TSTP Solution File: ALG434-1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : ALG434-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:12:40 EDT 2022
% Result : Unsatisfiable 2.43s 2.61s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__HOL_Ozero_0,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__HOL_Ozero]) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Power_Opower_0,plain,
( class_Power_Opower(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Power_Opower]) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Int_Onumber__ring_0,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Int_Onumber__ring]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd_0,plain,
( class_Ring__and__Field_Odvd(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odvd]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom_0,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring_0,plain,
( class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield_0,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ofield]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1_0,plain,
( class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add_0,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add_0,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring_0,plain,
( class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult_0,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring_0,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero_0,plain,
( class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add_0,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1_0,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one_0,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add_0,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring_0,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add_0,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult_0,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult_0,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult]) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra_0,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0_0,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1_0,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors_0,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors_0,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors_0,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add_0,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add]) ).
cnf(cls_CHAINED_0_01,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
input ).
fof(cls_CHAINED_0_01_0,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(cls_CHAINED_0,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)),
input ).
fof(cls_CHAINED_0_0,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))
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0]) ).
cnf(cls_pq_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
input ).
fof(cls_pq_0_0,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| $false ),
inference(orientation,[status(thm)],[cls_pq_0]) ).
fof(def_lhs_atom1,axiom,
( lhs_atom1
<=> c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[cls_pq_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
( lhs_atom2
<=> 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)) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
( lhs_atom2
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_0,def_lhs_atom2]) ).
fof(to_be_clausified_2,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_01_0,def_lhs_atom1]) ).
fof(def_lhs_atom3,axiom,
( lhs_atom3
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
( lhs_atom3
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
( lhs_atom4
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
( lhs_atom4
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
( lhs_atom5
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
( lhs_atom5
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
( lhs_atom6
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
( lhs_atom14
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
( lhs_atom14
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
( lhs_atom17
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom17
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
( lhs_atom18
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
( lhs_atom19
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
( lhs_atom19
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
( lhs_atom20
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
( lhs_atom21
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
( lhs_atom21
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
( lhs_atom22
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
( lhs_atom22
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
( lhs_atom23
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
( lhs_atom23
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
( lhs_atom24
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
( lhs_atom24
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
( lhs_atom25
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
( lhs_atom25
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
( lhs_atom26
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
( lhs_atom26
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
( lhs_atom27
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
( lhs_atom27
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ofield_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
( lhs_atom28
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
( lhs_atom28
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
( lhs_atom29
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
( lhs_atom29
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
( lhs_atom30
<=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
( lhs_atom30
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odvd_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
( lhs_atom31
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
( lhs_atom31
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Int_Onumber__ring_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
( lhs_atom32
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Power_Opower_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
( lhs_atom33
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
( lhs_atom33
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__HOL_Ozero_0,def_lhs_atom33]) ).
% Start CNF derivation
fof(c_0_0,axiom,
( lhs_atom33
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_1,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_2,axiom,
( lhs_atom31
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_3,axiom,
( lhs_atom30
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_4,axiom,
( lhs_atom29
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_5,axiom,
( lhs_atom28
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_6,axiom,
( lhs_atom27
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_7,axiom,
( lhs_atom26
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_8,axiom,
( lhs_atom25
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_9,axiom,
( lhs_atom24
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_10,axiom,
( lhs_atom23
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_11,axiom,
( lhs_atom22
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_12,axiom,
( lhs_atom21
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_13,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_14,axiom,
( lhs_atom19
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_15,axiom,
( lhs_atom18
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_16,axiom,
( lhs_atom17
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_17,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_18,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_19,axiom,
( lhs_atom14
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_20,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_21,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_22,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_23,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_24,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_25,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_26,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_27,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_28,axiom,
( lhs_atom5
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_29,axiom,
( lhs_atom4
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_30,axiom,
( lhs_atom3
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_31,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_32,axiom,
( lhs_atom2
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_33,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_34,plain,
lhs_atom33,
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_35,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_36,plain,
lhs_atom31,
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_37,plain,
lhs_atom30,
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_38,plain,
lhs_atom29,
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_39,plain,
lhs_atom28,
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_40,plain,
lhs_atom27,
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_41,plain,
lhs_atom26,
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_42,plain,
lhs_atom25,
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_43,plain,
lhs_atom24,
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_44,plain,
lhs_atom23,
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_45,plain,
lhs_atom22,
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_46,plain,
lhs_atom21,
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_47,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_48,plain,
lhs_atom19,
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_49,plain,
lhs_atom18,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_50,plain,
lhs_atom17,
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_51,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_52,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_53,plain,
lhs_atom14,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_54,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_55,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_56,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_57,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_58,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_59,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_60,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_61,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_62,plain,
lhs_atom5,
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_63,plain,
lhs_atom4,
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_64,plain,
lhs_atom3,
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_65,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_66,plain,
lhs_atom2,
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_67,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_68,plain,
lhs_atom33,
c_0_34 ).
fof(c_0_69,plain,
lhs_atom32,
c_0_35 ).
fof(c_0_70,plain,
lhs_atom31,
c_0_36 ).
fof(c_0_71,plain,
lhs_atom30,
c_0_37 ).
fof(c_0_72,plain,
lhs_atom29,
c_0_38 ).
fof(c_0_73,plain,
lhs_atom28,
c_0_39 ).
fof(c_0_74,plain,
lhs_atom27,
c_0_40 ).
fof(c_0_75,plain,
lhs_atom26,
c_0_41 ).
fof(c_0_76,plain,
lhs_atom25,
c_0_42 ).
fof(c_0_77,plain,
lhs_atom24,
c_0_43 ).
fof(c_0_78,plain,
lhs_atom23,
c_0_44 ).
fof(c_0_79,plain,
lhs_atom22,
c_0_45 ).
fof(c_0_80,plain,
lhs_atom21,
c_0_46 ).
fof(c_0_81,plain,
lhs_atom20,
c_0_47 ).
fof(c_0_82,plain,
lhs_atom19,
c_0_48 ).
fof(c_0_83,plain,
lhs_atom18,
c_0_49 ).
fof(c_0_84,plain,
lhs_atom17,
c_0_50 ).
fof(c_0_85,plain,
lhs_atom16,
c_0_51 ).
fof(c_0_86,plain,
lhs_atom15,
c_0_52 ).
fof(c_0_87,plain,
lhs_atom14,
c_0_53 ).
fof(c_0_88,plain,
lhs_atom13,
c_0_54 ).
fof(c_0_89,plain,
lhs_atom12,
c_0_55 ).
fof(c_0_90,plain,
lhs_atom11,
c_0_56 ).
fof(c_0_91,plain,
lhs_atom10,
c_0_57 ).
fof(c_0_92,plain,
lhs_atom9,
c_0_58 ).
fof(c_0_93,plain,
lhs_atom8,
c_0_59 ).
fof(c_0_94,plain,
lhs_atom7,
c_0_60 ).
fof(c_0_95,plain,
lhs_atom6,
c_0_61 ).
fof(c_0_96,plain,
lhs_atom5,
c_0_62 ).
fof(c_0_97,plain,
lhs_atom4,
c_0_63 ).
fof(c_0_98,plain,
lhs_atom3,
c_0_64 ).
fof(c_0_99,plain,
lhs_atom1,
c_0_65 ).
fof(c_0_100,plain,
lhs_atom2,
c_0_66 ).
fof(c_0_101,plain,
lhs_atom1,
c_0_67 ).
cnf(c_0_102,plain,
lhs_atom33,
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_103,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_104,plain,
lhs_atom31,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_105,plain,
lhs_atom30,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_106,plain,
lhs_atom29,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_107,plain,
lhs_atom28,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_108,plain,
lhs_atom27,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_109,plain,
lhs_atom26,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_110,plain,
lhs_atom25,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_111,plain,
lhs_atom24,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_112,plain,
lhs_atom23,
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_113,plain,
lhs_atom22,
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_114,plain,
lhs_atom21,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_115,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_116,plain,
lhs_atom19,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_117,plain,
lhs_atom18,
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_118,plain,
lhs_atom17,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_119,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_120,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_121,plain,
lhs_atom14,
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_122,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_123,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_124,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_125,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_126,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_127,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_128,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_129,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_130,plain,
lhs_atom5,
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_131,plain,
lhs_atom4,
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_132,plain,
lhs_atom3,
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_133,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_134,plain,
lhs_atom2,
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_135,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_136,plain,
lhs_atom33,
c_0_102,
[final] ).
cnf(c_0_137,plain,
lhs_atom32,
c_0_103,
[final] ).
cnf(c_0_138,plain,
lhs_atom31,
c_0_104,
[final] ).
cnf(c_0_139,plain,
lhs_atom30,
c_0_105,
[final] ).
cnf(c_0_140,plain,
lhs_atom29,
c_0_106,
[final] ).
cnf(c_0_141,plain,
lhs_atom28,
c_0_107,
[final] ).
cnf(c_0_142,plain,
lhs_atom27,
c_0_108,
[final] ).
cnf(c_0_143,plain,
lhs_atom26,
c_0_109,
[final] ).
cnf(c_0_144,plain,
lhs_atom25,
c_0_110,
[final] ).
cnf(c_0_145,plain,
lhs_atom24,
c_0_111,
[final] ).
cnf(c_0_146,plain,
lhs_atom23,
c_0_112,
[final] ).
cnf(c_0_147,plain,
lhs_atom22,
c_0_113,
[final] ).
cnf(c_0_148,plain,
lhs_atom21,
c_0_114,
[final] ).
cnf(c_0_149,plain,
lhs_atom20,
c_0_115,
[final] ).
cnf(c_0_150,plain,
lhs_atom19,
c_0_116,
[final] ).
cnf(c_0_151,plain,
lhs_atom18,
c_0_117,
[final] ).
cnf(c_0_152,plain,
lhs_atom17,
c_0_118,
[final] ).
cnf(c_0_153,plain,
lhs_atom16,
c_0_119,
[final] ).
cnf(c_0_154,plain,
lhs_atom15,
c_0_120,
[final] ).
cnf(c_0_155,plain,
lhs_atom14,
c_0_121,
[final] ).
cnf(c_0_156,plain,
lhs_atom13,
c_0_122,
[final] ).
cnf(c_0_157,plain,
lhs_atom12,
c_0_123,
[final] ).
cnf(c_0_158,plain,
lhs_atom11,
c_0_124,
[final] ).
cnf(c_0_159,plain,
lhs_atom10,
c_0_125,
[final] ).
cnf(c_0_160,plain,
lhs_atom9,
c_0_126,
[final] ).
cnf(c_0_161,plain,
lhs_atom8,
c_0_127,
[final] ).
cnf(c_0_162,plain,
lhs_atom7,
c_0_128,
[final] ).
cnf(c_0_163,plain,
lhs_atom6,
c_0_129,
[final] ).
cnf(c_0_164,plain,
lhs_atom5,
c_0_130,
[final] ).
cnf(c_0_165,plain,
lhs_atom4,
c_0_131,
[final] ).
cnf(c_0_166,plain,
lhs_atom3,
c_0_132,
[final] ).
cnf(c_0_167,plain,
lhs_atom1,
c_0_133,
[final] ).
cnf(c_0_168,plain,
lhs_atom2,
c_0_134,
[final] ).
cnf(c_0_169,plain,
lhs_atom1,
c_0_135,
[final] ).
% End CNF derivation
cnf(c_0_136_0,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_136,def_lhs_atom33]) ).
cnf(c_0_137_0,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_137,def_lhs_atom32]) ).
cnf(c_0_138_0,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_138,def_lhs_atom31]) ).
cnf(c_0_139_0,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_139,def_lhs_atom30]) ).
cnf(c_0_140_0,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_140,def_lhs_atom29]) ).
cnf(c_0_141_0,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_141,def_lhs_atom28]) ).
cnf(c_0_142_0,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_142,def_lhs_atom27]) ).
cnf(c_0_143_0,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_143,def_lhs_atom26]) ).
cnf(c_0_144_0,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_144,def_lhs_atom25]) ).
cnf(c_0_145_0,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_145,def_lhs_atom24]) ).
cnf(c_0_146_0,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_146,def_lhs_atom23]) ).
cnf(c_0_147_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_147,def_lhs_atom22]) ).
cnf(c_0_148_0,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_148,def_lhs_atom21]) ).
cnf(c_0_149_0,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_149,def_lhs_atom20]) ).
cnf(c_0_150_0,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_150,def_lhs_atom19]) ).
cnf(c_0_151_0,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_151,def_lhs_atom18]) ).
cnf(c_0_152_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_152,def_lhs_atom17]) ).
cnf(c_0_153_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_153,def_lhs_atom16]) ).
cnf(c_0_154_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_154,def_lhs_atom15]) ).
cnf(c_0_155_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_155,def_lhs_atom14]) ).
cnf(c_0_156_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_156,def_lhs_atom13]) ).
cnf(c_0_157_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_157,def_lhs_atom12]) ).
cnf(c_0_158_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_158,def_lhs_atom11]) ).
cnf(c_0_159_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_159,def_lhs_atom10]) ).
cnf(c_0_160_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_160,def_lhs_atom9]) ).
cnf(c_0_161_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_161,def_lhs_atom8]) ).
cnf(c_0_162_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_162,def_lhs_atom7]) ).
cnf(c_0_163_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_163,def_lhs_atom6]) ).
cnf(c_0_164_0,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_164,def_lhs_atom5]) ).
cnf(c_0_165_0,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_165,def_lhs_atom4]) ).
cnf(c_0_166_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_166,def_lhs_atom3]) ).
cnf(c_0_167_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unfold_definition,[status(thm)],[c_0_167,def_lhs_atom1]) ).
cnf(c_0_168_0,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)),
inference(unfold_definition,[status(thm)],[c_0_168,def_lhs_atom2]) ).
cnf(c_0_169_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unfold_definition,[status(thm)],[c_0_169,def_lhs_atom1]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X12,X7,X8,X22,X13,X23,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(X8,c_HOL_Otimes__class_Otimes(X7,X12,tc_Polynomial_Opoly(X5)),X23,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X22,tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5)),X5)
| ~ c_Polynomial_Opdivmod__rel(X6,X12,X23,X22,X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__mult_0) ).
fof(c_0_1_002,axiom,
! [X7,X8,X34,X35,X36,X37,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X37 = X36
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X36,X34,X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X37,X35,X5) ),
file('<stdin>',cls_pdivmod__rel__unique_0) ).
fof(c_0_2_003,axiom,
! [X7,X8,X34,X35,X36,X37,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X35 = X34
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X36,X34,X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X37,X35,X5) ),
file('<stdin>',cls_pdivmod__rel__unique_1) ).
fof(c_0_3_004,axiom,
! [X7,X8,X13,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X4,X8,X5),X7,c_Polynomial_Osmult(X4,X6,X5),c_Polynomial_Osmult(X4,X13,X5),X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__smult__left_0) ).
fof(c_0_4_005,axiom,
! [X7,X8,X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X7,X5),c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X4,X5),c_HOL_Ominus__class_Ominus(X7,X3,X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X4,X5),X3,X5),X5),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X7,X3,X5),X5),X5) ),
file('<stdin>',cls_mult_Oprod__diff__prod_0) ).
fof(c_0_5_006,axiom,
! [X7,X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X8 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X7,tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__def_0) ).
fof(c_0_6_007,axiom,
! [X7,X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)) = X13
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
file('<stdin>',cls_mod__poly__eq_0) ).
fof(c_0_7_008,axiom,
! [X7,X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)) = X6
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
file('<stdin>',cls_div__poly__eq_0) ).
fof(c_0_8_009,axiom,
! [X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,X13,X5)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_pdivmod__rel__def_1) ).
fof(c_0_9_010,axiom,
! [X7,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__0__iff_0) ).
fof(c_0_10_011,axiom,
! [X7,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__0__iff_1) ).
fof(c_0_11_012,axiom,
! [X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__by__0__iff_0) ).
fof(c_0_12_013,axiom,
! [X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X13 = X8
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,X13,X5) ),
file('<stdin>',cls_pdivmod__rel__by__0__iff_1) ).
fof(c_0_13_014,axiom,
! [X13,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X13,X5) ),
file('<stdin>',cls_pdivmod__rel__def_5) ).
fof(c_0_14_015,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_pdivmod__rel__def_6) ).
fof(c_0_15_016,axiom,
! [X7,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X7,tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X7,X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_pdivmod__rel__def_3) ).
fof(c_0_16_017,axiom,
! [X8,X32,X10,X15,X33,X5] :
( ~ class_Ring__and__Field_Odvd(X5)
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(X8,X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X10,X33,X5),X5),X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X33,X5) ),
file('<stdin>',cls_inf__period_I4_J_1) ).
fof(c_0_17_018,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(X8,X7,c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_pdivmod__rel_0) ).
fof(c_0_18_019,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_pdivmod__rel__0_0) ).
fof(c_0_19_020,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X8,X5) ),
file('<stdin>',cls_pdivmod__rel__by__0_0) ).
fof(c_0_20_021,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Otimes__class_Otimes(X7,X12,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),X12,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__mod__mult__right_0) ).
fof(c_0_21_022,axiom,
! [X8,X32,X10,X15,X33,X5] :
( ~ class_Ring__and__Field_Odvd(X5)
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X10,X33,X5),X5),X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(X8,X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X33,X5) ),
file('<stdin>',cls_inf__period_I4_J_0) ).
fof(c_0_22_023,axiom,
! [X20,X15,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X5),X20,X5),X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X15,X5) ),
file('<stdin>',cls_eq__add__iff2_1) ).
fof(c_0_23_024,axiom,
! [X20,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X5),X20,X5),X14,X5),X5) ),
file('<stdin>',cls_eq__add__iff1_1) ).
fof(c_0_24_025,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,X14,X5) ),
file('<stdin>',cls_div__mod__equality_0) ).
fof(c_0_25_026,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,X14,X5) ),
file('<stdin>',cls_div__mod__equality2_0) ).
fof(c_0_26_027,axiom,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,X14,X5) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X14,X5),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__eq__0__iff__dvd_1) ).
fof(c_0_27_028,axiom,
! [X20,X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),X14,X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X15,X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X5),X20,X5),X14,X5) = X15 ),
file('<stdin>',cls_eq__add__iff1_0) ).
fof(c_0_28_029,axiom,
! [X20,X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),X14,X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X15,X5)
| X14 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X5),X20,X5),X15,X5) ),
file('<stdin>',cls_eq__add__iff2_0) ).
fof(c_0_29_030,axiom,
! [X20,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Osemiring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X14,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X20,X5),X14,X5) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_30_031,axiom,
! [X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X15,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X15,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| X14 = X15
| X4 = X3 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_31_032,axiom,
! [X12,X7,X8,X19,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X7,X5),c_HOL_Otimes__class_Otimes(X8,X12,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X12,X5),c_HOL_Otimes__class_Otimes(X8,X7,X5),X5)
| X7 = X12
| X19 = X8 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_32_033,axiom,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X14,X5),X5) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X14,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__iff__poly__eq__0_0) ).
fof(c_0_33_034,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X14,X5),c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
file('<stdin>',cls_mod__add__eq_0) ).
fof(c_0_34_035,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X14,X5),c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
file('<stdin>',cls_mod__diff__eq_0) ).
fof(c_0_35_036,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X14,X5),c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
file('<stdin>',cls_mod__mult__eq_0) ).
fof(c_0_36_037,axiom,
! [X12,X7,X8,X19,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X7,X5),c_Divides_Odiv__class_Odiv(X19,X12,X5),X5) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X19,X5),c_HOL_Otimes__class_Otimes(X7,X12,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X19,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
file('<stdin>',cls_div__mult__div__if__dvd_0) ).
fof(c_0_37_038,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X6,X5),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X5),c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_mult__pCons__left_0) ).
fof(c_0_38_039,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(X2,c_Polynomial_OpCons(X4,X6,X5),tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X5),c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_mult__pCons__right_0) ).
fof(c_0_39_040,axiom,
! [X14,X17,X3,X18,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X14,X5) != c_Divides_Odiv__class_Omod(X17,X14,X5)
| c_Divides_Odiv__class_Omod(X4,X14,X5) != c_Divides_Odiv__class_Omod(X18,X14,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X5),X14,X5) ),
file('<stdin>',cls_mod__add__cong_0) ).
fof(c_0_40_041,axiom,
! [X14,X17,X3,X18,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X14,X5) != c_Divides_Odiv__class_Omod(X17,X14,X5)
| c_Divides_Odiv__class_Omod(X4,X14,X5) != c_Divides_Odiv__class_Omod(X18,X14,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X17,X5),X14,X5) ),
file('<stdin>',cls_mod__mult__cong_0) ).
fof(c_0_41_042,axiom,
! [X14,X17,X3,X18,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X14,X5) != c_Divides_Odiv__class_Omod(X17,X14,X5)
| c_Divides_Odiv__class_Omod(X4,X14,X5) != c_Divides_Odiv__class_Omod(X18,X14,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,X5),X14,X5) ),
file('<stdin>',cls_mod__diff__cong_0) ).
fof(c_0_42_043,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X4,X5),c_Divides_Odiv__class_Odiv(X14,X4,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_div__dvd__div_0) ).
fof(c_0_43_044,axiom,
! [X28,X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X29,X28,X5),X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_44_045,axiom,
! [X28,X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),X28,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_45_046,axiom,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,X14,X5) != c_HOL_Ozero__class_Ozero(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X14,X5),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__eq__0__iff__dvd_0) ).
fof(c_0_46_047,axiom,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X14,X5),X5) != c_HOL_Ozero__class_Ozero(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X14,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__iff__poly__eq__0_1) ).
fof(c_0_47_048,axiom,
! [X12,X7,X8,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,X7,X5),X12,X5) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X12,X5),c_Divides_Odiv__class_Odiv(X7,X12,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X8,X5) ),
file('<stdin>',cls_div__add_0) ).
fof(c_0_48_049,axiom,
! [X6,X2,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X4,X2,X5),c_Polynomial_OpCons(X3,X6,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X4,X3,X5),c_HOL_Ominus__class_Ominus(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_diff__pCons_0) ).
fof(c_0_49_050,axiom,
! [X6,X2,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X4,X2,X5),c_Polynomial_OpCons(X3,X6,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X4,X3,X5),c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_add__pCons_0) ).
fof(c_0_50_051,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X7,X5),c_HOL_Otimes__class_Otimes(X8,X12,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X12,X5),c_HOL_Otimes__class_Otimes(X8,X7,X5),X5) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_51_052,axiom,
! [X8,X15,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X14,X5),c_HOL_Otimes__class_Otimes(X8,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,X5),c_HOL_Otimes__class_Otimes(X8,X14,X5),X5) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_52_053,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X3,X5),X5),X3,X5) = c_HOL_Oplus__class_Oplus(X14,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__self1_0) ).
fof(c_0_53_054,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5),X3,X5) = c_HOL_Oplus__class_Oplus(X14,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__self2_0) ).
fof(c_0_54_055,axiom,
! [X8,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X4,X2,X5),X8,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X2,X8,X5),X5),X5) ),
file('<stdin>',cls_poly__pCons_0) ).
fof(c_0_55_056,axiom,
! [X28,X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X29,X5),c_HOL_Otimes__class_Otimes(X31,X28,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_56_057,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) ),
file('<stdin>',cls_zmod__simps_I2_J_0) ).
fof(c_0_57_058,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) ),
file('<stdin>',cls_zmod__simps_I1_J_0) ).
fof(c_0_58_059,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) ),
file('<stdin>',cls_zmod__simps_I4_J_0) ).
fof(c_0_59_060,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
file('<stdin>',cls_mod__add__right__eq_0) ).
fof(c_0_60_061,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) ),
file('<stdin>',cls_mod__add__left__eq_0) ).
fof(c_0_61_062,axiom,
! [X15,X14,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,X5),c_HOL_Oplus__class_Oplus(X3,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,X5),c_HOL_Ominus__class_Ominus(X14,X15,X5),X5) ),
file('<stdin>',cls_Deriv_Oadd__diff__add_0) ).
fof(c_0_62_063,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
file('<stdin>',cls_mod__mult__right__eq_0) ).
fof(c_0_63_064,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) ),
file('<stdin>',cls_mod__mult__left__eq_0) ).
fof(c_0_64_065,axiom,
! [X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),c_HOL_Oplus__class_Oplus(X14,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X14,X5),c_HOL_Oplus__class_Oplus(X3,X15,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_65_066,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) ),
file('<stdin>',cls_mod__diff__left__eq_0) ).
fof(c_0_66_067,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
file('<stdin>',cls_mod__diff__right__eq_0) ).
fof(c_0_67_068,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X4,X5),c_Divides_Odiv__class_Odiv(X14,X4,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_div__dvd__div_1) ).
fof(c_0_68_069,axiom,
! [X8,X13,X15,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X13,X14,X5),X5) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X13,X15,X5),X5)
| X14 = X15
| X13 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_69_070,axiom,
! [X7,X8,X9,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X8,X7,X5),X9,X5) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X8,X9,X5),c_Power_Opower__class_Opower(X7,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
file('<stdin>',cls_div__power_0) ).
fof(c_0_70_071,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5) ),
file('<stdin>',cls_mod__div__decomp_0) ).
fof(c_0_71_072,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5) = X4 ),
file('<stdin>',cls_mod__div__equality_0) ).
fof(c_0_72_073,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5) = X4 ),
file('<stdin>',cls_mod__div__equality2_0) ).
fof(c_0_73_074,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,X5),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),X5) = X4 ),
file('<stdin>',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(c_0_74_075,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
file('<stdin>',cls_dvd__mult__cancel__right_0) ).
fof(c_0_75_076,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5) ),
file('<stdin>',cls_dvd__mult__cancel__left_0) ).
fof(c_0_76_077,axiom,
! [X13,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X13,tc_Polynomial_Opoly(X5)),c_HOL_Otimes__class_Otimes(X6,X13,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_mult__poly__add__left_0) ).
fof(c_0_77_078,axiom,
! [X2,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X14,X2,X5),c_Polynomial_OpCons(X4,X2,X5),tc_Polynomial_Opoly(X5)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_offset__poly__eq__0__lemma_0) ).
fof(c_0_78_079,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ominus__class_Ominus(X2,X6,tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__diff__right_0) ).
fof(c_0_79_080,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X5) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__add__right_0) ).
fof(c_0_80_081,axiom,
! [X8,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X2,X8,X5),c_Polynomial_Opoly(X6,X8,X5),X5) ),
file('<stdin>',cls_poly__mult_0) ).
fof(c_0_81_082,axiom,
! [X8,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X2,X8,X5),c_Polynomial_Opoly(X6,X8,X5),X5) ),
file('<stdin>',cls_poly__add_0) ).
fof(c_0_82_083,axiom,
! [X8,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X2,X6,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X2,X8,X5),c_Polynomial_Opoly(X6,X8,X5),X5) ),
file('<stdin>',cls_poly__diff_0) ).
fof(c_0_83_084,axiom,
! [X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X15,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_mult__dvd__mono_0) ).
fof(c_0_84_085,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X4,X3,X5),X2,X5) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X3,X2,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__add__left_0) ).
fof(c_0_85_086,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X4,X3,X5),X2,X5) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X3,X2,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__diff__left_0) ).
fof(c_0_86_087,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X5),c_HOL_Otimes__class_Otimes(X7,X7,X5),X5) != c_HOL_Ozero__class_Ozero(X5)
| X8 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_87_088,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X5),c_HOL_Otimes__class_Otimes(X7,X7,X5),X5) != c_HOL_Ozero__class_Ozero(X5)
| X7 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_88_089,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_Polynomial_OpCons(X3,X2,X5),X5) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_Polynomial_Osmult(X4,X2,X5),X5) ),
file('<stdin>',cls_smult__pCons_0) ).
fof(c_0_89_090,axiom,
! [X7,X8,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X7,X5),X6,X5) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X6,X5),c_Power_Opower__class_Opower(X7,X6,X5),X5) ),
file('<stdin>',cls_class__semiring_Opwr__mul_0) ).
fof(c_0_90_091,axiom,
! [X9,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X4,X3,X5),X9,X5) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X9,X5),c_Power_Opower__class_Opower(X3,X9,X5),X5) ),
file('<stdin>',cls_power__mult__distrib_0) ).
fof(c_0_91_092,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_92_093,axiom,
! [X7,X25,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X8,X7,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X8,X5),c_HOL_Otimes__class_Otimes(X25,X7,X5),X5) ),
file('<stdin>',cls_mult__right_Oadd_0) ).
fof(c_0_93_094,axiom,
! [X17,X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X3,X17,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X4,X17,X5),X5) ),
file('<stdin>',cls_mult_Oadd__right_0) ).
fof(c_0_94_095,axiom,
! [X24,X7,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X7,X5),X24,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X24,X5),c_HOL_Otimes__class_Otimes(X7,X24,X5),X5) ),
file('<stdin>',cls_mult__left_Oadd_0) ).
fof(c_0_95_096,axiom,
! [X3,X18,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X18,X5),X3,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X18,X3,X5),X5) ),
file('<stdin>',cls_mult_Oadd__left_0) ).
fof(c_0_96_097,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X7,X5),c_HOL_Otimes__class_Otimes(X8,X12,X5),X5) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_97_098,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_98_099,axiom,
! [X11,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X11,X5),c_HOL_Otimes__class_Otimes(X3,X11,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X11,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_99_100,axiom,
! [X7,X25,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ominus__class_Ominus(X8,X7,X5),X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X25,X8,X5),c_HOL_Otimes__class_Otimes(X25,X7,X5),X5) ),
file('<stdin>',cls_mult__right_Odiff_0) ).
fof(c_0_100_101,axiom,
! [X17,X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X17,X5),X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X4,X17,X5),X5) ),
file('<stdin>',cls_mult_Odiff__right_0) ).
fof(c_0_101_102,axiom,
! [X3,X18,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X18,X5),X3,X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X18,X3,X5),X5) ),
file('<stdin>',cls_mult_Odiff__left_0) ).
fof(c_0_102_103,axiom,
! [X24,X7,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X7,X5),X24,X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X24,X5),c_HOL_Otimes__class_Otimes(X7,X24,X5),X5) ),
file('<stdin>',cls_mult__left_Odiff_0) ).
fof(c_0_103_104,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
file('<stdin>',cls_mod__mult__self2_0) ).
fof(c_0_104_105,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X3,X5),X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
file('<stdin>',cls_mod__mult__self1_0) ).
fof(c_0_105_106,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5) = c_HOL_Otimes__class_Otimes(X14,c_Divides_Odiv__class_Omod(X4,X3,X5),X5) ),
file('<stdin>',cls_mod__mult__mult1_0) ).
fof(c_0_106_107,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X3,X5),X14,X5) ),
file('<stdin>',cls_mod__mult__mult2_0) ).
fof(c_0_107_108,axiom,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oring__1(X5)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X4,X5),X9,X5) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X5),X5),X9,X5),c_Power_Opower__class_Opower(X4,X9,X5),X5) ),
file('<stdin>',cls_power__minus_0) ).
fof(c_0_108_109,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X5),X14,X5) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X14,X5),X4,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__div__mult_0) ).
fof(c_0_109_110,axiom,
! [X13,X6,X2,X14,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X14,X6,X5),tc_Polynomial_Opoly(X5)) != c_Polynomial_OpCons(X13,X6,X5)
| X13 = c_Polynomial_Opoly(X2,X14,X5) ),
file('<stdin>',cls_synthetic__div__unique_0) ).
fof(c_0_110_111,axiom,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5) ),
file('<stdin>',cls_dvd__mod__imp__dvd_0) ).
fof(c_0_111_112,axiom,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5) ),
file('<stdin>',cls_dvd__mod__iff_0) ).
fof(c_0_112_113,axiom,
! [X12,X7,X8,X21,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) != c_HOL_Oplus__class_Oplus(X7,X21,X5)
| c_HOL_Oplus__class_Oplus(X8,X12,X5) = X21 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_113_114,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X4,X3,X5),X5),X3,X5) ),
file('<stdin>',cls_mod__minus__eq_0) ).
fof(c_0_114_115,axiom,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X7,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X8,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__greatest_0) ).
fof(c_0_115_116,axiom,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X7,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X8,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__poly__gcd__iff_2) ).
fof(c_0_116_117,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Otimes__class_Otimes(X7,X12,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),X12,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__div__mult__right_0) ).
fof(c_0_117_118,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__mult__cancel__right_2) ).
fof(c_0_118_119,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__mult__cancel__left_2) ).
fof(c_0_119_120,axiom,
! [X7,X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X9,X5),c_Power_Opower__class_Opower(X7,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
file('<stdin>',cls_dvd__power__same_0) ).
fof(c_0_120_121,axiom,
! [X7,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X4,X8,X5),X7,tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_mod__smult__left_0) ).
fof(c_0_121_122,axiom,
! [X7,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X4,X8,X5),X7,tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_div__smult__left_0) ).
fof(c_0_122_123,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_mult__smult__right_0) ).
fof(c_0_123_124,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_mult__smult__left_0) ).
fof(c_0_124_125,axiom,
! [X11,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X11,X5),X11,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X5),X5),X11,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_125_126,axiom,
! [X11,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X4,X11,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X5),X5),X11,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_126_127,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__add_0) ).
fof(c_0_127_128,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X7,X12,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X12,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
file('<stdin>',cls_dvd__diff_0) ).
fof(c_0_128_129,axiom,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5) ),
file('<stdin>',cls_dvd__mod__iff_1) ).
fof(c_0_129_130,axiom,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5) ),
file('<stdin>',cls_dvd__mod_0) ).
fof(c_0_130_131,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X4,X5),X3,X5) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X3,X5),c_HOL_Oone__class_Oone(X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__add__self1_0) ).
fof(c_0_131_132,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X3,X5),X3,X5) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X3,X5),c_HOL_Oone__class_Oone(X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__add__self2_0) ).
fof(c_0_132_133,axiom,
! [X3,X18,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(X4,X3,X5) != c_Divides_Odiv__class_Omod(X18,X3,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X18,X5),X3,X5) ),
file('<stdin>',cls_mod__minus__cong_0) ).
fof(c_0_133_134,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X3,X5),X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X3,X5),X5) ),
file('<stdin>',cls_abs__add__abs_0) ).
fof(c_0_134_135,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__smult__cancel_0) ).
fof(c_0_135_136,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_dvd__smult__iff_0) ).
fof(c_0_136_137,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__dvd__iff_1) ).
fof(c_0_137_138,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5) = c_Divides_Odiv__class_Odiv(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__mult1_0) ).
fof(c_0_138_139,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) = c_Divides_Odiv__class_Odiv(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__mult2_0) ).
fof(c_0_139_140,axiom,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X7,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__poly__gcd__iff_1) ).
fof(c_0_140_141,axiom,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X8,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__poly__gcd__iff_0) ).
fof(c_0_141_142,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__dvd__cancel_0) ).
fof(c_0_142_143,axiom,
! [X8,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X4,X2,X5),X8,X5) = c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X2,X8,X5),X5) ),
file('<stdin>',cls_poly__smult_0) ).
fof(c_0_143_144,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_144_145,axiom,
! [X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),X29,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X29,X5),X31,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_145_146,axiom,
! [X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),X29,X5) = c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X31,X29,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_146_147,axiom,
! [X28,X29,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X29,X5),X28,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_147_148,axiom,
! [X28,X29,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(X30,X28,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_148_149,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X7,X12,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X8,X7,X5),X12,X5) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_149_150,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,c_Polynomial_Opoly__gcd(X7,X12,X5),X5) = c_Polynomial_Opoly__gcd(X7,c_Polynomial_Opoly__gcd(X8,X12,X5),X5) ),
file('<stdin>',cls_poly__gcd__left__commute_0) ).
fof(c_0_150_151,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X8,X7,X5),X12,X5) = c_Polynomial_Opoly__gcd(X8,c_Polynomial_Opoly__gcd(X7,X12,X5),X5) ),
file('<stdin>',cls_poly__gcd__assoc_0) ).
fof(c_0_151_152,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X5),X5) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_152_153,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_153_154,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X7,X5),X12,X5) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_154_155,axiom,
! [X12,X7,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X8,X12,X5),X5) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_155_156,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_156_157,axiom,
! [X15,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X14,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X14,X5),X15,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_157_158,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X14,X5),X3,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_158_159,axiom,
! [X15,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X14,X15,X5),X5) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X4,X15,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_159_160,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_160_161,axiom,
! [X9,X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X9,X5),X4,X5) = c_HOL_Otimes__class_Otimes(X4,c_Power_Opower__class_Opower(X4,X9,X5),X5) ),
file('<stdin>',cls_power__commutes_0) ).
fof(c_0_161_162,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X3,X2,X5),X5) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X4,X3,X5),X2,X5) ),
file('<stdin>',cls_smult__smult_0) ).
fof(c_0_162_163,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_163_164,axiom,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__dvd__iff_4) ).
fof(c_0_164_165,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) ),
file('<stdin>',cls_dvd__mult__right_0) ).
fof(c_0_165_166,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) ),
file('<stdin>',cls_dvd__mult__left_0) ).
fof(c_0_166_167,axiom,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X3,X5) ),
file('<stdin>',cls_mod__mod__cancel_0) ).
fof(c_0_167_168,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__mult1__if_0) ).
fof(c_0_168_169,axiom,
! [X6,X2,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5),X6,tc_Polynomial_Opoly(X5))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__dvd__iff_0) ).
fof(c_0_169_170,axiom,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X4,X5),X9,X5),X5) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X9,X5),X5) ),
file('<stdin>',cls_abs__power__minus_0) ).
fof(c_0_170,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5),X5) ),
file('<stdin>',cls_dvd__mult__cancel__left_1) ).
fof(c_0_171,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X5),X5),X5) ),
file('<stdin>',cls_dvd__mult__cancel__right_1) ).
fof(c_0_172,axiom,
! [X7,X8,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
file('<stdin>',cls_dvd__div__neg_0) ).
fof(c_0_173,axiom,
! [X7,X8,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
file('<stdin>',cls_dvd__neg__div_0) ).
fof(c_0_174,axiom,
! [X12,X7,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) != X7
| X8 = c_HOL_Ouminus__class_Ouminus(X12,X5) ),
file('<stdin>',cls_add__cancel__end_0) ).
fof(c_0_175,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__dvd_0) ).
fof(c_0_176,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_dvd__smult__iff_1) ).
fof(c_0_177,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_smult__dvd__iff_2) ).
fof(c_0_178,axiom,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_dvd__smult_0) ).
fof(c_0_179,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Odiv(X3,X4,X5),X5) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__mult__div__cancel_0) ).
fof(c_0_180,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X5),X4,X5) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__div__mult__self_0) ).
fof(c_0_181,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__mult2_0) ).
fof(c_0_182,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5) ),
file('<stdin>',cls_dvd__mult_0) ).
fof(c_0_183,axiom,
! [X2,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X4,X2,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X5)),X5) ),
file('<stdin>',cls_minus__pCons_0) ).
fof(c_0_184,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,X5),X5) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X4,X5),X5) ),
file('<stdin>',cls_abs__minus__commute_0) ).
fof(c_0_185,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X11,X11,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X5),c_HOL_Oone__class_Oone(X5),X5),X11,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_186,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) = c_Polynomial_Opoly__gcd(X7,c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),X5)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__code_1) ).
fof(c_0_187,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__div__minus__right_0) ).
fof(c_0_188,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X5)),X7,tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__div__minus__left_0) ).
fof(c_0_189,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X5)),X7,tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__mod__minus__left_0) ).
fof(c_0_190,axiom,
! [X7,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,c_Polynomial_Osmult(X4,X7,X5),tc_Polynomial_Opoly(X5)) = c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__smult__right_0) ).
fof(c_0_191,axiom,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__trans_0) ).
fof(c_0_192,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X3,X5),X5) ),
file('<stdin>',cls_abs__mult_0) ).
fof(c_0_193,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X5),X5) ),
file('<stdin>',cls_Lim_Ominus__diff__minus_0) ).
fof(c_0_194,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
file('<stdin>',cls_minus__add_0) ).
fof(c_0_195,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
file('<stdin>',cls_minus__add__distrib_0) ).
fof(c_0_196,axiom,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X4,X2,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__minus__right_0) ).
fof(c_0_197,axiom,
! [X7,X8,X5] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X8,X7,X5),X5) = c_HOL_Otimes__class_Otimes(X8,X7,X5) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_198,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
file('<stdin>',cls_mod__add__self1_0) ).
fof(c_0_199,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
file('<stdin>',cls_mod__add__self2_0) ).
fof(c_0_200,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X3,X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
file('<stdin>',cls_mod__mod__trivial_0) ).
fof(c_0_201,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5),X5) = X3 ),
file('<stdin>',cls_add__minus__cancel_0) ).
fof(c_0_202,axiom,
! [X8,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X2,X8,X5),X5) ),
file('<stdin>',cls_poly__minus_0) ).
fof(c_0_203,axiom,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X4,X5),X2,X5) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X4,X2,X5),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__minus__left_0) ).
fof(c_0_204,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) ),
file('<stdin>',cls_minus__mult__left_0) ).
fof(c_0_205,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
file('<stdin>',cls_minus__mult__right_0) ).
fof(c_0_206,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) ),
file('<stdin>',cls_mult_Ominus__left_0) ).
fof(c_0_207,axiom,
! [X7,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X7,X5),X5) ),
file('<stdin>',cls_mult__left_Ominus_0) ).
fof(c_0_208,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) ),
file('<stdin>',cls_mult_Ominus__right_0) ).
fof(c_0_209,axiom,
! [X25,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ouminus__class_Ouminus(X8,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X25,X8,X5),X5) ),
file('<stdin>',cls_mult__right_Ominus_0) ).
fof(c_0_210,axiom,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X9,X5),X5) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X5),X9,X5) ),
file('<stdin>',cls_power__abs_0) ).
fof(c_0_211,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__dvd__iff_3) ).
fof(c_0_212,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_HOL_Otimes__class_Otimes(X4,X4,X5) != c_HOL_Otimes__class_Otimes(X3,X3,X5)
| X4 = c_HOL_Ouminus__class_Ouminus(X3,X5)
| X4 = X3 ),
file('<stdin>',cls_square__eq__iff_0) ).
fof(c_0_213,axiom,
! [X12,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X12,X5),c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = X7 ),
file('<stdin>',cls_add__cancel__end_1) ).
fof(c_0_214,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Oplus__class_Oplus(X4,X3,X5),X5) = X3 ),
file('<stdin>',cls_minus__add__cancel_0) ).
fof(c_0_215,axiom,
! [X2,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X14,X2,X5) != c_Polynomial_OpCons(X4,X2,X5)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_synthetic__div__unique__lemma_0) ).
fof(c_0_216,axiom,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Oabs__class_Oabs(X10,X5),X5) ),
file('<stdin>',cls_dvd__abs__iff_0) ).
fof(c_0_217,axiom,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X11,X5),X10,X5) ),
file('<stdin>',cls_abs__dvd__iff_0) ).
fof(c_0_218,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5) ),
file('<stdin>',cls_minus__dvd__iff_0) ).
fof(c_0_219,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) ),
file('<stdin>',cls_dvd__minus__iff_0) ).
fof(c_0_220,axiom,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(X8,X7,X5) != c_HOL_Oplus__class_Oplus(X8,X12,X5)
| X7 = X12 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_221,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X5),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X5),X9,X5),X5) ),
file('<stdin>',cls_dvd__power_1) ).
fof(c_0_222,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X5),X5) = c_HOL_Ominus__class_Ominus(X3,X4,X5) ),
file('<stdin>',cls_minus__diff__eq_0) ).
fof(c_0_223,axiom,
! [X6,X2,X3,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_Polynomial_OpCons(X3,X6,X5)
| X4 = X3 ),
file('<stdin>',cls_pCons__eq__iff_0) ).
fof(c_0_224,axiom,
! [X6,X2,X3,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_Polynomial_OpCons(X3,X6,X5)
| X2 = X6 ),
file('<stdin>',cls_pCons__eq__iff_1) ).
fof(c_0_225,axiom,
! [X26,X27,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) != c_HOL_Ominus__class_Ominus(X27,X26,X5)
| X27 = X26 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_226,axiom,
! [X7,X25,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X25,X7,X5) != c_HOL_Ominus__class_Ominus(X8,X8,X5)
| X25 = X7 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_227,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Oplus__class_Oplus(X4,X14,X5)
| X3 = X14 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_228,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Oplus__class_Oplus(X4,X14,X5)
| X3 = X14 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_229,axiom,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(X3,X4,X5) != c_HOL_Oplus__class_Oplus(X14,X4,X5)
| X3 = X14 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_230,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X4,X5),X3,X5) = X4
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__self1__is__id_0) ).
fof(c_0_231,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X3,X5),X3,X5) = X4
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__mult__self2__is__id_0) ).
fof(c_0_232,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X8,X7,X5),X8,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__dvd1_0) ).
fof(c_0_233,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X8,X7,X5),X7,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__dvd2_0) ).
fof(c_0_234,axiom,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Oabs__class_Oabs(X10,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5) ),
file('<stdin>',cls_dvd__abs__iff_1) ).
fof(c_0_235,axiom,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X11,X5),X10,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5) ),
file('<stdin>',cls_abs__dvd__iff_1) ).
fof(c_0_236,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
file('<stdin>',cls_minus__dvd__iff_1) ).
fof(c_0_237,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
file('<stdin>',cls_dvd__minus__iff_1) ).
fof(c_0_238,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X4,X3,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__div__trivial_0) ).
fof(c_0_239,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__mult__self1__is__0_0) ).
fof(c_0_240,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__mult__self2__is__0_0) ).
fof(c_0_241,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,X5),X3,X5) = X4 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_242,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X3,X5) = X4 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_243,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X4,X5),X5) ),
file('<stdin>',cls_dvd__triv__right_0) ).
fof(c_0_244,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) ),
file('<stdin>',cls_dvd__triv__left_0) ).
fof(c_0_245,axiom,
! [X10,X3,X5] :
( ~ class_Ring__and__Field_Odvd(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X10,X5),X5) ),
file('<stdin>',cls_dvdI_0) ).
fof(c_0_246,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Otimes__class_Otimes(X3,X3,X5) ),
file('<stdin>',cls_square__eq__iff_1) ).
fof(c_0_247,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X3,X5) ),
file('<stdin>',cls_minus__mult__minus_0) ).
fof(c_0_248,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X4,X5) ),
file('<stdin>',cls_abs__mult__self_0) ).
fof(c_0_249,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
file('<stdin>',cls_minus__mult__commute_0) ).
fof(c_0_250,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__mod__minus__right_0) ).
fof(c_0_251,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X5)),X5) = c_Polynomial_Opoly__gcd(X8,X7,X5) ),
file('<stdin>',cls_poly__gcd__minus__right_0) ).
fof(c_0_252,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X5)),X7,X5) = c_Polynomial_Opoly__gcd(X8,X7,X5) ),
file('<stdin>',cls_poly__gcd__minus__left_0) ).
fof(c_0_253,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).
fof(c_0_254,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X4,X5) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
file('<stdin>',cls_dvd__imp__mod__0_0) ).
fof(c_0_255,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Oplus__class_Oplus(X4,X3,X5) ),
file('<stdin>',cls_diff__minus__eq__add_0) ).
fof(c_0_256,axiom,
! [X7,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X7,X5) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) ),
file('<stdin>',cls_diff__def_0) ).
fof(c_0_257,axiom,
! [X7,X8,X5] :
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Ominus__class_Ominus(X8,X7,X5) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) ),
file('<stdin>',cls_class__ring_Osub__add_0) ).
fof(c_0_258,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
file('<stdin>',cls_diff__minus_0) ).
fof(c_0_259,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
file('<stdin>',cls_ab__diff__minus_0) ).
fof(c_0_260,axiom,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_Power_Opower__class_Opower(X4,X9,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_261,axiom,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(X4,X2,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_smult__eq__0__iff_0) ).
fof(c_0_262,axiom,
! [X2,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_pCons__eq__0__iff_1) ).
fof(c_0_263,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__zero__iff_0) ).
fof(c_0_264,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__zero__iff_1) ).
fof(c_0_265,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X8,X7,X5) = c_HOL_Otimes__class_Otimes(X7,X8,X5) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_266,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) = c_HOL_Otimes__class_Otimes(X3,X4,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_267,axiom,
! [X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,X14,X5) = c_HOL_Oplus__class_Oplus(X14,X4,X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_268,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X8,X7,X5) = c_HOL_Oplus__class_Oplus(X7,X8,X5) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_269,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) = c_HOL_Oplus__class_Oplus(X3,X4,X5) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_270,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) = c_Polynomial_Opoly__gcd(X7,X8,X5) ),
file('<stdin>',cls_poly__gcd__commute_0) ).
fof(c_0_271,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) = X3 ),
file('<stdin>',cls_minus__unique_0) ).
fof(c_0_272,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ouminus__class_Ouminus(X3,X5) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_1) ).
fof(c_0_273,axiom,
! [X2,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_pCons__eq__0__iff_0) ).
fof(c_0_274,axiom,
! [X8,X5] :
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Ouminus__class_Ouminus(X8,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X5),X5),X8,X5) ),
file('<stdin>',cls_class__ring_Oneg__mul_0) ).
fof(c_0_275,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X3 = c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_276,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X3 = c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_277,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_278,axiom,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ominus__class_Ominus(X8,X7,X5) != c_HOL_Ozero__class_Ozero(X5)
| X8 = X7 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_279,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_poly__gcd__0__0_0) ).
fof(c_0_280,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
file('<stdin>',cls_dvd__0__left_0) ).
fof(c_0_281,axiom,
! [X8,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X8 != c_HOL_Oplus__class_Oplus(X8,X4,X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_282,axiom,
! [X16,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(X16,X5) != c_HOL_Oabs__class_Oabs(X10,X5)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X10,X5) ),
file('<stdin>',cls_dvd__if__abs__eq_0) ).
fof(c_0_283,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(X6,tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_diff__poly__code_I1_J_0) ).
fof(c_0_284,axiom,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X5)
| c_Power_Opower__class_Opower(X4,X9,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_285,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_286,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = X3 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_287,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = X3 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_288,axiom,
! [X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_pCons__0__0_0) ).
fof(c_0_289,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,tc_Polynomial_Opoly(X5)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_mult__poly__0__left_0) ).
fof(c_0_290,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_mult__poly__0__right_0) ).
fof(c_0_291,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_0) ).
fof(c_0_292,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_ab__left__minus_0) ).
fof(c_0_293,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_right__minus_0) ).
fof(c_0_294,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_left__minus_0) ).
fof(c_0_295,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__0__right_0) ).
fof(c_0_296,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__eq__0__iff_2) ).
fof(c_0_297,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = X2 ),
file('<stdin>',cls_diff__poly__code_I2_J_0) ).
fof(c_0_298,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,tc_Polynomial_Opoly(X5)) = X6 ),
file('<stdin>',cls_add__poly__code_I1_J_0) ).
fof(c_0_299,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = X2 ),
file('<stdin>',cls_add__poly__code_I2_J_0) ).
fof(c_0_300,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_order__root_1) ).
fof(c_0_301,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_poly__0_0) ).
fof(c_0_302,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5) ),
file('<stdin>',cls_group__add__class_Odiff__0_0) ).
fof(c_0_303,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_304,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__eq__0__iff_1) ).
fof(c_0_305,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_smult__0__left_0) ).
fof(c_0_306,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X5),X5) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_307,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_308,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__by__0_0) ).
fof(c_0_309,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__0_0) ).
fof(c_0_310,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__0_0) ).
fof(c_0_311,axiom,
! [X9,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X5),X9,X5) = c_HOL_Oone__class_Oone(X5) ),
file('<stdin>',cls_power__one_0) ).
fof(c_0_312,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_313,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_314,axiom,
! [X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X7,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__left_Ozero_0) ).
fof(c_0_315,axiom,
! [X3,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult_Ozero__left_0) ).
fof(c_0_316,axiom,
! [X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult_Ozero__right_0) ).
fof(c_0_317,axiom,
! [X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__right_Ozero_0) ).
fof(c_0_318,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_319,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_320,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_321,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_322,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_323,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__by__1_0) ).
fof(c_0_324,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_div__self_0) ).
fof(c_0_325,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_326,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
file('<stdin>',cls_mult__1__right_0) ).
fof(c_0_327,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
file('<stdin>',cls_mult__1__left_0) ).
fof(c_0_328,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
file('<stdin>',cls_mult__1_0) ).
fof(c_0_329,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X8,X5) = X8 ),
file('<stdin>',cls_class__semiring_Omul__1_0) ).
fof(c_0_330,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_331,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_332,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_333,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_334,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_335,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X8,X5) = X8 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_336,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_337,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_338,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_339,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
file('<stdin>',cls_div__by__1_0) ).
fof(c_0_340,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
file('<stdin>',cls_mod__by__0_0) ).
fof(c_0_341,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X5),X2,X5) = X2 ),
file('<stdin>',cls_smult__1__left_0) ).
fof(c_0_342,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
file('<stdin>',cls_dvd__0__right_0) ).
fof(c_0_343,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X5),X4,X5) ),
file('<stdin>',cls_one__dvd_0) ).
fof(c_0_344,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_345,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_346,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_347,axiom,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_mod__self_0) ).
fof(c_0_348,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| c_HOL_Otimes__class_Otimes(X8,X8,X5) = X8 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_349,axiom,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X5) ),
file('<stdin>',cls_dvd__refl_0) ).
fof(c_0_350,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
file('<stdin>',cls_abs__minus__cancel_0) ).
fof(c_0_351,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
file('<stdin>',cls_abs__idempotent_0) ).
fof(c_0_352,axiom,
! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('<stdin>',cls_minus__poly__code_I1_J_0) ).
fof(c_0_353,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != c_HOL_Ouminus__class_Ouminus(X3,X5)
| X4 = X3 ),
file('<stdin>',cls_neg__equal__iff__equal_0) ).
fof(c_0_354,axiom,
! [X7,X8,X5] :
( ~ class_Lattices_Oboolean__algebra(X5)
| c_HOL_Ouminus__class_Ouminus(X8,X5) != c_HOL_Ouminus__class_Ouminus(X7,X5)
| X8 = X7 ),
file('<stdin>',cls_compl__eq__compl__iff_0) ).
fof(c_0_355,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = X3 ),
file('<stdin>',cls_minus__equation__iff_1) ).
fof(c_0_356,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X4 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
file('<stdin>',cls_equation__minus__iff_1) ).
fof(c_0_357,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X3 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
file('<stdin>',cls_equation__minus__iff_0) ).
fof(c_0_358,axiom,
! [X8,X5] :
( ~ class_Lattices_Oboolean__algebra(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X5),X5) = X8 ),
file('<stdin>',cls_double__compl_0) ).
fof(c_0_359,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = X4 ),
file('<stdin>',cls_minus__minus_0) ).
fof(c_0_360,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_neg__equal__0__iff__equal_0) ).
fof(c_0_361,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Ouminus__class_Ouminus(X4,X5)
| c_HOL_Ozero__class_Ozero(X5) = X4 ),
file('<stdin>',cls_neg__0__equal__iff__equal_0) ).
fof(c_0_362,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_abs__eq__0_0) ).
fof(c_0_363,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != X4
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_neg__equal__zero_0) ).
fof(c_0_364,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Oone__class_Oone(X5) ),
file('<stdin>',cls_abs__one_0) ).
fof(c_0_365,axiom,
! [X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_abs__eq__0_1) ).
fof(c_0_366,axiom,
! [X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X5),X5) ),
file('<stdin>',cls_neg__0__equal__iff__equal_1) ).
fof(c_0_367,axiom,
! [X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_minus__zero_0) ).
fof(c_0_368,axiom,
! [X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_neg__equal__zero_1) ).
fof(c_0_369,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Oone__class_Oone(X5) != c_HOL_Ozero__class_Ozero(X5) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_370,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_371,axiom,
! [X1] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_372,axiom,
! [X1] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(c_0_373,axiom,
! [X1] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(c_0_374,axiom,
! [X1] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(c_0_375,axiom,
! [X1] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_376,axiom,
! [X1] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(c_0_377,axiom,
! [X1] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(c_0_378,axiom,
! [X1] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_379,axiom,
! [X1] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_380,axiom,
! [X1] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_381,axiom,
! [X1] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_382,axiom,
! [X1] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_383,axiom,
! [X1] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_384,axiom,
! [X1] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_385,axiom,
! [X1] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_386,axiom,
! [X1] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_387,axiom,
! [X1] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_388,axiom,
! [X1] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(c_0_389,axiom,
! [X1] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(c_0_390,axiom,
! [X1] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(c_0_391,axiom,
! [X1] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(c_0_392,axiom,
! [X1] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(c_0_393,axiom,
! [X1] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(c_0_394,axiom,
! [X1] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(c_0_395,axiom,
! [X1] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(c_0_396,axiom,
! [X1] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(c_0_397,axiom,
! [X1] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(c_0_398,axiom,
! [X1] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(c_0_399,axiom,
! [X1] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(c_0_400,axiom,
! [X1] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(c_0_401,axiom,
! [X1] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(c_0_402,axiom,
! [X1] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(c_0_403,axiom,
! [X1] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(c_0_404,axiom,
! [X1] :
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(c_0_405,axiom,
! [X1] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
file('<stdin>',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(c_0_406,plain,
! [X12,X7,X8,X22,X13,X23,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(X8,c_HOL_Otimes__class_Otimes(X7,X12,tc_Polynomial_Opoly(X5)),X23,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X22,tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5)),X5)
| ~ c_Polynomial_Opdivmod__rel(X6,X12,X23,X22,X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_407,plain,
! [X7,X8,X34,X35,X36,X37,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X37 = X36
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X36,X34,X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X37,X35,X5) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_408,plain,
! [X7,X8,X34,X35,X36,X37,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X35 = X34
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X36,X34,X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X37,X35,X5) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_409,plain,
! [X7,X8,X13,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X4,X8,X5),X7,c_Polynomial_Osmult(X4,X6,X5),c_Polynomial_Osmult(X4,X13,X5),X5)
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_410,plain,
! [X7,X8,X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X7,X5),c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X4,X5),c_HOL_Ominus__class_Ominus(X7,X3,X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X4,X5),X3,X5),X5),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X7,X3,X5),X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_411,plain,
! [X7,X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X8 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X7,tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_412,plain,
! [X7,X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)) = X13
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_413,plain,
! [X7,X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)) = X6
| ~ c_Polynomial_Opdivmod__rel(X8,X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_414,plain,
! [X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,X13,X5)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_415,plain,
! [X7,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_416,plain,
! [X7,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_417,plain,
! [X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_418,plain,
! [X8,X13,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X13 = X8
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_419,plain,
! [X13,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X13,X5) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_420,plain,
! [X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_421,plain,
! [X7,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X7,tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X7,X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_422,plain,
! [X8,X32,X10,X15,X33,X5] :
( ~ class_Ring__and__Field_Odvd(X5)
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(X8,X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X10,X33,X5),X5),X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X33,X5) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_423,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(X8,X7,c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_424,plain,
! [X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_425,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_426,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Otimes__class_Otimes(X7,X12,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),X12,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_427,plain,
! [X8,X32,X10,X15,X33,X5] :
( ~ class_Ring__and__Field_Odvd(X5)
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X10,X33,X5),X5),X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oplus__class_Oplus(X8,X32,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X33,X5) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_428,plain,
! [X20,X15,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X5),X20,X5),X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X15,X5) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_429,plain,
! [X20,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X5),X20,X5),X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_430,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_431,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_432,plain,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,X14,X5) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X14,X5),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_433,plain,
! [X20,X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),X14,X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X15,X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X5),X20,X5),X14,X5) = X15 ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_434,plain,
! [X20,X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),X14,X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X15,X5)
| X14 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X5),X20,X5),X15,X5) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_435,plain,
! [X20,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Osemiring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X20,X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X5),X14,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X20,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_436,plain,
! [X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X15,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X15,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| X14 = X15
| X4 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_437,plain,
! [X12,X7,X8,X19,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X7,X5),c_HOL_Otimes__class_Otimes(X8,X12,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X12,X5),c_HOL_Otimes__class_Otimes(X8,X7,X5),X5)
| X7 = X12
| X19 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_438,plain,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X14,X5),X5) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X14,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_439,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X14,X5),c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_440,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X14,X5),c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_441,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X14,X5),c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_442,plain,
! [X12,X7,X8,X19,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X7,X5),c_Divides_Odiv__class_Odiv(X19,X12,X5),X5) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X19,X5),c_HOL_Otimes__class_Otimes(X7,X12,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X19,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_443,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X6,X5),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X5),c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_444,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(X2,c_Polynomial_OpCons(X4,X6,X5),tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X5),c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_445,plain,
! [X14,X17,X3,X18,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X14,X5) != c_Divides_Odiv__class_Omod(X17,X14,X5)
| c_Divides_Odiv__class_Omod(X4,X14,X5) != c_Divides_Odiv__class_Omod(X18,X14,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_446,plain,
! [X14,X17,X3,X18,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X14,X5) != c_Divides_Odiv__class_Omod(X17,X14,X5)
| c_Divides_Odiv__class_Omod(X4,X14,X5) != c_Divides_Odiv__class_Omod(X18,X14,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X17,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_447,plain,
! [X14,X17,X3,X18,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X14,X5) != c_Divides_Odiv__class_Omod(X17,X14,X5)
| c_Divides_Odiv__class_Omod(X4,X14,X5) != c_Divides_Odiv__class_Omod(X18,X14,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_448,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X4,X5),c_Divides_Odiv__class_Odiv(X14,X4,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_449,plain,
! [X28,X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X29,X28,X5),X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_450,plain,
! [X28,X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),X28,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_451,plain,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,X14,X5) != c_HOL_Ozero__class_Ozero(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X14,X5),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_452,plain,
! [X2,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X14,X5),X5) != c_HOL_Ozero__class_Ozero(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X14,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X2,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_453,plain,
! [X12,X7,X8,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,X7,X5),X12,X5) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X12,X5),c_Divides_Odiv__class_Odiv(X7,X12,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_454,plain,
! [X6,X2,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X4,X2,X5),c_Polynomial_OpCons(X3,X6,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X4,X3,X5),c_HOL_Ominus__class_Ominus(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_455,plain,
! [X6,X2,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X4,X2,X5),c_Polynomial_OpCons(X3,X6,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X4,X3,X5),c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_456,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X7,X5),c_HOL_Otimes__class_Otimes(X8,X12,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X12,X5),c_HOL_Otimes__class_Otimes(X8,X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_457,plain,
! [X8,X15,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X14,X5),c_HOL_Otimes__class_Otimes(X8,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,X5),c_HOL_Otimes__class_Otimes(X8,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_458,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X3,X5),X5),X3,X5) = c_HOL_Oplus__class_Oplus(X14,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_459,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5),X3,X5) = c_HOL_Oplus__class_Oplus(X14,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_460,plain,
! [X8,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X4,X2,X5),X8,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X2,X8,X5),X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_461,plain,
! [X28,X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X29,X5),c_HOL_Otimes__class_Otimes(X31,X28,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_462,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_463,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_464,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_465,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_466,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_467,plain,
! [X15,X14,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,X5),c_HOL_Oplus__class_Oplus(X3,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,X5),c_HOL_Ominus__class_Ominus(X14,X15,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_468,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_469,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_470,plain,
! [X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),c_HOL_Oplus__class_Oplus(X14,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X14,X5),c_HOL_Oplus__class_Oplus(X3,X15,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_471,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X14,X5),X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_472,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,c_Divides_Odiv__class_Omod(X3,X14,X5),X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_473,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X4,X5),c_Divides_Odiv__class_Odiv(X14,X4,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_474,plain,
! [X8,X13,X15,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X13,X14,X5),X5) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X13,X15,X5),X5)
| X14 = X15
| X13 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_475,plain,
! [X7,X8,X9,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X8,X7,X5),X9,X5) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X8,X9,X5),c_Power_Opower__class_Opower(X7,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_476,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_477,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_478,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X4,X3,X5),X5),c_Divides_Odiv__class_Omod(X4,X3,X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_479,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,X5),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X3,X5),X3,X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_480,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_481,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_482,plain,
! [X13,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X13,tc_Polynomial_Opoly(X5)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X13,tc_Polynomial_Opoly(X5)),c_HOL_Otimes__class_Otimes(X6,X13,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_483,plain,
! [X2,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X14,X2,X5),c_Polynomial_OpCons(X4,X2,X5),tc_Polynomial_Opoly(X5)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_484,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ominus__class_Ominus(X2,X6,tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_485,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X5) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_486,plain,
! [X8,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X2,X8,X5),c_Polynomial_Opoly(X6,X8,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_487,plain,
! [X8,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X2,X6,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X2,X8,X5),c_Polynomial_Opoly(X6,X8,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_488,plain,
! [X8,X6,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X2,X6,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X2,X8,X5),c_Polynomial_Opoly(X6,X8,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_489,plain,
! [X15,X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X15,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_490,plain,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X4,X3,X5),X2,X5) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X3,X2,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_491,plain,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X4,X3,X5),X2,X5) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X4,X2,X5),c_Polynomial_Osmult(X3,X2,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_492,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X5),c_HOL_Otimes__class_Otimes(X7,X7,X5),X5) != c_HOL_Ozero__class_Ozero(X5)
| X8 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_493,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X5),c_HOL_Otimes__class_Otimes(X7,X7,X5),X5) != c_HOL_Ozero__class_Ozero(X5)
| X7 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_494,plain,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_Polynomial_OpCons(X3,X2,X5),X5) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_Polynomial_Osmult(X4,X2,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_495,plain,
! [X7,X8,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X7,X5),X6,X5) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X6,X5),c_Power_Opower__class_Opower(X7,X6,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_496,plain,
! [X9,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X4,X3,X5),X9,X5) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X9,X5),c_Power_Opower__class_Opower(X3,X9,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_497,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_498,plain,
! [X7,X25,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X8,X7,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X8,X5),c_HOL_Otimes__class_Otimes(X25,X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_499,plain,
! [X17,X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X3,X17,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X4,X17,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_500,plain,
! [X24,X7,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X7,X5),X24,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X24,X5),c_HOL_Otimes__class_Otimes(X7,X24,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_501,plain,
! [X3,X18,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X18,X5),X3,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X18,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_502,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X7,X5),c_HOL_Otimes__class_Otimes(X8,X12,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_503,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_504,plain,
! [X11,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X11,X5),c_HOL_Otimes__class_Otimes(X3,X11,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,X5),X11,X5) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_505,plain,
! [X7,X25,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ominus__class_Ominus(X8,X7,X5),X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X25,X8,X5),c_HOL_Otimes__class_Otimes(X25,X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_506,plain,
! [X17,X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X17,X5),X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X4,X17,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_507,plain,
! [X3,X18,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X18,X5),X3,X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X3,X5),c_HOL_Otimes__class_Otimes(X18,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_508,plain,
! [X24,X7,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X7,X5),X24,X5) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X24,X5),c_HOL_Otimes__class_Otimes(X7,X24,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_509,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_510,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X3,X5),X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_511,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5) = c_HOL_Otimes__class_Otimes(X14,c_Divides_Odiv__class_Omod(X4,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_512,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X4,X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_513,plain,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oring__1(X5)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X4,X5),X9,X5) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X5),X5),X9,X5),c_Power_Opower__class_Opower(X4,X9,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_514,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X5),X14,X5) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X14,X5),X4,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_515,plain,
! [X13,X6,X2,X14,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X14,X6,X5),tc_Polynomial_Opoly(X5)) != c_Polynomial_OpCons(X13,X6,X5)
| X13 = c_Polynomial_Opoly(X2,X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_516,plain,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_517,plain,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_518,plain,
! [X12,X7,X8,X21,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) != c_HOL_Oplus__class_Oplus(X7,X21,X5)
| c_HOL_Oplus__class_Oplus(X8,X12,X5) = X21 ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_519,plain,
! [X3,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X4,X3,X5),X5),X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_520,plain,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X7,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X8,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_521,plain,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X7,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X8,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_522,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Otimes__class_Otimes(X7,X12,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),X12,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_523,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_524,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_525,plain,
! [X7,X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X9,X5),c_Power_Opower__class_Opower(X7,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_526,plain,
! [X7,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X4,X8,X5),X7,tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_527,plain,
! [X7,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X4,X8,X5),X7,tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_528,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_529,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X4,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_530,plain,
! [X11,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X11,X5),X11,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X5),X5),X11,X5) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_531,plain,
! [X11,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X4,X11,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X5),X5),X11,X5) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_532,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_533,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X7,X12,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X12,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_534,plain,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_535,plain,
! [X9,X11,X10,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X11,X9,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X5) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_536,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X4,X5),X3,X5) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X3,X5),c_HOL_Oone__class_Oone(X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_537,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X3,X5),X3,X5) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X3,X5),c_HOL_Oone__class_Oone(X5),X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_538,plain,
! [X3,X18,X4,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Omod(X4,X3,X5) != c_Divides_Odiv__class_Omod(X18,X3,X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X18,X5),X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_539,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X3,X5),X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_540,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_541,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_542,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_543,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,X4,X5),c_HOL_Otimes__class_Otimes(X14,X3,X5),X5) = c_Divides_Odiv__class_Odiv(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_544,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X14,X5),c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) = c_Divides_Odiv__class_Odiv(X4,X3,X5)
| X14 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_545,plain,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X7,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_546,plain,
! [X7,X8,X10,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X8,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X8,X7,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_547,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_548,plain,
! [X8,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X4,X2,X5),X8,X5) = c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X2,X8,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_549,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_550,plain,
! [X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),X29,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X29,X5),X31,X5) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_551,plain,
! [X29,X31,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X5),X29,X5) = c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X31,X29,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_552,plain,
! [X28,X29,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X29,X5),X28,X5) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_553,plain,
! [X28,X29,X30,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X29,X28,X5),X5) = c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(X30,X28,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_554,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X7,X12,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X8,X7,X5),X12,X5) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_555,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,c_Polynomial_Opoly__gcd(X7,X12,X5),X5) = c_Polynomial_Opoly__gcd(X7,c_Polynomial_Opoly__gcd(X8,X12,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_556,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X8,X7,X5),X12,X5) = c_Polynomial_Opoly__gcd(X8,c_Polynomial_Opoly__gcd(X7,X12,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_557,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_558,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_559,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X7,X5),X12,X5) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_560,plain,
! [X12,X7,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X8,X12,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_561,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_562,plain,
! [X15,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X14,X15,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X14,X5),X15,X5) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_563,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X14,X5),X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_564,plain,
! [X15,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X14,X15,X5),X5) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X4,X15,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_565,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X14,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_566,plain,
! [X9,X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X9,X5),X4,X5) = c_HOL_Otimes__class_Otimes(X4,c_Power_Opower__class_Opower(X4,X9,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_567,plain,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X3,X2,X5),X5) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X4,X3,X5),X2,X5) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_568,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_569,plain,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_570,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_571,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X5),X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_572,plain,
! [X14,X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X3,X5),X14,X5) = c_Divides_Odiv__class_Omod(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_573,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_574,plain,
! [X6,X2,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5),X6,tc_Polynomial_Opoly(X5))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_575,plain,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X4,X5),X9,X5),X5) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X9,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_576,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_577,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X5),X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_578,plain,
! [X7,X8,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_579,plain,
! [X7,X8,X5] :
( ~ class_Divides_Oring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_580,plain,
! [X12,X7,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) != X7
| X8 = c_HOL_Ouminus__class_Ouminus(X12,X5) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_581,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_582,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_583,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X5),X6,tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_584,plain,
! [X6,X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X6,X5),tc_Polynomial_Opoly(X5))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_585,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Odiv(X3,X4,X5),X5) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_586,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X5),X4,X5) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_587,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_588,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X14,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_589,plain,
! [X2,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X4,X2,X5),tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X5)),X5) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_590,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,X5),X5) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X4,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_591,plain,
! [X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X11,X11,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X5),c_HOL_Oone__class_Oone(X5),X5),X11,X5) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_592,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) = c_Polynomial_Opoly__gcd(X7,c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),X5)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_593,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_594,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X5)),X7,tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_595,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X5)),X7,tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_596,plain,
! [X7,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,c_Polynomial_Osmult(X4,X7,X5),tc_Polynomial_Opoly(X5)) = c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_597,plain,
! [X14,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X14,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_598,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_599,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_600,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_601,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X5) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_602,plain,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X4,X2,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_603,plain,
! [X7,X8,X5] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X8,X7,X5),X5) = c_HOL_Otimes__class_Otimes(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_604,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_605,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_606,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X3,X5),X3,X5) = c_Divides_Odiv__class_Omod(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_607,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5),X5) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_608,plain,
! [X8,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X2,X8,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_609,plain,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X4,X5),X2,X5) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X4,X2,X5),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_610,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_611,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_612,plain,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_613,plain,
! [X7,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_614,plain,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_615,plain,
! [X25,X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ouminus__class_Ouminus(X8,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X25,X8,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_616,plain,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X9,X5),X5) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X5),X9,X5) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_617,plain,
! [X2,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_618,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_HOL_Otimes__class_Otimes(X4,X4,X5) != c_HOL_Otimes__class_Otimes(X3,X3,X5)
| X4 = c_HOL_Ouminus__class_Ouminus(X3,X5)
| X4 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_619,plain,
! [X12,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X12,X5),c_HOL_Oplus__class_Oplus(X7,X12,X5),X5) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_620,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Oplus__class_Oplus(X4,X3,X5),X5) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_621,plain,
! [X2,X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X14,X2,X5) != c_Polynomial_OpCons(X4,X2,X5)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_622,plain,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Oabs__class_Oabs(X10,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_623,plain,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X11,X5),X10,X5) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_624,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_625,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_626,plain,
! [X12,X7,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(X8,X7,X5) != c_HOL_Oplus__class_Oplus(X8,X12,X5)
| X7 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_627,plain,
! [X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X5),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X5),X9,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_628,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X5),X5) = c_HOL_Ominus__class_Ominus(X3,X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_629,plain,
! [X6,X2,X3,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_Polynomial_OpCons(X3,X6,X5)
| X4 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_630,plain,
! [X6,X2,X3,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_Polynomial_OpCons(X3,X6,X5)
| X2 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_631,plain,
! [X26,X27,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) != c_HOL_Ominus__class_Ominus(X27,X26,X5)
| X27 = X26 ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_632,plain,
! [X7,X25,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X25,X7,X5) != c_HOL_Ominus__class_Ominus(X8,X8,X5)
| X25 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_633,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Oplus__class_Oplus(X4,X14,X5)
| X3 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_634,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Oplus__class_Oplus(X4,X14,X5)
| X3 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_635,plain,
! [X14,X3,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| c_HOL_Oplus__class_Oplus(X3,X4,X5) != c_HOL_Oplus__class_Oplus(X14,X4,X5)
| X3 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_636,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X4,X5),X3,X5) = X4
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_637,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X3,X5),X3,X5) = X4
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_638,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X8,X7,X5),X8,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_639,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X8,X7,X5),X7,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_640,plain,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Oabs__class_Oabs(X10,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_641,plain,
! [X11,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X11,X5),X10,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X5) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_642,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X5),X7,X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_643,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_644,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X4,X3,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_645,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_646,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_647,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,X5),X3,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_648,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,X5),X3,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_649,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X4,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_650,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_651,plain,
! [X10,X3,X5] :
( ~ class_Ring__and__Field_Odvd(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X10,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_652,plain,
! [X3,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Otimes__class_Otimes(X3,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_653,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_654,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_655,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),X3,X5) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_656,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_Divides_Odiv__class_Omod(X8,X7,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_657,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X5)),X5) = c_Polynomial_Opoly__gcd(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_658,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X5)),X7,X5) = c_Polynomial_Opoly__gcd(X8,X7,X5) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_659,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_660,plain,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X3,X4,X5) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_661,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = c_HOL_Oplus__class_Oplus(X4,X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_662,plain,
! [X7,X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X7,X5) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_663,plain,
! [X7,X8,X5] :
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Ominus__class_Ominus(X8,X7,X5) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X7,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_664,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_665,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_666,plain,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_Power_Opower__class_Opower(X4,X9,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_667,plain,
! [X2,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(X4,X2,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_668,plain,
! [X2,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_669,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_670,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_671,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X8,X7,X5) = c_HOL_Otimes__class_Otimes(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_672,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) = c_HOL_Otimes__class_Otimes(X3,X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_673,plain,
! [X14,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,X14,X5) = c_HOL_Oplus__class_Oplus(X14,X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_674,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X8,X7,X5) = c_HOL_Oplus__class_Oplus(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_675,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) = c_HOL_Oplus__class_Oplus(X3,X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_676,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(X8,X7,X5) = c_Polynomial_Opoly__gcd(X7,X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_677,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_678,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ouminus__class_Ouminus(X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_679,plain,
! [X2,X4,X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(X4,X2,X5) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_680,plain,
! [X8,X5] :
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Ouminus__class_Ouminus(X8,X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X5),X5),X8,X5) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_681,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X3 = c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_682,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X3 = c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_683,plain,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| X3 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_684,plain,
! [X7,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ominus__class_Ominus(X8,X7,X5) != c_HOL_Ozero__class_Ozero(X5)
| X8 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_685,plain,
! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_686,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_687,plain,
! [X8,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X8 != c_HOL_Oplus__class_Oplus(X8,X4,X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_688,plain,
! [X16,X10,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(X16,X5) != c_HOL_Oabs__class_Oabs(X10,X5)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X10,X5) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_689,plain,
! [X6,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,tc_Polynomial_Opoly(X5)) = c_HOL_Ouminus__class_Ouminus(X6,tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_690,plain,
! [X9,X4,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X5)
| c_Power_Opower__class_Opower(X4,X9,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_691,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_692,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_693,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X3,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_694,plain,
! [X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_695,plain,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,tc_Polynomial_Opoly(X5)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_696,plain,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_697,plain,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_698,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_699,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_700,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_701,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_702,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_703,plain,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_704,plain,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6,tc_Polynomial_Opoly(X5)) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_705,plain,
! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_706,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_707,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_708,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_709,plain,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_710,plain,
! [X2,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_711,plain,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X5),X2,X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_712,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_713,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_714,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_715,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_716,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_717,plain,
! [X9,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X5),X9,X5) = c_HOL_Oone__class_Oone(X5) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_718,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_719,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_720,plain,
! [X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X7,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_721,plain,
! [X3,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_722,plain,
! [X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_723,plain,
! [X8,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_724,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_725,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_726,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_727,plain,
! [X3,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X3,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_728,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_729,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_730,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_731,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_732,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_733,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_734,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_735,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X8,X5) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_736,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_737,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_738,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_739,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_740,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_741,plain,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X8,X5) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_742,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_743,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_744,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_745,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_746,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_747,plain,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X5),X2,X5) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_748,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_749,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X5),X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_750,plain,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_751,plain,
! [X8,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X8,X8,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_752,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_753,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_754,plain,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| c_HOL_Otimes__class_Otimes(X8,X8,X5) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_755,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_756,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_757,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_758,plain,
! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_759,plain,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != c_HOL_Ouminus__class_Ouminus(X3,X5)
| X4 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_760,plain,
! [X7,X8,X5] :
( ~ class_Lattices_Oboolean__algebra(X5)
| c_HOL_Ouminus__class_Ouminus(X8,X5) != c_HOL_Ouminus__class_Ouminus(X7,X5)
| X8 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_761,plain,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X5),X5) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_762,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X4 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_763,plain,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X3 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_764,plain,
! [X8,X5] :
( ~ class_Lattices_Oboolean__algebra(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X5),X5) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_765,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_766,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_767,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Ouminus__class_Ouminus(X4,X5)
| c_HOL_Ozero__class_Ozero(X5) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_768,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_769,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != X4
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_770,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Oone__class_Oone(X5) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_771,plain,
! [X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_772,plain,
! [X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_773,plain,
! [X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_774,plain,
! [X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_775,plain,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Oone__class_Oone(X5) != c_HOL_Ozero__class_Ozero(X5) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_776,plain,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_777,plain,
! [X1] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_778,plain,
! [X1] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_779,plain,
! [X1] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_780,plain,
! [X1] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_781,plain,
! [X1] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_782,plain,
! [X1] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_783,plain,
! [X1] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_784,plain,
! [X1] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_785,plain,
! [X1] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_786,plain,
! [X1] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_787,plain,
! [X1] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_788,plain,
! [X1] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_789,plain,
! [X1] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_790,plain,
! [X1] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_791,plain,
! [X1] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_792,plain,
! [X1] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_793,plain,
! [X1] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_794,plain,
! [X1] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_795,plain,
! [X1] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_796,plain,
! [X1] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_797,plain,
! [X1] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_798,plain,
! [X1] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_799,plain,
! [X1] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_800,plain,
! [X1] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_801,plain,
! [X1] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_802,plain,
! [X1] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_803,plain,
! [X1] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_804,plain,
! [X1] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_805,plain,
! [X1] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_806,plain,
! [X1] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_807,plain,
! [X1] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_808,plain,
! [X1] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_809,plain,
! [X1] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_810,plain,
! [X1] :
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_811,plain,
! [X1] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_812,plain,
! [X24,X25,X26,X27,X28,X29,X30,X31] :
( ~ class_Ring__and__Field_Ofield(X31)
| c_Polynomial_Opdivmod__rel(X26,c_HOL_Otimes__class_Otimes(X25,X24,tc_Polynomial_Opoly(X31)),X29,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X27,tc_Polynomial_Opoly(X31)),X28,tc_Polynomial_Opoly(X31)),X31)
| ~ c_Polynomial_Opdivmod__rel(X30,X24,X29,X27,X31)
| ~ c_Polynomial_Opdivmod__rel(X26,X25,X30,X28,X31) ),
inference(variable_rename,[status(thm)],[c_0_406]) ).
fof(c_0_813,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( ~ class_Ring__and__Field_Ofield(X44)
| X43 = X42
| ~ c_Polynomial_Opdivmod__rel(X39,X38,X42,X40,X44)
| ~ c_Polynomial_Opdivmod__rel(X39,X38,X43,X41,X44) ),
inference(variable_rename,[status(thm)],[c_0_407]) ).
fof(c_0_814,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( ~ class_Ring__and__Field_Ofield(X44)
| X41 = X40
| ~ c_Polynomial_Opdivmod__rel(X39,X38,X42,X40,X44)
| ~ c_Polynomial_Opdivmod__rel(X39,X38,X43,X41,X44) ),
inference(variable_rename,[status(thm)],[c_0_408]) ).
fof(c_0_815,plain,
! [X14,X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X18,X15,X19),X14,c_Polynomial_Osmult(X18,X17,X19),c_Polynomial_Osmult(X18,X16,X19),X19)
| ~ c_Polynomial_Opdivmod__rel(X15,X14,X17,X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_816,plain,
! [X9,X10,X11,X12,X13] :
( ~ class_RealVector_Oreal__normed__algebra(X13)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X10,X9,X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X12,X13),c_HOL_Ominus__class_Ominus(X9,X11,X13),X13),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X12,X13),X11,X13),X13),c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X9,X11,X13),X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_410]) ).
fof(c_0_817,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| X15 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X14,tc_Polynomial_Opoly(X18)),X16,tc_Polynomial_Opoly(X18))
| ~ c_Polynomial_Opdivmod__rel(X15,X14,X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_411]) ).
fof(c_0_818,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Divides_Odiv__class_Omod(X15,X14,tc_Polynomial_Opoly(X18)) = X16
| ~ c_Polynomial_Opdivmod__rel(X15,X14,X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_412]) ).
fof(c_0_819,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Divides_Odiv__class_Odiv(X15,X14,tc_Polynomial_Opoly(X18)) = X17
| ~ c_Polynomial_Opdivmod__rel(X15,X14,X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_413]) ).
fof(c_0_820,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| ~ c_Polynomial_Opdivmod__rel(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X16,X15,X17)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_414]) ).
fof(c_0_821,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X14,X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_822,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X14,X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_416]) ).
fof(c_0_823,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| ~ c_Polynomial_Opdivmod__rel(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_417]) ).
fof(c_0_824,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| X15 = X14
| ~ c_Polynomial_Opdivmod__rel(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_418]) ).
fof(c_0_825,plain,
! [X14,X15] :
( ~ class_Ring__and__Field_Ofield(X15)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)),tc_Polynomial_Opoly(X15)),X14,tc_Polynomial_Opoly(X15)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_419]) ).
fof(c_0_826,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ofield(X9)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X8,tc_Polynomial_Opoly(X9)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),tc_Polynomial_Opoly(X9)),X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X9) ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_827,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,tc_Polynomial_Opoly(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),tc_Polynomial_Opoly(X10)),X8,X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X10) ),
inference(variable_rename,[status(thm)],[c_0_421]) ).
fof(c_0_828,plain,
! [X34,X35,X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Odvd(X39)
| ~ class_Ring__and__Field_Ocomm__ring(X39)
| c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Oplus__class_Oplus(X34,X35,X39),X39)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X34,c_HOL_Otimes__class_Otimes(X36,X38,X39),X39),X35,X39),X39)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X38,X39) ),
inference(variable_rename,[status(thm)],[c_0_422]) ).
fof(c_0_829,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opdivmod__rel(X10,X9,c_Divides_Odiv__class_Odiv(X10,X9,tc_Polynomial_Opoly(X11)),c_Divides_Odiv__class_Omod(X10,X9,tc_Polynomial_Opoly(X11)),X11) ),
inference(variable_rename,[status(thm)],[c_0_423]) ).
fof(c_0_830,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ofield(X9)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X9) ),
inference(variable_rename,[status(thm)],[c_0_424]) ).
fof(c_0_831,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opdivmod__rel(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_425]) ).
fof(c_0_832,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Divides_Odiv__class_Omod(X15,c_HOL_Otimes__class_Otimes(X14,X13,tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X15,X14,tc_Polynomial_Opoly(X16)),X13,tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16)),c_Divides_Odiv__class_Omod(X15,X14,tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_426]) ).
fof(c_0_833,plain,
! [X34,X35,X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Odvd(X39)
| ~ class_Ring__and__Field_Ocomm__ring(X39)
| c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X34,c_HOL_Otimes__class_Otimes(X36,X38,X39),X39),X35,X39),X39)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Oplus__class_Oplus(X34,X35,X39),X39)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X38,X39) ),
inference(variable_rename,[status(thm)],[c_0_427]) ).
fof(c_0_834,plain,
! [X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oring(X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X21,X25),X22,X25),X25) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X25),X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_428]) ).
fof(c_0_835,plain,
! [X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oring(X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X25),X22,X25) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X23,X25),X21,X25),X22,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_429]) ).
fof(c_0_836,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X17,X16,X18),X16,X18),c_Divides_Odiv__class_Omod(X17,X16,X18),X18),X15,X18) = c_HOL_Oplus__class_Oplus(X17,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_430]) ).
fof(c_0_837,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,c_Divides_Odiv__class_Odiv(X17,X16,X18),X18),c_Divides_Odiv__class_Omod(X17,X16,X18),X18),X15,X18) = c_HOL_Oplus__class_Oplus(X17,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_431]) ).
fof(c_0_838,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,X16,X17) = c_HOL_Ozero__class_Ozero(X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X16,X17),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_432]) ).
fof(c_0_839,plain,
! [X21,X22,X23,X24,X25,X26] :
( ~ class_Ring__and__Field_Oring(X26)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X24,X26),X21,X26),X23,X26) = X22 ),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_840,plain,
! [X21,X22,X23,X24,X25,X26] :
( ~ class_Ring__and__Field_Oring(X26)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26)
| X23 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X25,X26),X21,X26),X22,X26) ),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_841,plain,
! [X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Osemiring(X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X25),X22,X25),X25) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X24,X23,X25),X21,X25),X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_842,plain,
! [X16,X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oidom(X20)
| ~ class_Int_Onumber__ring(X20)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X17,X20),c_HOL_Otimes__class_Otimes(X18,X16,X20),X20) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,X20),c_HOL_Otimes__class_Otimes(X18,X17,X20),X20)
| X17 = X16
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_843,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Oidom(X24)
| ~ class_Int_Onumber__ring(X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X20,X24),X24) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
| X21 = X20
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_844,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,c_HOL_Ouminus__class_Ouminus(X16,X17),X17) = c_HOL_Ozero__class_Ozero(X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X16,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_438]) ).
fof(c_0_845,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X15,X18),c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_439]) ).
fof(c_0_846,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Oring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X17,X15,X18),c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_440]) ).
fof(c_0_847,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X15,X18),c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_441]) ).
fof(c_0_848,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Divides_Osemiring__div(X24)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X22,X21,X24),c_Divides_Odiv__class_Odiv(X23,X20,X24),X24) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X22,X23,X24),c_HOL_Otimes__class_Otimes(X21,X20,X24),X24)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X23,X24)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_442]) ).
fof(c_0_849,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X9,X8,X10),X7,tc_Polynomial_Opoly(X10)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X9,X7,X10),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X10),c_HOL_Otimes__class_Otimes(X8,X7,tc_Polynomial_Opoly(X10)),X10),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_850,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_HOL_Otimes__class_Otimes(X8,c_Polynomial_OpCons(X9,X7,X10),tc_Polynomial_Opoly(X10)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X9,X8,X10),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X10),c_HOL_Otimes__class_Otimes(X8,X7,tc_Polynomial_Opoly(X10)),X10),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_444]) ).
fof(c_0_851,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Divides_Osemiring__div(X24)
| c_Divides_Odiv__class_Omod(X21,X19,X24) != c_Divides_Odiv__class_Omod(X20,X19,X24)
| c_Divides_Odiv__class_Omod(X23,X19,X24) != c_Divides_Odiv__class_Omod(X22,X19,X24)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,X21,X24),X19,X24) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X22,X20,X24),X19,X24) ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_852,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Divides_Osemiring__div(X24)
| c_Divides_Odiv__class_Omod(X21,X19,X24) != c_Divides_Odiv__class_Omod(X20,X19,X24)
| c_Divides_Odiv__class_Omod(X23,X19,X24) != c_Divides_Odiv__class_Omod(X22,X19,X24)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,X21,X24),X19,X24) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X22,X20,X24),X19,X24) ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_853,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Divides_Oring__div(X24)
| c_Divides_Odiv__class_Omod(X21,X19,X24) != c_Divides_Odiv__class_Omod(X20,X19,X24)
| c_Divides_Odiv__class_Omod(X23,X19,X24) != c_Divides_Odiv__class_Omod(X22,X19,X24)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X23,X21,X24),X19,X24) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X22,X20,X24),X19,X24) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_854,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X16,X17,X18),c_Divides_Odiv__class_Odiv(X15,X17,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_855,plain,
! [X32,X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X36),c_HOL_Otimes__class_Otimes(X33,X32,X36),X36) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X36),X36),X36) ),
inference(variable_rename,[status(thm)],[c_0_449]) ).
fof(c_0_856,plain,
! [X32,X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X36),c_HOL_Otimes__class_Otimes(X33,X32,X36),X36) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X36),X32,X36),X36) ),
inference(variable_rename,[status(thm)],[c_0_450]) ).
fof(c_0_857,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,X16,X17) != c_HOL_Ozero__class_Ozero(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X16,X17),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_451]) ).
fof(c_0_858,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,c_HOL_Ouminus__class_Ouminus(X16,X17),X17) != c_HOL_Ozero__class_Ozero(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X16,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_859,plain,
! [X13,X14,X15,X16] :
( ~ class_Divides_Osemiring__div(X16)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X15,X14,X16),X13,X16) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X15,X13,X16),c_Divides_Odiv__class_Odiv(X14,X13,X16),X16)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X14,X16)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_453]) ).
fof(c_0_860,plain,
! [X7,X8,X9,X10,X11] :
( ~ class_OrderedGroup_Oab__group__add(X11)
| c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X10,X8,X11),c_Polynomial_OpCons(X9,X7,X11),tc_Polynomial_Opoly(X11)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X10,X9,X11),c_HOL_Ominus__class_Ominus(X8,X7,tc_Polynomial_Opoly(X11)),X11) ),
inference(variable_rename,[status(thm)],[c_0_454]) ).
fof(c_0_861,plain,
! [X7,X8,X9,X10,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X11)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X10,X8,X11),c_Polynomial_OpCons(X9,X7,X11),tc_Polynomial_Opoly(X11)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Oplus__class_Oplus(X8,X7,tc_Polynomial_Opoly(X11)),X11) ),
inference(variable_rename,[status(thm)],[c_0_455]) ).
fof(c_0_862,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oidom(X16)
| ~ class_Int_Onumber__ring(X16)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X14,X16),c_HOL_Otimes__class_Otimes(X15,X13,X16),X16) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X13,X16),c_HOL_Otimes__class_Otimes(X15,X14,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_863,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X17,X19),c_HOL_Otimes__class_Otimes(X16,X18,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_864,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X15,X16,X18),X18),X16,X18) = c_HOL_Oplus__class_Oplus(X15,c_Divides_Odiv__class_Odiv(X17,X16,X18),X18)
| X16 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_865,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18),X16,X18) = c_HOL_Oplus__class_Oplus(X15,c_Divides_Odiv__class_Odiv(X17,X16,X18),X18)
| X16 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_866,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X9,c_Polynomial_Opoly(X10,X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_867,plain,
! [X32,X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X36),c_HOL_Otimes__class_Otimes(X33,X32,X36),X36) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X36),c_HOL_Otimes__class_Otimes(X34,X32,X36),X36) ),
inference(variable_rename,[status(thm)],[c_0_461]) ).
fof(c_0_868,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_462]) ).
fof(c_0_869,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X15,X18),X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_463]) ).
fof(c_0_870,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X15,X18),X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_871,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_872,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X15,X18),X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_873,plain,
! [X16,X17,X18,X19,X20] :
( ~ class_OrderedGroup_Oab__group__add(X20)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X19,X17,X20),c_HOL_Oplus__class_Oplus(X18,X16,X20),X20) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X19,X18,X20),c_HOL_Ominus__class_Ominus(X17,X16,X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_874,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_875,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X15,X18),X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_469]) ).
fof(c_0_876,plain,
! [X16,X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X19,X18,X20),c_HOL_Oplus__class_Oplus(X17,X16,X20),X20) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X19,X17,X20),c_HOL_Oplus__class_Oplus(X18,X16,X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_877,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Oring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X17,X15,X18),X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_878,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Oring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,c_Divides_Odiv__class_Omod(X16,X15,X18),X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_472]) ).
fof(c_0_879,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X16,X17,X18),c_Divides_Odiv__class_Odiv(X15,X17,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_880,plain,
! [X16,X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oidom(X20)
| ~ class_Int_Onumber__ring(X20)
| c_HOL_Oplus__class_Oplus(X16,c_HOL_Otimes__class_Otimes(X17,X19,X20),X20) != c_HOL_Oplus__class_Oplus(X16,c_HOL_Otimes__class_Otimes(X17,X18,X20),X20)
| X19 = X18
| X17 = c_HOL_Ozero__class_Ozero(X20) ),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_881,plain,
! [X10,X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X11,X10,X13),X12,X13) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X11,X12,X13),c_Power_Opower__class_Opower(X10,X12,X13),X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_882,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| X7 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X6,X8),X6,X8),c_Divides_Odiv__class_Omod(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_476]) ).
fof(c_0_883,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X6,X8),X6,X8),c_Divides_Odiv__class_Omod(X7,X6,X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_884,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,c_Divides_Odiv__class_Odiv(X7,X6,X8),X8),c_Divides_Odiv__class_Omod(X7,X6,X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_885,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X7,X6,X8),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X6,X8),X6,X8),X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_886,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18)
| X15 = c_HOL_Ozero__class_Ozero(X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_887,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18)
| X15 = c_HOL_Ozero__class_Ozero(X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,X17,X18),c_HOL_Otimes__class_Otimes(X15,X16,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_888,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X17)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X16,X15,tc_Polynomial_Opoly(X17)),X14,tc_Polynomial_Opoly(X17)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X14,tc_Polynomial_Opoly(X17)),c_HOL_Otimes__class_Otimes(X15,X14,tc_Polynomial_Opoly(X17)),tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_889,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X16,X15,X18),c_Polynomial_OpCons(X17,X15,X18),tc_Polynomial_Opoly(X18)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_890,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__ring(X10)
| c_Polynomial_Osmult(X9,c_HOL_Ominus__class_Ominus(X8,X7,tc_Polynomial_Opoly(X10)),X10) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X9,X8,X10),c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_891,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_Polynomial_Osmult(X9,c_HOL_Oplus__class_Oplus(X8,X7,tc_Polynomial_Opoly(X10)),X10) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X9,X8,X10),c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_892,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X11,X10,tc_Polynomial_Opoly(X12)),X9,X12) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X11,X9,X12),c_Polynomial_Opoly(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_893,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X11,X10,tc_Polynomial_Opoly(X12)),X9,X12) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X11,X9,X12),c_Polynomial_Opoly(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_894,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__ring(X12)
| c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X11,X10,tc_Polynomial_Opoly(X12)),X9,X12) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X11,X9,X12),c_Polynomial_Opoly(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_895,plain,
! [X16,X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X19,X17,X20),c_HOL_Otimes__class_Otimes(X18,X16,X20),X20)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X20)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_896,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X9)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X8,X7,X9),X6,X9) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X8,X6,X9),c_Polynomial_Osmult(X7,X6,X9),tc_Polynomial_Opoly(X9)) ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_897,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__ring(X9)
| c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X8,X7,X9),X6,X9) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X8,X6,X9),c_Polynomial_Osmult(X7,X6,X9),tc_Polynomial_Opoly(X9)) ),
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_898,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X10,X11),c_HOL_Otimes__class_Otimes(X9,X9,X11),X11) != c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_899,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X10,X11),c_HOL_Otimes__class_Otimes(X9,X9,X11),X11) != c_HOL_Ozero__class_Ozero(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_900,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X9)
| c_Polynomial_Osmult(X8,c_Polynomial_OpCons(X7,X6,X9),X9) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X8,X7,X9),c_Polynomial_Osmult(X8,X6,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_901,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X10,X9,X12),X11,X12) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X11,X12),c_Power_Opower__class_Opower(X9,X11,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_902,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X13)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X12,X11,X13),X10,X13) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X12,X10,X13),c_Power_Opower__class_Opower(X11,X10,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_903,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_904,plain,
! [X26,X27,X28,X29] :
( ~ class_RealVector_Oreal__normed__algebra(X29)
| c_HOL_Otimes__class_Otimes(X27,c_HOL_Oplus__class_Oplus(X28,X26,X29),X29) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X28,X29),c_HOL_Otimes__class_Otimes(X27,X26,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_905,plain,
! [X18,X19,X20,X21] :
( ~ class_RealVector_Oreal__normed__algebra(X21)
| c_HOL_Otimes__class_Otimes(X20,c_HOL_Oplus__class_Oplus(X19,X18,X21),X21) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Otimes__class_Otimes(X20,X18,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_906,plain,
! [X25,X26,X27,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X28)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X27,X26,X28),X25,X28) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X25,X28),c_HOL_Otimes__class_Otimes(X26,X25,X28),X28) ),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_907,plain,
! [X19,X20,X21,X22] :
( ~ class_RealVector_Oreal__normed__algebra(X22)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X21,X20,X22),X19,X22) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_908,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Oplus__class_Oplus(X14,X13,X16),X16) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X14,X16),c_HOL_Otimes__class_Otimes(X15,X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_909,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring(X18)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_910,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_911,plain,
! [X26,X27,X28,X29] :
( ~ class_RealVector_Oreal__normed__algebra(X29)
| c_HOL_Otimes__class_Otimes(X27,c_HOL_Ominus__class_Ominus(X28,X26,X29),X29) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X27,X28,X29),c_HOL_Otimes__class_Otimes(X27,X26,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_912,plain,
! [X18,X19,X20,X21] :
( ~ class_RealVector_Oreal__normed__algebra(X21)
| c_HOL_Otimes__class_Otimes(X20,c_HOL_Ominus__class_Ominus(X19,X18,X21),X21) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Otimes__class_Otimes(X20,X18,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_913,plain,
! [X19,X20,X21,X22] :
( ~ class_RealVector_Oreal__normed__algebra(X22)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,X22),X19,X22) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_914,plain,
! [X25,X26,X27,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X28)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,X28),X25,X28) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X27,X25,X28),c_HOL_Otimes__class_Otimes(X26,X25,X28),X28) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_915,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_916,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X15,X16,X18),X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_917,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X15,X17,X18),c_HOL_Otimes__class_Otimes(X15,X16,X18),X18) = c_HOL_Otimes__class_Otimes(X15,c_Divides_Odiv__class_Omod(X17,X16,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_918,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_919,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oring__1(X12)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X12),X12),X10,X12),c_Power_Opower__class_Opower(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_920,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X16,X17,X18),X15,X18) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X16,X15,X18),X17,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_921,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X19)
| c_HOL_Oplus__class_Oplus(X17,c_Polynomial_Osmult(X18,X16,X19),tc_Polynomial_Opoly(X19)) != c_Polynomial_OpCons(X15,X16,X19)
| X15 = c_Polynomial_Opoly(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_922,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_923,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_924,plain,
! [X22,X23,X24,X25,X26] :
( ~ class_OrderedGroup_Oab__group__add(X26)
| c_HOL_Oplus__class_Oplus(X24,c_HOL_Oplus__class_Oplus(X23,X22,X26),X26) != c_HOL_Oplus__class_Oplus(X23,X25,X26)
| c_HOL_Oplus__class_Oplus(X24,X22,X26) = X25 ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_925,plain,
! [X6,X7,X8] :
( ~ class_Divides_Oring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X7,X6,X8),X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_926,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_Polynomial_Opoly__gcd(X12,X11,X14),tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X11,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X12,tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_927,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_Polynomial_Opoly__gcd(X12,X11,X14),tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X11,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X12,tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_928,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Divides_Odiv__class_Odiv(X15,c_HOL_Otimes__class_Otimes(X14,X13,tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X15,X14,tc_Polynomial_Opoly(X16)),X13,tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_929,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_930,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,X17,X18),c_HOL_Otimes__class_Otimes(X15,X16,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_931,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X11,X12,X13),c_Power_Opower__class_Opower(X10,X12,X13),X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X13) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_932,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X11,X10,X12),X9,tc_Polynomial_Opoly(X12)) = c_Polynomial_Osmult(X11,c_Divides_Odiv__class_Omod(X10,X9,tc_Polynomial_Opoly(X12)),X12) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_933,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X11,X10,X12),X9,tc_Polynomial_Opoly(X12)) = c_Polynomial_Osmult(X11,c_Divides_Odiv__class_Odiv(X10,X9,tc_Polynomial_Opoly(X12)),X12) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_934,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10)) = c_Polynomial_Osmult(X9,c_HOL_Otimes__class_Otimes(X8,X7,tc_Polynomial_Opoly(X10)),X10) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_935,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X9,X8,X10),X7,tc_Polynomial_Opoly(X10)) = c_Polynomial_Osmult(X9,c_HOL_Otimes__class_Otimes(X8,X7,tc_Polynomial_Opoly(X10)),X10) ),
inference(variable_rename,[status(thm)],[c_0_529]) ).
fof(c_0_936,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X12,X14),X12,X14) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X13,c_HOL_Oone__class_Oone(X14),X14),X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_530]) ).
fof(c_0_937,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X13,X12,X14),X14) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X13,c_HOL_Oone__class_Oone(X14),X14),X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_938,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_939,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X16)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Ominus__class_Ominus(X14,X13,X16),X16)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X13,X16)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_940,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_941,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_942,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X6,X7,X8),X6,X8) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X7,X6,X8),c_HOL_Oone__class_Oone(X8),X8)
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_943,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X7,X6,X8),X6,X8) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X7,X6,X8),c_HOL_Oone__class_Oone(X8),X8)
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_944,plain,
! [X19,X20,X21,X22] :
( ~ class_Divides_Oring__div(X22)
| c_Divides_Odiv__class_Omod(X21,X19,X22) != c_Divides_Odiv__class_Omod(X20,X19,X22)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X21,X22),X19,X22) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X20,X22),X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_538]) ).
fof(c_0_945,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X8)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X7,X8),c_HOL_Oabs__class_Oabs(X6,X8),X8),X8) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X7,X8),c_HOL_Oabs__class_Oabs(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_946,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_947,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_948,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X9,X8,X10),X7,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_949,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X15,X17,X18),c_HOL_Otimes__class_Otimes(X15,X16,X18),X18) = c_Divides_Odiv__class_Odiv(X17,X16,X18)
| X15 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_950,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) = c_Divides_Odiv__class_Odiv(X17,X16,X18)
| X15 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_951,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X11,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_Polynomial_Opoly__gcd(X12,X11,X14),tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_952,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X12,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_Polynomial_Opoly__gcd(X12,X11,X14),tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_953,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X9,X8,X10),X7,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_954,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X11,X10,X12),X9,X12) = c_HOL_Otimes__class_Otimes(X11,c_Polynomial_Opoly(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_955,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X18)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_956,plain,
! [X32,X33,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X35),X32,X35) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X32,X35),X33,X35) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_957,plain,
! [X32,X33,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X35),X32,X35) = c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_958,plain,
! [X31,X32,X33,X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X32,X31,X34),X34) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X34),X31,X34) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_959,plain,
! [X31,X32,X33,X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X32,X31,X34),X34) = c_HOL_Otimes__class_Otimes(X32,c_HOL_Otimes__class_Otimes(X33,X31,X34),X34) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_960,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X14,X13,X16),X16) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X14,X16),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_961,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Polynomial_Opoly__gcd(X15,c_Polynomial_Opoly__gcd(X14,X13,X16),X16) = c_Polynomial_Opoly__gcd(X14,c_Polynomial_Opoly__gcd(X15,X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_962,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X15,X14,X16),X13,X16) = c_Polynomial_Opoly__gcd(X15,c_Polynomial_Opoly__gcd(X14,X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_963,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
| c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18) = c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X17,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_964,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_965,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X14,X13,X16),X16) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X15,X14,X16),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_966,plain,
! [X13,X14,X15,X16] :
( ~ class_OrderedGroup_Oab__group__add(X16)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X14,X13,X16),X16) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X15,X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_967,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Oab__semigroup__add(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_968,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_969,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X15,X18),X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_970,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_971,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_972,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Omonoid__mult(X12)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X11,X10,X12),X11,X12) = c_HOL_Otimes__class_Otimes(X11,c_Power_Opower__class_Opower(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_973,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X9)
| c_Polynomial_Osmult(X8,c_Polynomial_Osmult(X7,X6,X9),X9) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X8,X7,X9),X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_974,plain,
! [X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),c_HOL_Ozero__class_Ozero(X6),X6),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),c_HOL_Ozero__class_Ozero(X6),X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_975,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X7,X6,X8),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),tc_Polynomial_Opoly(X8))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_976,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_977,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_978,plain,
! [X15,X16,X17,X18] :
( ~ class_Divides_Osemiring__div(X18)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X17,X16,X18),X15,X18) = c_Divides_Odiv__class_Omod(X17,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_979,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X8),X7,X8),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X8),X6,X8),X8) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_980,plain,
! [X7,X8,X9] :
( ~ class_Ring__and__Field_Ofield(X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X9),X8,X9),X7,tc_Polynomial_Opoly(X9))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_981,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12),X12) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_982,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X8),X7,X8),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_983,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X8),X8),c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X8),X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_984,plain,
! [X9,X10,X11] :
( ~ class_Divides_Oring__div(X11)
| c_Divides_Odiv__class_Odiv(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X10,X9,X11),X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_985,plain,
! [X9,X10,X11] :
( ~ class_Divides_Oring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X10,X9,X11),X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_986,plain,
! [X13,X14,X15,X16] :
( ~ class_OrderedGroup_Oab__group__add(X16)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X14,X13,X16),X16) != X14
| X15 = c_HOL_Ouminus__class_Ouminus(X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_987,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X9,X8,X10),X7,tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_988,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_989,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X9,X8,X10),X7,tc_Polynomial_Opoly(X10))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_990,plain,
! [X7,X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_Polynomial_Osmult(X9,X7,X10),tc_Polynomial_Opoly(X10))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_991,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Odiv(X6,X7,X8),X8) = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_992,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X6,X7,X8),X7,X8) = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_993,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_994,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_995,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X7,X6,X8),tc_Polynomial_Opoly(X8)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X7,X8),c_HOL_Ouminus__class_Ouminus(X6,tc_Polynomial_Opoly(X8)),X8) ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_996,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X8)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X6,X8),X8) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X6,X7,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_997,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_HOL_Oplus__class_Oplus(X12,X12,X13) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X13),c_HOL_Oone__class_Oone(X13),X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_998,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(X10,X9,X11) = c_Polynomial_Opoly__gcd(X9,c_Divides_Odiv__class_Omod(X10,X9,tc_Polynomial_Opoly(X11)),X11)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_999,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Divides_Odiv__class_Odiv(X10,c_HOL_Ouminus__class_Ouminus(X9,tc_Polynomial_Opoly(X11)),tc_Polynomial_Opoly(X11)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X10,X9,tc_Polynomial_Opoly(X11)),tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1000,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X11)),X9,tc_Polynomial_Opoly(X11)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X10,X9,tc_Polynomial_Opoly(X11)),tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1001,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X11)),X9,tc_Polynomial_Opoly(X11)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X10,X9,tc_Polynomial_Opoly(X11)),tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_1002,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_Divides_Odiv__class_Omod(X10,c_Polynomial_Osmult(X11,X9,X12),tc_Polynomial_Opoly(X12)) = c_Divides_Odiv__class_Omod(X10,X9,tc_Polynomial_Opoly(X12))
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1003,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1004,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X7,X6,X8),X8) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X7,X8),c_HOL_Oabs__class_Oabs(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1005,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X7,X8),c_HOL_Ouminus__class_Ouminus(X6,X8),X8) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1006,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X8) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X8),c_HOL_Ouminus__class_Ouminus(X7,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1007,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X8) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X8),c_HOL_Ouminus__class_Ouminus(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1008,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__ring(X8)
| c_Polynomial_Osmult(X7,c_HOL_Ouminus__class_Ouminus(X6,tc_Polynomial_Opoly(X8)),X8) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X7,X6,X8),tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1009,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X11)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) = c_HOL_Otimes__class_Otimes(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_1010,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X6,X7,X8),X6,X8) = c_Divides_Odiv__class_Omod(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_1011,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X6,X8),X6,X8) = c_Divides_Odiv__class_Omod(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1012,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X7,X6,X8),X6,X8) = c_Divides_Odiv__class_Omod(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1013,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8),X8) = X6 ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1014,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__ring(X11)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X11)),X9,X11) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_1015,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__ring(X8)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X7,X6,X8),tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1016,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring(X8)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X7,X6,X8),X8) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1017,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring(X8)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X7,X6,X8),X8) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Ouminus__class_Ouminus(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1018,plain,
! [X6,X7,X8] :
( ~ class_RealVector_Oreal__normed__algebra(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1019,plain,
! [X9,X10,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1020,plain,
! [X6,X7,X8] :
( ~ class_RealVector_Oreal__normed__algebra(X8)
| c_HOL_Otimes__class_Otimes(X7,c_HOL_Ouminus__class_Ouminus(X6,X8),X8) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1021,plain,
! [X26,X27,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X28)
| c_HOL_Otimes__class_Otimes(X26,c_HOL_Ouminus__class_Ouminus(X27,X28),X28) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X26,X27,X28),X28) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1022,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X11,X10,X12),X12) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X11,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1023,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X7),X6,X7),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1024,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_HOL_Otimes__class_Otimes(X7,X7,X8) != c_HOL_Otimes__class_Otimes(X6,X6,X8)
| X7 = c_HOL_Ouminus__class_Ouminus(X6,X8)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1025,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Oab__group__add(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X13,X15),c_HOL_Oplus__class_Oplus(X14,X13,X15),X15) = X14 ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1026,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X8),c_HOL_Oplus__class_Oplus(X7,X6,X8),X8) = X6 ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1027,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Osmult(X16,X15,X18) != c_Polynomial_OpCons(X17,X15,X18)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1028,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X13,X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Oabs__class_Oabs(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1029,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X13,X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X12,X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1030,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1031,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1032,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oidom(X16)
| ~ class_Int_Onumber__ring(X16)
| c_HOL_Oplus__class_Oplus(X15,X14,X16) != c_HOL_Oplus__class_Oplus(X15,X13,X16)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1033,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X11),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X11),X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1034,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X7,X6,X8),X8) = c_HOL_Ominus__class_Ominus(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1035,plain,
! [X7,X8,X9,X10,X11] :
( ~ class_HOL_Ozero(X11)
| c_Polynomial_OpCons(X10,X8,X11) != c_Polynomial_OpCons(X9,X7,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1036,plain,
! [X7,X8,X9,X10,X11] :
( ~ class_HOL_Ozero(X11)
| c_Polynomial_OpCons(X10,X8,X11) != c_Polynomial_OpCons(X9,X7,X11)
| X8 = X7 ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1037,plain,
! [X28,X29,X30,X31] :
( ~ class_OrderedGroup_Oab__group__add(X31)
| c_HOL_Ominus__class_Ominus(X30,X30,X31) != c_HOL_Ominus__class_Ominus(X29,X28,X31)
| X29 = X28 ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1038,plain,
! [X26,X27,X28,X29] :
( ~ class_OrderedGroup_Oab__group__add(X29)
| c_HOL_Ominus__class_Ominus(X27,X26,X29) != c_HOL_Ominus__class_Ominus(X28,X28,X29)
| X27 = X26 ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1039,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X18)
| c_HOL_Oplus__class_Oplus(X17,X16,X18) != c_HOL_Oplus__class_Oplus(X17,X15,X18)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1040,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X18)
| c_HOL_Oplus__class_Oplus(X17,X16,X18) != c_HOL_Oplus__class_Oplus(X17,X15,X18)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1041,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X18)
| c_HOL_Oplus__class_Oplus(X16,X17,X18) != c_HOL_Oplus__class_Oplus(X15,X17,X18)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1042,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X6,X7,X8),X6,X8) = X7
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1043,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X6,X8),X6,X8) = X7
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1044,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X10,X9,X11),X10,tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1045,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X10,X9,X11),X9,tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1046,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Oabs__class_Oabs(X13,X14),X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1047,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X12,X14),X13,X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1048,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1049,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1050,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X7,X6,X8),X6,X8) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1051,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X7,X8),X6,X8) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1052,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X8),X6,X8) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1053,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X7,X6,X8),X6,X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1054,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X6,X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1055,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X6,X7,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1056,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1057,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Odvd(X13)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1058,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X6,X7),c_HOL_Ouminus__class_Ouminus(X6,X7),X7) = c_HOL_Otimes__class_Otimes(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1059,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X8),c_HOL_Ouminus__class_Ouminus(X6,X8),X8) = c_HOL_Otimes__class_Otimes(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1060,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X6,X7),c_HOL_Oabs__class_Oabs(X6,X7),X7) = c_HOL_Otimes__class_Otimes(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1061,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Ouminus__class_Ouminus(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1062,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Divides_Odiv__class_Omod(X10,c_HOL_Ouminus__class_Ouminus(X9,tc_Polynomial_Opoly(X11)),tc_Polynomial_Opoly(X11)) = c_Divides_Odiv__class_Omod(X10,X9,tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1063,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(X10,c_HOL_Ouminus__class_Ouminus(X9,tc_Polynomial_Opoly(X11)),X11) = c_Polynomial_Opoly__gcd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1064,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X11)),X9,X11) = c_Polynomial_Opoly__gcd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1065,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(X6,X7,X8) != c_HOL_Ozero__class_Ozero(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1066,plain,
! [X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(X6,X7,X8) = c_HOL_Ozero__class_Ozero(X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1067,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ouminus__class_Ouminus(X6,X8),X8) = c_HOL_Oplus__class_Oplus(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1068,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Oab__group__add(X11)
| c_HOL_Ominus__class_Ominus(X10,X9,X11) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1069,plain,
! [X9,X10,X11] :
( ~ class_Int_Onumber__ring(X11)
| c_HOL_Ominus__class_Ominus(X10,X9,X11) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1070,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Ominus__class_Ominus(X7,X6,X8) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ouminus__class_Ouminus(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1071,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ominus__class_Ominus(X7,X6,X8) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ouminus__class_Ouminus(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1072,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ozero__neq__one(X12)
| ~ class_Ring__and__Field_Ono__zero__divisors(X12)
| ~ class_Ring__and__Field_Omult__zero(X12)
| ~ class_Power_Opower(X12)
| c_Power_Opower__class_Opower(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1073,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Polynomial_Osmult(X7,X6,X8) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1074,plain,
! [X6,X7,X8] :
( ~ class_HOL_Ozero(X8)
| c_Polynomial_OpCons(X7,X6,X8) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1075,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(X10,X9,X11) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1076,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(X10,X9,X11) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1077,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Otimes__class_Otimes(X10,X9,X11) = c_HOL_Otimes__class_Otimes(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1078,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_HOL_Otimes__class_Otimes(X7,X6,X8) = c_HOL_Otimes__class_Otimes(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1079,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| c_HOL_Oplus__class_Oplus(X16,X15,X17) = c_HOL_Oplus__class_Oplus(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1080,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Oplus__class_Oplus(X10,X9,X11) = c_HOL_Oplus__class_Oplus(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1081,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_HOL_Oplus__class_Oplus(X7,X6,X8) = c_HOL_Oplus__class_Oplus(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1082,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(X10,X9,X11) = c_Polynomial_Opoly__gcd(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1083,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Oplus__class_Oplus(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| c_HOL_Ouminus__class_Ouminus(X7,X8) = X6 ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1084,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Oplus__class_Oplus(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ouminus__class_Ouminus(X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1085,plain,
! [X6,X7,X8] :
( ~ class_HOL_Ozero(X8)
| c_Polynomial_OpCons(X7,X6,X8) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1086,plain,
! [X9,X10] :
( ~ class_Int_Onumber__ring(X10)
| c_HOL_Ouminus__class_Ouminus(X9,X10) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X10),X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1087,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X8)
| c_HOL_Otimes__class_Otimes(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X6 = c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1088,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X8)
| c_HOL_Otimes__class_Otimes(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X6 = c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1089,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X8)
| c_HOL_Otimes__class_Otimes(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(X8)
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1090,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Onumber__ring(X11)
| c_HOL_Ominus__class_Ominus(X10,X9,X11) != c_HOL_Ozero__class_Ozero(X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1091,plain,
! [X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X6) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1092,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1093,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Onumber__ring(X11)
| X9 != c_HOL_Oplus__class_Oplus(X9,X10,X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1094,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X19)
| c_HOL_Oabs__class_Oabs(X17,X19) != c_HOL_Oabs__class_Oabs(X18,X19)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1095,plain,
! [X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7,tc_Polynomial_Opoly(X8)) = c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1096,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X12)
| c_Power_Opower__class_Opower(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1097,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oplus__class_Oplus(X6,X6,X7) != c_HOL_Ozero__class_Ozero(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1098,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| c_HOL_Ominus__class_Ominus(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1099,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Ominus__class_Ominus(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1100,plain,
! [X6] :
( ~ class_HOL_Ozero(X6)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X6),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X6) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1101,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7,tc_Polynomial_Opoly(X8)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1102,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),tc_Polynomial_Opoly(X7)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1103,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1104,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1105,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ouminus__class_Ouminus(X6,X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1106,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1107,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X7)
| c_Polynomial_Osmult(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X7) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1108,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| c_Polynomial_Osmult(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X7) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1109,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),tc_Polynomial_Opoly(X7)) = X6 ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1110,plain,
! [X7,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7,tc_Polynomial_Opoly(X8)) = X7 ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1111,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),tc_Polynomial_Opoly(X7)) = X6 ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1112,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1113,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1114,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ouminus__class_Ouminus(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1115,plain,
! [X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X6),c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1116,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1117,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X7)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1118,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| ~ class_Int_Onumber__ring(X10)
| X9 = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1119,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| ~ class_Int_Onumber__ring(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1120,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(X6,c_HOL_Ozero__class_Ozero(X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1121,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1122,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1123,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Omonoid__mult(X11)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X11),X10,X11) = c_HOL_Oone__class_Oone(X11) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1124,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1125,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1126,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X9)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X9),X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1127,plain,
! [X6,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1128,plain,
! [X6,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1129,plain,
! [X9,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X10)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Ozero__class_Ozero(X10),X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1130,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X10),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1131,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Omult__zero(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1132,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Omult__zero(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1133,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1134,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1135,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Omod(X6,c_HOL_Oone__class_Oone(X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1136,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(X6,X6,X7) = c_HOL_Oone__class_Oone(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1137,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1138,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Oone__class_Oone(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1139,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1140,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1141,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1142,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Otimes__class_Otimes(X6,c_HOL_Oone__class_Oone(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1143,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1144,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1145,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1146,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1147,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1148,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1149,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1150,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1151,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Odiv(X6,c_HOL_Oone__class_Oone(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1152,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Omod(X6,c_HOL_Ozero__class_Ozero(X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1153,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X7),X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1154,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1155,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1156,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1157,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1158,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X6,X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1159,plain,
! [X6,X7] :
( ~ class_Divides_Osemiring__div(X7)
| c_Divides_Odiv__class_Omod(X6,X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1160,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X10)
| c_HOL_Otimes__class_Otimes(X9,X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1161,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1162,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X7)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X6,X7),X7) = c_HOL_Oabs__class_Oabs(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1163,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X7)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X6,X7),X7) = c_HOL_Oabs__class_Oabs(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1164,plain,
! [X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),tc_Polynomial_Opoly(X6)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1165,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Ogroup__add(X8)
| c_HOL_Ouminus__class_Ouminus(X7,X8) != c_HOL_Ouminus__class_Ouminus(X6,X8)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1166,plain,
! [X9,X10,X11] :
( ~ class_Lattices_Oboolean__algebra(X11)
| c_HOL_Ouminus__class_Ouminus(X10,X11) != c_HOL_Ouminus__class_Ouminus(X9,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1167,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1168,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| X6 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1169,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| X6 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1170,plain,
! [X9,X10] :
( ~ class_Lattices_Oboolean__algebra(X10)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1171,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1172,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ouminus__class_Ouminus(X6,X7) != c_HOL_Ozero__class_Ozero(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1173,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ozero__class_Ozero(X7) != c_HOL_Ouminus__class_Ouminus(X6,X7)
| c_HOL_Ozero__class_Ozero(X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1174,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X7)
| c_HOL_Oabs__class_Oabs(X6,X7) != c_HOL_Ozero__class_Ozero(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1175,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X7)
| c_HOL_Ouminus__class_Ouminus(X6,X7) != X6
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1176,plain,
! [X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X6),X6) = c_HOL_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1177,plain,
! [X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1178,plain,
! [X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ozero__class_Ozero(X6) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1179,plain,
! [X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1180,plain,
! [X6] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1181,plain,
! [X6] :
( ~ class_Ring__and__Field_Ozero__neq__one(X6)
| c_HOL_Oone__class_Oone(X6) != c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1182,plain,
! [X6] :
( ~ class_Ring__and__Field_Ozero__neq__one(X6)
| c_HOL_Ozero__class_Ozero(X6) != c_HOL_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1183,plain,
! [X2] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1184,plain,
! [X2] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1185,plain,
! [X2] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1186,plain,
! [X2] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1187,plain,
! [X2] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1188,plain,
! [X2] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1189,plain,
! [X2] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1190,plain,
! [X2] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1191,plain,
! [X2] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1192,plain,
! [X2] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1193,plain,
! [X2] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1194,plain,
! [X2] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1195,plain,
! [X2] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1196,plain,
! [X2] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1197,plain,
! [X2] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1198,plain,
! [X2] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1199,plain,
! [X2] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1200,plain,
! [X2] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1201,plain,
! [X2] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1202,plain,
! [X2] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1203,plain,
! [X2] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1204,plain,
! [X2] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1205,plain,
! [X2] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1206,plain,
! [X2] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1207,plain,
! [X2] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1208,plain,
! [X2] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1209,plain,
! [X2] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1210,plain,
! [X2] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1211,plain,
! [X2] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1212,plain,
! [X2] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1213,plain,
! [X2] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1214,plain,
! [X2] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1215,plain,
! [X2] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1216,plain,
! [X2] :
( class_Power_Opower(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1217,plain,
! [X2] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(variable_rename,[status(thm)],[c_0_811]) ).
cnf(c_0_1218,plain,
( c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X7,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X8,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)),X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X3,X6,X7,X8,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1219,plain,
( X3 = X6
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1220,plain,
( X4 = X7
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1221,plain,
( c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X6,X1,X5),X2,c_Polynomial_Osmult(X6,X3,X5),c_Polynomial_Osmult(X6,X4,X5),X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1222,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1223,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1224,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X5)) = X4
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1225,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X5)) = X3
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1226,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1227,plain,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1228,plain,
( X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1229,plain,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1230,plain,
( X4 = X1
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1231,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1232,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1233,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)),X2,X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1234,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1235,plain,
( c_Polynomial_Opdivmod__rel(X1,X2,c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_829]) ).
cnf(c_0_1236,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_830]) ).
cnf(c_0_1237,plain,
( c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1238,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1239,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_833]) ).
cnf(c_0_1240,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1241,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1242,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1243,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1244,plain,
( c_Polynomial_Opoly(X3,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1245,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1246,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1247,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1248,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1249,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1250,plain,
( c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1251,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_845]) ).
cnf(c_0_1252,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1253,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1254,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1255,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1256,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Polynomial_OpCons(X2,X3,X4),tc_Polynomial_Opoly(X4)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X1,X4),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1257,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1258,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1259,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1260,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1261,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1262,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1263,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1264,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1265,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1266,plain,
( c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,tc_Polynomial_Opoly(X3)),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1267,plain,
( c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_Polynomial_Opoly(X3)),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1268,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1269,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1270,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1271,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1272,plain,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X2,X4,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1273,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1274,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1275,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1276,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1277,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1278,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1279,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1280,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1281,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1282,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1283,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_877]) ).
cnf(c_0_1284,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_878]) ).
cnf(c_0_1285,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1286,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1287,plain,
( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1288,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1289,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1290,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_884]) ).
cnf(c_0_1291,plain,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_885]) ).
cnf(c_0_1292,plain,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_886]) ).
cnf(c_0_1293,plain,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1294,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_Polynomial_Opoly(X3)),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1295,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X4,X1,X2),tc_Polynomial_Opoly(X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1296,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1297,plain,
( c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1298,plain,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_892]) ).
cnf(c_0_1299,plain,
( c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_893]) ).
cnf(c_0_1300,plain,
( c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_894]) ).
cnf(c_0_1301,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_895]) ).
cnf(c_0_1302,plain,
( c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1303,plain,
( c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1304,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_898]) ).
cnf(c_0_1305,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1306,plain,
( c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1307,plain,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1308,plain,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1309,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_903]) ).
cnf(c_0_1310,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(split_conjunct,[status(thm)],[c_0_904]) ).
cnf(c_0_1311,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(split_conjunct,[status(thm)],[c_0_905]) ).
cnf(c_0_1312,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1313,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_907]) ).
cnf(c_0_1314,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1315,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1316,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1317,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1318,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1319,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1320,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1321,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1322,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1323,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1324,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1325,plain,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1326,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1327,plain,
( X1 = c_Polynomial_Opoly(X2,X3,X4)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X5,X4),tc_Polynomial_Opoly(X4)) != c_Polynomial_OpCons(X1,X5,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1328,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1329,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1330,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1331,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,X2),X2),X3,X2)
| ~ class_Divides_Oring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1332,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1333,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1334,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1335,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1336,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1337,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1338,plain,
( c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1339,plain,
( c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1340,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1341,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1342,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1343,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1344,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1345,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1346,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1347,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1348,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X3,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1349,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X1,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1350,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X2),X3,X2)
| c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Divides_Odiv__class_Omod(X4,X3,X2)
| ~ class_Divides_Oring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1351,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1352,plain,
( X2 = c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1353,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1354,plain,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1355,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1356,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1357,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1358,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1359,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1360,plain,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1361,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1362,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1363,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1364,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1365,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1366,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1367,plain,
( c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),X4) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1368,plain,
( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X3),X4,X3) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1369,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1370,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1371,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1372,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1373,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1374,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_968]) ).
cnf(c_0_1375,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1376,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1377,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1378,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1379,plain,
( c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1380,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1381,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1382,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1383,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1384,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1385,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1386,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1387,plain,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1388,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1389,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1390,plain,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1391,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1392,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) != X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1393,plain,
( X4 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X3),X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1394,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1395,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X3,X2),X4,tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1396,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X2,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1397,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1398,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1399,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1400,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1401,plain,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X1,X2,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1402,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1403,plain,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1404,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X3,X1,X2) = c_Polynomial_Opoly__gcd(X1,c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1405,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1406,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1407,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1408,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Omod(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1409,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1410,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1411,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1412,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1413,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1414,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X2,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1415,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1416,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1417,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1418,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1419,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1420,plain,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1421,plain,
( c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X3,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1422,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1423,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1424,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1425,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1426,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1427,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1428,plain,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1429,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1430,plain,
( X1 = X2
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Otimes__class_Otimes(X1,X1,X3) != c_HOL_Otimes__class_Otimes(X2,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1431,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) = X3
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1432,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1433,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1434,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1435,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1436,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1437,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1438,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1439,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1440,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1441,plain,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1442,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1443,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1444,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1445,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1446,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1447,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1448,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1449,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1450,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1451,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1452,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1046]) ).
cnf(c_0_1453,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1454,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1048]) ).
cnf(c_0_1455,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1456,plain,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1457,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1458,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1459,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1460,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1461,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1462,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1463,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1464,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1465,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X3,X2)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1466,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1467,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1468,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1469,plain,
( c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_Polynomial_Opoly__gcd(X1,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1470,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_Polynomial_Opoly__gcd(X1,X3,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1471,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1472,plain,
( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1473,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1474,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1475,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Int_Onumber__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1476,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1477,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1478,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1479,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1480,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1481,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1482,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1483,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1484,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1485,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1486,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1487,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1488,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X2,X1,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1489,plain,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1490,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1491,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1492,plain,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1493,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1494,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1495,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1496,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1497,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1498,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1499,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != c_HOL_Oplus__class_Oplus(X3,X1,X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1500,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1501,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1502,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1503,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1504,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1505,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1506,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1507,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1508,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1509,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1510,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1511,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1512,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1513,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1514,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1515,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1516,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1517,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1518,plain,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1519,plain,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1520,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1521,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1522,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1523,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1524,plain,
( X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1525,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1526,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1527,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1528,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1529,plain,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1530,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1531,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1532,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1533,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1534,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1535,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1536,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1537,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1538,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1539,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1540,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1541,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1542,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1543,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1544,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1545,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1546,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1547,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1548,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1549,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1550,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1551,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1552,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1553,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1554,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1555,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1556,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1557,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1558,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1559,plain,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1560,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1561,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1562,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1563,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1564,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1565,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1566,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1567,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1568,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1569,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1570,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1571,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1572,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1573,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1574,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1575,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1576,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1577,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1578,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1579,plain,
( c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1580,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1581,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1582,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1583,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1584,plain,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1585,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1586,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1587,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1588,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1589,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1590,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1591,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1592,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1593,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1594,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1595,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1596,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1597,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1598,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1599,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1600,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1601,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1602,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1603,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1604,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1605,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1606,plain,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1607,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1608,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1609,plain,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1610,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1611,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1612,plain,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1613,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1614,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1615,plain,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1616,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1617,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1618,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1619,plain,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1620,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1621,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1622,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1623,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1624,plain,
( c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X7,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X8,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)),X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X3,X6,X7,X8,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1218,
[final] ).
cnf(c_0_1625,plain,
( X3 = X6
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1219,
[final] ).
cnf(c_0_1626,plain,
( X4 = X7
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1220,
[final] ).
cnf(c_0_1627,plain,
( c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X6,X1,X5),X2,c_Polynomial_Osmult(X6,X3,X5),c_Polynomial_Osmult(X6,X4,X5),X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1221,
[final] ).
cnf(c_0_1628,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1222,
[final] ).
cnf(c_0_1629,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1223,
[final] ).
cnf(c_0_1630,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X5)) = X4
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1224,
[final] ).
cnf(c_0_1631,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X5)) = X3
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_1225,
[final] ).
cnf(c_0_1632,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1226,
[final] ).
cnf(c_0_1633,plain,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1227,
[final] ).
cnf(c_0_1634,plain,
( X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1228,
[final] ).
cnf(c_0_1635,plain,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1229,
[final] ).
cnf(c_0_1636,plain,
( X4 = X1
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1230,
[final] ).
cnf(c_0_1637,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1231,
[final] ).
cnf(c_0_1638,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1232,
[final] ).
cnf(c_0_1639,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)),X2,X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1233,
[final] ).
cnf(c_0_1640,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_1234,
[final] ).
cnf(c_0_1641,plain,
( c_Polynomial_Opdivmod__rel(X1,X2,c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1235,
[final] ).
cnf(c_0_1642,plain,
( c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1236,
[final] ).
cnf(c_0_1643,plain,
( c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1237,
[final] ).
cnf(c_0_1644,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
c_0_1238,
[final] ).
cnf(c_0_1645,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_1239,
[final] ).
cnf(c_0_1646,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1240,
[final] ).
cnf(c_0_1647,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1241,
[final] ).
cnf(c_0_1648,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1242,
[final] ).
cnf(c_0_1649,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1243,
[final] ).
cnf(c_0_1650,plain,
( c_Polynomial_Opoly(X3,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1244,
[final] ).
cnf(c_0_1651,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1245,
[final] ).
cnf(c_0_1652,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
c_0_1246,
[final] ).
cnf(c_0_1653,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
c_0_1247,
[final] ).
cnf(c_0_1654,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1248,
[final] ).
cnf(c_0_1655,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1249,
[final] ).
cnf(c_0_1656,plain,
( c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1250,
[final] ).
cnf(c_0_1657,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1251,
[final] ).
cnf(c_0_1658,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_1252,
[final] ).
cnf(c_0_1659,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1253,
[final] ).
cnf(c_0_1660,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1254,
[final] ).
cnf(c_0_1661,plain,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1255,
[final] ).
cnf(c_0_1662,plain,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X1,X4),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4),tc_Polynomial_Opoly(X4)) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_OpCons(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1256,
[final] ).
cnf(c_0_1663,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1257,
[final] ).
cnf(c_0_1664,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1258,
[final] ).
cnf(c_0_1665,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_1259,
[final] ).
cnf(c_0_1666,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1260,
[final] ).
cnf(c_0_1667,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1261,
[final] ).
cnf(c_0_1668,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1262,
[final] ).
cnf(c_0_1669,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1263,
[final] ).
cnf(c_0_1670,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1264,
[final] ).
cnf(c_0_1671,plain,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1265,
[final] ).
cnf(c_0_1672,plain,
( c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3))
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1266,
[final] ).
cnf(c_0_1673,plain,
( c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_1267,
[final] ).
cnf(c_0_1674,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1268,
[final] ).
cnf(c_0_1675,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1269,
[final] ).
cnf(c_0_1676,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1270,
[final] ).
cnf(c_0_1677,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1271,
[final] ).
cnf(c_0_1678,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X2,X4,X3),X3),X3) = c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1272,
[final] ).
cnf(c_0_1679,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1273,
[final] ).
cnf(c_0_1680,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_1274,
[final] ).
cnf(c_0_1681,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1275,
[final] ).
cnf(c_0_1682,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1276,
[final] ).
cnf(c_0_1683,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1277,
[final] ).
cnf(c_0_1684,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1278,
[final] ).
cnf(c_0_1685,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1279,
[final] ).
cnf(c_0_1686,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1280,
[final] ).
cnf(c_0_1687,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1281,
[final] ).
cnf(c_0_1688,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1282,
[final] ).
cnf(c_0_1689,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_1283,
[final] ).
cnf(c_0_1690,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_1284,
[final] ).
cnf(c_0_1691,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1285,
[final] ).
cnf(c_0_1692,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1286,
[final] ).
cnf(c_0_1693,plain,
( c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1287,
[final] ).
cnf(c_0_1694,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1288,
[final] ).
cnf(c_0_1695,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1289,
[final] ).
cnf(c_0_1696,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1290,
[final] ).
cnf(c_0_1697,plain,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1291,
[final] ).
cnf(c_0_1698,plain,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1292,
[final] ).
cnf(c_0_1699,plain,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1293,
[final] ).
cnf(c_0_1700,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_Polynomial_Opoly(X3)),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1294,
[final] ).
cnf(c_0_1701,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X4,X1,X2),tc_Polynomial_Opoly(X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1295,
[final] ).
cnf(c_0_1702,plain,
( c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
c_0_1296,
[final] ).
cnf(c_0_1703,plain,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1297,
[final] ).
cnf(c_0_1704,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1298,
[final] ).
cnf(c_0_1705,plain,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1299,
[final] ).
cnf(c_0_1706,plain,
( c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
c_0_1300,
[final] ).
cnf(c_0_1707,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1301,
[final] ).
cnf(c_0_1708,plain,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1302,
[final] ).
cnf(c_0_1709,plain,
( c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
c_0_1303,
[final] ).
cnf(c_0_1710,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1304,
[final] ).
cnf(c_0_1711,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1305,
[final] ).
cnf(c_0_1712,plain,
( c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),X4) = c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1306,
[final] ).
cnf(c_0_1713,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1307,
[final] ).
cnf(c_0_1714,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
c_0_1308,
[final] ).
cnf(c_0_1715,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1309,
[final] ).
cnf(c_0_1716,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
c_0_1310,
[final] ).
cnf(c_0_1717,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
c_0_1311,
[final] ).
cnf(c_0_1718,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1312,
[final] ).
cnf(c_0_1719,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1313,
[final] ).
cnf(c_0_1720,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1314,
[final] ).
cnf(c_0_1721,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
c_0_1315,
[final] ).
cnf(c_0_1722,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1316,
[final] ).
cnf(c_0_1723,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
c_0_1317,
[final] ).
cnf(c_0_1724,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
c_0_1318,
[final] ).
cnf(c_0_1725,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1319,
[final] ).
cnf(c_0_1726,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1320,
[final] ).
cnf(c_0_1727,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_1321,
[final] ).
cnf(c_0_1728,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_1322,
[final] ).
cnf(c_0_1729,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1323,
[final] ).
cnf(c_0_1730,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1324,
[final] ).
cnf(c_0_1731,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oring__1(X2) ),
c_0_1325,
[final] ).
cnf(c_0_1732,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1326,
[final] ).
cnf(c_0_1733,plain,
( X1 = c_Polynomial_Opoly(X2,X3,X4)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X5,X4),tc_Polynomial_Opoly(X4)) != c_Polynomial_OpCons(X1,X5,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1327,
[final] ).
cnf(c_0_1734,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_1328,
[final] ).
cnf(c_0_1735,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1329,
[final] ).
cnf(c_0_1736,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1330,
[final] ).
cnf(c_0_1737,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,X2),X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Divides_Oring__div(X2) ),
c_0_1331,
[final] ).
cnf(c_0_1738,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1332,
[final] ).
cnf(c_0_1739,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1333,
[final] ).
cnf(c_0_1740,plain,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
c_0_1334,
[final] ).
cnf(c_0_1741,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1335,
[final] ).
cnf(c_0_1742,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1336,
[final] ).
cnf(c_0_1743,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1337,
[final] ).
cnf(c_0_1744,plain,
( c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1338,
[final] ).
cnf(c_0_1745,plain,
( c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1339,
[final] ).
cnf(c_0_1746,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1340,
[final] ).
cnf(c_0_1747,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1341,
[final] ).
cnf(c_0_1748,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1342,
[final] ).
cnf(c_0_1749,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1343,
[final] ).
cnf(c_0_1750,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1344,
[final] ).
cnf(c_0_1751,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
c_0_1345,
[final] ).
cnf(c_0_1752,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1346,
[final] ).
cnf(c_0_1753,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1347,
[final] ).
cnf(c_0_1754,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X3,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1348,
[final] ).
cnf(c_0_1755,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X1,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1349,
[final] ).
cnf(c_0_1756,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X2),X3,X2)
| c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Divides_Odiv__class_Omod(X4,X3,X2)
| ~ class_Divides_Oring__div(X2) ),
c_0_1350,
[final] ).
cnf(c_0_1757,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_1351,
[final] ).
cnf(c_0_1758,plain,
( X2 = c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
c_0_1352,
[final] ).
cnf(c_0_1759,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1353,
[final] ).
cnf(c_0_1760,plain,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1354,
[final] ).
cnf(c_0_1761,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1355,
[final] ).
cnf(c_0_1762,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1356,
[final] ).
cnf(c_0_1763,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
c_0_1357,
[final] ).
cnf(c_0_1764,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
c_0_1358,
[final] ).
cnf(c_0_1765,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1359,
[final] ).
cnf(c_0_1766,plain,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1360,
[final] ).
cnf(c_0_1767,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
c_0_1361,
[final] ).
cnf(c_0_1768,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1362,
[final] ).
cnf(c_0_1769,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1363,
[final] ).
cnf(c_0_1770,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1364,
[final] ).
cnf(c_0_1771,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1365,
[final] ).
cnf(c_0_1772,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1366,
[final] ).
cnf(c_0_1773,plain,
( c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),X4) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ofield(X4) ),
c_0_1367,
[final] ).
cnf(c_0_1774,plain,
( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X3),X4,X3) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1368,
[final] ).
cnf(c_0_1775,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_1369,
[final] ).
cnf(c_0_1776,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_1370,
[final] ).
cnf(c_0_1777,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1371,
[final] ).
cnf(c_0_1778,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1372,
[final] ).
cnf(c_0_1779,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
c_0_1373,
[final] ).
cnf(c_0_1780,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1374,
[final] ).
cnf(c_0_1781,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1375,
[final] ).
cnf(c_0_1782,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_1376,
[final] ).
cnf(c_0_1783,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1377,
[final] ).
cnf(c_0_1784,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
c_0_1378,
[final] ).
cnf(c_0_1785,plain,
( c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1379,
[final] ).
cnf(c_0_1786,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1380,
[final] ).
cnf(c_0_1787,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1381,
[final] ).
cnf(c_0_1788,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1382,
[final] ).
cnf(c_0_1789,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1383,
[final] ).
cnf(c_0_1790,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1384,
[final] ).
cnf(c_0_1791,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1385,
[final] ).
cnf(c_0_1792,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1386,
[final] ).
cnf(c_0_1793,plain,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1387,
[final] ).
cnf(c_0_1794,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1388,
[final] ).
cnf(c_0_1795,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1389,
[final] ).
cnf(c_0_1796,plain,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_1390,
[final] ).
cnf(c_0_1797,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_1391,
[final] ).
cnf(c_0_1798,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) != X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1392,
[final] ).
cnf(c_0_1799,plain,
( X4 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X3),X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1393,
[final] ).
cnf(c_0_1800,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1394,
[final] ).
cnf(c_0_1801,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X3,X2),X4,tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1395,
[final] ).
cnf(c_0_1802,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X2,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1396,
[final] ).
cnf(c_0_1803,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1397,
[final] ).
cnf(c_0_1804,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1398,
[final] ).
cnf(c_0_1805,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1399,
[final] ).
cnf(c_0_1806,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1400,
[final] ).
cnf(c_0_1807,plain,
( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X1,X2,X3),tc_Polynomial_Opoly(X3))
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1401,
[final] ).
cnf(c_0_1808,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_1402,
[final] ).
cnf(c_0_1809,plain,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1403,
[final] ).
cnf(c_0_1810,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X1,c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Opoly__gcd(X3,X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1404,
[final] ).
cnf(c_0_1811,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1405,
[final] ).
cnf(c_0_1812,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1406,
[final] ).
cnf(c_0_1813,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1407,
[final] ).
cnf(c_0_1814,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Omod(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1408,
[final] ).
cnf(c_0_1815,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1409,
[final] ).
cnf(c_0_1816,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1410,
[final] ).
cnf(c_0_1817,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1411,
[final] ).
cnf(c_0_1818,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1412,
[final] ).
cnf(c_0_1819,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1413,
[final] ).
cnf(c_0_1820,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X2,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
c_0_1414,
[final] ).
cnf(c_0_1821,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
c_0_1415,
[final] ).
cnf(c_0_1822,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1416,
[final] ).
cnf(c_0_1823,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1417,
[final] ).
cnf(c_0_1824,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1418,
[final] ).
cnf(c_0_1825,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1419,
[final] ).
cnf(c_0_1826,plain,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
c_0_1420,
[final] ).
cnf(c_0_1827,plain,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X3,X2),tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
c_0_1421,
[final] ).
cnf(c_0_1828,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1422,
[final] ).
cnf(c_0_1829,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_1423,
[final] ).
cnf(c_0_1830,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
c_0_1424,
[final] ).
cnf(c_0_1831,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
c_0_1425,
[final] ).
cnf(c_0_1832,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1426,
[final] ).
cnf(c_0_1833,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_1427,
[final] ).
cnf(c_0_1834,plain,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1428,
[final] ).
cnf(c_0_1835,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1429,
[final] ).
cnf(c_0_1836,plain,
( X1 = X2
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Otimes__class_Otimes(X1,X1,X3) != c_HOL_Otimes__class_Otimes(X2,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1430,
[final] ).
cnf(c_0_1837,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) = X3
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1431,
[final] ).
cnf(c_0_1838,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1432,
[final] ).
cnf(c_0_1839,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1433,
[final] ).
cnf(c_0_1840,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1434,
[final] ).
cnf(c_0_1841,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1435,
[final] ).
cnf(c_0_1842,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
c_0_1436,
[final] ).
cnf(c_0_1843,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
c_0_1437,
[final] ).
cnf(c_0_1844,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
c_0_1438,
[final] ).
cnf(c_0_1845,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1439,
[final] ).
cnf(c_0_1846,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1440,
[final] ).
cnf(c_0_1847,plain,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_1441,
[final] ).
cnf(c_0_1848,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_1442,
[final] ).
cnf(c_0_1849,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1443,
[final] ).
cnf(c_0_1850,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1444,
[final] ).
cnf(c_0_1851,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
c_0_1445,
[final] ).
cnf(c_0_1852,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
c_0_1446,
[final] ).
cnf(c_0_1853,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
c_0_1447,
[final] ).
cnf(c_0_1854,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1448,
[final] ).
cnf(c_0_1855,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1449,
[final] ).
cnf(c_0_1856,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1450,
[final] ).
cnf(c_0_1857,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1451,
[final] ).
cnf(c_0_1858,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1452,
[final] ).
cnf(c_0_1859,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1453,
[final] ).
cnf(c_0_1860,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
c_0_1454,
[final] ).
cnf(c_0_1861,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
c_0_1455,
[final] ).
cnf(c_0_1862,plain,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1456,
[final] ).
cnf(c_0_1863,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1457,
[final] ).
cnf(c_0_1864,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1458,
[final] ).
cnf(c_0_1865,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1459,
[final] ).
cnf(c_0_1866,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1460,
[final] ).
cnf(c_0_1867,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1461,
[final] ).
cnf(c_0_1868,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1462,
[final] ).
cnf(c_0_1869,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_1463,
[final] ).
cnf(c_0_1870,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1464,
[final] ).
cnf(c_0_1871,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X3,X2)
| ~ class_Ring__and__Field_Oring(X2) ),
c_0_1465,
[final] ).
cnf(c_0_1872,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1466,
[final] ).
cnf(c_0_1873,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_Ring__and__Field_Oring(X2) ),
c_0_1467,
[final] ).
cnf(c_0_1874,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1468,
[final] ).
cnf(c_0_1875,plain,
( c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_Polynomial_Opoly__gcd(X1,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1469,
[final] ).
cnf(c_0_1876,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_Polynomial_Opoly__gcd(X1,X3,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1470,
[final] ).
cnf(c_0_1877,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1471,
[final] ).
cnf(c_0_1878,plain,
( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1472,
[final] ).
cnf(c_0_1879,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1473,
[final] ).
cnf(c_0_1880,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1474,
[final] ).
cnf(c_0_1881,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Int_Onumber__ring(X3) ),
c_0_1475,
[final] ).
cnf(c_0_1882,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1476,
[final] ).
cnf(c_0_1883,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1477,
[final] ).
cnf(c_0_1884,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_1478,
[final] ).
cnf(c_0_1885,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1479,
[final] ).
cnf(c_0_1886,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
c_0_1480,
[final] ).
cnf(c_0_1887,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1481,
[final] ).
cnf(c_0_1888,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_1482,
[final] ).
cnf(c_0_1889,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1483,
[final] ).
cnf(c_0_1890,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1484,
[final] ).
cnf(c_0_1891,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1485,
[final] ).
cnf(c_0_1892,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1486,
[final] ).
cnf(c_0_1893,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_1487,
[final] ).
cnf(c_0_1894,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X2,X1,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_1488,
[final] ).
cnf(c_0_1895,plain,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1489,
[final] ).
cnf(c_0_1896,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1490,
[final] ).
cnf(c_0_1897,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
c_0_1491,
[final] ).
cnf(c_0_1898,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_Int_Onumber__ring(X2) ),
c_0_1492,
[final] ).
cnf(c_0_1899,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_1493,
[final] ).
cnf(c_0_1900,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_1494,
[final] ).
cnf(c_0_1901,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_1495,
[final] ).
cnf(c_0_1902,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1496,
[final] ).
cnf(c_0_1903,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1497,
[final] ).
cnf(c_0_1904,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1498,
[final] ).
cnf(c_0_1905,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1499,
[final] ).
cnf(c_0_1906,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1500,
[final] ).
cnf(c_0_1907,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1501,
[final] ).
cnf(c_0_1908,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
c_0_1502,
[final] ).
cnf(c_0_1909,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1503,
[final] ).
cnf(c_0_1910,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1504,
[final] ).
cnf(c_0_1911,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1505,
[final] ).
cnf(c_0_1912,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_1506,
[final] ).
cnf(c_0_1913,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1507,
[final] ).
cnf(c_0_1914,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1508,
[final] ).
cnf(c_0_1915,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1509,
[final] ).
cnf(c_0_1916,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1510,
[final] ).
cnf(c_0_1917,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1511,
[final] ).
cnf(c_0_1918,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1512,
[final] ).
cnf(c_0_1919,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1513,
[final] ).
cnf(c_0_1920,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1514,
[final] ).
cnf(c_0_1921,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1515,
[final] ).
cnf(c_0_1922,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1516,
[final] ).
cnf(c_0_1923,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_1517,
[final] ).
cnf(c_0_1924,plain,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1518,
[final] ).
cnf(c_0_1925,plain,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1519,
[final] ).
cnf(c_0_1926,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1520,
[final] ).
cnf(c_0_1927,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1521,
[final] ).
cnf(c_0_1928,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1522,
[final] ).
cnf(c_0_1929,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1523,
[final] ).
cnf(c_0_1930,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1524,
[final] ).
cnf(c_0_1931,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1525,
[final] ).
cnf(c_0_1932,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1526,
[final] ).
cnf(c_0_1933,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1527,
[final] ).
cnf(c_0_1934,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1528,
[final] ).
cnf(c_0_1935,plain,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_1529,
[final] ).
cnf(c_0_1936,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1530,
[final] ).
cnf(c_0_1937,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1531,
[final] ).
cnf(c_0_1938,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1532,
[final] ).
cnf(c_0_1939,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1533,
[final] ).
cnf(c_0_1940,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
c_0_1534,
[final] ).
cnf(c_0_1941,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
c_0_1535,
[final] ).
cnf(c_0_1942,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1536,
[final] ).
cnf(c_0_1943,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_1537,
[final] ).
cnf(c_0_1944,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
c_0_1538,
[final] ).
cnf(c_0_1945,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_1539,
[final] ).
cnf(c_0_1946,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_1540,
[final] ).
cnf(c_0_1947,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1541,
[final] ).
cnf(c_0_1948,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1542,
[final] ).
cnf(c_0_1949,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1543,
[final] ).
cnf(c_0_1950,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
c_0_1544,
[final] ).
cnf(c_0_1951,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_1545,
[final] ).
cnf(c_0_1952,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_1546,
[final] ).
cnf(c_0_1953,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1547,
[final] ).
cnf(c_0_1954,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1548,
[final] ).
cnf(c_0_1955,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1549,
[final] ).
cnf(c_0_1956,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_1550,
[final] ).
cnf(c_0_1957,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1551,
[final] ).
cnf(c_0_1958,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_1552,
[final] ).
cnf(c_0_1959,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1553,
[final] ).
cnf(c_0_1960,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1554,
[final] ).
cnf(c_0_1961,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1555,
[final] ).
cnf(c_0_1962,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1556,
[final] ).
cnf(c_0_1963,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1557,
[final] ).
cnf(c_0_1964,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1558,
[final] ).
cnf(c_0_1965,plain,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1559,
[final] ).
cnf(c_0_1966,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1560,
[final] ).
cnf(c_0_1967,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1561,
[final] ).
cnf(c_0_1968,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1562,
[final] ).
cnf(c_0_1969,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1563,
[final] ).
cnf(c_0_1970,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1564,
[final] ).
cnf(c_0_1971,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1565,
[final] ).
cnf(c_0_1972,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_1566,
[final] ).
cnf(c_0_1973,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_1567,
[final] ).
cnf(c_0_1974,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_1568,
[final] ).
cnf(c_0_1975,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_1569,
[final] ).
cnf(c_0_1976,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1570,
[final] ).
cnf(c_0_1977,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1571,
[final] ).
cnf(c_0_1978,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_1572,
[final] ).
cnf(c_0_1979,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1573,
[final] ).
cnf(c_0_1980,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1574,
[final] ).
cnf(c_0_1981,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1575,
[final] ).
cnf(c_0_1982,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
c_0_1576,
[final] ).
cnf(c_0_1983,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1577,
[final] ).
cnf(c_0_1984,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1578,
[final] ).
cnf(c_0_1985,plain,
( c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1579,
[final] ).
cnf(c_0_1986,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_1580,
[final] ).
cnf(c_0_1987,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_1581,
[final] ).
cnf(c_0_1988,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1582,
[final] ).
cnf(c_0_1989,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_1583,
[final] ).
cnf(c_0_1990,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1584,
[final] ).
cnf(c_0_1991,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1585,
[final] ).
cnf(c_0_1992,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
c_0_1586,
[final] ).
cnf(c_0_1993,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1587,
[final] ).
cnf(c_0_1994,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1588,
[final] ).
cnf(c_0_1995,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_1589,
[final] ).
cnf(c_0_1996,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1590,
[final] ).
cnf(c_0_1997,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1591,
[final] ).
cnf(c_0_1998,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1592,
[final] ).
cnf(c_0_1999,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_1593,
[final] ).
cnf(c_0_2000,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1594,
[final] ).
cnf(c_0_2001,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1595,
[final] ).
cnf(c_0_2002,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_1596,
[final] ).
cnf(c_0_2003,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1597,
[final] ).
cnf(c_0_2004,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1598,
[final] ).
cnf(c_0_2005,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1599,
[final] ).
cnf(c_0_2006,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1600,
[final] ).
cnf(c_0_2007,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1601,
[final] ).
cnf(c_0_2008,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1602,
[final] ).
cnf(c_0_2009,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1603,
[final] ).
cnf(c_0_2010,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1604,
[final] ).
cnf(c_0_2011,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1605,
[final] ).
cnf(c_0_2012,plain,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1606,
[final] ).
cnf(c_0_2013,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_1607,
[final] ).
cnf(c_0_2014,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1608,
[final] ).
cnf(c_0_2015,plain,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1609,
[final] ).
cnf(c_0_2016,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_1610,
[final] ).
cnf(c_0_2017,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1611,
[final] ).
cnf(c_0_2018,plain,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1612,
[final] ).
cnf(c_0_2019,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1613,
[final] ).
cnf(c_0_2020,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1614,
[final] ).
cnf(c_0_2021,plain,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_1615,
[final] ).
cnf(c_0_2022,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1616,
[final] ).
cnf(c_0_2023,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_1617,
[final] ).
cnf(c_0_2024,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1618,
[final] ).
cnf(c_0_2025,plain,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1619,
[final] ).
cnf(c_0_2026,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_1620,
[final] ).
cnf(c_0_2027,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_1621,
[final] ).
cnf(c_0_2028,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1622,
[final] ).
cnf(c_0_2029,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_1623,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1624_0,axiom,
( c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X7,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X8,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)),X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X3,X6,X7,X8,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X7,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X8,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)),X5)
| ~ c_Polynomial_Opdivmod__rel(X3,X6,X7,X8,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_2,axiom,
( ~ c_Polynomial_Opdivmod__rel(X3,X6,X7,X8,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X7,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X8,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)),X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_3,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X3,X6,X7,X8,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X6,tc_Polynomial_Opoly(X5)),X7,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X8,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1625_0,axiom,
( X3 = X6
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X3 = X6
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_2,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X3 = X6
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_3,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1626_0,axiom,
( X4 = X7
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X4 = X7
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_2,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X4 = X7
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_3,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X6,X7,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X4 = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1627_0,axiom,
( c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X6,X1,X5),X2,c_Polynomial_Osmult(X6,X3,X5),c_Polynomial_Osmult(X6,X4,X5),X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X6,X1,X5),X2,c_Polynomial_Osmult(X6,X3,X5),c_Polynomial_Osmult(X6,X4,X5),X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_2,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X6,X1,X5),X2,c_Polynomial_Osmult(X6,X3,X5),c_Polynomial_Osmult(X6,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1628_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1629_0,axiom,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5))
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_2,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X5)),X4,tc_Polynomial_Opoly(X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1630_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X5)) = X4
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X5)) = X4
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_2,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X5)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1631_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X5)) = X3
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1631_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X5)) = X3
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1631_2,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X5)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1632_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1633_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1634_0,axiom,
( X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X4,X1)
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1635_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1636_0,axiom,
( X4 = X1
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_1,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| X4 = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X2)
| X4 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1637_0,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1638_0,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1639_0,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)),X2,X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)),X2,X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)),X2,X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1640_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_4,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1641_0,axiom,
( c_Polynomial_Opdivmod__rel(X1,X2,c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X1,X2,c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1642_0,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1643_0,axiom,
( c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1644_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_1,axiom,
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)),c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1645_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_4,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1646_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1647_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1648_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1648_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1649_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1650_0,axiom,
( c_Polynomial_Opoly(X3,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1651_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_2,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1652_0,axiom,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_2,axiom,
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1653_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_1,axiom,
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1654_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1655_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1656_0,axiom,
( c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1657_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1658_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1659_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1660_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1661_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1661_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1662_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X1,X4),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4),tc_Polynomial_Opoly(X4)) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_OpCons(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X1,X4),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4),tc_Polynomial_Opoly(X4)) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_OpCons(X2,X3,X4),tc_Polynomial_Opoly(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1663_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_2,axiom,
( c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1664_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_2,axiom,
( c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1665_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_2,axiom,
( c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_3,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1666_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_4,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1667_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1668_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1669_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_1,axiom,
( c_Polynomial_Opoly(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Opoly(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1670_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_1,axiom,
( c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Opoly(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),X3,tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1671_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1672_0,axiom,
( c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3))
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1673_0,axiom,
( c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X4,X5,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1674_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1675_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1676_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1677_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1678_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X2,X4,X3),X3),X3) = c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X2,X4,X3),X3),X3) = c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1679_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1680_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_1,axiom,
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1681_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1682_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1682_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1683_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1684_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1685_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1686_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1687_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1688_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1689_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1690_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1691_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_4,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1692_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_1,axiom,
( X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_2,axiom,
( c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_3,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_4,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1693_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1694_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1695_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1696_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1697_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),X3) = X1
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1698_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1699_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1700_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_Polynomial_Opoly(X3)),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_Polynomial_Opoly(X3)),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1701_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X4,X1,X2),tc_Polynomial_Opoly(X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X4,X1,X2),tc_Polynomial_Opoly(X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X4,X1,X2),tc_Polynomial_Opoly(X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1702_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1703_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1704_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1706_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X1,X4,X3),c_Polynomial_Opoly(X2,X4,X3),X3) = c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1708_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1709_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X1,X4,X3),c_Polynomial_Osmult(X2,X4,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1710_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_0,axiom,
( c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),X4) = c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4),X4) = c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1713_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1715_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1716_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1717_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1718_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1719_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1720_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1721_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1722_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1723_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1724_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1725_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1727_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_1,axiom,
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1728_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_1,axiom,
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1729_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_1,axiom,
( ~ class_Ring__and__Field_Oring__1(X2)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1732_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1733_0,axiom,
( X1 = c_Polynomial_Opoly(X2,X3,X4)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X5,X4),tc_Polynomial_Opoly(X4)) != c_Polynomial_OpCons(X1,X5,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X5,X4),tc_Polynomial_Opoly(X4)) != c_Polynomial_OpCons(X1,X5,X4)
| X1 = c_Polynomial_Opoly(X2,X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X5,X4),tc_Polynomial_Opoly(X4)) != c_Polynomial_OpCons(X1,X5,X4)
| X1 = c_Polynomial_Opoly(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1734_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_3,axiom,
( ~ class_Divides_Osemiring__div(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1735_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1736_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1737_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,X2),X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Divides_Oring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_1,axiom,
( ~ class_Divides_Oring__div(X2)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,X2),X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1738_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_3,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1739_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_3,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1740_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_1,axiom,
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X4)),X3,tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1741_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1742_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1743_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1744_0,axiom,
( c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1745_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1745_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1746_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1747_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1748_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1749_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1750_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1751_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1752_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1753_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1754_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X3,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X3,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X3,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1755_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X1,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X1,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X1,X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1756_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X2),X3,X2)
| c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Divides_Odiv__class_Omod(X4,X3,X2)
| ~ class_Divides_Oring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Divides_Odiv__class_Omod(X4,X3,X2)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X2),X3,X2)
| ~ class_Divides_Oring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_2,axiom,
( ~ class_Divides_Oring__div(X2)
| c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Divides_Odiv__class_Omod(X4,X3,X2)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1757_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1758_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| X2 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| X2 = c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_3,axiom,
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1759_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1760_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_3,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1761_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1762_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1763_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_2,axiom,
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1764_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_2,axiom,
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1765_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1766_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1767_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1768_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1769_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1770_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1771_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1772_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1773_0,axiom,
( c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),X4) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ofield(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_1,axiom,
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X4),X4) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1774_0,axiom,
( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X3),X4,X3) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X3),X4,X3) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1775_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1775_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1776_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1777_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1778_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1779_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1779_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1780_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1781_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1782_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1783_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1784_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1785_0,axiom,
( c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1786_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1787_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1788_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1789_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1790_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1791_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1792_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1793_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1794_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1795_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_1,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1796_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_2,axiom,
( ~ class_Divides_Oring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1797_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_2,axiom,
( ~ class_Divides_Oring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1798_0,axiom,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) != X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) != X4
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) != X4
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1799_0,axiom,
( X4 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X3),X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X3),X2,tc_Polynomial_Opoly(X3))
| X4 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X3),X2,tc_Polynomial_Opoly(X3))
| X4 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_3,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X3),X2,tc_Polynomial_Opoly(X3))
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1800_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1801_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X3,X2),X4,tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X3,X2),X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X3,X2),X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X3,X2),X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1802_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X2,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X2,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X2,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1803_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1804_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1805_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1806_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1807_0,axiom,
( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X1,X2,X3),tc_Polynomial_Opoly(X3))
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X1,X2,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1808_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1808_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1809_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1809_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1810_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X1,c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Opoly__gcd(X3,X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_1,axiom,
( c_Polynomial_Opoly__gcd(X1,c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Opoly__gcd(X3,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Opoly__gcd(X1,c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Opoly__gcd(X3,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1811_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1812_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1813_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1814_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Omod(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_1,axiom,
( c_Divides_Odiv__class_Omod(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Divides_Odiv__class_Omod(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1815_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1816_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1819_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1820_0,axiom,
( c_Polynomial_Osmult(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X2,X3),tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_Polynomial_Osmult(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X2,X3),tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1823_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1824_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1826_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X2)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1827_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X3,X2),tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X2)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X3,X2),tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1830_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1831_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1832_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1833_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1835_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1836_0,axiom,
( X1 = X2
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Otimes__class_Otimes(X1,X1,X3) != c_HOL_Otimes__class_Otimes(X2,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_1,axiom,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X1,X3) != c_HOL_Otimes__class_Otimes(X2,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X1,X3) != c_HOL_Otimes__class_Otimes(X2,X2,X3)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(X1,X1,X3) != c_HOL_Otimes__class_Otimes(X2,X2,X3)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) = X3
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1838_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_1,axiom,
( c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1840_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_2,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_2,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1844_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_2,axiom,
( ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_3,axiom,
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_1,axiom,
( c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1848_0,axiom,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1853_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1855_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X1,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1857_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X3),X2,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1858_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1859_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_2,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_2,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1865_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1866_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_1,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1870_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_1,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1871_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X3,X2)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_1,axiom,
( ~ class_Ring__and__Field_Oring(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1872_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1872_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1873_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_1,axiom,
( ~ class_Ring__and__Field_Oring(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
( c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_Polynomial_Opoly__gcd(X1,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X3)),X3) = c_Polynomial_Opoly__gcd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_0,axiom,
( c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_Polynomial_Opoly__gcd(X1,X3,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_Polynomial_Opoly__gcd(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1877_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_1,axiom,
( c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Int_Onumber__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1882_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1885_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_2,axiom,
( c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_1,axiom,
( c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1887_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_1,axiom,
( c_Polynomial_Opoly__gcd(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Opoly__gcd(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_1,axiom,
( c_Polynomial_Opoly__gcd(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Opoly__gcd(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1893_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1894_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X2,X1,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1896_0,axiom,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1897_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_1,axiom,
( c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1898_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1898_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2),X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1899_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1900_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_3,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1901_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1902_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1903_0,axiom,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1906_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1907_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1908_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_2,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1913_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1914_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1916_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1916_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1917_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1919_0,axiom,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_1,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1922_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1923_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1928_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1931_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1932_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1935_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1936_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1937_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1938_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1939_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1940_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1941_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1943_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1944_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1945_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1946_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1947_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1948_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_1,axiom,
( c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1949_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1950_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1951_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1953_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1954_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1955_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1956_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1957_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1958_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1960_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1961_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1962_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1963_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1964_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1965_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1966_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1967_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1968_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1969_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1970_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1971_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1972_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
| c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1975_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1976_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1977_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1978_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_2,axiom,
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1979_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1979_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1980_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1982_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1982_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1983_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1990_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1992_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_0,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_1,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1996_0,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_0,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_1,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_0,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2007_0,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_0,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_0,axiom,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2025_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2026_0,axiom,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2027_0,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_0,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2029_0,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_171,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('<stdin>',cls_conjecture_0) ).
fof(c_0_1_172,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)),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_173,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)),
c_0_1 ).
cnf(c_0_3_174,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)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_175,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)),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_473,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X3,X2,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_07657f.p',c_0_1802_0) ).
cnf(c_1853,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X3,X2,X0),tc_Polynomial_Opoly(X0)) ),
inference(copy,[status(esa)],[c_473]) ).
cnf(c_16791,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(X0,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(instantiation,[status(thm)],[c_1853]) ).
cnf(c_40016,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))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(instantiation,[status(thm)],[c_16791]) ).
cnf(c_1001,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_07657f.p',c_0_167_0) ).
cnf(c_1008,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/iprover_modulo_07657f.p',c_0_160_0) ).
cnf(c_1033,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/sandbox2/tmp/iprover_modulo_07657f.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_40016,c_1001,c_1008,c_1033]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG434-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 02:46:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.46 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.46 % Orientation found
% 0.19/0.46 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_3dbcda.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_07657f.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_e55350 | grep -v "SZS"
% 0.19/0.48
% 0.19/0.48 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.48
% 0.19/0.48 %
% 0.19/0.48 % ------ iProver source info
% 0.19/0.48
% 0.19/0.48 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.48 % git: non_committed_changes: true
% 0.19/0.48 % git: last_make_outside_of_git: true
% 0.19/0.48
% 0.19/0.48 %
% 0.19/0.48 % ------ Input Options
% 0.19/0.48
% 0.19/0.48 % --out_options all
% 0.19/0.48 % --tptp_safe_out true
% 0.19/0.48 % --problem_path ""
% 0.19/0.48 % --include_path ""
% 0.19/0.48 % --clausifier .//eprover
% 0.19/0.48 % --clausifier_options --tstp-format
% 0.19/0.48 % --stdin false
% 0.19/0.48 % --dbg_backtrace false
% 0.19/0.48 % --dbg_dump_prop_clauses false
% 0.19/0.48 % --dbg_dump_prop_clauses_file -
% 0.19/0.48 % --dbg_out_stat false
% 0.19/0.48
% 0.19/0.48 % ------ General Options
% 0.19/0.48
% 0.19/0.48 % --fof false
% 0.19/0.48 % --time_out_real 150.
% 0.19/0.48 % --time_out_prep_mult 0.2
% 0.19/0.48 % --time_out_virtual -1.
% 0.19/0.48 % --schedule none
% 0.19/0.48 % --ground_splitting input
% 0.19/0.48 % --splitting_nvd 16
% 0.19/0.48 % --non_eq_to_eq false
% 0.19/0.48 % --prep_gs_sim true
% 0.19/0.48 % --prep_unflatten false
% 0.19/0.48 % --prep_res_sim true
% 0.19/0.48 % --prep_upred true
% 0.19/0.48 % --res_sim_input true
% 0.19/0.48 % --clause_weak_htbl true
% 0.19/0.48 % --gc_record_bc_elim false
% 0.19/0.48 % --symbol_type_check false
% 0.19/0.48 % --clausify_out false
% 0.19/0.48 % --large_theory_mode false
% 0.19/0.48 % --prep_sem_filter none
% 0.19/0.48 % --prep_sem_filter_out false
% 0.19/0.48 % --preprocessed_out false
% 0.19/0.48 % --sub_typing false
% 0.19/0.48 % --brand_transform false
% 0.19/0.48 % --pure_diseq_elim true
% 0.19/0.48 % --min_unsat_core false
% 0.19/0.48 % --pred_elim true
% 0.19/0.48 % --add_important_lit false
% 0.19/0.48 % --soft_assumptions false
% 0.19/0.49 % --reset_solvers false
% 0.19/0.49 % --bc_imp_inh []
% 0.19/0.49 % --conj_cone_tolerance 1.5
% 0.19/0.49 % --prolific_symb_bound 500
% 0.19/0.49 % --lt_threshold 2000
% 0.19/0.49
% 0.19/0.49 % ------ SAT Options
% 0.19/0.49
% 0.19/0.49 % --sat_mode false
% 0.19/0.49 % --sat_fm_restart_options ""
% 0.19/0.49 % --sat_gr_def false
% 0.19/0.49 % --sat_epr_types true
% 0.19/0.49 % --sat_non_cyclic_types false
% 0.19/0.49 % --sat_finite_models false
% 0.19/0.49 % --sat_fm_lemmas false
% 0.19/0.49 % --sat_fm_prep false
% 0.19/0.49 % --sat_fm_uc_incr true
% 0.19/0.49 % --sat_out_model small
% 0.19/0.49 % --sat_out_clauses false
% 0.19/0.49
% 0.19/0.49 % ------ QBF Options
% 0.19/0.49
% 0.19/0.49 % --qbf_mode false
% 0.19/0.49 % --qbf_elim_univ true
% 0.19/0.49 % --qbf_sk_in true
% 0.19/0.49 % --qbf_pred_elim true
% 0.19/0.49 % --qbf_split 32
% 0.19/0.49
% 0.19/0.49 % ------ BMC1 Options
% 0.19/0.49
% 0.19/0.49 % --bmc1_incremental false
% 0.19/0.49 % --bmc1_axioms reachable_all
% 0.19/0.49 % --bmc1_min_bound 0
% 0.19/0.49 % --bmc1_max_bound -1
% 0.19/0.49 % --bmc1_max_bound_default -1
% 0.19/0.49 % --bmc1_symbol_reachability true
% 0.19/0.49 % --bmc1_property_lemmas false
% 0.19/0.49 % --bmc1_k_induction false
% 0.19/0.49 % --bmc1_non_equiv_states false
% 0.19/0.49 % --bmc1_deadlock false
% 0.19/0.49 % --bmc1_ucm false
% 0.19/0.49 % --bmc1_add_unsat_core none
% 0.19/0.49 % --bmc1_unsat_core_children false
% 0.19/0.49 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.49 % --bmc1_out_stat full
% 0.19/0.49 % --bmc1_ground_init false
% 0.19/0.49 % --bmc1_pre_inst_next_state false
% 0.19/0.49 % --bmc1_pre_inst_state false
% 0.19/0.49 % --bmc1_pre_inst_reach_state false
% 0.19/0.49 % --bmc1_out_unsat_core false
% 0.19/0.49 % --bmc1_aig_witness_out false
% 0.19/0.49 % --bmc1_verbose false
% 0.19/0.49 % --bmc1_dump_clauses_tptp false
% 0.38/0.58 % --bmc1_dump_unsat_core_tptp false
% 0.38/0.58 % --bmc1_dump_file -
% 0.38/0.58 % --bmc1_ucm_expand_uc_limit 128
% 0.38/0.58 % --bmc1_ucm_n_expand_iterations 6
% 0.38/0.58 % --bmc1_ucm_extend_mode 1
% 0.38/0.58 % --bmc1_ucm_init_mode 2
% 0.38/0.58 % --bmc1_ucm_cone_mode none
% 0.38/0.58 % --bmc1_ucm_reduced_relation_type 0
% 0.38/0.58 % --bmc1_ucm_relax_model 4
% 0.38/0.58 % --bmc1_ucm_full_tr_after_sat true
% 0.38/0.58 % --bmc1_ucm_expand_neg_assumptions false
% 0.38/0.58 % --bmc1_ucm_layered_model none
% 0.38/0.58 % --bmc1_ucm_max_lemma_size 10
% 0.38/0.58
% 0.38/0.58 % ------ AIG Options
% 0.38/0.58
% 0.38/0.58 % --aig_mode false
% 0.38/0.58
% 0.38/0.58 % ------ Instantiation Options
% 0.38/0.58
% 0.38/0.58 % --instantiation_flag true
% 0.38/0.58 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.38/0.58 % --inst_solver_per_active 750
% 0.38/0.58 % --inst_solver_calls_frac 0.5
% 0.38/0.58 % --inst_passive_queue_type priority_queues
% 0.38/0.58 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.38/0.58 % --inst_passive_queues_freq [25;2]
% 0.38/0.58 % --inst_dismatching true
% 0.38/0.58 % --inst_eager_unprocessed_to_passive true
% 0.38/0.58 % --inst_prop_sim_given true
% 0.38/0.58 % --inst_prop_sim_new false
% 0.38/0.58 % --inst_orphan_elimination true
% 0.38/0.58 % --inst_learning_loop_flag true
% 0.38/0.58 % --inst_learning_start 3000
% 0.38/0.58 % --inst_learning_factor 2
% 0.38/0.58 % --inst_start_prop_sim_after_learn 3
% 0.38/0.58 % --inst_sel_renew solver
% 0.38/0.58 % --inst_lit_activity_flag true
% 0.38/0.58 % --inst_out_proof true
% 0.38/0.58
% 0.38/0.58 % ------ Resolution Options
% 0.38/0.58
% 0.38/0.58 % --resolution_flag true
% 0.38/0.58 % --res_lit_sel kbo_max
% 0.38/0.58 % --res_to_prop_solver none
% 0.38/0.58 % --res_prop_simpl_new false
% 0.38/0.58 % --res_prop_simpl_given false
% 0.38/0.58 % --res_passive_queue_type priority_queues
% 0.38/0.58 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.38/0.58 % --res_passive_queues_freq [15;5]
% 0.38/0.58 % --res_forward_subs full
% 0.38/0.58 % --res_backward_subs full
% 0.38/0.58 % --res_forward_subs_resolution true
% 0.38/0.58 % --res_backward_subs_resolution true
% 0.38/0.58 % --res_orphan_elimination false
% 0.38/0.58 % --res_time_limit 1000.
% 0.38/0.58 % --res_out_proof true
% 0.38/0.58 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_3dbcda.s
% 0.38/0.58 % --modulo true
% 0.38/0.58
% 0.38/0.58 % ------ Combination Options
% 0.38/0.58
% 0.38/0.58 % --comb_res_mult 1000
% 0.38/0.58 % --comb_inst_mult 300
% 0.38/0.58 % ------
% 0.38/0.58
% 0.38/0.58 % ------ Parsing...% successful
% 0.38/0.58
% 0.38/0.58 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.38/0.58
% 0.38/0.58 % ------ Proving...
% 0.38/0.58 % ------ Problem Properties
% 0.38/0.58
% 0.38/0.58 %
% 0.38/0.58 % EPR false
% 0.38/0.58 % Horn false
% 0.38/0.58 % Has equality true
% 0.38/0.58
% 0.38/0.58 % % ------ Input Options Time Limit: Unbounded
% 0.38/0.58
% 0.38/0.58
% 0.38/0.58 % % ------ Current options:
% 0.38/0.58
% 0.38/0.58 % ------ Input Options
% 0.38/0.58
% 0.38/0.58 % --out_options all
% 0.38/0.58 % --tptp_safe_out true
% 0.38/0.58 % --problem_path ""
% 0.38/0.58 % --include_path ""
% 0.38/0.58 % --clausifier .//eprover
% 0.38/0.58 % --clausifier_options --tstp-format
% 0.38/0.58 % --stdin false
% 0.38/0.58 % --dbg_backtrace false
% 0.38/0.58 % --dbg_dump_prop_clauses false
% 0.38/0.58 % --dbg_dump_prop_clauses_file -
% 0.38/0.58 % --dbg_out_stat false
% 0.38/0.58
% 0.38/0.58 % ------ General Options
% 0.38/0.58
% 0.38/0.58 % --fof false
% 0.38/0.58 % --time_out_real 150.
% 0.38/0.58 % --time_out_prep_mult 0.2
% 0.38/0.58 % --time_out_virtual -1.
% 0.38/0.58 % --schedule none
% 0.38/0.58 % --ground_splitting input
% 0.38/0.58 % --splitting_nvd 16
% 0.38/0.58 % --non_eq_to_eq false
% 0.38/0.58 % --prep_gs_sim true
% 0.38/0.58 % --prep_unflatten false
% 0.38/0.58 % --prep_res_sim true
% 0.38/0.58 % --prep_upred true
% 0.38/0.58 % --res_sim_input true
% 0.38/0.58 % --clause_weak_htbl true
% 0.38/0.58 % --gc_record_bc_elim false
% 0.38/0.58 % --symbol_type_check false
% 0.38/0.58 % --clausify_out false
% 0.38/0.58 % --large_theory_mode false
% 0.38/0.58 % --prep_sem_filter none
% 0.38/0.58 % --prep_sem_filter_out false
% 0.38/0.58 % --preprocessed_out false
% 0.38/0.58 % --sub_typing false
% 0.38/0.58 % --brand_transform false
% 0.38/0.58 % --pure_diseq_elim true
% 0.38/0.58 % --min_unsat_core false
% 0.38/0.58 % --pred_elim true
% 0.38/0.58 % --add_important_lit false
% 0.38/0.58 % --soft_assumptions false
% 0.38/0.58 % --reset_solvers false
% 0.38/0.58 % --bc_imp_inh []
% 0.38/0.58 % --conj_cone_tolerance 1.5
% 0.38/0.58 % --prolific_symb_bound 500
% 0.38/0.58 % --lt_threshold 2000
% 0.38/0.58
% 0.38/0.58 % ------ SAT Options
% 0.38/0.58
% 0.38/0.58 % --sat_mode false
% 0.38/0.58 % --sat_fm_restart_options ""
% 0.38/0.58 % --sat_gr_def false
% 0.38/0.58 % --sat_epr_types true
% 0.38/0.58 % --sat_non_cyclic_types false
% 0.38/0.58 % --sat_finite_models false
% 0.38/0.58 % --sat_fm_lemmas false
% 0.38/0.58 % --sat_fm_prep false
% 0.38/0.58 % --sat_fm_uc_incr true
% 0.38/0.58 % --sat_out_model small
% 0.38/0.58 % --sat_out_clauses false
% 0.38/0.58
% 0.38/0.58 % ------ QBF Options
% 0.38/0.58
% 0.38/0.58 % --qbf_mode false
% 0.38/0.58 % --qbf_elim_univ true
% 0.38/0.58 % --qbf_sk_in true
% 0.38/0.58 % --qbf_pred_elim true
% 0.38/0.58 % --qbf_split 32
% 0.38/0.58
% 0.38/0.58 % ------ BMC1 Options
% 0.38/0.58
% 0.38/0.58 % --bmc1_incremental false
% 0.38/0.58 % --bmc1_axioms reachable_all
% 0.38/0.58 % --bmc1_min_bound 0
% 0.38/0.58 % --bmc1_max_bound -1
% 0.38/0.58 % --bmc1_max_bound_default -1
% 0.38/0.58 % --bmc1_symbol_reachability true
% 0.38/0.58 % --bmc1_property_lemmas false
% 0.38/0.58 % --bmc1_k_induction false
% 0.38/0.58 % --bmc1_non_equiv_states false
% 0.38/0.58 % --bmc1_deadlock false
% 0.38/0.58 % --bmc1_ucm false
% 0.38/0.58 % --bmc1_add_unsat_core none
% 0.38/0.58 % --bmc1_unsat_core_children false
% 0.38/0.58 % --bmc1_unsat_core_extrapolate_axioms false
% 0.38/0.58 % --bmc1_out_stat full
% 0.38/0.58 % --bmc1_ground_init false
% 0.38/0.58 % --bmc1_pre_inst_next_state false
% 0.38/0.58 % --bmc1_pre_inst_state false
% 0.38/0.58 % --bmc1_pre_inst_reach_state false
% 0.38/0.58 % --bmc1_out_unsat_core false
% 0.38/0.58 % --bmc1_aig_witness_out false
% 0.38/0.58 % --bmc1_verbose false
% 0.38/0.58 % --bmc1_dump_clauses_tptp false
% 0.38/0.58 % --bmc1_dump_unsat_core_tptp false
% 0.38/0.58 % --bmc1_dump_file -
% 0.38/0.58 % --bmc1_ucm_expand_uc_limit 128
% 0.38/0.58 % --bmc1_ucm_n_expand_iterations 6
% 0.38/0.58 % --bmc1_ucm_extend_mode 1
% 0.38/0.58 % --bmc1_ucm_init_mode 2
% 0.38/0.58 % --bmc1_ucm_cone_mode none
% 0.38/0.58 % --bmc1_ucm_reduced_relation_type 0
% 0.38/0.58 % --bmc1_ucm_relax_model 4
% 0.38/0.58 % --bmc1_ucm_full_tr_after_sat true
% 0.38/0.58 % --bmc1_ucm_expand_neg_assumptions false
% 0.38/0.58 % --bmc1_ucm_layered_model none
% 0.38/0.58 % --bmc1_ucm_max_lemma_size 10
% 0.38/0.58
% 0.38/0.58 % ------ AIG Options
% 0.38/0.58
% 0.38/0.58 % --aig_mode false
% 0.38/0.58
% 0.38/0.58 % ------ Instantiation Options
% 0.38/0.58
% 0.38/0.58 % --instantiation_flag true
% 0.38/0.58 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.38/0.58 % --inst_solver_per_active 750
% 0.38/0.58 % --inst_solver_calls_frac 0.5
% 0.38/0.58 % --inst_passive_queue_type priority_queues
% 0.38/0.58 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.38/0.58 % --inst_passive_queues_freq [25;2]
% 0.38/0.58 % --inst_dismatching true
% 0.38/0.58 % --inst_eager_unprocessed_to_passive true
% 0.38/0.58 % --inst_prop_sim_given true
% 2.43/2.61 % --inst_prop_sim_new false
% 2.43/2.61 % --inst_orphan_elimination true
% 2.43/2.61 % --inst_learning_loop_flag true
% 2.43/2.61 % --inst_learning_start 3000
% 2.43/2.61 % --inst_learning_factor 2
% 2.43/2.61 % --inst_start_prop_sim_after_learn 3
% 2.43/2.61 % --inst_sel_renew solver
% 2.43/2.61 % --inst_lit_activity_flag true
% 2.43/2.61 % --inst_out_proof true
% 2.43/2.61
% 2.43/2.61 % ------ Resolution Options
% 2.43/2.61
% 2.43/2.61 % --resolution_flag true
% 2.43/2.61 % --res_lit_sel kbo_max
% 2.43/2.61 % --res_to_prop_solver none
% 2.43/2.61 % --res_prop_simpl_new false
% 2.43/2.61 % --res_prop_simpl_given false
% 2.43/2.61 % --res_passive_queue_type priority_queues
% 2.43/2.61 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.43/2.61 % --res_passive_queues_freq [15;5]
% 2.43/2.61 % --res_forward_subs full
% 2.43/2.61 % --res_backward_subs full
% 2.43/2.61 % --res_forward_subs_resolution true
% 2.43/2.61 % --res_backward_subs_resolution true
% 2.43/2.61 % --res_orphan_elimination false
% 2.43/2.61 % --res_time_limit 1000.
% 2.43/2.61 % --res_out_proof true
% 2.43/2.61 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_3dbcda.s
% 2.43/2.61 % --modulo true
% 2.43/2.61
% 2.43/2.61 % ------ Combination Options
% 2.43/2.61
% 2.43/2.61 % --comb_res_mult 1000
% 2.43/2.61 % --comb_inst_mult 300
% 2.43/2.61 % ------
% 2.43/2.61
% 2.43/2.61
% 2.43/2.61
% 2.43/2.61 % ------ Proving...
% 2.43/2.61 %
% 2.43/2.61
% 2.43/2.61
% 2.43/2.61 % ------ Statistics
% 2.43/2.61
% 2.43/2.61 % ------ General
% 2.43/2.61
% 2.43/2.61 % num_of_input_clauses: 1034
% 2.43/2.61 % num_of_input_neg_conjectures: 1
% 2.43/2.61 % num_of_splits: 0
% 2.43/2.61 % num_of_split_atoms: 0
% 2.43/2.61 % num_of_sem_filtered_clauses: 0
% 2.43/2.61 % num_of_subtypes: 0
% 2.43/2.61 % monotx_restored_types: 0
% 2.43/2.61 % sat_num_of_epr_types: 0
% 2.43/2.61 % sat_num_of_non_cyclic_types: 0
% 2.43/2.61 % sat_guarded_non_collapsed_types: 0
% 2.43/2.61 % is_epr: 0
% 2.43/2.61 % is_horn: 0
% 2.43/2.61 % has_eq: 1
% 2.43/2.61 % num_pure_diseq_elim: 0
% 2.43/2.61 % simp_replaced_by: 0
% 2.43/2.61 % res_preprocessed: 2
% 2.43/2.61 % prep_upred: 0
% 2.43/2.61 % prep_unflattend: 0
% 2.43/2.61 % pred_elim_cands: 0
% 2.43/2.61 % pred_elim: 0
% 2.43/2.61 % pred_elim_cl: 0
% 2.43/2.61 % pred_elim_cycles: 0
% 2.43/2.61 % forced_gc_time: 0
% 2.43/2.61 % gc_basic_clause_elim: 0
% 2.43/2.61 % parsing_time: 0.056
% 2.43/2.61 % sem_filter_time: 0.
% 2.43/2.61 % pred_elim_time: 0.
% 2.43/2.61 % out_proof_time: 0.
% 2.43/2.61 % monotx_time: 0.
% 2.43/2.61 % subtype_inf_time: 0.
% 2.43/2.61 % unif_index_cands_time: 0.004
% 2.43/2.61 % unif_index_add_time: 0.005
% 2.43/2.61 % total_time: 2.139
% 2.43/2.61 % num_of_symbols: 86
% 2.43/2.61 % num_of_terms: 59175
% 2.43/2.61
% 2.43/2.61 % ------ Propositional Solver
% 2.43/2.61
% 2.43/2.61 % prop_solver_calls: 3
% 2.43/2.61 % prop_fast_solver_calls: 3
% 2.43/2.61 % prop_num_of_clauses: 2102
% 2.43/2.61 % prop_preprocess_simplified: 5993
% 2.43/2.61 % prop_fo_subsumed: 0
% 2.43/2.61 % prop_solver_time: 0.
% 2.43/2.61 % prop_fast_solver_time: 0.
% 2.43/2.61 % prop_unsat_core_time: 0.
% 2.43/2.61
% 2.43/2.61 % ------ QBF
% 2.43/2.61
% 2.43/2.61 % qbf_q_res: 0
% 2.43/2.61 % qbf_num_tautologies: 0
% 2.43/2.61 % qbf_prep_cycles: 0
% 2.43/2.61
% 2.43/2.61 % ------ BMC1
% 2.43/2.61
% 2.43/2.61 % bmc1_current_bound: -1
% 2.43/2.61 % bmc1_last_solved_bound: -1
% 2.43/2.61 % bmc1_unsat_core_size: -1
% 2.43/2.61 % bmc1_unsat_core_parents_size: -1
% 2.43/2.61 % bmc1_merge_next_fun: 0
% 2.43/2.61 % bmc1_unsat_core_clauses_time: 0.
% 2.43/2.61
% 2.43/2.61 % ------ Instantiation
% 2.43/2.61
% 2.43/2.61 % inst_num_of_clauses: 1476
% 2.43/2.61 % inst_num_in_passive: 680
% 2.43/2.61 % inst_num_in_active: 740
% 2.43/2.61 % inst_num_in_unprocessed: 54
% 2.43/2.61 % inst_num_of_loops: 742
% 2.43/2.61 % inst_num_of_learning_restarts: 0
% 2.43/2.61 % inst_num_moves_active_passive: 0
% 2.43/2.61 % inst_lit_activity: 125
% 2.43/2.61 % inst_lit_activity_moves: 0
% 2.43/2.61 % inst_num_tautologies: 0
% 2.43/2.61 % inst_num_prop_implied: 0
% 2.43/2.61 % inst_num_existing_simplified: 0
% 2.43/2.61 % inst_num_eq_res_simplified: 0
% 2.43/2.61 % inst_num_child_elim: 0
% 2.43/2.61 % inst_num_of_dismatching_blockings: 1143
% 2.43/2.61 % inst_num_of_non_proper_insts: 646
% 2.43/2.61 % inst_num_of_duplicates: 2097
% 2.43/2.61 % inst_inst_num_from_inst_to_res: 0
% 2.43/2.61 % inst_dismatching_checking_time: 0.001
% 2.43/2.61
% 2.43/2.61 % ------ Resolution
% 2.43/2.61
% 2.43/2.61 % res_num_of_clauses: 10581
% 2.43/2.61 % res_num_in_passive: 8732
% 2.43/2.61 % res_num_in_active: 1264
% 2.43/2.61 % res_num_of_loops: 3000
% 2.43/2.61 % res_forward_subset_subsumed: 1363
% 2.43/2.61 % res_backward_subset_subsumed: 0
% 2.43/2.61 % res_forward_subsumed: 2158
% 2.43/2.61 % res_backward_subsumed: 0
% 2.43/2.61 % res_forward_subsumption_resolution: 764
% 2.43/2.61 % res_backward_subsumption_resolution: 0
% 2.43/2.61 % res_clause_to_clause_subsumption: 151941
% 2.43/2.61 % res_orphan_elimination: 0
% 2.43/2.61 % res_tautology_del: 420
% 2.43/2.61 % res_num_eq_res_simplified: 0
% 2.43/2.61 % res_num_sel_changes: 0
% 2.43/2.61 % res_moves_from_active_to_pass: 0
% 2.43/2.61
% 2.43/2.61 % Status Unsatisfiable
% 2.43/2.61 % SZS status Unsatisfiable
% 2.43/2.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------