( c_Polynomial_Osmult @ SV713 @ ( c_Polynomial_Osmult @ SV993 @ SV1177 @ SV317 ) @ SV317 )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ SV713 @ SV993 @ SV317 ) @ SV1177 @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3411,plain,
! [SV1178: $i,SV994: $i,SV714: $i,SV353: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV353 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV353 )
| ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
| ( SV994 = SV1178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3412,plain,
! [SV1179: $i,SV995: $i,SV715: $i,SV354: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SV995 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SV715 @ SV1179 @ SV354 ) )
| ( SV995 = SV1179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3413,plain,
! [SV355: $i,SV996: $i,SV716: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV716 @ SV996 @ SV355 )
!= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV996 @ SV716 @ SV355 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3414,plain,
! [SV356: $i,SV997: $i,SV717: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SV997 @ SV356 )
!= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
= $true )
| ( ( ( SV997
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3199]) ).
thf(3415,plain,
! [SV357: $i,SV998: $i,SV718: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SV998 @ SV357 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $true )
| ( ( ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV998
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3200]) ).
thf(3416,plain,
! [SV358: $i,SV999: $i,SV719: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV719 @ SV999 @ SV358 )
!= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
= $true )
| ( ( SV719
= ( c_HOL_Ouminus__class_Ouminus @ SV999 @ SV358 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3417,plain,
! [SV1222: $i,SV1180: $i,SV1000: $i,SV720: $i,SV359: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV359 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
| ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3418,plain,
! [SV1223: $i,SV1181: $i,SV1001: $i,SV721: $i,SV360: $i] :
( ( ( ~ ( class_HOL_Ozero @ SV360 ) )
= $true )
| ( ( ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
!= ( c_Polynomial_OpCons @ SV1181 @ SV1223 @ SV360 ) )
| ( SV1001 = SV1223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3419,plain,
! [SV361: $i,SV722: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV722 @ SV722 @ SV361 )
= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
= $false )
| ( ( SV722
= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3420,plain,
! [SV1002: $i,SV362: $i,SV723: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV723 @ SV362 )
!= ( c_HOL_Oabs__class_Oabs @ SV1002 @ SV362 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV723 @ SV1002 @ SV362 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3421,plain,
! [SV363: $i,SV1003: $i,SV724: $i] :
( ( ( ( c_Polynomial_Opoly @ SV724 @ ( c_HOL_Ouminus__class_Ouminus @ SV1003 @ SV363 ) @ SV363 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV1003 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SV724 @ ( tc_Polynomial_Opoly @ SV363 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3422,plain,
! [SV725: $i,SV364: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= ( c_HOL_Ouminus__class_Ouminus @ SV725 @ SV364 ) )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV364 )
= SV725 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3423,plain,
! [SV1240: $i,SV1224: $i,SV1182: $i,SV1004: $i,SV726: $i,SV365: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV365 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1224 @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
| ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1224 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3424,plain,
! [SV1241: $i,SV1225: $i,SV1183: $i,SV1005: $i,SV727: $i,SV366: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV366 )
| ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3425,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV367 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3426,plain,
! [SV1184: $i,SV1007: $i,SV729: $i,SV368: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
= $false )
| ( ( ( ( c_Polynomial_Osmult @ SV729 @ SV1007 @ SV368 )
!= ( c_Polynomial_OpCons @ SV1184 @ SV1007 @ SV368 ) )
| ( SV1007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3427,plain,
! [SV1185: $i,SV1008: $i,SV730: $i,SV369: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SV1008 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SV1185 @ SV1008 @ SV369 ) )
| ( SV730 = SV1185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3428,plain,
! [SV370: $i,SV1009: $i,SV731: $i] :
( ( ( ( c_Polynomial_Opoly__gcd @ SV731 @ SV1009 @ SV370 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
= $true )
| ( ( SV1009
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV370 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3429,plain,
! [SV1010: $i,SV732: $i,SV371: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV371 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SV732 = SV1010 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV371 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3430,plain,
! [SV372: $i,SV1011: $i,SV733: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV733 @ SV1011 @ SV372 )
!= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
= $true )
| ( ( SV733
= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3431,plain,
! [SV1012: $i,SV373: $i,SV734: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV734 @ SV734 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1012 @ SV373 ) @ SV373 )
!= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
= $true )
| ( ( SV1012
= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3432,plain,
! [SV1186: $i,SV1013: $i,SV735: $i,SV374: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SV1013 @ SV374 ) @ ( c_Polynomial_OpCons @ SV1186 @ SV1013 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
| ( SV1013
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3433,plain,
! [SV376: $i,SV1014: $i,SV736: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SV1014 @ SV376 )
!= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
= $true )
| ( ( ( SV1014
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3218]) ).
thf(3434,plain,
! [SV1226: $i,SV1187: $i,SV1015: $i,SV737: $i,SV377: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV377 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3219]) ).
thf(3435,plain,
! [SV378: $i,SV1016: $i,SV738: $i] :
( ( ( ( c_Polynomial_OpCons @ SV738 @ SV1016 @ SV378 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
= $true )
| ( ( SV1016
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
= $true )
| ( ( class_HOL_Ozero @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3436,plain,
! [SV1188: $i,SV1017: $i,SV739: $i,SV379: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1017 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1188 @ SV379 ) )
| ( SV1017 = SV1188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3437,plain,
! [SV380: $i,SV740: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV740 @ SV380 )
= SV740 )
= $false )
| ( ( SV740
= ( c_HOL_Ozero__class_Ozero @ SV380 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__ab__group__add @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3438,plain,
! [SV1018: $i,SV381: $i,SV741: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
!= ( c_HOL_Otimes__class_Otimes @ SV1018 @ SV1018 @ SV381 ) )
= $true )
| ( ( ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SV1018 @ SV381 ) )
| ( SV741 = SV1018 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3439,plain,
! [SV1019: $i,SV382: $i,SV742: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV742 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SV1019 @ SV1019 @ SV382 ) @ SV382 )
!= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
= $true )
| ( ( SV742
= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3224]) ).
thf(3440,plain,
! [SV1242: $i,SV1227: $i,SV1189: $i,SV1020: $i,SV743: $i,SV383: $i] :
( ( ~ ( class_Divides_Oring__div @ SV383 )
| ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3441,plain,
! [SV1228: $i,SV1190: $i,SV1021: $i,SV744: $i,SV384: $i] :
( ( ( ~ ( class_HOL_Ozero @ SV384 ) )
= $true )
| ( ( ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
!= ( c_Polynomial_OpCons @ SV1190 @ SV1228 @ SV384 ) )
| ( SV744 = SV1190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3442,plain,
! [SV385: $i,SV1022: $i,SV745: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1022 @ SV385 )
!= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ SV745 @ SV385 )
= SV1022 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV385 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3443,plain,
! [SV386: $i,SV746: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV746 @ SV386 )
= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
= $false )
| ( ( SV746
= ( c_HOL_Ozero__class_Ozero @ SV386 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3444,plain,
! [SV387: $i,SV1023: $i,SV747: $i] :
( ( ( ( c_Polynomial_Osmult @ SV747 @ SV1023 @ SV387 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
= $true )
| ( ( ( SV1023
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV387 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3445,plain,
! [SV1191: $i,SV1024: $i,SV748: $i,SV388: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV388 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SV1024 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV388 ) )
| ( SV748 = SV1024 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3446,plain,
! [SV389: $i,SV1025: $i,SV749: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV749 @ SV1025 @ SV389 )
!= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
= $true )
| ( ( SV749 = SV1025 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3231]) ).
thf(3447,plain,
! [SV1243: $i,SV1229: $i,SV1192: $i,SV1026: $i,SV750: $i,SV390: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV390 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1229 @ SV1026 @ SV390 ) @ SV1243 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SV1229 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SV1243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3448,plain,
! [SV391: $i,SV1027: $i,SV751: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV751 @ SV1027 @ SV391 )
!= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
= $true )
| ( ( SV751 = SV1027 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3449,plain,
! [SV1230: $i,SV1193: $i,SV1028: $i,SV752: $i,SV392: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SV1193 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SV1230 @ SV1193 @ SV392 ) )
| ( SV1230
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3234]) ).
thf(3450,plain,
! [SV1231: $i,SV1194: $i,SV1029: $i,SV753: $i,SV393: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV393 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3235]) ).
thf(3451,plain,
! [SV395: $i,SV1030: $i,SV754: $i] :
( ( ( ( c_Polynomial_Opoly @ SV754 @ SV1030 @ SV395 )
!= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV1030 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SV754 @ ( tc_Polynomial_Opoly @ SV395 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV395 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3452,plain,
! [SV396: $i,SV1031: $i,SV755: $i] :
( ( ( ( c_Polynomial_Opoly__gcd @ SV755 @ SV1031 @ SV396 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
= $true )
| ( ( SV755
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV396 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3237]) ).
thf(3453,plain,
! [SV1195: $i,SV1032: $i,SV756: $i,SV397: $i] :
( ( ( class_Divides_Oring__div @ SV397 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV756 @ SV1032 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SV1195 @ SV1032 @ SV397 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ SV397 ) @ SV1032 @ SV397 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3454,plain,
! [SV1232: $i,SV1196: $i,SV1033: $i,SV757: $i,SV398: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV398 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1196 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1232 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SV1196 @ SV398 )
= SV1232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3455,plain,
! [SV399: $i,SV758: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV758 @ SV399 )
= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
= $false )
| ( ( SV758
= ( c_HOL_Ozero__class_Ozero @ SV399 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV399 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3456,plain,
! [SV1197: $i,SV1034: $i,SV759: $i,SV400: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV400 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SV1034 @ SV1197 @ SV400 ) @ SV400 )
!= SV1034 )
| ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SV1197 @ SV400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3457,plain,
! [SV1244: $i,SV1233: $i,SV1198: $i,SV1035: $i,SV760: $i,SV401: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV401 )
| ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3458,plain,
! [SV1199: $i,SV1036: $i,SV761: $i,SV402: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV402 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV1199 @ SV402 ) )
| ( SV1036 = SV1199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3459,plain,
! [SV1037: $i,SV762: $i,SV403: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV403 ) )
= $true )
| ( ( ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
| ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3244]) ).
thf(3460,plain,
! [SV1038: $i,SV404: $i,SV763: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV763 @ SV404 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1038 @ SV404 ) )
= $true )
| ( ( SV763 = SV1038 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3461,plain,
! [SV405: $i,SV1039: $i,SV764: $i] :
( ( ( ( c_Polynomial_OpCons @ SV764 @ SV1039 @ SV405 )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
= $true )
| ( ( SV764
= ( c_HOL_Ozero__class_Ozero @ SV405 ) )
= $true )
| ( ( class_HOL_Ozero @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3462,plain,
! [SV1040: $i,SV406: $i,SV765: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV765 @ SV406 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1040 @ SV406 ) )
= $true )
| ( ( SV765 = SV1040 )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3463,plain,
! [SV1200: $i,SV1046: $i,SV772: $i,SV415: $i,SV9: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV9 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Polynomial_OpCons @ SV415 @ SV772 @ SV9 ) @ ( c_Polynomial_OpCons @ SV1046 @ SV1200 @ SV9 ) @ ( tc_Polynomial_Opoly @ SV9 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ominus__class_Ominus @ SV415 @ SV1046 @ SV9 ) @ ( c_HOL_Ominus__class_Ominus @ SV772 @ SV1200 @ ( tc_Polynomial_Opoly @ SV9 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3464,plain,
! [SV1201: $i,SV1047: $i,SV774: $i,SV417: $i,SV11: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_OpCons @ SV417 @ SV774 @ SV11 ) @ ( c_Polynomial_OpCons @ SV1047 @ SV1201 @ SV11 ) @ ( tc_Polynomial_Opoly @ SV11 ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Oplus__class_Oplus @ SV417 @ SV1047 @ SV11 ) @ ( c_HOL_Oplus__class_Oplus @ SV774 @ SV1201 @ ( tc_Polynomial_Opoly @ SV11 ) ) @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3465,plain,
! [SV419: $i,SV14: $i,SV776: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV776 @ SV14 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV14 ) ) @ SV14 ) @ SV14 ) @ SV419 @ ( tc_Polynomial_Opoly @ SV14 ) )
= $false )
| ( ( ( c_Polynomial_Opoly @ SV419 @ SV776 @ SV14 )
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3466,plain,
! [SV420: $i,SV15: $i,SV777: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV777 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV15 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV15 ) ) @ SV15 ) @ SV15 ) @ SV420 @ ( tc_Polynomial_Opoly @ SV15 ) )
= $false )
| ( ( ( c_Polynomial_Opoly @ SV420 @ ( c_HOL_Ouminus__class_Ouminus @ SV777 @ SV15 ) @ SV15 )
= ( c_HOL_Ozero__class_Ozero @ SV15 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3467,plain,
! [SV1202: $i,SV1049: $i,SV780: $i,SV423: $i,SV18: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV780 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV1049 @ SV1202 @ SV18 ) @ SV18 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV423 @ SV1049 @ SV18 ) @ ( c_HOL_Otimes__class_Otimes @ SV780 @ SV1202 @ SV18 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3468,plain,
! [SV1203: $i,SV1050: $i,SV781: $i,SV424: $i,SV19: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV424 @ SV781 @ SV19 ) @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SV1203 @ SV19 ) @ SV19 )
= ( c_HOL_Otimes__class_Otimes @ SV424 @ ( c_HOL_Otimes__class_Otimes @ SV781 @ ( c_HOL_Otimes__class_Otimes @ SV1050 @ SV1203 @ SV19 ) @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3469,plain,
! [SV1204: $i,SV1051: $i,SV782: $i,SV425: $i,SV20: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1204 @ SV20 ) @ SV20 )
= ( c_HOL_Otimes__class_Otimes @ SV1051 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV782 @ SV20 ) @ SV1204 @ SV20 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3470,plain,
! [SV1245: $i,SV1234: $i,SV1205: $i,SV1052: $i,SV783: $i,SV426: $i,SV21: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV21 )
| ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3471,plain,
! [SV1246: $i,SV1235: $i,SV1206: $i,SV1053: $i,SV784: $i,SV427: $i,SV22: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV22 )
| ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3472,plain,
! [SV1207: $i,SV1054: $i,SV791: $i,SV434: $i,SV30: $i] :
( ( ( class_Divides_Osemiring__div @ SV30 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3473,plain,
! [SV1055: $i,SV31: $i,SV792: $i,SV435: $i] :
( ( ( SV435 = SV792 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV792 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SV1055 @ SV435 @ SV31 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3474,plain,
! [SV1057: $i,SV798: $i,SV38: $i,SV442: $i] :
( ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SV798 @ SV1057 @ SV38 ) )
= $true )
| ( ( SV798
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3475,plain,
! [SV1058: $i,SV799: $i,SV39: $i,SV443: $i] :
( ( ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SV799 @ SV443 @ SV1058 @ SV39 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3476,plain,
! [SV1059: $i,SV800: $i,SV40: $i,SV444: $i] :
( ( ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SV800 @ SV1059 @ SV444 @ SV40 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3477,plain,
! [SV1060: $i,SV801: $i,SV41: $i,SV445: $i] :
( ( ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV801 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SV1060 @ SV41 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3478,plain,
! [SV1236: $i,SV1208: $i,SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV46 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3479,plain,
! [SV1237: $i,SV1209: $i,SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV47 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3480,plain,
! [SV52: $i,SV456: $i,SV811: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV811 @ SV456 @ SV52 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV456 @ ( c_HOL_Ouminus__class_Ouminus @ SV811 @ SV52 ) @ SV52 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV456 @ SV811 @ SV52 ) @ SV52 ) )
= $true )
| ( ( class_Divides_Oring__div @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3481,plain,
! [SV53: $i,SV457: $i,SV812: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV812 @ SV457 @ SV53 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ SV457 @ SV53 ) @ SV812 @ SV53 )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ SV457 @ SV812 @ SV53 ) @ SV53 ) )
= $true )
| ( ( class_Divides_Oring__div @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3482,plain,
! [SV1082: $i,SV79: $i,SV836: $i,SV482: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV836 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV482 @ SV1082 @ SV79 ) @ SV79 )
= ( c_Divides_Odiv__class_Odiv @ SV836 @ SV1082 @ SV79 ) )
= $true )
| ( ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV79 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3483,plain,
! [SV1083: $i,SV80: $i,SV837: $i,SV483: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV483 @ SV837 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1083 @ SV837 @ SV80 ) @ SV80 )
= ( c_Divides_Odiv__class_Odiv @ SV483 @ SV1083 @ SV80 ) )
= $true )
| ( ( SV837
= ( c_HOL_Ozero__class_Ozero @ SV80 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3484,plain,
! [SV1210: $i,SV1086: $i,SV841: $i,SV498: $i,SV95: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV95 )
= $false )
| ( ( ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SV1086 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SV1210 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
| ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SV1086 @ SV841 @ SV1210 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3485,plain,
! [SV1211: $i,SV1088: $i,SV843: $i,SV500: $i,SV97: $i] :
( ( ( class_Ring__and__Field_Oring @ SV97 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV843 @ SV97 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV500 @ SV97 ) @ SV843 @ SV97 ) @ SV1211 @ SV97 ) @ SV97 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1088 @ SV843 @ SV97 ) @ SV1211 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3486,plain,
! [SV1089: $i,SV98: $i,SV844: $i,SV501: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3487,plain,
! [SV1091: $i,SV847: $i,SV511: $i,SV108: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV108 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ SV108 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3488,plain,
! [SV1092: $i,SV848: $i,SV512: $i,SV109: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV109 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ SV109 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3489,plain,
! [SV1212: $i,SV1107: $i,SV870: $i,SV534: $i,SV133: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV133 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SV1107 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SV1212 @ SV1107 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3490,plain,
! [SV1213: $i,SV1108: $i,SV871: $i,SV535: $i,SV134: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV134 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV535 @ SV871 @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ SV1213 @ SV134 ) @ SV134 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SV1213 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV535 @ SV1108 @ SV134 ) @ SV1213 @ SV134 ) @ SV134 ) @ ( c_HOL_Otimes__class_Otimes @ SV1108 @ ( c_HOL_Ominus__class_Ominus @ SV871 @ SV1213 @ SV134 ) @ SV134 ) @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3491,plain,
! [SV1214: $i,SV1109: $i,SV872: $i,SV536: $i,SV135: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV135 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV536 @ SV872 @ SV135 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1109 @ SV872 @ SV135 ) @ SV1214 @ SV135 ) @ SV135 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV536 @ SV1109 @ SV135 ) @ SV872 @ SV135 ) @ SV1214 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3492,plain,
! [SV1215: $i,SV1114: $i,SV877: $i,SV545: $i,SV144: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV144 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV877 @ SV144 ) @ ( c_HOL_Oplus__class_Oplus @ SV1114 @ SV1215 @ SV144 ) @ SV144 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV545 @ SV1114 @ SV144 ) @ ( c_HOL_Ominus__class_Ominus @ SV877 @ SV1215 @ SV144 ) @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3493,plain,
! [SV1115: $i,SV145: $i,SV878: $i,SV546: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SV878 @ SV145 ) @ SV1115 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SV1115 @ SV145 ) @ SV878 @ SV145 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV878 @ SV546 @ SV145 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3331]) ).
thf(3494,plain,
! [SV1247: $i,SV1238: $i,SV1216: $i,SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ! [SY2849: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SY2849 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SY2849 @ SV1247 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3495,plain,
! [SV150: $i,SV883: $i,SV551: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV551 @ SV883 @ SV150 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV551 @ ( c_Divides_Odiv__class_Odiv @ SV883 @ SV551 @ SV150 ) @ SV150 )
= SV883 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3496,plain,
! [SV151: $i,SV552: $i,SV884: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV884 @ SV552 @ SV151 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV552 @ SV884 @ SV151 ) @ SV884 @ SV151 )
= SV552 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3497,plain,
! [SV1121: $i,SV155: $i,SV888: $i,SV556: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
= $true )
| ( ( ( SV1121
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV1121 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SV1121 @ SV155 ) @ SV155 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3498,plain,
! [SV1122: $i,SV156: $i,SV889: $i,SV557: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
= $true )
| ( ( ( SV1122
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV889 @ SV156 ) @ SV156 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3499,plain,
! [SV1217: $i,SV1123: $i,SV892: $i,SV576: $i,SV175: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV175 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV892 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1123 @ SV1217 @ SV175 ) @ SV175 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV576 @ SV1123 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV892 @ SV1217 @ SV175 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3500,plain,
! [SV183: $i,SV584: $i,SV898: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV898 @ SV584 @ SV183 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV584 @ SV898 @ SV183 )
= ( c_HOL_Ozero__class_Ozero @ SV183 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3501,plain,
! [SV187: $i,SV1127: $i,SV901: $i,SV588: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV588 @ ( c_Polynomial_Osmult @ SV901 @ SV1127 @ SV187 ) @ ( tc_Polynomial_Opoly @ SV187 ) )
= ( c_Divides_Odiv__class_Omod @ SV588 @ SV1127 @ ( tc_Polynomial_Opoly @ SV187 ) ) )
= $true )
| ( ( SV901
= ( c_HOL_Ozero__class_Ozero @ SV187 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3502,plain,
! [SV1218: $i,SV1128: $i,SV904: $i,SV594: $i,SV193: $i] :
( ( ( class_Ring__and__Field_Oring @ SV193 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV594 @ SV904 @ SV193 ) @ SV1128 @ SV193 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1218 @ SV904 @ SV193 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV594 @ SV1218 @ SV193 ) @ SV904 @ SV193 ) @ SV1128 @ SV193 ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3503,plain,
! [SV207: $i,SV1132: $i,SV914: $i,SV608: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV608 @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV1132 @ SV207 ) @ SV207 ) @ SV1132 @ SV207 )
= ( c_HOL_Oplus__class_Oplus @ SV914 @ ( c_Divides_Odiv__class_Odiv @ SV608 @ SV1132 @ SV207 ) @ SV207 ) )
= $true )
| ( ( SV1132
= ( c_HOL_Ozero__class_Ozero @ SV207 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3352]) ).
thf(3504,plain,
! [SV208: $i,SV1133: $i,SV915: $i,SV609: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV609 @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1133 @ SV208 ) @ SV208 ) @ SV915 @ SV208 )
= ( c_HOL_Oplus__class_Oplus @ SV1133 @ ( c_Divides_Odiv__class_Odiv @ SV609 @ SV915 @ SV208 ) @ SV208 ) )
= $true )
| ( ( SV915
= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3505,plain,
! [SV1219: $i,SV1134: $i,SV916: $i,SV611: $i,SV210: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV210 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SV1134 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SV1134 @ SV1219 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3506,plain,
! [SV1136: $i,SV212: $i,SV918: $i,SV613: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SV918 @ SV212 ) @ SV1136 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SV1136 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV918 @ SV1136 @ SV212 ) @ SV212 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV918 @ SV613 @ SV212 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3507,plain,
! [SV1220: $i,SV1140: $i,SV940: $i,SV652: $i,SV256: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3362]) ).
thf(3508,plain,
! [SV1141: $i,SV259: $i,SV941: $i,SV655: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SV941 @ SV259 ) @ SV1141 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SV1141 @ SV259 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1141 @ SV941 @ SV259 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3363]) ).
thf(3509,plain,
! [SV260: $i,SV1142: $i,SV942: $i,SV656: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3510,plain,
! [SV261: $i,SV1143: $i,SV943: $i,SV657: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3511,plain,
! [SV946: $i,SV660: $i,SV264: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV660 @ SV264 ) @ SV946 @ ( tc_Polynomial_Opoly @ SV264 ) )
= $false )
| ( ( SV946
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV264 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3512,plain,
! [SV265: $i,SV947: $i,SV661: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ SV947 @ SV265 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV661 @ ( c_HOL_Oabs__class_Oabs @ SV947 @ SV265 ) @ SV265 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3513,plain,
! [SV266: $i,SV948: $i,SV662: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ ( c_HOL_Oabs__class_Oabs @ SV948 @ SV266 ) @ SV266 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV662 @ SV948 @ SV266 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3514,plain,
! [SV267: $i,SV949: $i,SV663: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV663 @ SV949 @ SV267 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV663 @ SV267 ) @ SV949 @ SV267 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3515,plain,
! [SV950: $i,SV268: $i,SV664: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV664 @ SV268 ) @ SV950 @ SV268 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV664 @ SV950 @ SV268 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3516,plain,
! [SV1145: $i,SV271: $i,SV952: $i,SV667: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SV952 @ ( tc_Polynomial_Opoly @ SV271 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SV1145 @ SV952 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3517,plain,
! [SV1146: $i,SV272: $i,SV953: $i,SV668: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SV953 @ ( tc_Polynomial_Opoly @ SV272 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SV953 @ SV1146 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3518,plain,
! [SV1147: $i,SV273: $i,SV954: $i,SV669: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV954 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1147 @ SV954 @ SV273 ) @ SV273 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SV1147 @ SV273 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3519,plain,
! [SV1148: $i,SV274: $i,SV955: $i,SV670: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV955 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV1148 @ SV274 ) @ SV274 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV955 @ SV1148 @ SV274 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3520,plain,
! [SV277: $i,SV957: $i,SV673: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV673 @ SV957 @ SV277 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV673 @ SV277 ) @ SV957 @ SV277 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3521,plain,
! [SV958: $i,SV278: $i,SV674: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ SV674 @ SV278 ) @ SV958 @ SV278 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV674 @ SV958 @ SV278 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3378]) ).
thf(3522,plain,
! [SV279: $i,SV959: $i,SV675: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ SV959 @ SV279 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV675 @ ( c_HOL_Ouminus__class_Ouminus @ SV959 @ SV279 ) @ SV279 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3523,plain,
! [SV280: $i,SV960: $i,SV676: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ ( c_HOL_Ouminus__class_Ouminus @ SV960 @ SV280 ) @ SV280 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV676 @ SV960 @ SV280 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3524,plain,
! [SV1149: $i,SV281: $i,SV961: $i,SV677: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3525,plain,
! [SV1150: $i,SV282: $i,SV962: $i,SV678: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3526,plain,
! [SV283: $i,SV1151: $i,SV963: $i,SV679: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3527,plain,
! [SV1153: $i,SV286: $i,SV965: $i,SV682: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
= $true )
| ( ( ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SV1153 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3528,plain,
! [SV1154: $i,SV287: $i,SV966: $i,SV683: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
= $true )
| ( ( ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3529,plain,
! [SV1155: $i,SV288: $i,SV967: $i,SV684: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SV1155 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
| ( SV1155
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3530,plain,
! [SV289: $i,SV1156: $i,SV968: $i,SV685: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SV1156 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SV1156 @ ( tc_Polynomial_Opoly @ SV289 ) )
| ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3388]) ).
thf(3531,plain,
! [SV1157: $i,SV290: $i,SV969: $i,SV686: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
= $true )
| ( ( ( SV1157
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1157 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3389]) ).
thf(3532,plain,
! [SV1158: $i,SV291: $i,SV970: $i,SV687: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3533,plain,
! [SV688: $i,SV292: $i,SV971: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV971 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV688 @ SV971 @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV292 ) ) @ ( tc_Polynomial_Opoly @ SV292 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3534,plain,
! [SV1159: $i,SV293: $i,SV972: $i,SV689: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SV972 @ SV293 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1159 @ SV689 @ SV293 ) @ SV972 @ SV293 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3535,plain,
! [SV1160: $i,SV294: $i,SV973: $i,SV690: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SV973 @ SV294 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV1160 @ SV294 ) @ SV973 @ SV294 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3536,plain,
! [SV295: $i,SV1161: $i,SV974: $i,SV691: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV974 @ SV1161 @ SV295 ) @ SV295 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SV974 @ SV295 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3537,plain,
! [SV296: $i,SV1162: $i,SV975: $i,SV692: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SV975 @ SV1162 @ SV296 ) @ SV296 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SV1162 @ SV296 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3395]) ).
thf(3538,plain,
! [SV1163: $i,SV298: $i,SV976: $i,SV694: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3539,plain,
! [SV1239: $i,SV1221: $i,SV1164: $i,SV977: $i,SV697: $i,SV301: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV301 ) )
= $true )
| ( ( ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SV1221 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SV1239 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SV1221 @ SV1239 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3540,plain,
! [SV302: $i,SV1165: $i,SV978: $i,SV698: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3541,plain,
! [SV1167: $i,SV304: $i,SV980: $i,SV700: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3542,plain,
! [SV305: $i,SV1168: $i,SV981: $i,SV701: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3401]) ).
thf(3543,plain,
! [SV1169: $i,SV306: $i,SV982: $i,SV702: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3402]) ).
thf(3544,plain,
! [SV307: $i,SV1170: $i,SV983: $i,SV703: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(3545,plain,
! [SV1172: $i,SV312: $i,SV988: $i,SV708: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1172 @ SV708 @ SV312 ) @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3405]) ).
thf(3546,plain,
! [SV313: $i,SV1173: $i,SV989: $i,SV709: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SV989 @ SV1173 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SV1173 @ ( tc_Polynomial_Opoly @ SV313 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3406]) ).
thf(3547,plain,
! [SV1174: $i,SV314: $i,SV990: $i,SV710: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SV990 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SV1174 @ SV990 @ SV314 ) @ SV314 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SV1174 @ SV314 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3407]) ).
thf(3548,plain,
! [SV1178: $i,SV994: $i,SV714: $i,SV353: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV353 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
| ( SV994 = SV1178 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3411]) ).
thf(3549,plain,
! [SV1179: $i,SV354: $i,SV995: $i,SV715: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SV995 @ SV354 )
!= ( c_HOL_Oplus__class_Oplus @ SV715 @ SV1179 @ SV354 ) )
= $true )
| ( ( SV995 = SV1179 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3412]) ).
thf(3550,plain,
! [SV355: $i,SV996: $i,SV716: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV716 @ SV996 @ SV355 )
= ( c_HOL_Ozero__class_Ozero @ SV355 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV996 @ SV716 @ SV355 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3551,plain,
! [SV356: $i,SV997: $i,SV717: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SV997 @ SV356 )
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
= $false )
| ( ( ( SV997
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3552,plain,
! [SV357: $i,SV998: $i,SV718: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SV998 @ SV357 )
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $false )
| ( ( ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV998
= ( c_HOL_Ozero__class_Ozero @ SV357 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3553,plain,
! [SV358: $i,SV999: $i,SV719: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV719 @ SV999 @ SV358 )
= ( c_HOL_Ozero__class_Ozero @ SV358 ) )
= $false )
| ( ( SV719
= ( c_HOL_Ouminus__class_Ouminus @ SV999 @ SV358 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3554,plain,
! [SV1222: $i,SV1180: $i,SV1000: $i,SV720: $i,SV359: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV359 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV359 )
| ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
| ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3555,plain,
! [SV1223: $i,SV1181: $i,SV1001: $i,SV721: $i,SV360: $i] :
( ( ( class_HOL_Ozero @ SV360 )
= $false )
| ( ( ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
!= ( c_Polynomial_OpCons @ SV1181 @ SV1223 @ SV360 ) )
| ( SV1001 = SV1223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3556,plain,
! [SV1002: $i,SV362: $i,SV723: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV723 @ SV362 )
= ( c_HOL_Oabs__class_Oabs @ SV1002 @ SV362 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV723 @ SV1002 @ SV362 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3420]) ).
thf(3557,plain,
! [SV363: $i,SV1003: $i,SV724: $i] :
( ( ( ( c_Polynomial_Opoly @ SV724 @ ( c_HOL_Ouminus__class_Ouminus @ SV1003 @ SV363 ) @ SV363 )
= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ SV1003 @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV363 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV363 ) ) @ SV363 ) @ SV363 ) @ SV724 @ ( tc_Polynomial_Opoly @ SV363 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3558,plain,
! [SV1240: $i,SV1224: $i,SV1182: $i,SV1004: $i,SV726: $i,SV365: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV365 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1224 @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
| ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1224 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(3559,plain,
! [SV1241: $i,SV1225: $i,SV1183: $i,SV1005: $i,SV727: $i,SV366: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV366 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(3560,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV367 )
| ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3561,plain,
! [SV1184: $i,SV368: $i,SV1007: $i,SV729: $i] :
( ( ( ( c_Polynomial_Osmult @ SV729 @ SV1007 @ SV368 )
!= ( c_Polynomial_OpCons @ SV1184 @ SV1007 @ SV368 ) )
= $true )
| ( ( SV1007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(3562,plain,
! [SV1185: $i,SV369: $i,SV1008: $i,SV730: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SV1008 @ SV369 )
!= ( c_HOL_Oplus__class_Oplus @ SV1185 @ SV1008 @ SV369 ) )
= $true )
| ( ( SV730 = SV1185 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(3563,plain,
! [SV370: $i,SV1009: $i,SV731: $i] :
( ( ( ( c_Polynomial_Opoly__gcd @ SV731 @ SV1009 @ SV370 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
= $false )
| ( ( SV1009
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV370 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3428]) ).
thf(3564,plain,
! [SV1010: $i,SV732: $i,SV371: $i] :
( ( ( class_Int_Onumber__ring @ SV371 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
| ( SV732 = SV1010 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3429]) ).
thf(3565,plain,
! [SV372: $i,SV1011: $i,SV733: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV733 @ SV1011 @ SV372 )
= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
= $false )
| ( ( SV733
= ( c_HOL_Ozero__class_Ozero @ SV372 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(3566,plain,
! [SV1012: $i,SV373: $i,SV734: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV734 @ SV734 @ SV373 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1012 @ SV373 ) @ SV373 )
= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
= $false )
| ( ( SV1012
= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3567,plain,
! [SV1186: $i,SV374: $i,SV1013: $i,SV735: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SV1013 @ SV374 ) @ ( c_Polynomial_OpCons @ SV1186 @ SV1013 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
= $true )
| ( ( SV1013
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3432]) ).
thf(3568,plain,
! [SV376: $i,SV1014: $i,SV736: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SV1014 @ SV376 )
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
= $false )
| ( ( ( SV1014
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
| ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3569,plain,
! [SV1226: $i,SV1187: $i,SV1015: $i,SV737: $i,SV377: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3570,plain,
! [SV378: $i,SV1016: $i,SV738: $i] :
( ( ( ( c_Polynomial_OpCons @ SV738 @ SV1016 @ SV378 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
= $false )
| ( ( SV1016
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV378 ) ) )
= $true )
| ( ( class_HOL_Ozero @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3435]) ).
thf(3571,plain,
! [SV1188: $i,SV379: $i,SV1017: $i,SV739: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1017 @ SV379 )
!= ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1188 @ SV379 ) )
= $true )
| ( ( SV1017 = SV1188 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3436]) ).
thf(3572,plain,
! [SV1018: $i,SV381: $i,SV741: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
= ( c_HOL_Otimes__class_Otimes @ SV1018 @ SV1018 @ SV381 ) )
= $false )
| ( ( ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SV1018 @ SV381 ) )
| ( SV741 = SV1018 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3573,plain,
! [SV1019: $i,SV382: $i,SV742: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV742 @ SV382 ) @ ( c_HOL_Otimes__class_Otimes @ SV1019 @ SV1019 @ SV382 ) @ SV382 )
= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
= $false )
| ( ( SV742
= ( c_HOL_Ozero__class_Ozero @ SV382 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(3574,plain,
! [SV1242: $i,SV1227: $i,SV1189: $i,SV1020: $i,SV743: $i,SV383: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV383 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(3575,plain,
! [SV1228: $i,SV1190: $i,SV1021: $i,SV744: $i,SV384: $i] :
( ( ( class_HOL_Ozero @ SV384 )
= $false )
| ( ( ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
!= ( c_Polynomial_OpCons @ SV1190 @ SV1228 @ SV384 ) )
| ( SV744 = SV1190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3441]) ).
thf(3576,plain,
! [SV385: $i,SV1022: $i,SV745: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1022 @ SV385 )
= ( c_HOL_Ozero__class_Ozero @ SV385 ) )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ SV745 @ SV385 )
= SV1022 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV385 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3577,plain,
! [SV387: $i,SV1023: $i,SV747: $i] :
( ( ( ( c_Polynomial_Osmult @ SV747 @ SV1023 @ SV387 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
= $false )
| ( ( ( SV1023
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3578,plain,
! [SV1191: $i,SV388: $i,SV1024: $i,SV748: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SV1024 @ SV388 )
!= ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV388 ) )
= $true )
| ( ( SV748 = SV1024 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(3579,plain,
! [SV389: $i,SV1025: $i,SV749: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV749 @ SV1025 @ SV389 )
= ( c_HOL_Ozero__class_Ozero @ SV389 ) )
= $false )
| ( ( SV749 = SV1025 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3580,plain,
! [SV1243: $i,SV1229: $i,SV1192: $i,SV1026: $i,SV750: $i,SV390: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV390 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1229 @ SV1026 @ SV390 ) @ SV1243 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SV1229 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SV1243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3447]) ).
thf(3581,plain,
! [SV391: $i,SV1027: $i,SV751: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV751 @ SV1027 @ SV391 )
= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
= $false )
| ( ( SV751 = SV1027 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(3582,plain,
! [SV1230: $i,SV1193: $i,SV1028: $i,SV752: $i,SV392: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SV1193 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SV1230 @ SV1193 @ SV392 ) )
| ( SV1230
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3449]) ).
thf(3583,plain,
! [SV1231: $i,SV1194: $i,SV1029: $i,SV753: $i,SV393: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV393 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV393 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3450]) ).
thf(3584,plain,
! [SV395: $i,SV1030: $i,SV754: $i] :
( ( ( ( c_Polynomial_Opoly @ SV754 @ SV1030 @ SV395 )
= ( c_HOL_Ozero__class_Ozero @ SV395 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ SV1030 @ SV395 ) @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ SV395 ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV395 ) ) @ SV395 ) @ SV395 ) @ SV754 @ ( tc_Polynomial_Opoly @ SV395 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV395 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3585,plain,
! [SV396: $i,SV1031: $i,SV755: $i] :
( ( ( ( c_Polynomial_Opoly__gcd @ SV755 @ SV1031 @ SV396 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
= $false )
| ( ( SV755
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV396 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3586,plain,
! [SV1195: $i,SV397: $i,SV1032: $i,SV756: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV756 @ SV1032 @ SV397 )
!= ( c_Divides_Odiv__class_Omod @ SV1195 @ SV1032 @ SV397 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ SV397 ) @ SV1032 @ SV397 ) )
= $true )
| ( ( class_Divides_Oring__div @ SV397 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3453]) ).
thf(3587,plain,
! [SV1232: $i,SV1196: $i,SV1033: $i,SV757: $i,SV398: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV398 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1196 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1232 @ SV398 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SV1196 @ SV398 )
= SV1232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3588,plain,
! [SV400: $i,SV1197: $i,SV1034: $i,SV759: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SV1034 @ SV1197 @ SV400 ) @ SV400 )
!= SV1034 )
= $true )
| ( ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SV1197 @ SV400 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV400 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3456]) ).
thf(3589,plain,
! [SV1244: $i,SV1233: $i,SV1198: $i,SV1035: $i,SV760: $i,SV401: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV401 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(3590,plain,
! [SV1199: $i,SV1036: $i,SV402: $i,SV761: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
!= ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV1199 @ SV402 ) )
= $true )
| ( ( SV1036 = SV1199 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3458]) ).
thf(3591,plain,
! [SV1037: $i,SV762: $i,SV403: $i] :
( ( ( class_Int_Onumber__ring @ SV403 )
= $false )
| ( ( ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
| ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3592,plain,
! [SV1038: $i,SV404: $i,SV763: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV763 @ SV404 )
= ( c_HOL_Ouminus__class_Ouminus @ SV1038 @ SV404 ) )
= $false )
| ( ( SV763 = SV1038 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3593,plain,
! [SV405: $i,SV1039: $i,SV764: $i] :
( ( ( ( c_Polynomial_OpCons @ SV764 @ SV1039 @ SV405 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV405 ) ) )
= $false )
| ( ( SV764
= ( c_HOL_Ozero__class_Ozero @ SV405 ) )
= $true )
| ( ( class_HOL_Ozero @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3594,plain,
! [SV1040: $i,SV406: $i,SV765: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV765 @ SV406 )
= ( c_HOL_Ouminus__class_Ouminus @ SV1040 @ SV406 ) )
= $false )
| ( ( SV765 = SV1040 )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3595,plain,
! [SV1245: $i,SV1234: $i,SV1205: $i,SV1052: $i,SV783: $i,SV426: $i,SV21: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV21 ) )
= $true )
| ( ( ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(3596,plain,
! [SV1246: $i,SV1235: $i,SV1206: $i,SV1053: $i,SV784: $i,SV427: $i,SV22: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV22 ) )
= $true )
| ( ( ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(3597,plain,
! [SV1207: $i,SV1054: $i,SV30: $i,SV791: $i,SV434: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3472]) ).
thf(3598,plain,
! [SV435: $i,SV1055: $i,SV31: $i,SV792: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV792 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV31 ) ) @ SV1055 @ SV435 @ SV31 )
= $false )
| ( ( SV435 = SV792 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3599,plain,
! [SV1057: $i,SV798: $i,SV38: $i,SV442: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV442 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) @ SV798 @ SV1057 @ SV38 )
= $false )
| ( ( SV798
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV38 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3600,plain,
! [SV1058: $i,SV443: $i,SV799: $i,SV39: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) @ SV799 @ SV443 @ SV1058 @ SV39 )
= $false )
| ( ( SV443
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV39 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3601,plain,
! [SV444: $i,SV1059: $i,SV800: $i,SV40: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) @ SV800 @ SV1059 @ SV444 @ SV40 )
= $false )
| ( ( SV444
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV40 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3602,plain,
! [SV1060: $i,SV445: $i,SV41: $i,SV801: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV801 @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) @ SV445 @ SV1060 @ SV41 )
= $false )
| ( ( SV445
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV41 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3603,plain,
! [SV1236: $i,SV1208: $i,SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3604,plain,
! [SV1237: $i,SV1209: $i,SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3605,plain,
! [SV1210: $i,SV95: $i,SV1086: $i,SV841: $i,SV498: $i] :
( ( ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SV1086 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SV1210 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV498 @ SV1086 @ SV841 @ SV1210 @ SV95 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3606,plain,
! [SV501: $i,SV98: $i,SV844: $i,SV1089: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3486]) ).
thf(3607,plain,
! [SV1091: $i,SV847: $i,SV511: $i,SV108: $i] :
( ( ( class_Int_Onumber__ring @ SV108 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ SV108 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV1091 @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV511 @ SV847 @ SV108 ) @ SV108 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3608,plain,
! [SV1092: $i,SV848: $i,SV512: $i,SV109: $i] :
( ( ( class_Int_Onumber__ring @ SV109 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ SV109 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV1092 @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV512 @ SV848 @ SV109 ) @ SV109 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3609,plain,
! [SV1212: $i,SV1107: $i,SV133: $i,SV870: $i,SV534: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SV1107 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SV1212 @ SV1107 @ SV133 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3489]) ).
thf(3610,plain,
! [SV1115: $i,SV145: $i,SV546: $i,SV878: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV878 @ SV546 @ SV145 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV546 @ SV878 @ SV145 ) @ SV1115 @ SV145 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV546 @ SV1115 @ SV145 ) @ SV878 @ SV145 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3611,plain,
! [SV1248: $i,SV1247: $i,SV1238: $i,SV1216: $i,SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(3612,plain,
! [SV888: $i,SV556: $i,SV155: $i,SV1121: $i] :
( ( ( SV1121
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV1121 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SV1121 @ SV155 ) @ SV155 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3497]) ).
thf(3613,plain,
! [SV889: $i,SV557: $i,SV156: $i,SV1122: $i] :
( ( ( SV1122
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV889 @ SV156 ) @ SV156 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3498]) ).
thf(3614,plain,
! [SV1219: $i,SV1134: $i,SV210: $i,SV916: $i,SV611: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SV1134 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SV1134 @ SV1219 @ SV210 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3505]) ).
thf(3615,plain,
! [SV1136: $i,SV212: $i,SV613: $i,SV918: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV918 @ SV613 @ SV212 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV613 @ SV918 @ SV212 ) @ SV1136 @ SV212 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV613 @ SV1136 @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV918 @ SV1136 @ SV212 ) @ SV212 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3616,plain,
! [SV1220: $i,SV1140: $i,SV256: $i,SV940: $i,SV652: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(3617,plain,
! [SV655: $i,SV259: $i,SV941: $i,SV1141: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1141 @ SV941 @ SV259 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV655 @ SV941 @ SV259 ) @ SV1141 @ SV259 )
= ( c_Divides_Odiv__class_Omod @ SV655 @ SV1141 @ SV259 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(3618,plain,
! [SV942: $i,SV260: $i,SV1142: $i,SV656: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3619,plain,
! [SV943: $i,SV261: $i,SV1143: $i,SV657: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3510]) ).
thf(3620,plain,
! [SV271: $i,SV952: $i,SV1145: $i,SV667: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ ( c_Polynomial_Opoly__gcd @ SV1145 @ SV952 @ SV271 ) @ ( tc_Polynomial_Opoly @ SV271 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV667 @ SV952 @ ( tc_Polynomial_Opoly @ SV271 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3621,plain,
! [SV272: $i,SV1146: $i,SV953: $i,SV668: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ ( c_Polynomial_Opoly__gcd @ SV953 @ SV1146 @ SV272 ) @ ( tc_Polynomial_Opoly @ SV272 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV668 @ SV953 @ ( tc_Polynomial_Opoly @ SV272 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(3622,plain,
! [SV954: $i,SV273: $i,SV1147: $i,SV669: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV669 @ SV1147 @ SV273 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV954 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1147 @ SV954 @ SV273 ) @ SV273 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3623,plain,
! [SV670: $i,SV274: $i,SV1148: $i,SV955: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV955 @ SV1148 @ SV274 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV955 @ SV274 ) @ ( c_HOL_Otimes__class_Otimes @ SV670 @ SV1148 @ SV274 ) @ SV274 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3624,plain,
! [SV961: $i,SV281: $i,SV1149: $i,SV677: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3524]) ).
thf(3625,plain,
! [SV962: $i,SV282: $i,SV1150: $i,SV678: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3525]) ).
thf(3626,plain,
! [SV963: $i,SV283: $i,SV1151: $i,SV679: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(3627,plain,
! [SV965: $i,SV682: $i,SV286: $i,SV1153: $i] :
( ( ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SV1153 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(3628,plain,
! [SV1154: $i,SV966: $i,SV287: $i,SV683: $i] :
( ( ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(3629,plain,
! [SV288: $i,SV967: $i,SV1155: $i,SV684: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SV1155 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) ) )
= $true )
| ( ( SV1155
= ( c_HOL_Ozero__class_Ozero @ SV288 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(3630,plain,
! [SV968: $i,SV289: $i,SV1156: $i,SV685: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SV1156 @ ( tc_Polynomial_Opoly @ SV289 ) ) )
= $true )
| ( ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SV1156 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(3631,plain,
! [SV969: $i,SV686: $i,SV290: $i,SV1157: $i] :
( ( ( SV1157
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1157 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(3632,plain,
! [SV687: $i,SV291: $i,SV1158: $i,SV970: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) ) )
= $true )
| ( ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(3633,plain,
! [SV972: $i,SV293: $i,SV689: $i,SV1159: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1159 @ SV689 @ SV293 ) @ SV972 @ SV293 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV689 @ SV972 @ SV293 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3634,plain,
! [SV973: $i,SV294: $i,SV1160: $i,SV690: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV1160 @ SV294 ) @ SV973 @ SV294 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV690 @ SV973 @ SV294 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3635,plain,
! [SV1161: $i,SV295: $i,SV974: $i,SV691: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ SV974 @ SV295 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV974 @ SV1161 @ SV295 ) @ SV295 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3636,plain,
! [SV975: $i,SV296: $i,SV1162: $i,SV692: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ SV1162 @ SV296 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV692 @ ( c_HOL_Otimes__class_Otimes @ SV975 @ SV1162 @ SV296 ) @ SV296 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(3637,plain,
! [SV694: $i,SV298: $i,SV976: $i,SV1163: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(3638,plain,
! [SV1239: $i,SV1221: $i,SV1164: $i,SV977: $i,SV697: $i,SV301: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV301 )
= $false )
| ( ( ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SV1221 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SV1239 @ SV301 ) @ SV301 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SV1221 @ SV1239 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3539]) ).
thf(3639,plain,
! [SV978: $i,SV302: $i,SV1165: $i,SV698: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(3640,plain,
! [SV980: $i,SV304: $i,SV1167: $i,SV700: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3641,plain,
! [SV1168: $i,SV305: $i,SV981: $i,SV701: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(3642,plain,
! [SV306: $i,SV1169: $i,SV982: $i,SV702: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(3643,plain,
! [SV983: $i,SV307: $i,SV1170: $i,SV703: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3644,plain,
! [SV988: $i,SV312: $i,SV708: $i,SV1172: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1172 @ SV708 @ SV312 ) @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV988 @ ( tc_Polynomial_Opoly @ SV312 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3545]) ).
thf(3645,plain,
! [SV989: $i,SV313: $i,SV1173: $i,SV709: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ SV1173 @ ( tc_Polynomial_Opoly @ SV313 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV709 @ ( c_Polynomial_Osmult @ SV989 @ SV1173 @ SV313 ) @ ( tc_Polynomial_Opoly @ SV313 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3646,plain,
! [SV990: $i,SV314: $i,SV1174: $i,SV710: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV710 @ SV1174 @ SV314 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV710 @ SV990 @ SV314 ) @ ( c_Power_Opower__class_Opower @ SV1174 @ SV990 @ SV314 ) @ SV314 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3647,plain,
! [SV1178: $i,SV994: $i,SV714: $i,SV353: $i] :
( ( ( class_Int_Onumber__ring @ SV353 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
| ( SV994 = SV1178 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3648,plain,
! [SV1179: $i,SV354: $i,SV995: $i,SV715: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV715 @ SV995 @ SV354 )
= ( c_HOL_Oplus__class_Oplus @ SV715 @ SV1179 @ SV354 ) )
= $false )
| ( ( SV995 = SV1179 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3649,plain,
! [SV717: $i,SV356: $i,SV997: $i] :
( ( ( SV997
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
= $true )
| ( ( SV717
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV717 @ SV997 @ SV356 )
= ( c_HOL_Ozero__class_Ozero @ SV356 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3551]) ).
thf(3650,plain,
! [SV998: $i,SV357: $i,SV718: $i] :
( ( ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $true )
| ( ( SV998
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV718 @ SV998 @ SV357 )
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(3651,plain,
! [SV1222: $i,SV1180: $i,SV1000: $i,SV720: $i,SV359: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV359 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
| ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3652,plain,
! [SV1223: $i,SV1181: $i,SV360: $i,SV1001: $i,SV721: $i] :
( ( ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
!= ( c_Polynomial_OpCons @ SV1181 @ SV1223 @ SV360 ) )
= $true )
| ( ( SV1001 = SV1223 )
= $true )
| ( ( class_HOL_Ozero @ SV360 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(3653,plain,
! [SV1240: $i,SV1224: $i,SV1182: $i,SV1004: $i,SV726: $i,SV365: $i] :
( ( ( class_Ring__and__Field_Oring @ SV365 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1224 @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
| ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1224 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3654,plain,
! [SV1241: $i,SV1225: $i,SV1183: $i,SV1005: $i,SV727: $i,SV366: $i] :
( ( ( class_Divides_Osemiring__div @ SV366 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3655,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV367 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3656,plain,
! [SV1184: $i,SV368: $i,SV1007: $i,SV729: $i] :
( ( ( ( c_Polynomial_Osmult @ SV729 @ SV1007 @ SV368 )
= ( c_Polynomial_OpCons @ SV1184 @ SV1007 @ SV368 ) )
= $false )
| ( ( SV1007
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV368 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3561]) ).
thf(3657,plain,
! [SV1185: $i,SV369: $i,SV1008: $i,SV730: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV730 @ SV1008 @ SV369 )
= ( c_HOL_Oplus__class_Oplus @ SV1185 @ SV1008 @ SV369 ) )
= $false )
| ( ( SV730 = SV1185 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3658,plain,
! [SV371: $i,SV1010: $i,SV732: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
!= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
= $true )
| ( ( SV732 = SV1010 )
= $true )
| ( ( class_Int_Onumber__ring @ SV371 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV371 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3659,plain,
! [SV1186: $i,SV374: $i,SV1013: $i,SV735: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Osmult @ SV735 @ SV1013 @ SV374 ) @ ( c_Polynomial_OpCons @ SV1186 @ SV1013 @ SV374 ) @ ( tc_Polynomial_Opoly @ SV374 ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
= $false )
| ( ( SV1013
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV374 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3660,plain,
! [SV736: $i,SV376: $i,SV1014: $i] :
( ( ( SV1014
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
= $true )
| ( ( SV736
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV736 @ SV1014 @ SV376 )
= ( c_HOL_Ozero__class_Ozero @ SV376 ) )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(3661,plain,
! [SV1226: $i,SV1187: $i,SV1015: $i,SV737: $i,SV377: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV377 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(3662,plain,
! [SV1188: $i,SV379: $i,SV1017: $i,SV739: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1017 @ SV379 )
= ( c_HOL_Oplus__class_Oplus @ SV739 @ SV1188 @ SV379 ) )
= $false )
| ( ( SV1017 = SV1188 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3571]) ).
thf(3663,plain,
! [SV381: $i,SV1018: $i,SV741: $i] :
( ( ( SV741
= ( c_HOL_Ouminus__class_Ouminus @ SV1018 @ SV381 ) )
= $true )
| ( ( SV741 = SV1018 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV741 @ SV741 @ SV381 )
= ( c_HOL_Otimes__class_Otimes @ SV1018 @ SV1018 @ SV381 ) )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(3664,plain,
! [SV1242: $i,SV1227: $i,SV1189: $i,SV1020: $i,SV743: $i,SV383: $i] :
( ( ( class_Divides_Oring__div @ SV383 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3665,plain,
! [SV1228: $i,SV1190: $i,SV384: $i,SV1021: $i,SV744: $i] :
( ( ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
!= ( c_Polynomial_OpCons @ SV1190 @ SV1228 @ SV384 ) )
= $true )
| ( ( SV744 = SV1190 )
= $true )
| ( ( class_HOL_Ozero @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3575]) ).
thf(3666,plain,
! [SV747: $i,SV387: $i,SV1023: $i] :
( ( ( SV1023
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
= $true )
| ( ( SV747
= ( c_HOL_Ozero__class_Ozero @ SV387 ) )
= $true )
| ( ( ( c_Polynomial_Osmult @ SV747 @ SV1023 @ SV387 )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ SV387 ) ) )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV387 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3577]) ).
thf(3667,plain,
! [SV1191: $i,SV388: $i,SV1024: $i,SV748: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV748 @ SV1024 @ SV388 )
= ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV388 ) )
= $false )
| ( ( SV748 = SV1024 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3668,plain,
! [SV1243: $i,SV1229: $i,SV1192: $i,SV1026: $i,SV750: $i,SV390: $i] :
( ( ( class_Ring__and__Field_Oring @ SV390 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1229 @ SV1026 @ SV390 ) @ SV1243 @ SV390 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SV1229 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SV1243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3580]) ).
thf(3669,plain,
! [SV1230: $i,SV392: $i,SV1193: $i,SV1028: $i,SV752: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SV1193 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
!= ( c_Polynomial_OpCons @ SV1230 @ SV1193 @ SV392 ) )
= $true )
| ( ( SV1230
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3582]) ).
thf(3670,plain,
! [SV1231: $i,SV1194: $i,SV1029: $i,SV753: $i,SV393: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV393 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3671,plain,
! [SV1195: $i,SV397: $i,SV1032: $i,SV756: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV756 @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ SV1195 @ SV1032 @ SV397 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV756 @ SV397 ) @ SV1032 @ SV397 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ SV397 ) @ SV1032 @ SV397 ) )
= $true )
| ( ( class_Divides_Oring__div @ SV397 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3672,plain,
! [SV1232: $i,SV398: $i,SV1196: $i,SV1033: $i,SV757: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1196 @ SV398 ) @ SV398 )
!= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1232 @ SV398 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SV1196 @ SV398 )
= SV1232 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV398 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(3673,plain,
! [SV400: $i,SV1197: $i,SV1034: $i,SV759: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Oplus__class_Oplus @ SV1034 @ SV1197 @ SV400 ) @ SV400 )
= SV1034 )
= $false )
| ( ( SV759
= ( c_HOL_Ouminus__class_Ouminus @ SV1197 @ SV400 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(3674,plain,
! [SV1244: $i,SV1233: $i,SV1198: $i,SV1035: $i,SV760: $i,SV401: $i] :
( ( ( class_Divides_Osemiring__div @ SV401 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3675,plain,
! [SV1199: $i,SV1036: $i,SV402: $i,SV761: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV761 @ SV761 @ SV402 )
= ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV1199 @ SV402 ) )
= $false )
| ( ( SV1036 = SV1199 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3676,plain,
! [SV403: $i,SV1037: $i,SV762: $i] :
( ( ( SV762
!= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
= $true )
| ( ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV403 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(3677,plain,
! [SV1245: $i,SV1234: $i,SV1205: $i,SV1052: $i,SV783: $i,SV426: $i,SV21: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV21 )
= $false )
| ( ( ( SV426 = SV783 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3595]) ).
thf(3678,plain,
! [SV1246: $i,SV1235: $i,SV1206: $i,SV1053: $i,SV784: $i,SV427: $i,SV22: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV22 )
= $false )
| ( ( ( SV427 = SV784 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3596]) ).
thf(3679,plain,
! [SV434: $i,SV791: $i,SV30: $i,SV1054: $i,SV1207: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(3680,plain,
! [SV1236: $i,SV1208: $i,SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV46 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(3681,plain,
! [SV1237: $i,SV1209: $i,SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV47 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3604]) ).
thf(3682,plain,
! [SV95: $i,SV1210: $i,SV841: $i,SV1086: $i,SV498: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV498 @ SV1086 @ SV841 @ SV1210 @ SV95 )
= $false )
| ( ( SV498
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV841 @ SV1086 @ ( tc_Polynomial_Opoly @ SV95 ) ) @ SV1210 @ ( tc_Polynomial_Opoly @ SV95 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3605]) ).
thf(3683,plain,
! [SV501: $i,SV98: $i,SV844: $i,SV1089: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3684,plain,
! [SV133: $i,SV1107: $i,SV1212: $i,SV870: $i,SV534: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV534 @ SV870 @ SV1212 @ SV1107 @ SV133 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV534 @ SV870 @ ( tc_Polynomial_Opoly @ SV133 ) )
= SV1107 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3609]) ).
thf(3685,plain,
! [SV1248: $i,SV1247: $i,SV1238: $i,SV1216: $i,SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV149 ) )
= $true )
| ( ( ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3611]) ).
thf(3686,plain,
! [SV888: $i,SV155: $i,SV1121: $i,SV556: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV1121 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV888 @ SV1121 @ SV155 ) @ SV155 )
= $false )
| ( ( SV1121
= ( c_HOL_Ozero__class_Ozero @ SV155 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV556 @ SV888 @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3687,plain,
! [SV889: $i,SV156: $i,SV557: $i,SV1122: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV557 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV889 @ SV156 ) @ SV156 )
= $false )
| ( ( SV1122
= ( c_HOL_Ozero__class_Ozero @ SV156 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV557 @ SV889 @ SV156 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(3688,plain,
! [SV210: $i,SV1219: $i,SV1134: $i,SV916: $i,SV611: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV611 @ SV916 @ SV1134 @ SV1219 @ SV210 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV611 @ SV916 @ ( tc_Polynomial_Opoly @ SV210 ) )
= SV1134 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3689,plain,
! [SV1140: $i,SV652: $i,SV256: $i,SV1220: $i,SV940: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(3690,plain,
! [SV942: $i,SV260: $i,SV1142: $i,SV656: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3691,plain,
! [SV943: $i,SV261: $i,SV1143: $i,SV657: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3692,plain,
! [SV961: $i,SV281: $i,SV1149: $i,SV677: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3693,plain,
! [SV962: $i,SV282: $i,SV1150: $i,SV678: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3694,plain,
! [SV963: $i,SV283: $i,SV1151: $i,SV679: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3626]) ).
thf(3695,plain,
! [SV286: $i,SV965: $i,SV1153: $i,SV682: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ ( c_Polynomial_Osmult @ SV1153 @ SV965 @ SV286 ) @ ( tc_Polynomial_Opoly @ SV286 ) )
= $false )
| ( ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV965 @ ( tc_Polynomial_Opoly @ SV286 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3696,plain,
! [SV683: $i,SV287: $i,SV1154: $i,SV966: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV966 @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
= $false )
| ( ( SV683
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV683 @ SV966 @ SV287 ) @ SV1154 @ ( tc_Polynomial_Opoly @ SV287 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(3697,plain,
! [SV288: $i,SV967: $i,SV1155: $i,SV684: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ ( c_Polynomial_Osmult @ SV1155 @ SV967 @ SV288 ) @ ( tc_Polynomial_Opoly @ SV288 ) )
= $false )
| ( ( SV1155
= ( c_HOL_Ozero__class_Ozero @ SV288 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV684 @ SV967 @ ( tc_Polynomial_Opoly @ SV288 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3698,plain,
! [SV968: $i,SV289: $i,SV1156: $i,SV685: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ SV1156 @ ( tc_Polynomial_Opoly @ SV289 ) )
= $false )
| ( ( SV968
= ( c_HOL_Ozero__class_Ozero @ SV289 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV685 @ ( c_Polynomial_Osmult @ SV968 @ SV1156 @ SV289 ) @ ( tc_Polynomial_Opoly @ SV289 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3699,plain,
! [SV969: $i,SV290: $i,SV686: $i,SV1157: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV1157 @ SV686 @ SV290 ) @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
= $false )
| ( ( SV1157
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV686 @ SV969 @ ( tc_Polynomial_Opoly @ SV290 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3631]) ).
thf(3700,plain,
! [SV687: $i,SV291: $i,SV1158: $i,SV970: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV970 @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
= $false )
| ( ( SV687
= ( c_HOL_Ozero__class_Ozero @ SV291 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Polynomial_Osmult @ SV687 @ SV970 @ SV291 ) @ SV1158 @ ( tc_Polynomial_Opoly @ SV291 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3632]) ).
thf(3701,plain,
! [SV694: $i,SV298: $i,SV976: $i,SV1163: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3637]) ).
thf(3702,plain,
! [SV1239: $i,SV1221: $i,SV1164: $i,SV301: $i,SV977: $i,SV697: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SV1221 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SV1239 @ SV301 ) @ SV301 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SV1221 @ SV1239 @ SV301 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(3703,plain,
! [SV978: $i,SV302: $i,SV1165: $i,SV698: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3704,plain,
! [SV980: $i,SV304: $i,SV1167: $i,SV700: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3640]) ).
thf(3705,plain,
! [SV1168: $i,SV305: $i,SV981: $i,SV701: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(3706,plain,
! [SV306: $i,SV1169: $i,SV982: $i,SV702: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3707,plain,
! [SV983: $i,SV307: $i,SV1170: $i,SV703: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3643]) ).
thf(3708,plain,
! [SV1178: $i,SV353: $i,SV994: $i,SV714: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
!= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
= $true )
| ( ( SV994 = SV1178 )
= $true )
| ( ( class_Int_Onumber__ring @ SV353 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(3709,plain,
! [SV1222: $i,SV1180: $i,SV1000: $i,SV720: $i,SV359: $i] :
( ( ( class_Int_Onumber__ring @ SV359 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
| ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(3710,plain,
! [SV1223: $i,SV1181: $i,SV360: $i,SV1001: $i,SV721: $i] :
( ( ( ( c_Polynomial_OpCons @ SV721 @ SV1001 @ SV360 )
= ( c_Polynomial_OpCons @ SV1181 @ SV1223 @ SV360 ) )
= $false )
| ( ( SV1001 = SV1223 )
= $true )
| ( ( class_HOL_Ozero @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3711,plain,
! [SV1240: $i,SV1224: $i,SV1182: $i,SV365: $i,SV1004: $i,SV726: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1224 @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
= $true )
| ( ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1224 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3653]) ).
thf(3712,plain,
! [SV1241: $i,SV1225: $i,SV1183: $i,SV366: $i,SV1005: $i,SV727: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(3713,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV367 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV367 )
| ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(3714,plain,
! [SV371: $i,SV1010: $i,SV732: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV732 @ SV1010 @ SV371 )
= ( c_HOL_Ozero__class_Ozero @ SV371 ) )
= $false )
| ( ( SV732 = SV1010 )
= $true )
| ( ( class_Int_Onumber__ring @ SV371 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3715,plain,
! [SV1226: $i,SV1187: $i,SV1015: $i,SV737: $i,SV377: $i] :
( ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
| ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(3716,plain,
! [SV1242: $i,SV1227: $i,SV1189: $i,SV383: $i,SV1020: $i,SV743: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) )
= $true )
| ( ( class_Divides_Oring__div @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(3717,plain,
! [SV1228: $i,SV1190: $i,SV384: $i,SV1021: $i,SV744: $i] :
( ( ( ( c_Polynomial_OpCons @ SV744 @ SV1021 @ SV384 )
= ( c_Polynomial_OpCons @ SV1190 @ SV1228 @ SV384 ) )
= $false )
| ( ( SV744 = SV1190 )
= $true )
| ( ( class_HOL_Ozero @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3718,plain,
! [SV1243: $i,SV1229: $i,SV1192: $i,SV390: $i,SV1026: $i,SV750: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1229 @ SV1026 @ SV390 ) @ SV1243 @ SV390 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SV1229 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SV1243 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV390 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3719,plain,
! [SV1230: $i,SV392: $i,SV1193: $i,SV1028: $i,SV752: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV752 @ ( c_Polynomial_Osmult @ SV1028 @ SV1193 @ SV392 ) @ ( tc_Polynomial_Opoly @ SV392 ) )
= ( c_Polynomial_OpCons @ SV1230 @ SV1193 @ SV392 ) )
= $false )
| ( ( SV1230
= ( c_Polynomial_Opoly @ SV752 @ SV1028 @ SV392 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV392 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(3720,plain,
! [SV1231: $i,SV1194: $i,SV1029: $i,SV753: $i,SV393: $i] :
( ( ( class_Int_Onumber__ring @ SV393 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
| ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(3721,plain,
! [SV1232: $i,SV398: $i,SV1196: $i,SV1033: $i,SV757: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1196 @ SV398 ) @ SV398 )
= ( c_HOL_Oplus__class_Oplus @ SV1033 @ SV1232 @ SV398 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV757 @ SV1196 @ SV398 )
= SV1232 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(3722,plain,
! [SV1244: $i,SV1233: $i,SV1198: $i,SV401: $i,SV1035: $i,SV760: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3674]) ).
thf(3723,plain,
! [SV403: $i,SV1037: $i,SV762: $i] :
( ( ( SV762
= ( c_HOL_Oplus__class_Oplus @ SV762 @ SV1037 @ SV403 ) )
= $false )
| ( ( SV1037
= ( c_HOL_Ozero__class_Ozero @ SV403 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV403 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3724,plain,
! [SV1245: $i,SV21: $i,SV1234: $i,SV1205: $i,SV1052: $i,SV783: $i,SV426: $i] :
( ( ( SV426 = SV783 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3725,plain,
! [SV1246: $i,SV22: $i,SV1235: $i,SV1206: $i,SV1053: $i,SV784: $i,SV427: $i] :
( ( ( SV427 = SV784 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(3726,plain,
! [SV434: $i,SV791: $i,SV30: $i,SV1054: $i,SV1207: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(3727,plain,
! [SV1236: $i,SV1208: $i,SV1065: $i,SV806: $i,SV450: $i,SV46: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV46 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(3728,plain,
! [SV1237: $i,SV1209: $i,SV1066: $i,SV807: $i,SV451: $i,SV47: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV47 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(3729,plain,
! [SV844: $i,SV98: $i,SV501: $i,SV1089: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV501 @ SV98 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1089 @ SV844 @ SV98 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV844 @ SV98 ) @ SV1089 @ SV98 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ SV501 @ SV1089 @ SV98 ) @ ( c_Divides_Odiv__class_Odiv @ SV844 @ SV1089 @ SV98 ) @ SV98 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(3730,plain,
! [SV1248: $i,SV1247: $i,SV1238: $i,SV1216: $i,SV1118: $i,SV882: $i,SV550: $i,SV149: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false )
| ( ( ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(3731,plain,
! [SV1140: $i,SV652: $i,SV256: $i,SV1220: $i,SV940: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(3732,plain,
! [SV1142: $i,SV260: $i,SV942: $i,SV656: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV942 @ ( tc_Polynomial_Opoly @ SV260 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV1142 @ ( tc_Polynomial_Opoly @ SV260 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ ( c_Polynomial_Opoly__gcd @ SV942 @ SV1142 @ SV260 ) @ ( tc_Polynomial_Opoly @ SV260 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(3733,plain,
! [SV1143: $i,SV261: $i,SV943: $i,SV657: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV943 @ ( tc_Polynomial_Opoly @ SV261 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ SV1143 @ ( tc_Polynomial_Opoly @ SV261 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV657 @ ( c_Polynomial_Opoly__gcd @ SV943 @ SV1143 @ SV261 ) @ ( tc_Polynomial_Opoly @ SV261 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3691]) ).
thf(3734,plain,
! [SV677: $i,SV281: $i,SV1149: $i,SV961: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(3735,plain,
! [SV678: $i,SV282: $i,SV962: $i,SV1150: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(3736,plain,
! [SV1151: $i,SV283: $i,SV963: $i,SV679: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV963 @ SV283 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV1151 @ SV283 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1151 @ SV283 ) @ SV283 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3737,plain,
! [SV976: $i,SV298: $i,SV1163: $i,SV694: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV1163 @ SV298 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1163 @ SV976 @ SV298 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV694 @ SV976 @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(3738,plain,
! [SV697: $i,SV301: $i,SV1239: $i,SV1221: $i,SV1164: $i,SV977: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV977 @ SV1164 @ SV1221 @ SV1239 @ SV301 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ ( c_Polynomial_Osmult @ SV697 @ SV977 @ SV301 ) @ SV1164 @ ( c_Polynomial_Osmult @ SV697 @ SV1221 @ SV301 ) @ ( c_Polynomial_Osmult @ SV697 @ SV1239 @ SV301 ) @ SV301 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3739,plain,
! [SV1165: $i,SV302: $i,SV978: $i,SV698: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV978 @ SV302 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ SV1165 @ SV302 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV698 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ SV1165 @ SV302 ) @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(3740,plain,
! [SV304: $i,SV1167: $i,SV980: $i,SV700: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV980 @ SV1167 @ SV304 ) @ SV304 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1167 @ SV304 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV980 @ SV304 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(3741,plain,
! [SV981: $i,SV305: $i,SV1168: $i,SV701: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1168 @ SV305 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV981 @ SV305 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV981 @ SV1168 @ SV305 ) @ SV305 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(3742,plain,
! [SV982: $i,SV306: $i,SV1169: $i,SV702: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1169 @ SV306 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV982 @ SV1169 @ SV306 ) @ SV306 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV982 @ SV306 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(3743,plain,
! [SV1170: $i,SV307: $i,SV983: $i,SV703: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV983 @ SV307 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ SV1170 @ SV307 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV703 @ ( c_Divides_Odiv__class_Omod @ SV983 @ SV1170 @ SV307 ) @ SV307 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3744,plain,
! [SV1178: $i,SV353: $i,SV994: $i,SV714: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV994 @ SV353 )
= ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1178 @ SV353 ) )
= $false )
| ( ( SV994 = SV1178 )
= $true )
| ( ( class_Int_Onumber__ring @ SV353 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(3745,plain,
! [SV1222: $i,SV359: $i,SV1180: $i,SV1000: $i,SV720: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
!= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
= $true )
| ( ( ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV359 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3746,plain,
! [SV1240: $i,SV1224: $i,SV1182: $i,SV365: $i,SV1004: $i,SV726: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1004 @ SV365 ) @ SV1182 @ SV365 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1224 @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
= $false )
| ( ( SV1182
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1224 @ SV726 @ SV365 ) @ SV1004 @ SV365 ) @ SV1240 @ SV365 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3747,plain,
! [SV1241: $i,SV1225: $i,SV1183: $i,SV366: $i,SV1005: $i,SV727: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3748,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( ~ ( class_Power_Opower @ SV367 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3713]) ).
thf(3749,plain,
! [SV1226: $i,SV1187: $i,SV377: $i,SV1015: $i,SV737: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
= $true )
| ( ( ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3715]) ).
thf(3750,plain,
! [SV1242: $i,SV1227: $i,SV1189: $i,SV383: $i,SV1020: $i,SV743: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) ) )
= $true )
| ( ( class_Divides_Oring__div @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(3751,plain,
! [SV1243: $i,SV1229: $i,SV1192: $i,SV390: $i,SV1026: $i,SV750: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV750 @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1229 @ SV1026 @ SV390 ) @ SV1243 @ SV390 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV750 @ SV1229 @ SV390 ) @ SV1026 @ SV390 ) @ SV1192 @ SV390 )
= SV1243 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV390 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3752,plain,
! [SV1231: $i,SV1194: $i,SV393: $i,SV1029: $i,SV753: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
= $true )
| ( ( ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV393 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(3753,plain,
! [SV1244: $i,SV1233: $i,SV1198: $i,SV401: $i,SV1035: $i,SV760: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(3754,plain,
! [SV1245: $i,SV426: $i,SV21: $i,SV1234: $i,SV783: $i,SV1205: $i,SV1052: $i] :
( ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 ) )
= $true )
| ( ( SV426 = SV783 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(3755,plain,
! [SV427: $i,SV1246: $i,SV22: $i,SV784: $i,SV1235: $i,SV1206: $i,SV1053: $i] :
( ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 ) )
= $true )
| ( ( SV427 = SV784 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(3756,plain,
! [SV1054: $i,SV1207: $i,SV30: $i,SV434: $i,SV791: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV791 @ SV434 @ SV30 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1207 @ SV1054 @ SV30 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV434 @ SV791 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV1054 @ SV1207 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV434 @ SV1054 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV791 @ SV1207 @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3726]) ).
thf(3757,plain,
! [SV1236: $i,SV46: $i,SV1208: $i,SV1065: $i,SV806: $i,SV450: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV46 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3727]) ).
thf(3758,plain,
! [SV1237: $i,SV1209: $i,SV47: $i,SV1066: $i,SV807: $i,SV451: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV47 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3728]) ).
thf(3759,plain,
! [SV1248: $i,SV1247: $i,SV1238: $i,SV1216: $i,SV149: $i,SV1118: $i,SV882: $i,SV550: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
| ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(3760,plain,
! [SV1220: $i,SV940: $i,SV256: $i,SV1140: $i,SV652: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV652 @ SV1140 @ SV256 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV940 @ SV1220 @ SV256 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV652 @ SV940 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV1140 @ SV1220 @ SV256 ) @ SV256 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3761,plain,
! [SV677: $i,SV281: $i,SV1149: $i,SV961: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3734]) ).
thf(3762,plain,
! [SV678: $i,SV282: $i,SV962: $i,SV1150: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(3763,plain,
! [SV1222: $i,SV359: $i,SV1180: $i,SV1000: $i,SV720: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
= $false )
| ( ( ( SV1180 = SV1222 )
| ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV359 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3764,plain,
! [SV1183: $i,SV727: $i,SV1241: $i,SV366: $i,SV1005: $i,SV1225: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
!= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3747]) ).
thf(3765,plain,
! [SV1006: $i,SV728: $i,SV367: $i] :
( ( ( class_Power_Opower @ SV367 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
| ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(3766,plain,
! [SV1226: $i,SV1187: $i,SV377: $i,SV1015: $i,SV737: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
= $false )
| ( ( ( SV1015 = SV1226 )
| ( SV737 = SV1187 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(3767,plain,
! [SV1189: $i,SV743: $i,SV1242: $i,SV383: $i,SV1020: $i,SV1227: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
!= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
= $false )
| ( ( class_Divides_Oring__div @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3750]) ).
thf(3768,plain,
! [SV1231: $i,SV1194: $i,SV393: $i,SV1029: $i,SV753: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
= $false )
| ( ( ( SV1029 = SV1231 )
| ( SV753 = SV1194 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV393 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3769,plain,
! [SV1198: $i,SV760: $i,SV1244: $i,SV401: $i,SV1035: $i,SV1233: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
!= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(3770,plain,
! [SV1245: $i,SV426: $i,SV21: $i,SV1234: $i,SV783: $i,SV1205: $i,SV1052: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
= $false )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 ) )
= $true )
| ( ( SV426 = SV783 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3771,plain,
! [SV427: $i,SV1246: $i,SV22: $i,SV784: $i,SV1235: $i,SV1206: $i,SV1053: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
= $false )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 ) )
= $true )
| ( ( SV427 = SV784 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3772,plain,
! [SV1065: $i,SV1208: $i,SV46: $i,SV1236: $i,SV806: $i,SV450: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV46 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3773,plain,
! [SV1066: $i,SV47: $i,SV1237: $i,SV1209: $i,SV807: $i,SV451: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV47 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(3774,plain,
! [SV1247: $i,SV882: $i,SV550: $i,SV149: $i,SV1238: $i,SV1216: $i,SV1118: $i,SV1248: $i] :
( ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 ) )
= $true )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3759]) ).
thf(3775,plain,
! [SV1149: $i,SV281: $i,SV677: $i,SV961: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV677 @ SV281 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV961 @ SV1149 @ SV281 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV1149 @ SV281 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV677 @ SV961 @ SV281 ) @ ( c_Divides_Odiv__class_Odiv @ SV1149 @ SV961 @ SV281 ) @ SV281 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3776,plain,
! [SV962: $i,SV282: $i,SV678: $i,SV1150: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV678 @ SV282 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1150 @ SV962 @ SV282 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV678 @ SV1150 @ SV282 ) @ ( c_Divides_Odiv__class_Odiv @ SV962 @ SV1150 @ SV282 ) @ SV282 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV678 @ SV962 @ SV282 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(3777,plain,
! [SV720: $i,SV359: $i,SV1000: $i,SV1222: $i,SV1180: $i] :
( ( ( SV1180 = SV1222 )
= $true )
| ( ( SV1000
= ( c_HOL_Ozero__class_Ozero @ SV359 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1180 @ SV359 ) @ SV359 )
= ( c_HOL_Oplus__class_Oplus @ SV720 @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1222 @ SV359 ) @ SV359 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV359 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(3778,plain,
! [SV1183: $i,SV727: $i,SV1241: $i,SV366: $i,SV1005: $i,SV1225: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1225 @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1005 @ SV366 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1225 @ SV727 @ SV366 ) @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1241 @ SV1183 @ SV366 ) @ SV1005 @ SV366 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV727 @ SV1005 @ SV366 )
= ( c_Divides_Odiv__class_Omod @ SV1183 @ SV1005 @ SV366 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3779,plain,
! [SV367: $i,SV1006: $i,SV728: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
!= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
= $true )
| ( ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
= $true )
| ( ( class_Power_Opower @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(3780,plain,
! [SV377: $i,SV1187: $i,SV737: $i,SV1226: $i,SV1015: $i] :
( ( ( SV1015 = SV1226 )
= $true )
| ( ( SV737 = SV1187 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1015 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1226 @ SV377 ) @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV737 @ SV1226 @ SV377 ) @ ( c_HOL_Otimes__class_Otimes @ SV1187 @ SV1015 @ SV377 ) @ SV377 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(3781,plain,
! [SV1189: $i,SV743: $i,SV1242: $i,SV383: $i,SV1020: $i,SV1227: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1227 @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1020 @ SV383 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1227 @ SV743 @ SV383 ) @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1242 @ SV1189 @ SV383 ) @ SV1020 @ SV383 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV743 @ SV1020 @ SV383 )
= ( c_Divides_Odiv__class_Omod @ SV1189 @ SV1020 @ SV383 ) )
= $false )
| ( ( class_Divides_Oring__div @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(3782,plain,
! [SV393: $i,SV1194: $i,SV753: $i,SV1231: $i,SV1029: $i] :
( ( ( SV1029 = SV1231 )
= $true )
| ( ( SV753 = SV1194 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1029 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1231 @ SV393 ) @ SV393 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1231 @ SV393 ) @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1029 @ SV393 ) @ SV393 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV393 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3768]) ).
thf(3783,plain,
! [SV1198: $i,SV760: $i,SV1244: $i,SV401: $i,SV1035: $i,SV1233: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1035 @ SV401 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV760 @ SV401 ) @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1244 @ SV1198 @ SV401 ) @ SV1035 @ SV401 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV760 @ SV1035 @ SV401 )
= ( c_Divides_Odiv__class_Omod @ SV1198 @ SV1035 @ SV401 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(3784,plain,
! [SV1234: $i,SV783: $i,SV21: $i,SV1245: $i,SV426: $i,SV1205: $i,SV1052: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV426 @ SV1245 @ SV21 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ SV1052 @ SV1205 @ SV783 @ SV1234 @ SV21 )
= $false )
| ( ( SV426 = SV783 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3785,plain,
! [SV784: $i,SV1235: $i,SV22: $i,SV427: $i,SV1246: $i,SV1206: $i,SV1053: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1246 @ SV427 @ SV22 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ SV1053 @ SV1206 @ SV1235 @ SV784 @ SV22 )
= $false )
| ( ( SV427 = SV784 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3786,plain,
! [SV1065: $i,SV1208: $i,SV46: $i,SV1236: $i,SV806: $i,SV450: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV46 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(3787,plain,
! [SV1066: $i,SV47: $i,SV1237: $i,SV1209: $i,SV807: $i,SV451: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV47 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3788,plain,
! [SV1247: $i,SV882: $i,SV550: $i,SV149: $i,SV1238: $i,SV1216: $i,SV1118: $i,SV1248: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
= $false )
| ( ( ~ ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 ) )
= $true )
| ( ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3789,plain,
! [SV367: $i,SV1006: $i,SV728: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV728 @ SV1006 @ SV367 )
= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
= $false )
| ( ( SV728
= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
= $true )
| ( ( class_Power_Opower @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV367 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(3790,plain,
! [SV1065: $i,SV1236: $i,SV806: $i,SV46: $i,SV1208: $i,SV450: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ SV1208 @ SV46 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1236 @ SV46 ) @ SV46 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV450 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV806 @ ( c_HOL_Otimes__class_Otimes @ SV1065 @ SV1208 @ SV46 ) @ SV46 ) @ SV1236 @ SV46 ) @ SV46 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV46 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3791,plain,
! [SV1066: $i,SV1209: $i,SV807: $i,SV47: $i,SV1237: $i,SV451: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ SV1237 @ SV47 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV807 @ ( c_HOL_Otimes__class_Otimes @ SV1209 @ SV1237 @ SV47 ) @ SV47 ) @ SV1066 @ SV47 ) @ SV47 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1066 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV47 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3792,plain,
! [SV1238: $i,SV1216: $i,SV1118: $i,SV149: $i,SV1247: $i,SV1248: $i,SV882: $i,SV550: $i] :
( ( ( c_Polynomial_Opdivmod__rel @ SV550 @ SV882 @ SV1248 @ SV1247 @ SV149 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ SV1248 @ SV1118 @ SV1216 @ SV1238 @ SV149 )
= $false )
| ( ( c_Polynomial_Opdivmod__rel @ SV550 @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1118 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1216 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV882 @ SV1238 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV1247 @ ( tc_Polynomial_Opoly @ SV149 ) ) @ SV149 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3793,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1258,3792,3791,3790,3789,3785,3784,3783,3782,3781,3780,3778,3777,3776,3775,3760,3756,3751,3746,3744,3743,3742,3741,3740,3739,3738,3737,3736,3733,3732,3729,3723,3721,3719,3717,3714,3710,3700,3699,3698,3697,3696,3695,3688,3687,3686,3684,3682,3675,3673,3671,3667,3666,3663,3662,3660,3659,3657,3656,3650,3649,3648,3646,3645,3644,3636,3635,3634,3633,3623,3622,3621,3620,3617,3615,3610,3608,3607,3602,3601,3600,3599,3598,3594,3593,3592,3585,3584,3581,3579,3576,3573,3570,3566,3565,3563,3557,3556,3553,3550,3533,3523,3522,3521,3520,3515,3514,3513,3512,3511,3504,3503,3502,3501,3500,3499,3496,3495,3492,3491,3490,3485,3483,3482,3481,3480,3469,3468,3467,3466,3465,3464,3463,3455,3443,3437,3422,3419,3410,3409,3408,3404,3399,3384,3376,3371,3361,3360,3359,3358,3357,3355,3351,3350,3349,3346,3345,3343,3341,3338,3337,3333,3332,3329,3328,3327,3326,3322,3321,3320,3319,3318,3317,3316,3315,3314,3313,3312,3311,3310,3309,3306,3303,3301,3300,3299,3296,3295,3294,3293,3292,3291,3290,3289,3288,3287,3286,3285,3284,3283,3282,3281,3280,3275,3274,3273,3272,3267,3259,3258,3255,3252,3251,3250,3249,3248,3189,3188,3187,3157,3146,3145,3140,3139,3136,3134,3133,3132,3131,3129,3127,3126,3125,3124,3123,3122,3121,3120,3114,3112,3111,3110,3109,3108,3104,3103,3102,3096,3095,3094,3093,3091,3090,3084,3078,3066,3065,3054,3053,3052,3051,3050,3045,3036,3033,3032,3031,3030,3029,3025,3008,3007,3006,2994,2993,2992,2991,2988,2987,2986,2985,2984,2983,2971,2968,2951,2932,2892,2891,2889,2876,2861,2850,2849,2835,2834,2827,2823,2822,2821,2820,2819,2818,2817,2816,2815,2814,2813,2812,2811,2810,2806,2796,2795,2794,2791,2786,2785,2781,2779,2778,2770,2769,2768,2767,2766,2765,2763,2762,2761,2760,2758,2757,2756,2755,2754,2736,2735,2734,2733,2706,2704,2703,2702,2701,2700,2699,2693,2691,2690,2689,2688,2687,2686,2685,2682,2681,2676,2651,2637,2605,2604,2548,2547,2546,2545,2544,2543,2542,2541,2540,2539,2538,2537,2536,2535,2534,2533,2532,2531,2530,2529,2528,2527,2526,2525,2524,2523,2522,2521,2520,2519,2518,2517,2516,2515,2514,2445,2435,2434,2433,2430,2315,2312,2267,2221,2209,1736,1383,1293,1292,1291,1290,1289,1288,1287,1286,1285,1284,1283,1282,1281,1280,1279,1278,1277,1276,1275,1274,1273,1272,1271,1270,1269,1268,1267,1266,1265,1264,1263,1261,1260]) ).
thf(3794,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG434-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 18:20:13 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.38/13.98 ...
% 81.38/13.98
% 81.38/13.98 No.of.Axioms: 441
% 81.38/13.98
% 81.38/13.98 Length.of.Defs: 0
% 81.38/13.98
% 81.38/13.98 Contains.Choice.Funs: false
% 81.38/13.98 .............................................................................................................................
% 81.38/13.98
% 81.38/13.98 ********************************
% 81.38/13.98 * All subproblems solved! *
% 81.38/13.98 ********************************
% 81.38/13.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:441,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3793,loop_count:0,foatp_calls:1,translation:fof_full)
% 81.38/13.98
% 81.38/13.98 %**** Beginning of derivation protocol ****
% 81.38/13.98 % SZS output start CNFRefutation
% See solution above
% 81.38/14.01
% 81.38/14.01 %**** End of derivation protocol ****
% 81.38/14.01 %**** no. of clauses in derivation: 3794 ****
% 81.38/14.01 %**** clause counter: 3793 ****
% 81.38/14.01
% 81.38/14.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:441,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3793,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------